Nanophosphor Coatings: Technology and Applications, Opportunities and Challenges

Abstract

The particle size of conventional commercial phosphor powders used in lighting and displays is in the range from several micrometers to tens of micrometers and it is known that submicrometer-sized phosphors can facilitate a decrease in their consumption and improved resolution of phosphor screens. When the particle size becomes comparable to wavelengths of light, the optical properties of phosphor powders undergo remarkable qualitative changes so that the luminescence performance of nanophosphor screens, along with a very pronounced influence of the particle size, becomes dependent on several additional parameters such as packing density of nanoparticles, refractive index and chemical composition of the medium between them. This brings about both advantages and disadvantages which are discussed in this review of recent literature on the synthesis, deposition, and applications of nanophosphors.

1. Introduction

The general function of any phosphor is to convert a certain kind of external energy into visible light. This conversion process can serve different purposes and, from this point of view, all practical applications of phosphors can be classified into several main groups:

• • Light sources (fluorescent lamps, backlights of liquid crystal displays (LCDs), light-emitting diodes (LEDs) including phosphor-converted white LEDs (pc-WLEDs), etc.).
• • Information displays (plasma display panels (PDPs), field emission displays (FEDs), cathode-ray tubes (CRTs), etc.).
• • Radiation converters (X-ray intensifying screens and other image intensifiers, spectral converters for solar cells, down-converters for excimer laser beam profilers and photolithography mask inspection tools, viewing screens for electron microscopy, etc.).
• • Fluorescent pigments and tracers (non-destructive testing, biolabeling, security labeling, leisure goods, etc.).

Luminescent substances are very often utilized in the form of a powder coating, i.e. a continuous particulate film of relatively small thickness extended in the other two dimensions. Such a coating deposited on a transparent substrate is usually referred to as a screen, if it is used for representation of any visual information. Each application imposes an appropriate set of requirements on the properties of the phosphor coating, e.g. its chemical composition, homogeneous or patterned structure, and its thickness. Usually, a trade-off between the maximum light output for the given excitation conditions, desired transient characteristics, quality of image reproduction, mechanical and environmental stability, and costs of the phosphors and their processing has to be found.

The size of phosphor particles is one of the main parameters affecting the performance of phosphor screens. Phosphors produced by conventional methods usually consist of particles with the sizes ranging from several micrometers to several tens of micrometers, i.e. significantly larger than the wavelengths of light they emit. The reduction of phosphor particle size into the subwavelength regime could be advantageous in many applications provided that the luminescent properties of the chosen material are still appropriate and the technological route is economical.

The purpose of this review is to point out the general qualitative differences between conventional phosphors and nanophosphors and to show potential advantages of the latter. Nanophosphors can be defined as nanoparticles of transparent dielectrics (hosts) doped with optically active ions (activators), so that the emission of light happens due to the electronic transitions between the levels of the impurity ions inside the bandgap of the host (characteristic luminescence). They have to be distinguished from the luminescent quantum dots as these emit light upon band-to-band transitions (bandgap luminescence) and are affected much more strongly by quantum confinement effects. Semiconductor quantum dots are not dealt with directly in this article although certain conclusions could also be applied to them. Interested readers can be directed to the reviews of physics and applications of quantum dots, such as Samokhvalov et al. (2013), Geszke-Moritz and Moritz (2013), Bera et al. (2010), Gaponik et al. (2010), and Liu et al. (2010). We will also not devote much attention to phosphor powders with particles of intermediate size between 100 nm and 1–2 μm. Their properties and synthesis were recently treated in (Kubrin, 2012) including an extended discussion of modeling methods and spray-based deposition techniques partially repeated here. Previous reviews of the physics and technology of luminescent nanoparticles can be found, e.g. in Ronda (2008), Tissue (2007), Liu and Chen (2007a), Tanner (2005), Chander (2005), and Tissue (1998).

2. Basic optics of phosphor screens

For the given excitation conditions (constant intensity of the incident X-Rays, UV-light, or an electron beam), the perceived brightness of a phosphor screen is determined by the geometrical configuration of the screen, the excitation source, and the observer. Generally, one distinguishes two different modes of screen observation. In the transmission (T-) mode, the screen is placed between the excitation source and the observer (Fig. 1, Observer A). In the reflection (R-) mode, the observer and the source of excitation are situated on the same side of the screen (Fig. 1, Observer B). The intensity of light exiting the screen in both modes depends on the screen thickness.

Fig. 1

Transmission and reflection modes of screen observation (Kubrin, 2012), © Cuvillier Verlag.

2.1 Perfect non-scattering screens

Let us consider the simplest model of the phosphor screen—an infinite continuous plate with even, perfectly smooth boundaries. If we assume a uniform excitation by unpolarized light (from one side of the screen), the time-averaged spatial distribution of intensity of luminescence from any volume element inside of the phosphor plate should by fully isotropic. We also assume a perfect match between refractive indices of the phosphor and surrounding medium, so that the light reflection at the boundaries of the phosphor layer can be neglected. In such cases, the intensities of light emitted forward (T-mode) and backward (R-mode) should be equal and constant everywhere outside of the screen   

$$I_T=I_R,$$(1)

where I_T and I_R stand for the transmission-mode and reflection-mode intensities, respectively, expressed as a number of photons emitted in a unit of time. Their sum equals the total intensity of luminescence and it can be related to the intensity of exciting radiation absorbed in the phosphor coating I′_A by the quantum efficiency q of the phosphor (number ratio of emitted and absorbed photons). From now on, symbols with a prime will be used for exciting radiation   

$$I_T=I_R=q\frac{{I^{\prime }}_A}{2}.$$(2)

Exciting radiation incident on the phosphor screen is either absorbed or transmitted through the screen. The sum of corresponding contributions equals the initial intensity of excitation   

$${I^{\prime }}_0={I^{\prime }}_A+{I^{\prime }}_T.$$(3)

The part of exciting radiation transmitted through the phosphor is given by the Beer-Lambert law   

$${I^{\prime }}_T={I^{\prime }}_0\text{exp}(-{\alpha }^{\prime }d),$$(4)

where α′ is the coefficient of absorption measured in the units of inverse length and d is the thickness of the screen. We obtain the following final expression   

$$I_T=I_R=q\frac{{I^{\prime }}_0(1-\text{exp}(-{\alpha }^{\prime }d))}{2}.$$(5)

Obviously, both R- and T-mode brightness increase for thicker phosphor screens and asymptotically approach the values corresponding to complete absorption of exciting radiation (Fig. 2). When considering the brightness of a perfect non-scattering screen, there is no definite optimal value of the screen thickness; the phosphor layer theoretically should be as thick as possible.

Fig. 2

Theoretical thickness dependence curves for non-scattering and single scattering models of phosphor screens.

In most practical cases, the refractive index of the luminescent material is substantially higher than that of the surrounding medium and the resulting light intensities should be corrected for the Fresnel reflection at the interface between the media. Eq. 4, which describes transmission of the exciting radiation (for the normal incidence on the screen), should now become (Nakazawa et al., 2007)   

$$\begin{array}{l}{I^{\prime }}_T=\frac{{\left(1-R_0\right)}^2\left(1+{\kappa }^2/n^2\right)\text{exp}(-{\alpha }^{\prime }d)}{1-R_0^2\text{exp}(-2{\alpha }^{\prime }d)}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\approx \frac{{\left(1-R_0\right)}^2\text{exp}(-{\alpha }^{\prime }d)}{1-R_0^2\text{exp}(-2{\alpha }^{\prime }d)},\end{array}$$(6)

where n and κ are the real and imaginary part of the refractive index, respectively; and R₀ is the normal surface reflectivity   

$$R_0=\frac{{\left(n-1\right)}^2+{\kappa }^2}{{\left(n+1\right)}^2+{\kappa }^2}.$$(7)

Equation 3 should now include a part of radiation I′_R reflected from the surface of the phosphor plate   

$${I^{\prime }}_0={I^{\prime }}_A+{I^{\prime }}_T+{I^{\prime }}_R,$$(8)

which equals   

$${I^{\prime }}_R=R_0\left(1+{I^{\prime }}_T\text{exp}(-{\alpha }^{\prime }d)\right).$$(9)

The emitted light undergoes reflection from the layer boundaries and a significant fraction of all light quanta cannot escape the phosphor plate due to the total internal reflection because their angle of incidence exceeds the critical angle   

$${\theta }_C=\text{arcsin}\left(n_A/n_P\right),$$(10)

where n_A and n_P are the refractive indices of the ambient medium and phosphor material, respectively. Such photons experience multiple reflections inside of the phosphor plate, while propagating towards the lateral edges of the structure (this phenomenon is often referred to as waveguiding), until they are finally absorbed and transformed into heat. Eq. 2 does not hold anymore and we obtain   

$$I_T=I_R<q\frac{{I^{\prime }}_A}{2}.$$(11)

The trapping of light inside of the luminescent layer (or in an adjacent transparent substrate) can have a dramatic effect on device performance. For example, the light extraction efficiency of semiconductor light-emitting diodes (LEDs) (i.e. the ratio between the intensity of light emitted into the ambience and the total intensity of light generated by the device) would come to only 2–4% if no special design measures were taken (Fujii et al., 2004; Windisch et al., 2001). Such inefficient light outcoupling results from high refractive indices of semiconductors (e.g. n[GaN] = 2.5). However, even for organic LEDs (OLEDs) which employ materials with moderate values of refractive index (n∼1.5), only about 20–30% of light would escape into air (Wei et al., 2006). Refractive indices of dielectrics used as phosphor hosts fall into the range between 1.5 and 2.5 and, therefore, the brightness of any single-crystalline phosphor screen should also be strongly affected by the internal reflection. Enhancement of the light extraction can be achieved by optimization of the device structure, e.g., “flip-chip” LEDs (Krames et al., 2007) or truncated cone patterns in single-crystalline phosphor screens (Jianbo et al., 2000), and/or intentional roughening of the emitting surfaces, which is applied in order to disrupt waveguiding by means of light scattering. LEDs with extraction efficiencies of 80% have been demonstrated (Krames et al., 2007). Elimination of the effect of the total internal reflection led to a remarkable improvement in performance, so that power efficiencies of semiconductor LEDs and OLEDs could exceed that of conventional fluorescent lamps (60–70 lm/W) (Krames et al., 2007; Reineke et al., 2009). This can be considered a great success because the light extraction efficiency of the fluorescent tubes is close to unity. It has to be mentioned that the improvement of device architecture and phosphor materials already allowed the production of LEDs with luminous efficacies approaching the predicted maximum values of 260–300 lm/W (Tan et al., 2012).

2.2 Single scattering model

The fluorescent lamps and many other devices in which phosphors are used in a powder form are practically not affected by waveguiding due to the absence of sufficiently smooth layer boundaries. Intensive scattering at the surface of phosphor particles, pores, and other inhomogeneities has a drastic influence on propagation of both the exciting radiation and emitted light. The equations describing the relation between the thickness of a screen and its brightness have to be changed accordingly.

Mathematically, the simplest case of the scattering phosphor screen is when the entire intensity of scattered light is immediately lost without any further effect on resulting screen brightness. The Beer-Lambert law for the exciting light (Eq. 4) should now include the scattering coefficient β′:   

$${I^{\prime }}_T={I^{\prime }}_0\text{exp}(-({\alpha }^{\prime }+{\beta }^{\prime })d).$$(12)

The scattering coefficient is not a material-specific constant; it is determined by processing-dependent properties of the phosphor powder. The absorption coefficient α′ in Eq. 12 also depends on the condition of the phosphor powder and, therefore, it should be distinguished from α′ for the bulk phosphor material in Eq. 4.

The assumption of equality of the T- and R-mode intensities of the emitted light (Eq. 1) does not hold anymore, especially for thick screens (i.e. when the intensity of excitation substantially changes with the screen depth) due to the effects of scattering. The T-mode intensity changes with the increasing thickness of the phosphor layer as follows   

$${\mathit{dI}}_T=\mathit{aq}{\alpha }^{\prime }{I^{\prime }}_T\mathit{dx}-\beta I_T\mathit{dx},$$(13)

where a is a fraction of light emitted in the forward direction, q is the quantum efficiency of the phosphor, β is the scattering coefficient for the light at the wavelength of emission. When combined with Eq. 12, this results in a differential equation   

$${\dot{I}}_T+\beta I_T=\mathit{aq}{\alpha }^{\prime }{I^{\prime }}_0\text{exp}(-({\alpha }^{\prime }+{\beta }^{\prime })d).$$(14)

The solution of Eq. 14 is   

$$I_T=\frac{\mathit{aq}{\alpha }^{\prime }{I^{\prime }}_0}{{\alpha }^{\prime }+{\beta }^{\prime }-\beta }[\text{exp}(-\beta d)-\text{exp}(-({\alpha }^{\prime }+{\beta }^{\prime })d)].$$(15)

This is a pulse function of the general form   

$$y=A\left[1-\text{exp}\left(-\frac{x}{t_1}\right)\right]\text{exp}\left(-\frac{x}{t_2}\right),$$(16)

which can be easily reformulated to match with Eq. 15 by setting   

$$A=\frac{\mathit{aq}{\alpha }^{\prime }{I^{\prime }}_0}{{\alpha }^{\prime }+{\beta }^{\prime }-\beta },t_1=\frac{1}{{\alpha }^{\prime }+{\beta }^{\prime }-\beta },t_2=\frac{1}{\beta }.$$(17)

For the R-mode,   

$${\mathit{dI}}_R={\mathit{dI}}_{\mathit{Rx}}\text{exp}(-\beta x),$$(18)

where I_R is the intensity of light coming out from the phosphor plate in the backward direction and I_Rx is the intensity of light emitted in the backward direction at the depth x in the screen. Eq. 18 results in a differential equation   

$${\dot{I}}_R=\mathit{aq}{\alpha }^{\prime }{I^{\prime }}_0\text{exp}(-({\alpha }^{\prime }+{\beta }^{\prime }+\beta )x),$$(19)

which is solved with   

$$I_R=\frac{\mathit{aq}{\alpha }^{\prime }{I^{\prime }}_0}{{\alpha }^{\prime }+{\beta }^{\prime }+\beta }[1-\text{exp}(-({\alpha }^{\prime }+{\beta }^{\prime }+\beta )d)].$$(20)

The R-mode curve is a single exponential decay curve.

