The Temperature-Dependent Interface States and the Reverse Current Conduction Mechanism of Single-Crystal ZnO Schottky Diodes

Abstract

The various current conduction mechanisms of Ag/ZnO Schottky diodes were explored by measuring the current–voltage characteristics from 100 to 300 K. In terms of thermionic emission, a comparison of the Schottky barrier height (SBH) to the ideality factor revealed two linear regions within 100–160 K and 200–300 K. Thus, the forward current characteristics feature two SBH sets with Gaussian distributions. The experimental ideality factor was approximated using the tunneling-related characteristic energy (E₀₀) (31 meV). Locally enhanced electric fields were associated with local low-barrier regions that enhanced the tunneling probability. The reverse current characteristics revealed that Poole–Frenkel (not Schottky) emission predominated, attributable to Zn_i-associated defects. Localized electric fields affected both the forward and reverse current characteristics and enhanced the internal electric field about five-fold.

Fig. 7 Fitting results of the reverse leakage current using the Poole–Frenkel emission (PFE) model. The inset shows a schematic of the band diagram under reverse bias. (online color)

1. Introduction

Wide band-gap semiconductors (band gap E_g > 3 eV), including SiC, β-Ga₂O₃, GaN, ZnO, and diamond, have attracted attention for use in high-performance optoelectronic devices and high-power, high-frequency electronic components [1–3]. ZnO is a wide band-gap oxide semiconductor that is transparent to visible light and exhibits high conductivity and elevated electron mobility [4]. Two-dimensional electron gas (ZnO/ZnMgO) microwave devices have been successfully constructed [5]. ZnO exhibits a higher exciton-binding energy (60 meV) than GaN (∼25 meV); the emitted light is brighter than that of GaN-based devices [6, 7]. High-quality single crystal ZnO wafers are now commercially available [8]. ZnO films of reasonable quality can thus be deposited at low temperatures on cheap substrates such as glass [9].

Metal/semiconductor (MS) contacts are basic components of semiconductor devices. Both a high Schottky barrier height (SBH, qϕ_B) and a low reverse leakage current that ensure high performance. In most practical devices, the SBH does not greatly depend on the work functions of metal contacts but rather the Fermi-level pinning is observed that is attributable to MS interface states [10, 11]. Most reported SBHs of n-ZnO Schottky diodes are 0.6∼0.9 eV regardless of the metal contacts used [6, 12]. A near-ideal Schottky diode (ideality factor 1.09) has been described [13], but most published ideality factors exceed 1.2 [12, 14]. ZnO exhibits ambient-dependent surface conductivity. For example, Schmidt et al. [15] showed that conductive bulk ZnO under vacuum exhibited reversible air resistivity; the conductive surface layer underwent passivation by acceptor-like adsorbates [13]. Oxidized metal contacts stabilized the metal/ZnO interface by passivating oxygen vacancies [16, 17].

In many studies, the SBHs of metal/n-ZnO Schottky contacts were determined at room temperature or above. However, studying diode characteristics under only such conditions does not yield comprehensive information on the current conduction mechanisms, barrier formation, or interface defects at the MS interface. For instance, Hyland et al. [18] monitored ZnO Schottky contacts with oxidized palladium PdO_x (x = 1.4) and iridium IrO_x (x = 1.9) from 20 to 180°C. In addition, Yadav et al. [19] examined the temperature-dependent electrical characteristics of Pd/ZnO Schottky diodes on n-Si from 294 to 443 K. The behavior of semimetal graphite/ZnO Schottky diodes was dominated by thermionic emission (TE) at 300–420 K [20]. Few studies have evaluated diode characteristics below room temperature [21–23]. Most such works used the barrier inhomogeneities to extract Richardson constants.

Here, the diode properties of Ag/ZnO Schottky contacts (the interface states and the reverse current conduction mechanism) were characterized using current–voltage (I–V) characteristics from 100 to 300 K.

2. Experimental

A hydrothermally grown ZnO ($11\bar{2}0$) single crystal (unintentionally n-type-doped: 1–2 × 10¹⁵ cm⁻³, thickness: 500 µm) served as the starting material. Before metallization, native oxide was removed by dipping into a HCl:H₂O (1:1) solution. An electron-beam evaporator was used to place Schottky and ohmic contacts (50-nm-thick Ag and 100-nm-thick Al) on the front and rear surfaces, respectively. Contact size was controlled using a metal shadow mask. I–V data were collected with the aid of an HP 4156B semiconductor parameter analyzer.