Fig. 2 shows the curves of the R- and T-mode brightness, which were obtained by the fitting of published experimental data (Fran and Tseng, 1999; Ozawa, 2007). This is a rather special case of the thickness dependence curves, which could only be obtained in the extremely rare conditions when the scattered photons did not reach the detector.

Even though the single scattering scenario is an over-simplification in most of the practical cases, it allows us to draw a conclusion which is generally valid. For any powder phosphor screen with non-negligible scattering which is observed in the T-mode (the usual way of operation of displays, fluorescent lamps, and phosphor-converted white LEDs), there always exists an optimal screen thickness corresponding to the maximum emission brightness at given conditions of excitation. When the exciting radiation is almost completely absorbed inside the phosphor plaque, each additional infinitesimal phosphor layer in excess of the optimal thickness introduces a net decrease of the perceived intensity because losses due to scattering exceed the intensity of light generated in this layer.

2.3 Multiple scattering of light in the powder screens

Even though the shape of the T- and R-mode curves in Fig. 2 could be predicted by simple mathematical derivations, the obtained equations (Eqs. 15 and 20) do not describe the general case of light generation in a powder phosphor screen because usually, photons are not lost immediately upon the first scattering event and can still contribute to the light output of the screen after being scattered several times. Even for a relatively low concentration of scatterers (e.g. atmospheric aerosols), this causes significant deviations from the Beer-Lambert law (Tam and Zardecki, 1982; Wind and Szymanski, 2002). In the case of densely packed particles, the propagation of light does not practically obey the Beer-Lambert law (Dick, 1998).

Fig. 3 shows an example of the typical dependence of the intensity of photoluminescence on the thickness of the strongly scattering screen. As opposed to the single scattering model, the R-mode intensity neither obeys the exponential law nor reaches saturation when the exciting radiation is fully absorbed in the screen. Both the T- and R-mode curves have an approximately linear character in the range of large screen thickness, while the sum of the corresponding intensities stays approximately constant. The comprehensive mathematical description of the process of light generation in the layers of packed phosphor particles is rather complicated. The most frequently implemented theoretical approaches to this problem are based on Kubelka-Munk’s theory and the Monte Carlo method (Yen et al., 2007). In some cases, simple practical techniques for optimization of the screen weight could be developed. For example, for strongly absorbed exciting radiation, the maximum of the T-mode intensity corresponds to the minimum thickness of the powder screen fully covering the substrate (i.e. there should be no direct transmission of exciting radiation via the voids between the particles, Donofrio and Rehkopf, 1979).

Fig. 3

Thickness dependence curves of strongly scattering Y₂O₃:Eu phosphor coatings (average phosphor particle size 440 nm, Kubrin, 2012), © Cuvillier Verlag.

In any case, it is expected that the T-mode thickness dependence curve has a maximum for a certain optimal screen thickness. Screen brightness in the R-mode asymptotically approaches a constant value, as for the non-scattering and single scattering models. However, for the multiple scattering of light emitted by a semi-infinite phosphor layer, the ratio between the light intensity detected in the R-mode and the total intensity of light generated in the screen could reach unity, if self-absorption of luminescence is negligible:   

$$I_R\to {\mathit{qI}}^{\prime }(0),$$(21)

whereas for non-scattering screens the limit is half as small (see Eq. 2, internal reflection is disregarded):   

$$I_R\to \frac{1}{2}{\mathit{qI}}^{\prime }(0),$$(22)

and it is even smaller in the single scattering model (see Eq. 20)   

$$I_R\to \frac{{\alpha }^{\prime }}{{\alpha }^{\prime }+{\beta }^{\prime }+\beta }\frac{1}{2}{\mathit{qI}}^{\prime }(0).$$(23)

The brightness of the non-scattering screen in the T-mode is equal to that in the R-mode and tends to the same maximum value (Eq. 22). When taking into account any losses, e.g. due to the unintended waveguiding, one obtains   

$$I_T<\frac{1}{2}q{I^{\prime }}_0.$$(24)

This inequality also holds for both single and multiple scattering models because the T-mode intensity would never exceed the R-mode intensity for any given screen thickness of isotropically emitting phosphor, and their sum cannot exceed the total intensity of emitted light.

Practical calculations for the phosphor coatings of finite thickness require more rigorous treatment. The Kubelka-Munk two-flux approach, which is discussed below based on the derivation in Narita (2007), is commonly applied for various kinds of pigment coatings or any other optical coatings with non-negligible multiple scattering. Its theoretical framework can be used in many fields of application of phosphor screens. Along with modeling of the performance of fluorescent tubes (Grossman, 1998; Narita, 2007), it was successfully adopted for LEDs (Ishida et al., 2008), X-ray and vacuum UV (VUV)-excitation (Baciero et al., 1999; Jeon et al., 2000; Kandarakis et al., 1996), and cathodoluminescence (Narita, 2007). Discussion of other modeling approaches of phosphor powder coatings can be found in Yen et al. (2007) and (Kubrin, 2012).

In the approximation of the infinite screen uniformly excited from one side, scattered light produces a diffuse light flux opposite to the initial direction of propagation of the exciting radiation or emitted light. In the standard Kubelka-Munk theory, the optical properties of a particle layer (e.g. a pigment coating, Buxbaum, 2005), which is assumed to be a continuous optical medium, are completely determined by two optical constants: the absorption coefficient K and the scattering coefficient S. These coefficients correspond to the previously introduced coefficients α and β generalized to three dimensions, i.e. when incident light is diffuse and scattering takes place in all directions (Narita, 2007).

In order to perform calculations, a value of either the absorption coefficient K or the scattering coefficient S must be known. The other constant can be determined from the value of the Kubelka-Munk function F(R_∞) by the equation   

$$F\left(R_{\infty }\right)=\frac{{\left(1-R_{\infty }\right)}^2}{2R_{\infty }}=\frac{K}{S},$$(25)

where R_∞ is reflectance of a semi-infinite powder layer obtained from experiments   

$$\left(R_{\infty }\right)=\frac{1-{\beta }_0}{1+{\beta }_0}.$$(26)

Usually, the scattering coefficient is obtained by measuring the reflectance R₀ of a relatively thin layer coated on a black plate (which has negligible reflectance)   

$$S=\frac{R_{\infty }}{d\left(1-R_{\infty }^2\right)}\text{ln}\frac{R_{\infty }\left(1-R_0{R}_{\infty }\right)}{R_{\infty }-R_0},$$(27)

where d is the thickness of the layer (Narita, 2007).

In a one-dimensional case, the light incident on the layer of non-luminescent particles is scattered in the forward and backward directions with intensities which we will denote by I′(x) and J′(x) instead of I′_T and I′_R, respectively. For the forward direction, the light absorbed in an infinitesimal layer of thickness dx is α′I′(x)dx, and the scattered light is β′I′(x)dx. A part of J′(x) is scattered back and has to be added to I′(x). One obtains   

$$\frac{d{I}^{\prime }(x)}{\mathit{dx}}=-({\alpha }^{\prime }+{\beta }^{\prime })I^{\prime }(x)+{\beta }^{\prime }{J}^{\prime }(x).$$(28)

For the backward direction, a similar equation can be written   

$$\frac{d{J}^{\prime }(x)}{\mathit{dx}}=({\alpha }^{\prime }+{\beta }^{\prime })J^{\prime }(x)-{\beta }^{\prime }{I}^{\prime }(x).$$(29)

The general solutions to this set of differential equations, known as Schuster-Kubelka-Munk equations, are   

$$I^{\prime }(x)=A^{\prime }\left(1-{{\beta }^{\prime }}_0\right)\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)+B^{\prime }\left(1+{{\beta }^{\prime }}_0\right)\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right),$$(30)

  

$$J^{\prime }(x)=A^{\prime }\left(1+{{\beta }^{\prime }}_0\right)\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)+B^{\prime }\left(1-{{\beta }^{\prime }}_0\right)\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right),$$(31)

where constants A and B are determined by boundary conditions, and α′₀ and β′₀ are defined as   

$${{\alpha }^{\prime }}_0=\sqrt{{\alpha }^{\prime }({\alpha }^{\prime }+2{\beta }^{\prime })},$$(32)

  

$${{\beta }^{\prime }}_0=\sqrt{{\alpha }^{\prime }/({\alpha }^{\prime }+2{\beta }^{\prime })}.$$(33)

Kubelka showed that the same equations can be derived for diffuse light and scattering in all directions. As light does not always have normal incidence on the phosphor layer, the mean light path dξ is longer than dx. It was shown that   

$$d\xi =2\mathit{dx}.$$(34)

If one defines the new coefficients K′ and S′ by   

$$K^{\prime }=2{\alpha }^{\prime },S^{\prime }=2{\beta }^{\prime },$$(35)

Eqs. 32 and 33 can be replaced with   

$${{\alpha }^{\prime }}_0=\sqrt{K^{\prime }(K^{\prime }+2S^{\prime })},$$(36)

  

$${{\beta }^{\prime }}_0=\sqrt{K^{\prime }/(K^{\prime }+2S^{\prime })},$$(37)

and then, general solutions of Schuster-Kubelka-Munk equations can be expressed by Eqs. 30 and 31 again.

In the case of photoluminescence, one has to account for both exciting and emitted light. There are the following contributions to the light emitted in the forward direction (T-mode)   

$$\mathit{dI}(x)=-{\mathit{dI}}_A-{\mathit{dI}}_S^I+{\mathit{dI}}_S^J+{\mathit{dI}}_E,$$(38)

where dI_A denotes changes due to absorption of emitted light; ${\mathit{dI}}_S^I$ and ${\mathit{dI}}_S^J$ stand for scattering from the forward and backward modes, respectively; dI_E accounts for the process of light generation from the absorbed exciting radiation. For the backward direction, it holds   

$$\mathit{dJ}(x)={\mathit{dJ}}_A+{\mathit{dJ}}_S^J-{\mathit{dJ}}_S^I-{\mathit{dJ}}_E.$$(39)

The intensity of the light emitted by the infinitesimal phosphor layer of thickness dx is   

$${\mathit{dI}}_E(x)+{\mathit{dJ}}_E(x)={\mathit{qK}}^{\prime }[I^{\prime }(x)+J^{\prime }(x)]\mathit{dx},$$(40)

where q is the efficiency of luminescence, K′ is the absorption coefficient of the exciting radiation, and I′(x) and J′(x) are the intensities of the exciting light in the forward and backward directions, respectively. By combining Eqs. 30 and 31, one obtains   

$${\mathit{dI}}_E(x)+{\mathit{dJ}}_E(x)=2{\mathit{qK}}^{\prime }\left[A^{\prime }\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)+B^{\prime }\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right)\right]\mathit{dx}.$$(41)

For infinitesimal phosphor layers,   

$$\mathit{dI}{(x)}_E={\mathit{dJ}}_E(x),{\mathit{dI}}_S^I={\mathit{dJ}}_S^I,{\mathit{dI}}_S^J={\mathit{dJ}}_S^J.$$(42)

As a result, one obtains a set of differential equations   

$$\begin{array}{l}\frac{\mathit{dI}(x)}{\mathit{dx}}=-(K+S)I(x)+\mathit{SJ}(x)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+{\mathit{qK}}^{\prime }\left[A^{\prime }\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)+B^{\prime }\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right)\right],\end{array}$$(43)

  

$$\begin{array}{l}\frac{\mathit{dJ}(x)}{\mathit{dx}}=(K+S)J(x)-\mathit{SI}(x)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-{\mathit{qK}}^{\prime }\left[A^{\prime }\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)+B^{\prime }\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right)\right].\end{array}$$(44)

The general solutions of these equations are   

$$\begin{array}{l}I(x)=\frac{q{K}^{\prime }{A}^{\prime }}{{\beta }_0}.\frac{{{\alpha }^{\prime }}_0{\beta }_0-{\alpha }_0}{{{\alpha }_0^{\prime }}^2-{{\alpha }_0}^2}\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-\frac{q{K}^{\prime }{B}^{\prime }}{{\beta }_0}.\frac{{{\alpha }^{\prime }}_0{\beta }_0+{\alpha }_0}{{{\alpha }_0^{\prime }}^2-{{\alpha }_0}^2}\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+A\text{exp}\left({\alpha }_{0}x\right)+B\text{exp}\left(-{\alpha }_{0}x\right),\end{array}$$(45)

  

$$\begin{array}{l}J(x)=-\frac{q{K}^{\prime }{A}^{\prime }}{{\beta }_0}.\frac{{{\alpha }^{\prime }}_0{\beta }_0+{\alpha }_0}{{{\alpha }_0^{\prime }}^2-{{\alpha }_0}^2}\text{exp}\left({{\alpha }^{\prime }}_{0}x\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+\frac{q{K}^{\prime }{B}^{\prime }}{{\beta }_0}.\frac{{{\alpha }^{\prime }}_0{\beta }_0-{\alpha }_0}{{{\alpha }_0^{\prime }}^2-{{\alpha }_0}^2}\text{exp}\left(-{{\alpha }^{\prime }}_{0}x\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}+\frac{A}{R_{\infty }}\text{exp}\left({\alpha }_{0}x\right)+B{R}_{\infty }\text{exp}\left(-{\alpha }_{0}x\right).\end{array}$$(46)

The values of A and B are determined by the boundary conditions. This allows for, e.g. taking into account the presence of the substrate or reflecting coatings, which are sometimes deposited over one side of the screen in order to increase the light output from the other side.

If absorption is not strong, the scattering coefficient S is practically independent of the absorption coefficient K. Furthermore, for conventional phosphor particles which are larger than the wavelengths of emitted light, the scattering coefficient is approximately constant over a wide wavelength range (Kortüm et al., 1963; ter Vrugt, 1965). However, in the ranges of strong absorption (e.g. for the UV-light), the described method of measuring the scattering constant cannot be used. The Kubelka-Munk theory does not predict the interdependence of K and S and requires special care when applied to the UV-range (Narita, 2007).

Another shortcoming of the Kubelka-Munk theory is that it completely disregards the size and shape of phosphor particles, as well as their mutual arrangement inside of the screen. It is known from experiments that S is reciprocally proportional to the particle size between 1 and 10 μm (Kortüm et al., 1963; Narita, 2007). In many practically relevant circumstances, the absorption coefficient K linearly depends on the volume concentration of particles f_V (volume fraction filled by particles, Buxbaum, 2005). However, the onset of multiple scattering results in a strong deviation from the linear dependence between the concentration f_V and the scattering coefficient S. It was shown that S/f_V is linearly dependent on f_V^2/3 (Buxbaum, 2005). Several authors attempted to derive the relations between the coefficients K and S and the properties of single particles (Liu et al., 2005; Mudgett and Richards, 1971).

The assumption of symmetric and semi-isotropic (two-flux) scattering made in the Kubelka-Munk theory is not always valid. In some cases, a many-flux (> 2) radiative transfer calculation procedure can produce noticeably more accurate results (Mudgett and Richards, 1971). Some further alternative approaches, such as Johnson’s theory or the p-layer model, make reference to the phosphor particle size where the phosphor screen is treated as a stack of particle monolayers (Fonger, 1982a; Fran and Tseng, 1999; ter Vrugt, 1965; Yen et al., 2007). Once the reflection and transmission of such monolayers are defined, one can calculate the optical properties of the phosphor coating of any thickness. In this case, recursion formulas are used instead of differential equations. However, it should be noted that there are no strict reasons for the unit particle layer to be related to the phosphor particle size, when used for the purposes of modeling the optical properties of phosphor screens. The thickness of such an elementary layer may actually be chosen arbitrarily small. For example, a single phosphor layer can be assumed infinitesimally thin, and then the recursive formulas reduce to differential equations equivalent to the Schuster-Kubelka-Munk equations (Fonger, 1982b). In other words, Johnson’s theory and other “discontinuous” models based on the notion of the particle layer are very similar to the “continuous” theory of Kubelka and Munk, and also do not explicitly account for the size and shape of phosphor particles.

The simplest bottom-up approach to modeling the collective properties of packed phosphor particles is based on stochastic computational algorithms explicitly using random numbers—generally termed as the Monte-Carlo method. It can be applied to any problem, which allows for probabilistic formulation. It was used for spherical and polyhedral particles, monosized ones and those possessing a size distribution, ordered and randomly distributed on the substrate (Konrad et al., 1999a; Soules and Klatt, 1988; Urabe, 1980). There are numerous reports on the Monte-Carlo modeling of properties of CRTs (Busselt and Raue, 1988), X-ray imaging systems (Badano, 2003; Liaparinos et al., 2006), and LEDs (Borbely and Johnson, 2005; Chang et al., 2005). Along with the possibility to explicitly account for the size, shape, and arrangement of phosphor particles on the substrate, it allows further parameters (e.g. roughness of particle surface, Konrad et al., 1999a) to be added and can be combined with theoretical methods (e.g. Mie scattering theory, Soules and Klatt, 1988; Liaparinos et al., 2006). The very important advantage of the Monte-Carlo method over the two-flux methods is that it can be used for calculations of the angular distribution of light intensity, for assessing the quality of image reproduction by the information displays and radiation converters, and can handle powder screens with a complicated structure (Urabe, 2007).

2.4 Resolution of the phosphor screens

Along with high efficiency of the conversion of external energy into visible light, phosphor screens used for acquiring or displaying any visual information have to satisfy several additional requirements. The imaging performance of a phosphor screen is determined by the amount of the information it can convey and is usually assessed by the limit of resolution, i.e. by the size of the finest structural details of an image that a display or an image converter is able to reproduce.

The smallest element of an image is a single point. In an ideal imaging system, excitation by a radiation beam of infinitesimal diameter would result in a perfect infinitesimal image point. In reality, the smallest point always has a certain finite size. Therefore, the resolution of the screen can be characterized by defining a corresponding point spread function (PSF), i.e. measuring the size of the spot produced by the point-like excitation source. The PSF is a unique characteristic of the imaging performance of a phosphor screen. The intensity distribution in the entire image, which should be considered as an aggregate of image points, can be obtained by convolution of the intensity distribution of exciting radiation with the PSF of the phosphor screen. When two image points are spaced by less than the width of the PSF, they cannot be fully resolved. Such blurring of an image leads to losses of visual information.

For isotropic imaging systems, the two-dimensional point spread function is rotationally symmetric (Rossmann, 1969) and can be described by a curve for one spatial dimension (Fig. 4a). Often a simple Gaussian intensity profile is assumed and the full width of the PSF at half the maximum intensity (FWHM) is commonly used as the representative value. The shape of the PSF of different screens, however, may vary significantly, so that it is advisable to measure it down to at least several percent of the peak intensity (Gruner et al., 2002), and the full width corresponding to 1–5% of the maximum is sometimes specified as well (e.g., Pokric and Allinson, 2002).

Fig. 4

Example of a point spread function (a) and the corresponding modulation transfer function (b) (Kubrin, 2012), © Cuvillier Verlag.

Direct measurement of the PSF is quite cumbersome because it requires a point source of excitation. In many applications, it is difficult to reduce the area of the screen exposed to the exciting radiation to a vanishingly small size and to have sufficient intensity at the same time. It can be more convenient to measure the line spread function (LSF)—another transfer characteristic of phosphor screens. Similarly to the PSF, which describes the transfer of intensity distribution from the point source of excitation to its image, the LSF defines the intensity profile of the image of a line source. The LSF is related to the PSF by the expression (Gruner et al., 2002)   

$$\mathit{LSF}(x)={\int }_{-\infty }^{+\infty }\mathit{PSF}(x,y)\mathit{dy}.$$(47)

The LSF is a one-dimensional function but, for the iso-tropic imaging systems, the two-dimensional PSF can be obtained from the single LSF by the Abel transform (Koch et al., 1998; Rossmann, 1969). If a PSF has a Gaussian shape, the corresponding LSF is a Gaussian function as well. Width of the LSF is also usually measured by its FWHM value and by the full width at some intensity in the range of several percent of the peak response (Busselt and Raue, 1988). Sometimes, the full width comprising most of the area of the integrated LSF (e.g. 90%) is applied (Koch et al., 1998).

How much overlap of the spread functions is needed for adjacent points/lines in the image to become irresolvable? There are several resolution criteria used in various fields of applied optics. The most well-known is the Rayleigh criterion, which states that two equally bright point objects can be resolved if the maximum of the PSF of the first point falls into the first minimum of the PSF of the second one (Sayanna et al., 2003). This definition of the limit of resolution was developed for diffraction-limited optical systems where the PSF is represented by the Airy pattern of concentric rings with multiple minima. For the PSFs without local minima (e.g. those of Gaussian shape), the Rayleigh criterion is ambiguous. Furthermore, it cannot be applied to the resolution of unequally bright point objects. Very often the limit of resolution is simply identified with the FWHM of the PSF. The so-defined Houston criterion can be used with the spread functions of any shape. However, it is also impractical for resolving the points/lines of different brightness. In many cases, the Sparrow criterion is preferred (Sayanna et al., 2003). Sparrow has suggested that the natural definition of resolution is the point separation at which the saddle point between the two maxima first develops, i.e. when the second derivative of the sum of the PSFs in the midpoint between the points vanishes. If the distance between the points is less or equal to the Sparrow limit, they will be perceived as a single elon-gated point. The same applies to the LSFs. For example, it is known that a series of equidistant Gaussian profiles separated by 2σ, where σ is a standard deviation of the spatial intensity distribution, should produce a uniform intensity (2σ ≈ 0.85FWHM). This property, referred to as a merging raster, is utilized for the reproduction of images with pixelated screens, i.e. screens composed of an array of pixels (discrete picture elements). If the distance between the lines increases, a variation of intensity with the corresponding spatial frequency will be observed as soon as this variation exceeds some perceivable threshold, i.e. the lines will be resolved.

For a general case of an arbitrary LSF, any quantitative treatment would require extensive calculations and it has long been recognized that the problem can be simplified by solving it in the (spatial) frequency domain. This approach is based on the notion of the optical transfer function (OTF), a representation of the frequency response of the optical system. The one-dimensional OTF can be obtained by the Fourier transform of the LSF (or of the PSF for two dimensions) (Koch et al., 1998; Williams and Becklund, 1989). It can also be directly measured for sinusoidal excitation patterns. As the emission and excitation of luminescence are incoherent, only the modulus of the OTF, termed modulation transfer function (MTF), has importance and its phase component (phase transfer function) can be disregarded. Modulation is defined as a ratio of the amplitude of the sinusoid to its average value and, therefore, cannot be greater than unity (Rossmann, 1969). An example of MTF is shown in Fig. 4b. The limit of resolution of a phosphor screen is usually associated with the spatial frequency (measured in cycles per unit length) at which the MTF decreases to 3–5%.

The contrast transfer function (CTF) is another transfer characteristic conventionally applied to phosphor screens. The CTF quantifies the frequency response of an imaging system for a square-wave input instead of the sine wave, which is more convenient for experiments (e.g. with bar charts or rectangular slits, Franks et al., 2003). For the same reason of simpler experimental procedure, the line spread function is sometimes obtained by differentiating an edge trace, i.e. intensity distribution on a boundary between “black” and “white” half-planes in the image of the knife edge (Williams and Becklund, 1989). The CTF equal to one designates perfect transfer of contrast. The limit of resolution of the imaging system is specified in lines per unit length. Such units are very convenient for pixelated displays and radiation converters where the smallest resolvable details of an image are inherently limited by the size of single pixels. However, when two neighboring lines of pixels have the same intensity, they cannot be resolved. “Black” lines should be interlaced with “white” lines, i.e. at least two lines of pixels are needed for the reproduction of each line in the image. In the sampling theory, this is justified by the Nyquist-Shannon theorem. In order to avoid confusion in the specification of resolution, the units of line pairs per unit length (e.g. lp/mm) are widely accepted. Generally, the cut-off spatial frequency for pixelated screens is in the best case approximately equal to half of the density of lines in the raster (or pixels in the line). It is somewhat worse if there is any cross-talk of the neighboring pixels, i.e. if their PSFs significantly overlap.

The resolution of homogeneous unpixelated screens is determined by several parameters. The following primitive example reveals the major factors of influence for a screen consisting of superwavelength-sized particles. Let us consider a single layer of phosphor particles deposited on the transparent substrate (Fig. 5a). Light emitted inside of the phosphor particle experiences multiple internal reflections and can escape the volume of the particle in any direction at an arbitrary point of its surface. Therefore, even for a single layer of phosphor particles, the smallest light emission spot would be approximately equal to the phosphor particle size. However, if neighboring particles have equal intensity, it is impossible to say whether those are two separate points or a single elongated one (Particles 1 and 2 in Fig. 5a). Similarly to the pixelated screens, two image points should be separated by at least one more “pixel” — in this case, another phosphor particle (Particles 2, 3, and 4 in Fig. 5a). The diameter D_IP of the smallest resolvable image point can be approximately expressed as follows:   

$$D_{\mathit{IP}}=2\varphi +2c,$$(48)

where ϕ is the phosphor particle size and c is the inter-particle clearance. Obviously, both the phosphor particles themselves and the gaps between them must be kept as small as possible for improved resolution.

Fig. 5

Schematic illustration of the influence of phosphor particle size, packing density and screen thickness on image resolution. The darker appearance corresponds to a higher intensity of emitted light. See text for explanation.

The influence of phosphor layer thickness on screen resolution is illustrated in Fig. 5b. It is assumed that the coated side of the screen is exposed to excitation with electrons or strongly absorbed photons which are completely absorbed in the top layer of phosphor particles, and particles in the deeper layer(s) merely scatter emitted light without contributing to the emission of luminescence. Nearly 50 percent of produced light is emitted towards the substrate and these photons impinge upon the particles in the second and the third layers and are either reflected or refracted on their surface. Light diffuses inside of the phosphor coating in all directions until it escapes on either side of the screen. If the screen is observed in the T-mode, the light intensity pattern (the image) produced in the top particle layer undergoes gradual degradation (blur), which makes closely spaced image points unresolvable, as in the bottom layer of the screen in Fig. 5b. The image observed in the R-mode is much less prone to the optical blur, although light scattered back from the deeper particle layers may escape from the screen at the spots which were not excited (Particle 3 in Fig. 5b) and in this way slightly impair the MTF. Experiments show that for powder phosphor screens exposed to the strongly absorbed exciting radiation, the MTF in the R-mode is almost independent of the screen thickness. The reflecting CRTs have 3–4 times better resolution as compared to the conventional transmitting ones (Zege et al., 1991).

Obviously, the resolution of unpixelated screens can be improved by decreasing the thickness of the phosphor screen, increasing the packing density of phosphor particles and, finally, by reducing the phosphor particle size. This conclusion is generally valid for any cathodo- or photoluminescent powder screens as well as for those excited by X-rays. However, each parameter affecting the screen resolution can be varied only within a certain limited range determined by other application-specific requirements or available technology. For example, X-rays are weakly absorbed by phosphors, and a considerable thickness of the screen may be required for sufficient efficiency of conversion into visible light. Usually in such cases, a trade-off between better resolution and fainter emission intensity has to be found. On the other hand, the penetration depth of an electron beam into the phosphor is often much smaller than the size of a single phosphor particle. However, from the point of view of manufacturing CRTs, it is difficult to deposit such thin phosphor coatings free of voids and irregularities. The thickness of phosphor screens in conventional CRTs often has to be increased in order to assure uniformity and thus the obtained resolution is compromised due to technological constraints.

A general relation for the optimum screen density W_opt of CRTs, which accounts for the non-close packing of phosphor particles, was obtained by Busselt and Raue (1988)   

$$W_{\mathit{opt}}=2{\overline{\varphi }}_{V50}\rho {f_V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.},$$(49)

where ϕ̄_V50 is the volume median diameter (measured by sedimentation), ρ is the phosphor density, and f_V is the packing density of the phosphor screen. In the same work, a simple relation between the width of the LSF at 5% peak intensity L₀₅ and the geometric thickness d of the screen was found for practical CRT phosphors (Busselt and Raue, 1988)   

$$L_{05}=4.5d.$$(50)

This equation may be rewritten for the optimum screen density W_opt and combined with Eq. 47 to obtain   

$$L_{05}=4.5\frac{W_{\mathit{opt}}}{\rho f_V}=9\frac{{\overline{\varphi }}_{\mathit{VM}}}{{f_V}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}.$$(51)

Therefore, an increase in the packing density of phosphor particles in the screens of optimized density leads to a “sharpening” of reproduced images. It can be considered as a general trend that screens with a high packing density of particles have a better resolution but decreased brightness (Sasaki and Talbot, 1999). It should be emphasized that Eqs. 47–49 are valid only for the T-mode of screen observation.

A combined effect of the size and packing density of phosphor particles can be expressed by the change of the scattering mean free path of the emitted photons (Busselt and Raue, 1988). Intensive optical scattering is found to suppress the tails of the spread functions, i.e. to decrease the L₀₅ in Eq. 47. As a result, the MTF of the powder phosphor screens at low spatial frequencies often surpasses that of non-scattering ones (e.g. single-crystalline or glass plates, Faruqi et al., 1995; Gruner et al., 2002; Swank, 1973).

Scattering of the exciting radiation usually has a minor effect on the quality of image reproduction in most of the applications. For example, in the case of CRTs, changes of the MTF introduced by an increase of the energy of electrons from 5 to 40 keV were less than 15% (Zege et al., 1991). For the X-ray excitation, the scattering of X-rays can be completely neglected.

If the exciting radiation is weakly absorbed, the resolution of the screen is still to a large extent determined by its geometric thickness, so that the values of the MTF corresponding to the same product of spatial frequency and phosphor thickness stay unchanged (Swank, 1973). The necessity of large values of thickness for the complete absorption of X-rays leads to a relatively low resolution of powder phosphor screens, which usually is limited to the range of 10–20 lp/mm (Badano, 2003; Sklensky et al., 1975). For a given thickness of the X-ray intensifying screen, the resolution may be improved by several methods, e.g. by depositing a reflective or absorbing coating (backing) over the rear side of the screen or by introducing small amounts of impurities which provide weak self-absorption of luminescence in the phosphor material, thus removing long tails of the LSF without strongly impairing the light output (Swank, 1973; Zege et al., 1991). Also for the X-ray excitation, the resolution of the screens in the R-mode is somewhat better than that for the T-mode (Zege et al., 1991).

Although the R-mode seems to be preferable for high-resolution imaging, it is highly impractical in most of the applications. In order to achieve superior resolution in the T-mode without sacrificing the efficiency of detection of X-rays, special structured screens are sometimes used. Columnar (needle-like) phosphor particles aligned parallel to the incident X-rays allow elimination of the strong interdependence between the width of the LSF and the screen thickness (Badano, 2003). Alternatively, a mask with an array of thin holes filled with a phosphor can be used. Screens with the resolution on the order of 1 μm were realized based on the latter approach (Flannery et al., 1987). Nonetheless, the screens with a spatial resolution close to the optical diffraction limit could be obtained only by decreasing the thickness of the phosphor film to 1 μm (Koch et al., 1998; Martin and Koch, 2006).

3. Limits of performance of the luminescent screens

Let us consider a powder phosphor screen which is excited by the UV-light (the wavelength and intensity are fixed). What can be its highest brightness and resolution?

For a semi-infinite phosphor plaque, the R-mode brightness is at most (see Sec. 2.3 and Eq. 21)   

$$I_R\to q{I}^{\prime }(0),$$(52)

where q is the quantum efficiency of the phosphor and I′(0) is the intensity of the incident exciting radiation. For the T-mode, the maximum achievable intensity (for the optimized screen thickness and without reflecting coatings on the rear side of the screen) would be   

$$I_T\le \frac{1}{2}q{I}^{\prime }(0).$$(53)

Thus, the maximum brightness of the phosphor screen is ultimately limited by the quantum efficiency of the phosphor. The quantum efficiency of phosphors used in fluorescent lamps, PDPs, and LEDs is about 100% (Ronda, 2008). In this aspect, the performance of the state-of-theart inorganic phosphors is quite close to the physical limits. One has to distinguish, however, between the quantum efficiency and energy efficiency of a phosphor. If luminescence is excited with photons which have energy exceeding that of the emitted photons by more than a factor of 2, the quantum efficiency may reach 200% in certain luminescent materials, i.e. two photons could be emitted per each incident exciting photon. This process is referred to as quantum cutting. Quantum-cutting phosphors have attracted a lot of attention in the past decade, particularly in the fields of photovoltaics and mercury-free fluorescent lamps (Huang et al., 2013; Meltzer, 2007; Ronda, 2008; Zhang and Huang, 2010).

Resolution of the screen is another major figure of performance. For the screens designed for observation with the naked human eye, the resolution of 20 lp/mm is usually sufficient. However, there are several imaging applications such as the excimer laser beam profiling, inspection of photolithographic masks, tunneling electron microscopy, and X-ray microtomography where the phosphor screens with a resolution beyond 1000 lp/mm would provide a definite advantage.

The resolution of the unpixelated phosphor screens is mainly determined by their geometric thickness (see Sec. 2.4). In principle, any desired resolution could be obtained with an appropriately thin phosphor coating, provided that it absorbs a sufficient amount of exciting radiation for a detectable light output. However, the ultimate limit of resolution is set by the diffraction of light and not by the screen thickness. If no special super-resolution techniques are utilized, the resolution of an optical system cannot be better than   

$$k\approx \frac{2n}{\lambda },$$(54)

where k is the Abbe limit of detection (measured in spatial frequency), n is the refractive index of the surrounding medium, and λ is the wavelength of emitted light (Evanko, 2009). The highest spatial frequency that can be optically resolved (for λ=400 nm) is therefore, about 5000 cycles/mm. For longer wavelengths and a finite aperture of the detector, the limit of detection can significantly decrease. If we assume, for simplicity, that the FWHM of the LSF exactly equals the thickness of the phosphor coating (Koch et al., 1998), the corresponding thickness threshold of the diffraction-limited phosphor screen would be on the order of 200 nm. For the pixelated phosphors, this is also the value of the smallest pixel pitch that could ever be needed for the optical imaging.

On one hand, several works on phosphor screens with submicrometer resolution very close to theoretical limits were already reported (Koch et al., 1998; Martin and Koch, 2006; Martin et al., 2012), so that the room for improvement of the spatial resolution per se is also rather limited. On the other hand, high-resolution phosphor radiation converters in the form of non-scattering single crystal films or transparent ceramics are much more difficult to produce (Kuntz et al., 2007; Martin et al., 2012; Park et al., 2012b; Touš et al., 2007) as compared to the conventional processing methods of phosphor powder coatings. It would be beneficial to find a means to manufacture phosphor screens with submicrometer optical resolution by simpler, more economical methods.

As follows from the discussion above, phosphor powder screens may approach diffraction-limited imaging if their thickness could be reduced below 200 nm. Obviously, the manufacturing of such screens would require the application of nanophosphors with a much smaller particle size.

The reduction of phosphor particle size in the super-wavelength regime is relatively straightforward because it does not affect the luminescent properties of particular phosphor materials. Submicrometer-sized phosphor particles are used, e.g. in plasma display panels, because they can be processed in smaller pixels than for conventional phosphors produced by solid-state firing and retain the same brightness for significantly lower screen weights (Kubrin et al., 2007; Kubrin, 2012), thus allowing for a reduced consumption of sometimes extremely costly phosphors. However, when their particle size enters the nano-range, many physical properties of solids undergo dramatic changes. These size effects are summarized in the next sections.

4. Physical implications of reducing the phosphor particle size

4.1 Independent scattering and absorption of light by nanoparticles

As discussed in Sec. 2.4, the scattering of light inside the phosphor layer degrades the resolution of powder screens. We also learned in Sec. 2.2 and 2.3 that scattering affects the thickness dependence curves of light emitted from the screen in the R- and T-modes. It is therefore desirable to derive a mathematical relation between the particle size and the scattering coefficient β (as used in Sec. 2.2 and 2.3) and to compare the behavior of conventional phosphor powders and nanophosphors.

It is convenient to introduce a quantity that specifies the ability of a single phosphor particle to scatter light. The amount of light removed from the incident light by a single phosphor particle is proportional to its geometric projected area A_P   

$$C_{\mathit{SCA}}=Q_{\mathit{SCA}}{A}_P$$(55)

where C_SCA is the scattering cross-section of the particle (measured in the units of area), the proportionality factor Q_SCA is termed scattering efficiency. In the general case of particles that both absorb and scatter, the attenuation cross-section (also called extinction cross-section) should be used instead of C_SCA   

$$C_{\mathit{ATT}}=Q_{\mathit{ATT}}{A}_P=C_{\mathit{ABS}}+C_{\mathit{SCA}}=\left(Q_{\mathit{ABS}}+Q_{\mathit{SCA}}\right)A_P,$$(56)

where Q_ATT and Q_ABS are the attenuation and absorption efficiencies, respectively; C_ATT and C_ABS are the corresponding cross-sections.

Calculation of the scattering and absorption efficiency factors is the central problem of the Mie scattering theory. The theory provides the exact solution of the Maxwell equations, describing the propagation of electromagnetic radiation for a plane wave incident on spherically symmetric particles. The intensity of scattered light at any angle can be calculated for a particle with the given relative refractive index n_R and size parameter x, defined by expressions   

$$n_R=\frac{n_P}{n_A},$$(57)

where n_P and n_A are the refractive indices of the phosphor material and ambient medium, respectively; and   

$$x=\frac{\pi \varphi }{\lambda },$$(58)

where ϕ is the particle diameter and λ is the wavelength of light incident on the particle. The desired attenuation/scattering efficiency factors are obtained in the form of a series of Legendre polynomials. If no additional simplifying assumptions can be made, the required calculations are computationally quite intensive. The comprehensive description of the procedure may be found in numerous textbooks on the scattering of light by small particles, e.g. in Bohren and Huffman (2004) Mishchenko et al. (2002), or van de Hulst (2009). An important outcome is that the scattering efficiency factor asymptotically tends to a value of 2 as the size parameter increases (i.e. for particles much larger than the wavelength of light). In the range of small values of the size parameter, a steep decrease of the scattering efficiency is observed.

For particles which are much smaller than the wavelength of light (ϕ < 50 nm), the intensity and pattern of scattering can be obtained by a much simpler Rayleigh scattering theory. For such particles, the incident electromagnetic field behaves almost as an electrostatic field and is homogeneous inside of the particle. This results in the following equations for the scattering and absorption efficiencies (Mishchenko et al., 2002)   

$$Q_{\mathit{SCA}}=\frac{8}{3}{x}^4{\left|\frac{n_R^2-1}{n_R^2+2}\right|}^2,$$(59)

  

$$Q_{\mathit{ABS}}=4x\text{Im}\left(\frac{n_R^2-1}{n_R^2+2}\right).$$(60)

It is important to note here that the scattering efficiency scales with the fourth power of the size parameter, whereas the absorption efficiency has a linear dependence. This means that the decrease in size of the nanoparticles strongly increases the contribution of absorption to the overall attenuation.

If the effective attenuation cross-section of phosphor particles is known, it can be used for assessing the collective optical properties of ensembles of particles. For the idealized scenario of single scattering by N particles per unit of volume (particles are assumed to be sparsely spaced), the Beer-Lambert law (see Eq. 12) can be rewritten to yield (Hinds, 1999)   

$$I_T=I_0\text{exp}(-(\alpha +\beta )d)=I_0\text{exp}\left(-N{Q}_{\mathit{ATT}}{A}_{P}d\right).$$(61)

Alternatively, it could be reformulated for the particle volume fraction f_V by assuming particles of spherical shape and diameter ϕ   

$$f_V=\frac{\pi N{\varphi }^3}{6},$$(62)

  

$$A_P=\frac{\pi {\varphi }^2}{4},$$(63)

  

$$I_T=I_0\text{exp}\left(-\frac{3f_V{Q}_{\mathit{ATT}}}{2\varphi }d\right).$$(64)

For non-absorbing particles substantially larger than the wavelength of light,   

$$Q_{\mathit{ATT}}=Q_{\mathit{SCA}}=2.$$(65)

one obtains a simple relation between β and ϕ   

$$\beta =-\frac{3f_V{Q}_{\mathit{SCA}}}{2\varphi }=\frac{3f_V}{\varphi }.$$(66)

If the volume concentration of particles (i.e. f_V) does not change, the scattering constant in the Beer-Lambert law is inversely proportional to the phosphor particle size. For nanoparticles (see Eq. 59),   

$$\beta =\frac{3f_V{Q}_{\mathit{SCA}}}{2\varphi }=\frac{4f_V}{\varphi }{x}^4{\left|\frac{n_R^2-1}{n_R^2+2}\right|}^2=\frac{4{\pi }^4{f}_V{\varphi }^3}{{\lambda }^4}{\left|\frac{n_R^2-1}{n_R^2+2}\right|}^2,$$(67)

it is expected that the scattering constant scales in direct proportion to ϕ³. For the absorption constant (Eq. 60), we have   

$$\alpha =\frac{3f_V{Q}_{\mathit{ABS}}}{2\varphi }=\frac{6f_V}{\varphi }x\text{Im}\left(\frac{n_R^2-1}{n_R^2+2}\right)=\frac{6\pi f_V}{\lambda }\text{Im}\left(\frac{n_R^2-1}{n_R^2+2}\right),$$(68)

which seems not to be affected by the size of nanoparticles. It is important that both α and β become dependent on the wavelength light. We should also keep in mind that the refractive index is also a function of the wavelength.

For superwavelength-sized particles, expressions of the general form   

$$S=\frac{\mathit{const}.}{\varphi }$$(69)

relating the scattering coefficient S with the size of phosphor particles can also be applied in the framework of the Kubelka-Munk theory (Butler, 1980). When particles are separated from each other by sufficiently large distances so that the scattering from each single particle is not affected by the proximity of its neighbors, it is possible to directly relate the parameters of the Kubelka-Munk theory with those of the Mie theory by introducing additional parameters (Liu et al., 2005)   

$$K=N\overline{\xi }{C}_{\mathit{ABS}}=\frac{3f_V}{2\varphi }\overline{\xi }{Q}_{\mathit{ABS}},$$(70)

  

$$S=N\overline{\xi }\left(1-{\overline{\sigma }}_d\right)C_{\mathit{SCA}}=\frac{3f_V}{2\varphi }\overline{\xi }\left(1-{\overline{\sigma }}_d\right)Q_{\mathit{SCA}},$$(71)

where ξ̄ is the average path-length parameter (assumed equal to 2 in the original Kubelka-Munk theory), and σ̄_d is the forward-scattering ratio for diffuse radiation (i.e. a fraction of energy that each particle scatters in the forward direction; it can also be determined by the Mie theory). It is possible to derive K and S for nanophosphors similar to Eqs. 67 and 68. However, such expressions cannot properly describe light propagation in the nanophosphor screens because the previously made assumption of independent light scattering by each particle, which requires their large separation, is never fulfilled for packed nanoparticles.

4.2 Dependent scattering and absorption in densely packed powders

In some cases, the collective optical properties of densely packed particles can still be treated as if these particles were attenuating incident light independently from each other. In many cases, however, the influence of the neighboring particles cannot be neglected. For example, effects generally termed as particle crowding play a very significant role in the technology of pigments (Auger et al., 2009; Koleske, 1995). With increasing packing density, the distances between neighboring particles decrease and more and more particles come into contact with each other. The mean free path of the photons between two successive scattering events is determined by the average interparticle spacing and thus it should decrease as well. If it becomes comparable to the particle size, the wavefront of the scattered light incident on the next particle along its path can be appreciably different from the plane wave. As a consequence, the accuracy of calculations based on the efficiency factors obtained from the Mie theory can be impaired. Furthermore, in such a case phosphor particles cannot be treated as point-like scatterers. The absorption and scattering coefficients (see Eq. 66) should be corrected for volume scattering (Brewster, 2004)   

$$\alpha =\frac{3f_V{Q}_{\mathit{ABS}}}{\left(1-f_V\right)2\varphi ,}\hspace{0.17em}\hspace{0.17em}\beta =\frac{3f_V{Q}_{\mathit{SCA}}}{\left(1-f_V\right)2\varphi }.$$(72)

These expressions differ from those derived for the point scattering by the factor (1−f_V) in denominator, which is introduced in order to account for shadowing of particles by each other for f_V > 0.1.

Significant qualitative changes in the interaction of light with particulate matter occur when the interparticle distances enter the size range of a single wavelength of incident light. At this scale, the scattered fields of the neighboring particles can become spatially coherent even for an incoherent radiation source. Coherent addition of the scattered light strongly affects the scattering characteristics of particles in the far field (Tien, 1988). At the same time, the near-field interactions become pronounced (McNeil et al., 2001). At a subwavelength distance from the particle surface, electromagnetic fields include contributions from non-propagating evanescent waves (Li et al., 2005; Mendes et al., 2010). Their influence on the radiation transfer is manifested, for example, by a phenomenon known as the frustrated total internal reflection, which causes transmission of light between two media with high refractive indices separated by a small gap filled with material of lower refractive index at the angles of incidence, for which the total internal reflection would occur in the absence of the second high-index medium. The near-field interactions affect both absorption and scattering of light by particulate matter (Tien, 1988).

The onset of the dependent scattering and absorption is usually determined by a 5% deviation from the independent Mie theory. It was found that this threshold is usually surpassed when the interparticle clearance decreases below approximately one half of the wavelength of the incident radiation (Tien and Drolen, 1987)   

$$c_d\le 0.5\lambda ,$$(73)

where c_d denotes the clearance for which the dependent effects are significant, and λ is the wavelength of light in the medium between the particles (not λ₀ for vacuum). It was shown that the criterion given by Eq. 73 approximately corresponds to the clearance at which the near-field zones of scattering particles begin to overlap (Kamiuto, 1984).

Although in general particles are randomly packed and have different sizes and shapes, the ratio of the average interparticle clearance to the wavelength is very often assessed by a formula derived for a periodical rhombohedral arrangement of monosized spheres (Tien, 1988)   

$$\frac{c}{\lambda }=\frac{x}{\pi }\left(\frac{0.905}{{f_V}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}-1\right),$$(74)

where f_V is the particle volume fraction, x is the particle size parameter. For nanoparticles, the clearance and the distance between the centers of the particles are practically equal. The position of the boundary between the independent and dependent regimes almost does not change with the particles size parameter, and therefore for Rayleigh particles, the critical particle volume fraction of 0.006 is generally assumed.

The “dependent” effects described above result in a decrease of the effective scattering cross-section of particles. For small absorbing particles, the absorption efficiency factor was found to increase (Kumar and Tien, 1990; Prasher, 2007). In the range of Rayleigh scattering, the contribution of absorption to the total attenuation dominates over scattering, and therefore the dependent attenuation efficiency of absorbing particles increases as well (Kumar and Tien, 1990; Prasher, 2007; Siegel and Howell, 1992).

Quantitatively, the problems of radiation transfer in the regime of dependent multiple scattering are usually solved by numerical simulations (Tien and Drolen, 1987). In several cases, analytical relations between the dependent scattering efficiency factor $Q_{\mathit{SCA}}^D$ and the independent (i.e. Mie-) scattering efficiency $Q_{\mathit{SCA}}^M$ could be obtained. For example, the pioneering work by Hottel et al. (Hottel et al., 1971) resulted in the following empirical expression for c/λ > 0.092   

$$\text{log log}\left(\frac{Q_{\mathit{SCA}}^M}{Q_{\mathit{SCA}}^D}\right)=0.25-3.8\frac{c}{\lambda },$$(75)

which was verified for x < 1 (Tien and Drolen, 1987). For the size parameter x→0, an analytic relation between $Q_{\mathit{SCA}}^D$ and $Q_{\mathit{SCA}}^M$ could be derived for the Percus-Yevick hard-sphere model (Tien and Drolen, 1987)   

$$\frac{Q_{\mathit{SCA}}^D}{Q_{\mathit{SCA}}^M}=\frac{{\left(1-f_V\right)}^4}{{\left(1+2f_V\right)}^2}.$$(76)

An approximate expression for the dependent absorption efficiencies $Q_{\mathit{ABS}}^D$ in the limit of Rayleigh particles (i.e. x→0) was identical for several different models (Kumar and Tien, 1990)   

$$Q_{\mathit{ABS}}^D=4x\text{Im}\left(\delta \frac{n_R^2-1}{n_R^2+2}\right),$$(77)

where   

$$\delta =\left[1-\frac{n_R^2-1}{n_R^2+2}{f}_V\right].$$(78)

Recently, it was shown that changes to the effective refractive index of a nanoparticulate medium should be taken into account when modeling the radiation transfer with dependent absorption and scattering (Prasher, 2007). A turbid medium filled with particles much smaller than the wavelength of light acts upon photons, which traverse it, as an optically homogeneous medium with a refractive index determined by the refractive indices of constituting media and the particle volume fraction. From this point of view, the influence of the volume concentration of nanoparticles on the effective refractive index can be considered as a further effect of dependent scattering and absorption.

Assuming a substantial number concentration N of nanoparticles in vacuum (there should be many nanoparticles in a sphere with a radius equal to the wavelength of light), the effective refractive index n_EFF can be related by the Lorentz-Lorenz equation (van de Hulst, 2009), also known as the Clausius-Mossotti relation (Meltzer et al., 1999)   

$$\frac{4\pi \alpha }{3}N=\frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2},$$(79)

where N is the number concentration of particles and α is the polarizability of the nanoparticles. The polarizability defines a dipole moment of the Rayleigh particles induced by an external electric field and can be used to describe their scattering. Alternatively, the effective refractive index can be derived from the volume concentration of particles f_V and their refractive index n_P   

$$\frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2}=f_V\frac{n_P^2-1}{n_P^2+2}.$$(80)

For particles dispersed in a medium with refractive index n_A it becomes (Klein, 1988)   

$$\frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2}=f_V\frac{n_P^2-1}{n_P^2+2}+\left(1-f_V\right)\frac{n_A^2-1}{n_A^2+2}.$$(81)

In many cases, however, a simplified expression below is applied (Meltzer et al., 1999; Vollath, 2008)   

$$n_{\mathit{EFF}}=f_V{n}_P+\left(1-f_V\right)n_A.$$(82)

The imaginary part of the effective refractive index (usually referred to as the extinction coefficient k) can be transformed into the absorption coefficient of the nanophosphor layer by the expression (Bohren and Huffman, 2004)   

$$\alpha =\frac{4\pi \text{Im}\left(n_{\mathit{EFF}}\right)}{{\lambda }_0}=\frac{4\pi k_{\mathit{EFF}}}{{\lambda }_0},$$(83)

where λ₀ is the wavelength of light in vacuum.

A potentially more exact expression can be derived from Eq. 68 and 77   

$$\begin{array}{l}\alpha =\frac{3f_V{Q}_{\mathit{ABS}}^D}{2\varphi }=\frac{6f_V}{\varphi }x\text{Im}\left(\delta \frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2}\right)\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\frac{6\pi f_V}{\lambda }\text{Im}\left(\delta \frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2}\right).\end{array}$$(84)

For the scattering coefficient, we combine Eq. 67 and 76   

$$\begin{array}{l}\beta =\frac{3f_V{Q}_{\mathit{SCA}}^D}{2\varphi }=\frac{4f_V}{\varphi }{x}^4{\left|\frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2}\right|}^2\frac{{\left(1-f_V\right)}^4}{{\left(1+2f_V\right)}^2}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=\frac{4{\pi }^4{f}_V{\varphi }^3}{{\lambda }^4}{\left|\frac{n_{\mathit{EFF}}^2-1}{n_{\mathit{EFF}}^2+2}\right|}^2\frac{{\left(1-f_V\right)}^4}{{\left(1+2f_V\right)}^2}.\end{array}$$(85)

The coefficients K and S for the Kubelka-Munk model could be derived in similar way. However, their complexity precludes convenient comparison of the scattering and absorption properties of conventional phosphors and nanophosphors. To complete this section, the experimentally observed wavelength dependence of the attenuance of coatings made of the same phosphor with different particle sizes is shown in Fig. 6. One can see that the values measured in the range of strong absorption (λ < 280 nm) are very close, whereas near the main emission peaks (λ ≈ 590–650 nm), scattering of the nanophosphor coating (i.e. attenuance minus absorbance, the latter is negligible in this wavelength range) is two orders of magnitude lower than that of phosphors with larger particle sizes. Furthermore, an increase of the particle volume fraction from 0.03 to 0.1 does not practically affect the curve in the short wavelength range but the scattering in the red part of the spectra substantially decreases due to the more pronounced dependent effects. The scattering of conventional phosphors is practically independent of the wavelength. For nanophosphors, a steep decrease is observed toward longer wavelengths in agreement with the predictions of Eq. 67. A consequence of the dramatically decreased scattering can be seen in the shape of the thickness dependence curve for the T-mode intensity of luminescence in Fig. 7. Once the maximal value is reached, the brightness of the screen stays virtually constant for any thicker phosphor coating, very similar to the theoretically expected behavior for non-scattering screens (Fig. 2).

Fig. 6

Attenuance spectra Y₂O₃:Eu nanophosphor coatings (NP) of different coating densities and particle volume fractions deposited by flame aerosol deposition. For comparison, spectra of a commercial phosphor powder (CP) and a fine phosphor powder produced by flame-assisted spray pyrolysis (FP) are also shown. Their thickness was optimized for the highest T-mode output. The figure is a compilation of data published in Fig. 7 and 9, Kubrin et al. (2010), © IOP Publishing.

Fig. 7

T-mode thickness dependence curve of Y₂O₃:Eu nano-phosphor coatings normalized to the highest brightness of the screen made of the commercial phosphor powder. The figure is a modified version of Fig. 8, Kubrin et al. (2010), © IOP Publishing.

As shown above, the intensity of scattering in the nanoparticle coating dramatically decreases with increasing wavelength of scattered light, decreasing the size of particles and increasing their packing density. Theoretically it should be possible to almost completely eliminate the scattering of light emitted by nanophosphor, if the particles could be made arbitrarily small and/or the particle volume fraction in the screen could be increased to values that are as high as possible (ideally up to the bulk density of the phosphor material). In this way, non-scattering phosphor screens suitable for diffraction-limited imaging could be obtained. At the same time, nanophosphor screens are less prone to losses due to internal reflection (see Sec. 2.1) because their surface is not smooth (or can be made deliberately rough, if needed), and their effective refractive index is usually much lower than that of single crystal films or fully sintered transparent ceramic phosphor plates. Now we can try to figure out the limiting factors, which counteract the advantages of weak light scattering by nanoparticulate matter.

4.3 Influence of particle size on emission of luminescence

How do the particle size and packing density influence the process of light emission by the particles of doped dielectrics? The quantum efficiency of a phosphor is determined by the competing processes of radiative and non-radiative relaxation of excited states. It can be expressed by the corresponding contributions to the decay times of luminescence   

$$q=\frac{\tau }{{\tau }_R},$$(86)

where τ_R is the radiative decay time constant (without non-radiative processes) and τ is the observed emission decay time constant. In the simplest case, when both the radiative and non-radiative contributions can be represented by a first-order exponential decay, τ would change according to   

$$\frac{1}{\tau }=\frac{1}{{\tau }_R}+\frac{1}{{\tau }_{\mathit{NR}}},$$(87)

where τ_NR is the non-radiative decay time constant.

Changes to the quantum efficiency and the luminescence decay time of doped phosphors are not very pronounced until they enter the size range of nanoparticles (i.e. < 100 nm). A further reduction of the size of phosphor particles usually has a profound effect on the performance of doped phosphors.

In the deep subwavelength size regime, the emission rate usually decreases with decreasing phosphor particle size. It is mainly attributed to the changes in the effective refractive index of the particulate medium (see Eqs. 80–82) (Liu and Chen, 2007a). The radiative decay time of an excited ion embedded in a medium with a refractive index n can be expressed as follows (Henderson and Imbusch, 1989; Meltzer et al., 1999)   

$${\tau }_R=\frac{1}{f(\mathit{ED})}\frac{{\lambda }_0^2}{{\left[\frac{1}{3}\left(n^2+2\right)\right]}^{2}n},$$(88)

where f(ED) is the oscillator strength of the electric dipole transition. In the case of nanoparticles, the effective refractive index n_EFF defined in the previous section should be used. Thus it can be expected that for vanishingly small phosphor particles separated by large distances (c > λ, i.e., f_V→0), the radiative lifetime of electronic transitions can be increased from its bulk value by a factor of   

$$\frac{n_P}{9}{\left(n_P^2+2\right)}^2.$$(89)

For the magnetic dipole transitions, Equation 88 should be replaced by (Liu and Chen, 2007b)   

$${\tau }_R=\frac{1}{f(\mathit{MD})}\frac{{\lambda }_0^2}{n^3},$$(90)

i.e. the radiative lifetime of the nanoparticles could differ from that of the bulk phosphor by a factor of $n_P^3$.

According to Eqs. 86 and 87, the decrease of the radiative decay rate due to the typically low effective refraction index can cause substantial reduction of the quantum efficiency. This effect has to be taken into account while measuring the efficiency (Mialon et al., 2009) because it becomes dependent on the packing density of nanophosphor. Compaction of the porous nanophosphor layer from 3 to 10 vol.% particle volume fraction discussed in the previous section, not only decreased its scattering but also increased the T-mode brightness of luminescence by 13% (Kubrin et al., 2010).

The non-radiative decay time of luminescence for conventional phosphors also affects quantum efficiency. It is usually described by the temperature-dependent multi-phonon relaxation rate (Liu and Chen, 2007a)   

$$\frac{1}{{\tau }_{NR}}=C\text{exp}\left(\frac{-\alpha \mathrm{\Delta }E}{\hslash {\omega }_m}\right){\left[\frac{\text{exp}\left(\hslash {\omega }_m/\mathit{kT}\right)}{\text{exp}\left(\hslash {\omega }_m/kT\right)-1}\right]}^{\raisebox{1ex}{$\mathrm{\Delta }E$}\!\left/ \!\raisebox{-1ex}{$\hslash {\omega }_m$}\right.},$$(91)

where ħω_m is the maximum phonon energy of the lattice vibrations, ΔE is the energy gap between the populated state and the next low-lying state, k is the Boltzmann constant, T is the temperature, and C and α are empirical parameters characteristic for the particular crystals. In nanocrystals, the phonon density of states becomes discrete and the low-energy acoustic phonons are gradually eliminated with decreasing particle size so that the non-radiative relaxation rate of excited states and the efficiency of the phonon-assisted energy transfer in nanophosphors can be substantially reduced as compared to that in bulk materials (Liu and Chen, 2007a).

The excited state can also migrate between the activator ions in insulating hosts due to the resonant energy transfer (Liu and Chen, 2007a). However, a slight variation of the energy levels of the embedded ions due to lattice stress and defects noticeably decreases the probability of the resonant energy transfer, especially for particles with a size below 40 nm (Chen et al., 2003). As a result, both mechanisms of migration of excitation energy are inhibited in nanophosphors.

On one hand, the decreased efficiency of the phonon-assisted energy transfer impairs sensitized or upconversion luminescence (Chen et al., 2003). And on the other hand, the increase of the non-radiative lifetime of luminescence due to restricted energy transfer should favorably influence the overall quantum efficiency of conventional downconverting phosphors by postponing the onset of the concentration quenching, especially when the size of the particles approaches 1–2 nm (Mutelet et al., 2011). As a general observation, nanophosphors are significantly less efficient than their micrometer-sized counterparts (Liu and Chen, 2007a; Ronda, 2008), which means that the non-radiative decay rate either does not decrease with the size of nanoparticles or it decreases too slowly to counteract the decrease of the radiative decay rate discussed earlier in this section. It is widely accepted that the main obstacle for achieving the performance of bulk materials is constituted by the increased specific surface area of nanoparticles (i.e. by large values of surface-to-volume ratio).

In the presence of migration of excitation, the non-radiative relaxation rate is determined not only by the efficiency of the inter-ionic energy transfer but also by the concentration of lattice defects acting as emission quenchers. The particle surface itself should be considered as a distortion of the crystalline structure. Atoms within several lattice constants from the surface are displaced due to the surface reconstruction, and dangling bonds are often terminated by chemical species with high phonon frequencies (e.g. OH-, CO₃- or NH-groups) adsorbed from the ambience (Bogdan et al., 2011; Igarashi et al., 2000; Liu and Chen, 2007a; Nayak et al., 2007; Ronda, 2008). The phonon spectra of nanoparticles are further modified by the introduction of surface phonon modes which are localized at the interface with surrounding medium and can provide new channels for non-radiative relaxations (Prasad, 2004). For nanoparticles dispersed in solvents, polymers, or glasses, the effect of size confinement leading to inhibition of the energy transfer does not play any significant role and the non-radiative decay time of luminescence is usually shorter than that of the same particles not embedded in any medium (Liu and Chen, 2007a). All these effects generally referred to as surface quenching effects become more pronounced with decreasing phosphor particle size and may dramatically change the dynamics of the luminescence emission of ultrafine phosphor powders.

One of the size effects attributed to the surface quenching consists in deviation of the luminescence decay curve from single-exponential behavior (Zhang et al., 2003). It was discovered that even for relatively low concentrations of activator, the decay of emission of nanophosphors is much better fitted with a second-order exponent (Kubrin, 2012). Following the explanation proposed in Zhang et al. (2003), the shorter decay time constant should correspond to activator ions situated on or near the particle surface. However, it is very unlikely that there are only two dissimilar kinds of activator ions (on the surface and in the volume of nanoparticles) without any intermediate states. It was suggested that the decay time constants gradually increase from the surface into the depth so that it could be described by a stretched exponential function (also called Kohlrausch function)   

$$I(t)=I_0\text{exp}\left[-{\left(\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$\tau $}\right.\right)}^{\beta }\right],$$(92)

where 0 < β ≤ 1 (Kubrin, 2012). The parameter β characterizes the width of distribution of the lifetimes and is often used as a measure of “disorder” present in the system under investigation. The Kohlrausch function is successfully applied to describe relaxation processes in many areas of physics including molecular fluorescence and luminescence of nanoscale semiconductors (Berberan-Santos et al., 2005; Chen, 2003; Martin and Shea-Rohwer, 2006).

Obviously, it is desirable to have a means to suppress the surface quenching. A simple strategy was proposed, which allows the quantum efficiency of nanophosphors to be improved. A thin shell of undoped host material or some other dielectric with low-as-possible maximum phonon frequency and similar lattice constant has to be grown around each nanoparticle. The external layer efficiently reduces the energy transfer to the quenching centers at the surface (Gnach and Bednarkiewicz, 2012; Liu and Chen, 2007a, Ronda, 2008, Wang et al., 2010). This strategy made it possible to achieve an exceptionally high quantum efficiency of 70% for CePO₄:Tb/LaPO₄ core-shell nanoparticles (Kömpe et al., 2003). The same method has been successfully applied for semiconductor quantum dots with a high quantum yield (Liu and Chen, 2007a). In certain cases, an undoped shell around phosphor nanoparticles can perform some further functions, e.g. protect the dopant ions from oxidation to a non-luminescent state (Buissette et al., 2006). It should be noted that “finishing” of the surface of phosphor particles is sometimes also used for conventional micrometer-sized phosphors in order to improve their maintenance or stability in suspensions (Jüstel et al., 1998). For coarse-grained phosphor powders, passivating coatings do not directly affect the luminescent properties.

Although the large surface-to-volume ratio of nanophosphors is usually a problem, it also can provide unique opportunities. For example, it has been demonstrated that the surface of Y₂O₃:Eu nanophosphor, which usually emits pure red light and is efficiently excited with only UV-light of wavelengths below 280 nm, can be passivated with organic ligands acting as a molecular antenna (Dai et al., 2011). Acetylacetonate ligands increase the absorption cross-section of phosphor nanoparticles so that the emission from Eu-ions and oxygen vacancies can be excited by a UV-LED (λ=350–370 nm) resulting in white luminescence.

The number of emitting ions inside of each nanoparticle decreases with its size and it becomes possible to observe emission from single ions of the activator. The constant intensity of emission under the constant excitation and exponential decay of luminescence, when excitation ceases, turns into discrete on-off blinking events (Barnes et al., 2000). Studies of luminescence of single phosphor nanoparticles offer additional opportunities for research. For example, they provided evidence of the dipole nature of electronic transitions involved in the emission of light (Bartko et al., 2002).

The luminescence spectra of nanophosphors are practically not affected by quantum confinement, as opposed to semiconductor quantum dots. Characteristic luminescence results from electron transitions inside of single impurity ions, which are strongly localized (this is especially true for rare earth ions predominantly used as activators for nanophosphors). As a result, the positions of the energy levels participating in radiative transitions hardly change even for nanophosphors with particle sizes well below 10 nm (Liu and Chen, 2007a; Ronda, 2008). This is the reason why the terms nanophosphors and quantum dots should not be used interchangeably. A sometimes reported broadening of the peaks in the spectra of emission is mostly attributed to distortions of the crystalline structure of nanoparticles (Lebbou et al., 2005; Tanner, 2005). The most pronounced changes related to quantum confinement of electronic states are reported for the peaks in the spectra of excitation of photoluminescence which involve the edges of the bandgap of the host material, such as shifts of the charge transfer bands (Shang et al., 2011).

4.4 Non-optical effects of reduced particle size

It is not only the optical properties of phosphors that are modified by the downscaling of phosphor particle size. There are several further particle size effects which can have implications for the technology of manufacturing and which indirectly influence the performance of the powder screens.

The increase of the surface-to-volume ratio affects the thermodynamics of the phase transformation. The Gibbs-Thomson effect favors crystallization of nanoparticles in high-pressure polymorphs due to additional hydrostatic pressure P (Dosev et al., 2006; Skandan et al., 1992)   

$$P=\frac{4\gamma }{\varphi },$$(93)

where γ is the surface energy (value of 1.5 J/m² is typical for many ceramic materials) and ϕ is the size of nanoparticle. More generally, it can be stated that reduction of the particle size decreases the temperature of phase transformations (Vollath, 2008). The melting points of nanoparticles are lower than those of the bulk substances (Kondepudi, 2008; Vollath, 2008). In addition, it can result in a particle size limit for the crystallization of some ceramic hosts (e.g. 8 nm for Al₂O₃, Vollath, 2008).

The contact mechanics of solid particles undergoes major changes when their size decreases. For nanoparticles, the adhesive forces can exceed other common forces by orders of magnitude. As a result, they stick firmly to any surface they contact (Hinds, 1999). Furthermore, such particles become cohesive, i.e. they tend to agglomerate with each other. For example, a clustering of nanoparticles dispersed in transparent matrices can cause a dramatic increase of light scattering (Vollath, 2008). Agglomeration and large interparticle friction forces are also responsible for the extremely low filling fraction of a random loose packing of fine and ultrafine powders (Valverde and Castellanos, 2006) as well as for low density of compacted nanopowders (< 45% of the theoretical values) (Gonzalez and Piermarini, 2000).

The size of phosphor particles directly influences their stability in colloidal suspensions. A particle in a liquid of lower density settles with a velocity that is proportional to the square of its size (Stokes’ law, Hinds, 1999). For well-dispersed nanoparticles, this velocity becomes extremely small. This has a strong impact on the technology of phosphor screens. On one hand, it renders screen deposition methods based on sedimentation, which are otherwise very popular in the manufacturing of monochromatic displays, highly impractical. On the other hand, by using colloidal methods, nanophosphors could be processed into special elaborate structures with the feature sizes on the order or below the wavelengths of incident/emitted light to gain additional functionality, e.g. to produce luminescent 3D photonic crystals with a morphology of inverse opal (Zhang et al., 2010). The technology-related issues will be reviewed in the next section.

5. Manufacturing of nanophosphor screens

5.1 Synthesis of nanophosphors

Many research groups all over the world are currently investigating different methods for the synthesis of nanophosphors. The most popular approaches have been reviewed several times (Chander, 2005; Dosev et al., 2008; Tan, 2012; Tanner, 2005; Tissue, 1998; Tissue, 2007) and are only briefly summarized here.

According to Tissue (2007), two main groups of synthesis methods can be defined. The first one includes different ways of producing nanophosphors in the gas phase, including synthesis in a vacuum, inert or reactive gas atmospheres. A source of heat for the vaporization of elements of the synthesized compounds is implied. This function can be performed by an electron beam, a laser beam, or a flame. Solid nanoparticles condense in the gas phase upon cooling. Such methods as laser-assisted gas-phase condensation (Bihari et al., 1997, Tissue, 2007), chemical vapor condensation (Konrad et al., 1999b; Schmechel et al., 2001), and flame spray pyrolysis (Laine et al., 2000; Camenzind et al., 2007; Kubrin et al., 2010; Sotiriou et al., 2011, 2012) fall under this category. Somewhat ambiguous is the assignment of pulsed laser deposition (Bär et al., 2005; Jones et al., 1997; Rajan and Gopchandran, 2009, Xu et al., 2011) and related laser ablation methods (Masenelli et al., 2013), which are sometimes included in this group of methods although they rather produce dense solid films and not nanopowders.

In the second group of synthesis methods, phosphor nanoparticles are obtained in a liquid solution. The group includes various realizations of chemical precipitation (Bazzi et al., 2004; Buissette et al., 2006; Khan et al., 2008; Lebbou et al., 2005; Mutelet et al., 2011; Wang et al., 2011), hydrothermal (Jacobsohn et al., 2007; Huang et al., 2012b; Riwotzki and Haase, 2001; Song et al., 2011; Zhang et al., 2010) or solvothermal (Gong et al., 2013; Kasuya et al., 2007; Nyman et al., 2009; Vorsthove and Kynast, 2011) synthesis, thermal (Si et al., 2006; Ye et al., 2010) or microwave (Dai et al., 2011) decomposition, solgel methods (Back et al., 2012; Dhanaraj et al., 2001; Eid et al., 2005; Gupta et al., 2010; Zhang et al., 2002), inverse micelle method (Barnes et al., 2000; Hirai et al., 2004), laser ablation in liquid media (Mhin et al., 2009; Singh et al., 2010), and combustion synthesis (Jacobsohn et al., 2007; Qi et al., 2002; Vu et al., 2007; Ye et al., 2009; Zhang et al., 2003), including flame-assisted spray pyrolysis, which is also capable of producing nanoparticles if the precursor solution is appropriately modified (Purwanto et al., 2008).

Chemical precipitation, sol-gel and some other methods of wet chemistry are very attractive because of simple and the relatively cheap process arrangement, but the collected products often require thermal post-treatment to improve their crystallinity and quantum efficiency. From this point of view, hydrothermal and solvothermal methods have a crucial advantage as they can facilitate the synthesis of well-dispersed crystalline nanoparticles at low temperatures (usually in the range 100–300°C). Another common shortcoming of many synthesis methods is a relatively low production rate of nanopowders. Upscaling of batchwise wet chemical processing is not always straightforward although for some methods this limitation is less pronounced. For example, sol-gel techniques are known for a high yield of the products. High production rates can be achieved with flame spray pyrolysis, where values on the order of 1 kg/h were already demonstrated (Mueller et al., 2003; Mueller et al., 2004).

As a next step towards the practical application of phosphors with decreased particle size, the optical performance of screens and coatings made of the new materials should be investigated. The choice of the screening technique is crucial because it affects both the optical and mechanical properties of phosphor coatings.

5.2 Deposition of separately produced nanophosphor powders

The simplest and most widely used method for depositing flat monochrome screens is gravitational settling (or sedimentation) of a suspension of phosphor particles in a solution containing a binder, e.g. potassium silicate buffered by barium nitrate or barium acetate (Sadowsky, 1949; Sasaki and Talbot, 1999; Tomita, 2007; Widdel, 1992). However, it is suitable only for large particles which settle fast. For particles smaller than 5 μm down to 1 μm, a centrifugal force should be applied in order to reduce the sedimentation time and to increase the packing density. Settling could hardly be applied for nanophosphors.

Electrophoretic deposition (EPD) is often used with fine particle size phosphors (Sadowsky, 1949; Sasaki and Talbot, 1999; Sluzky and Hesse, 1989; Yum et al., 2003). In this method, the phosphor in liquid suspension (e.g. isopropyl alcohol) is attracted to an immersed electrode. Phosphor particles should be electrically charged (e.g. by the introduction of charging ions such as Mg²⁺); the particles will then deposit onto the electrode of the opposite charge. Therefore, EPD requires a conductive substrate (e.g. ITO glass). Deposited samples are dried and baked. Smooth, dense phosphor layers with exceptional resolution and low noise can be deposited by EPD from conventional micrometer-sized phosphors, although the adhesive strength of EPD coatings is relatively weak (Yum et al., 2003). The deposition of luminescent nanoparticles by EPD and similar approaches has been reported (Lee et al., 2000; Smith et al., 2003; Wakefield et al., 2001; Zhang et al., 2006) but it does not seem to gain much popularity, which could be at least partly explained by the fact that the need for transparent and uniformly conductive substrates diminishes the attractiveness of the method for currently developing applications of nanophosphors other than field emission displays.

One of these applications (we will discuss them later in this review) is in phosphor-converted LEDs and there is ongoing research on the processing of nanophosphors by the corresponding standard manufacturing methods. Phosphor powders deposited onto UV- or blue LED chips are usually encapsulated by epoxy or silicone resins. This approach was successfully tested not only with epoxy (Nyman et al., 2009) and silicone (Revaux et al., 2011a) but also with poly(methyl methacrylate) (PMMA, Saladino et al., 2010), derivatives of ethyl methacrylate (Davion et al., 2011), poly-N-vinylpyrrolidone (PVP, Potdevin et al., 2012), and cyanoacrylate (Super Glue, Dai et al., 2011). In an interesting recent publication by Mutlugun et al. (2012), InP/ZnS quantum dots embedded in PMMA were processed into free-standing film with an area exceeding 50 cm × 50 cm. Requirements imposed on the encapsulation of nanophosphors and semiconductor quantum dot are very similar, so that the results obtained for the latter should be taken into account for the future work on nanophosphor-converted white LEDs. Furthermore, this knowledge could also be useful for X-Ray or UV-enhanced CCD image sensors, where similar strategies for the deposition of phosphor layers were proposed (Franks et al., 2000; Franks et al., 2003). Properties of the encapsulant are crucial because it may impair the quantum efficiency of the nanophosphor as discussed in Sec. 4.3. Nanophosphors should not agglomerate in the polymeric phase, which substantially limits the achievable particle volume fractions (e.g. < 20% w/w for CdSe quantum dots in 13 different polymers, Schreuder et al., 2008). Another related common problem is the photodegradation of encapsulants which lose their transparency under exposure to UV-light (Edwards et al., 2001; Koh et al., 2013, Narendran et al., 2004).

Thick layers of nanophosphors could be deposited with the well-known Doctor Blade method (Fujiwara et al., 2008) or by pressing a viscous paste between two substrates (Kasuya et al., 2007; Park et al., 2012a). The screen printing technique, in which a concentrated phosphor ink containing a liquid organic vehicle is applied to a substrate through a mesh screen and then calcinated to remove organic additives, could also be implemented for nanophopshor plasma display panels (Song et al., 2012a; Song et al., 2012b), field emission screens (Wang et al., 2011), and X-Ray imaging systems (Kim et al., 2007). Sol-gel coatings and pastes can be applied by dip-coating (Pang et al., 2003; Wu et al., 2007) or spin-coating (Bedekar et al., 2010; Buissette et al., 2006; Huang et al., 2012a; Khan et al., 2008; Klausch et al., 2012; Psuja et al., 2009; Revaux et al., 2011b; Song et al., 2011). Wet spraying, known for many decades (Sadowsky, 1949), could be adopted for the deposition of nanophosphors as well (Fleury et al., 2012; Revaux et al., 2011a).

In all the above-mentioned techniques, phosphor nanoparticles have to be dispersed in liquids and therefore obey the principles of colloidal chemistry. The composition of the solvent plays an extremely important role because it should prevent the agglomeration of nanoparticles (to ensure low scattering in the deposited screens and low viscosity of the phosphor slurry/ink/paste during processing) as well as the contamination of the screen by non-luminescent substances (residues of dispersants, surfactants, and chemical species adsorbed on the particle surface), which could decrease its quantum efficiency. Furthermore, the solvent is usually removed in the final step of deposition. Drying can cause substantial shrinkage of the phosphor layer potentially leading to the formation of cracks. For example, sol-gel coatings are especially prone to drying-induced cracks so that the crack-free deposits can be obtained only if the layer thickness does not exceed a certain critical value (typically on the order of 1 μm, Brinker and Scherer, 1990).

On the other hand, colloidal methods offer unique opportunities for processing nanophosphors such as shape-directed self-assembly (Si et al., 2006, Ye et al., 2010) and templating of colloidal crystals (Zhang et al., 2010). It also facilitates novel methods of the deposition of nanoparticles which are not applicable for conventional phosphors: layer-by-layer assembly (Camacho et al., 2012; Jang and Grunlan, 2005, Varahramyan and Lvov, 2006), Langmuir-Blodgett technique (Lu et al., 2005), and ink-jet printing (Fuller et al., 2002).

5.3 Simultaneous synthesis and deposition of nanophosphors

Not all methods of processing conventional coarse-grained phosphors require wet processing of powders. For example, in dry spraying, a fine spray of dry phosphor powder is blown from a gun onto the tacky surface (Sadowsky, 1949). This technique is hardly feasible for nanophosphors because dry nanoparticles tend to build agglomerates so that the advantages of reduced particle size could not be fully utilized even if spraying would succeed. However, premature agglomeration of ultrafine particles can be precluded by combining processes of gas-phase synthesis and film deposition in a single technology step. In such a way, all intermediate steps are excluded (i.e. dispersion in liquids is not required), and the deposition of phosphor coatings can be performed very rapidly. This approach is exploited in laser-assisted gas-phase condensation (Tissue, 2007) and electrostatic-directed deposition (Tsai et al., 2005), microwave plasma synthesis (Milewski et al., 1998) and hypersonic plasma particle deposition (Hafiz et al., 2004), as well as in flame aerosol deposition (FAD, Kubrin et al., 2010).

Flame aerosol deposition, also known as direct nanoparticle deposition (DND), is the best studied method as it was already tested for manufacturing advanced gas sensors (Kuehne et al., 2008; Mädler et al., 2006; Sahm et al., 2007), porous catalysts (Kavitha et al., 2007; Thybo et al., 2004), and battery electrodes (Chew et al., 2009), as well as for the deposition of anti-fogging films (Tricoli et al., 2009) and optical coatings (Pimenoff et al., 2006). It is also industrially applied in the fabrication of optical fiber preforms (Mendez and Morse, 2007; Tammela et al., 2006).

FAD is derived from flame spray pyrolysis and should be distinguished from other spray-based coating methods which could also be used for the deposition of phosphors but do not produce dispersed nanoparticles. One such method is spray deposition, where inorganic films are deposited by spraying solutions of appropriate reagents over a heated substrate. The chemical transformation occurs directly on the surface of the substrate. Phosphors can be deposited in this way (e.g. Y₂O₃:RE, Hao et al., 2001) but this method produces continuous films rather than powder coatings.

Flame spray pyrolysis (FSP) can be defined as a spray process where the high-temperature environment for chemical reactions is provided by heat released by a burning spray. FSP of flammable precursors should be opposed to the flame-assisted spray pyrolysis (FASP) of precursors that are not combustible themselves (e.g. aqueous solutions), and where heat is generated exclusively by an external flame. Different methods of synthesis of inorganic powders by FSP can be further classified into processes of direct droplet-to-particle conversion (DPC) and chemical vapor condensation (CVC). The droplet-to-particle conversion occurs when the precursor solute is not volatile. In such cases, the final weight of each single particle is proportional to the initial size of the droplet. The DPC usually produces submicrometer-sized particles. The CVC involves the combustion of volatile precursors which evaporate, react in the gas-phase, and condense to produce nanoparticles of the desired compounds. In the context of this review, both FSP and FAD refer to the CVC-type of particle formation. Latest reviews on the subject can be found in Pratsinis (2010); Teoh et al., (2010) and Strobel and Pratsinis (2007).

For the purposes of the deposition of particulate coatings, a substrate can be placed directly into the flame. Under certain conditions, this could result in the heterogeneous condensation of pyrolyzed compounds from the vapor-phase directly on the surface of the substrate, i.e. without producing free nanoparticles. This deposition technique, first published in 1993 (Hunt et al., 1993), is called combustion chemical vapor deposition (CCVD). It could also be used for the deposition of phosphors (e.g. Zn₂SiO₄:Mn, Kang et al., 2006) in the form of solid films. However, when the substrate is placed outside the reaction volume, airborne nanoparticles can be formed. In this way, the high temperature of the flame required to obtain particles with improved crystallinity is separated from the deposition zone. The substrate temperature can be decreased down to 150°C so that it can facilitate the direct deposition of nanopowders onto electronic chips (Tricoli et al., 2008).

FAD essentially shares the main strengths and weaknesses of FSP. On the one hand, it is exceptionally rapid and allows producing relatively thick deposits within minutes (Kubrin et al., 2010). From this point of view, FAD-deposited nanophosphor screens probably could compete with conventional phosphors even for applications which do not require optical transparency or high image resolution. On the other hand, due to the inherent limitation of all combustion synthesis methods, FAD/FSP is best suited for the production of oxides. Nevertheless, certain important non-oxide phosphors can still be obtained by appropriate post-treatment (Y₂O₂S:Er, Chen et al., 2003; Liu et al., 2002), flame pyrolysis in controlled inert atmosphere (ZnS:Mn, Athanassiou et al., 2010), or by simply using an appropriate halide source (NaYF:RE, Stepuk et al., 2013). The size of produced nanoparticles is controlled by parameters of the flame and, if needed, can be further decreased by charging them during the synthesis with a corona discharge (Vemury and Pratsinis, 1995). The deposits are extremely porous (particle volume fraction < 3 vol.%) but could be manually compacted to at least 10 vol.% without destroying the integrity of the phosphor layer (Kubrin et al., 2010). Further compaction should be possible through the elaboration of proper techniques. Even for the thickness on the order of 100 μm, the deposits were fairly homogeneous and free of cracks. FAD should be considered a powerful tool for future studies on nanophosphors, and can certainly inspire research on other functional nanoparticle coatings and other methods for the rapid processing of nanopowders.

6. Applications of nanophosphor screens

Phosphor-converted white LEDs was probably the field where the advantage of low scattering of light was recognized first. Most of work here is focused on YAG:Ce nanophosphor, which converts blue light from the LED chip into yellow so that white light is obtained by color addition. Kasuya et al. (2007) demonstrated a 200-μm-thick nanophosphor film with 82% transparency at the emission wavelength. No absolute figures of conversion efficiency or quantum efficiency were reported, but the doubling of photoluminescence intensity by placing a mirror on the rear side of the sample was pointed out. In the case of conventional micrometer-sized phosphor, the use of the mirror had no appreciable effect on screen performance. Nyman et al. (2009) reported an increase of quantum efficiency of YAG:Ce nanopowder to 57% and its successful epoxy-encapsulation. The quantum yield of the phosphor was further increased to 60% by a “protected annealing” in porous silica by Revaux et al. (2011c). The same group investigated the incorporation of nanophosphors into a TiO₂ sol-gel coating in order to match the refractive index and thus further decrease scattering (Revaux et al., 2011a; Revaux et al., 2011b). A systematic comparison of the performance of pc-LEDs incorporating YAG:Ce with the morphology of a nanophosphor, thin-film phosphor, ceramic plate and micrometer-sized powder was performed by Park et al. (2012a), also including a 2D photonic crystal layer for improving the extraction efficiency and short-wave pass filters for recovering the light emitted backwards. Nanophosphor-based LEDs showed a conversion efficiency of 31%, packaging efficiency of 82%, and luminous efficacy of 40.2 lm/W, not much worse than that of the ceramic plate or conventional phosphor powder and outperforming the thin-film phosphor. Recently, a luminosity of 100 lm/W was obtained with ligand-passivated Y₂O₃:Eu nanophosphor (Dai et al., 2011) discussed in Sec 4.3. This performance is competitive with current commercial products.

The optical transparency of nanophosphor layers was crucial in the development of transparent plasma display devices (PDD) first published in 2010 by the group of H. Yang at the Hongik University, Seoul, Korea (Song et al., 2010). Initially starting with monochrome green-emitting nanophosphor LaPO₄:Ce,Tb, they reached a luminance of 97 cd/m² (Song et al., 2011). The transparency of the phosphor layer in the wavelength range of emission exceeded 90% and that of the fully assembled test devices was at least 40%. The work on red-emitting Y(V,P)O₄:Eu followed soon after (Song et al., 2012b) and finally, the full-color PDDs based on LaPO₄:Ce,Tb, Y(V,P)O₄:Eu, and blue-emitting Y(V,P)O₄:Tm were reported (Song et al., 2012a). The phosphors were deposited by means of screen printing and combined by line patterning. The brightness of white emission was 96 cd/m² and could be increased to 137 cd/m² by the application of a 2D photonic crystal (a monolayer of ordered polystyrene micro-spheres of a uniform size). Transparency could be held on the level of 30%.

The advantageous properties of nanophosphors for field emission displays (FED) were demonstrated more than a decade ago (Lee et al., 2000; Wakefield et al., 2001). In this case, however, the main benefit was the increased phosphor efficiency attributed to the improved crystallinity and surface microstructure, not the decreased scattering. New works on nanophosphors for low-voltage cathodoluminescence have occasionally been published since then (Chang et al., 2010; Shang et al., 2012; Wang et al., 2011).

There were a few reports on the application of nanophosphors for X-ray imaging (Cha et al., 2011; Kalyvas et al., 2012; Kim et al., 2007), but none of them clearly addressed the effects of phosphor particle size. A comprehensive theoretical treatment applying the Mie scattering theory and Monte Carlo simulations showed that the best imaging performance should be expected from scintillator powders with a particle size greater than 200 nm (Liaparinos, 2012). It should be concluded that there is no advantage of utilizing nanophosphor screens for conventional digital radiography with a resolution lower than 20 lp/mm. This does not apply to X-ray microtomography and other imaging applications with submicrometer resolution (discussed in Sec. 2.4.), because nanophosphors have a great potential in this area.

Another promising application of nanophosphor screens is in the technology of solar cells, which absorb electromagnetic radiation and convert it into electricity. The efficiency of this process cannot exceed a so-called Shockley-Queisser limit (usually about 30%) unless they are enhanced by appropriate spectral converters (SC, Richards, 2006; van der Ende et al., 2009). Downshifting (conventional photoluminescence) and downconverting (quantum-cutting luminescence) SCs absorb high-energy photons and convert them to photons of wavelengths more efficiently absorbed by the corresponding solar cells. Such coatings are placed in front of the cell and ideally they should not interfere with light which does not need to be converted. Obviously, transparency of the converter layer is strongly desired so that nanophosphor coatings should be preferred over conventional phosphors (Huang et al., 2012a; Khan et al., 2008; Peng et al., 2011; Takeshita et al., 2009). Upconverting SCs perform a complimentary function of absorbing low-energy photons, for which the solar cell itself is transparent, and convert to photons of shorter wavelength so that they could also be absorbed by the solar cell. Upconverters are usually mounted on the rear side of the cell and can be processed from phosphor nanoparticles as well (Chen et al., 2012). It was predicted that the Shockley-Queisser limit for the efficiency of a single junction solar cell can be raised to 40% (using downconversion) or even 50% (using upconversion, van der Ende et al., 2009).

One more potential application of nanophosphors which relies on the transparency of powder coatings is in flat dielectric discharge lamps published recently (Klausch et al., 2012). A nanophosphor layer of YVO₄:Eu with > 90% transmittance in the visible range was tested as a prototype of a light-emitting window.

The luminescent properties of nanophosphors are affected by environmental conditions. For example, the intensity and decay time of luminescence or ratio of intensities of certain peaks in the spectra may substantially change for different ambient temperatures. Such effects further extend the list of possible applications of nanophosphor coatings, e.g. by scanning nanothermometry (Jaque and Vetrone, 2012). The options here are almost unlimited: if a high sensitivity in the physiological range is required, one can use upconverting nanoparticles (Fischer et al., 2011). In the range of extreme temperatures, nanoparticles of refractory phosphors could probably be applied even above 1000°C because the emission of bulk thermographic phosphors such as YAG:Dy can be measured up to 1700°C (Chambers and Clarke, 2009). The resolution of nanothermometry is approaching the size of the single nanoparticle and allows the temperature inside the living cells to be measured (Vetrone et al., 2010). The small size of nanoparticles facilitates numerous further ways of their utilization in biomedical imaging as fluorescent labels (Dosev et al., 2008), but these methods do not involve phosphor screens and thus will not be further discussed here.

7. Conclusions

In this review, we try to present the advantages of phosphor nanopowders for applications where continuous phosphor layers—screens—are used. The basic optics of phosphor screens is treated in detail so that the influence of particle size on the screen performance can be comprehensively explained. We discuss various further effects of particle size which modify the quantum efficiency of luminescent devices and have implications for the manufacturing technology. The most popular methods of deposition and suggested applications of phosphor screens/coatings are analyzed. Here, we summarize the main outcomes.

First of all, nanoparticles barely scatter light. This means that even relatively thick coatings can be virtually transparent and thus, nanophosphors are preferred for application as spectral converters in photovoltaics, and could potentially be applied in “augmented reality” displays including, e.g. contact lens displays (Lingley et al., 2011). Vanishingly weak scattering leads also to a dramatic qualitative change in the shape of the thickness dependence curves for the brightness of phosphor screens. Nanophosphor layers behave similarly to non-scattering screens (e.g. single crystalline films). It can be expected that their T-mode performance will only weakly depend on the thickness, both in terms of brightness and resolution, especially when excited by strongly absorbed radiation. Ideally, the excitation energy should be absorbed within some 200 nm from the exposed surface of the screen so that the emitting volume corresponding to a single image point could be kept smaller than the limit of diffraction. If emitted light was not scattered, the perfect image point could be observed from any direction, thus approaching the diffraction-limited image resolution, irrespective of the total screen thickness. For X-ray applications or other weakly absorbed radiation, the full thickness of the diffraction-limited nanophosphot screen would have to be kept below 200 nm.

The quantum efficiency of nanophosphors is usually lower than that of the corresponding bulk materials. This is explained to a large extent by the increased surface-to-volume ratio of the nanoparticles, which promotes the surface quenching effects. However, it is possible to turn this drawback into an advantage, e.g. by improving the efficiency of excitation of photoluminescence through appropriate functionalization of the particle surface with organic ligands. The same approach would not work with conventional coarse-grained phosphors.

A thorough characterization of the quantum efficiency of the luminescence lifetime of nanophosphors requires special care regarding the porosity of the deposits and refractive index of the medium filling the pores, because the observed luminescent properties are strongly affected by the effective refractive index of the surroundings of emitting ions. For example, compaction of the nanophosphor layer leads to improvement of the quantum efficiency as well as shortening of the emission decay time.

Nanophosphors offer special opportunities for processing the screens as their small particle size can facilitate untypical deposition methods such as self-assembly, templating of colloidal crystals, and ink-jet printing. Due to their cohesive nature, they could also be directly attached to a substrate in a very rapid process of flame aerosol deposition without using any adhesive or a binder. Moreover, we observed that the nanophosphor coating itself can act as an adhesive when we investigated compaction of the deposits between two substrates.

Continuous progress in the technology of nanophosphors will surely stimulate development of numerous new imaging applications. There is still ‘plenty of room’ spanning all possible excitation sources and all conceivable dimensions of the nanophosphor screens—starting from single nanoparticles excited by X-rays, as in recently published X-ray luminescence computed tomography (Cong et al., 2011; Carpenter et al., 2012), and ending with macroscopic volumes excited by infrared radiation, as in solid-state 3D displays (Downing et al., 1996).

Author’s short biography

Roman Kubrin

Roman Kubrin graduated from the North-Caucasus State Technical University in Stavropol, Russia, in 2002 and received his M.Sc. degree in Microelectronics and Microsystems from the Hamburg University of Technology (TUHH) in 2005. He later worked on the technology of phosphors with reduced particle size at the Institute of Optical and Electronic Materials at the TUHH, was a visiting researcher at the Particle Technology Laboratory at the Swiss Federal Institute of Technology (ETH Zurich), and received his Ph.D. (Dr.-Ing.) in 2012. He is currently working at the Institute of Advanced Ceramics at the TUHH on the synthesis of ceramic nanostructures for high-temperature photonics.

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