3. Results and Discussion

Figure 1 shows the I–V curves at 100 and 300 K; the numbers and arrows are the voltage sweep sequences and directions, respectively. Regardless of the sweep direction, the I–V curves did not exhibit hysteric behavior at 300 K but did at 100 and 140 K. The hysteric I–V characteristics of a GaN Schottky contact were associated with the presence of deep traps [24]. Orfao et al. [25] also observed low-temperature hysteresis in a GaN Schottky diode and attributed this to bias-dependent deep trap occupancy. This reduced the current when the diode was under a high negative voltage. The occupancy rate of deep traps at the Ag/ZnO interface might be associated with sweep direction-dependent current variations. Therefore, to derive the current conduction mechanism using the I–V data, the voltage sweep direction ran from 0 V to high positive or negative values.

Fig. 1

Current–voltage (I–V) hysteresis curves at (a) 100 and (b) 300 K. The numbers and the arrows indicate the voltage sweep sequences and directions, respectively. (online color)

The forward ln(J)–V data shown in Fig. 2(a) were used to extract both the SBH and ideality factor (n) using the TE model; the current density (J) is that of [10]:

  

\begin{equation} J = J_{S}\left[\exp\left(\frac{q(V - IR_{S})}{nkT}\right) - 1\right] \end{equation} (1)

  

\begin{equation} J_{S} = A^{*}T^{2}\exp \left(\frac{-q\phi_{B}}{kT}\right) \end{equation} (2)

where J_S is the saturation current density and A^* the effective Richardson constant (32 A/cm² K² for n-ZnO). Figure 2(b) shows a plot of qϕ_B versus n; linear correlations are apparent in two distinct regions at a low (100–160 K) and a high (200–300 K) temperature. Plot extrapolation to n = 1 yielded homogeneous SBHs of 0.662 and 1.262 eV at the low and high temperatures, respectively. A linear relationship between qϕ_B and n indicates that SBHs exhibit Gaussian distributions [26]. As there are two linear regions, there are two sets of Gaussian distributions [22, 27, 28].

Fig. 2

(a) Current density–voltage (J–V) curves at different temperatures and (b) plot of barrier height versus ideality factor. (online color)

The ideality factor exceeds unity [Fig. 2(b)], and thus may affect the generation/recombination or tunneling currents. When the forward current characteristics are dominated by the tunneling current, the current density is [29, 30]:

  

\begin{equation} J = J_{S}\exp \left[\left(\frac{q(V - IR_{S}}{E_{0}}\right) - 1\right] \end{equation} (3)

  

\begin{equation} E_{0} = n_{\textit{tunn}}kT = E_{00}\coth \left(\frac{E_{00}}{kT}\right) \end{equation} (4)

where E₀₀ = qħ/2(N_D/m_eε_S)^1/2 is the characteristic tunneling-related energy and n_tunn is the tunneling ideality factor, which can be written as [30, 31]:

  

\begin{equation} n_{\textit{tunn}} = \frac{E_{0}}{kT(1 - \beta)} \end{equation} (5)

where β is the SBH bias coefficient. Linear fitting of the nkT versus kT curve [Fig. 3(a)] yielded a slope of 0.188, thus smaller than the ideal (n = 1) (i.e., that of a pure TE model). The solid lines of Fig. 3(b) were derived from eq. (5) using different E₀₀ values with β = 0. The experimental values were approximated when E₀₀ = 31 meV [Fig. 3(b)]. This corresponds to an N_D = 6.16 × 10¹⁸ cm⁻³, which is much greater than the carrier concentration of bulk ZnO. Importantly, the calculated E₀₀ of an Ag/ZnO Schottky diode with N_D = 1 × 10¹⁵ cm⁻³, m_e = 0.26m₀, and ε_S = 8.5ε₀ (for ZnO) [32] was 0.39 meV.

Fig. 3

(a) A plot of nkT versus kT and (b) the calculated ideality factors with the characteristic energy (E₀₀) values given by eq. (5) (solid lines). (online color)

Current transport mechanisms can be classified into three groups by the carrier concentration and the temperature. TE dominates at E₀₀/kT ≪ 1 and field emission (FE) at E₀₀/kT ≫ 1; thermionic field emission (TFE) occurs between these values [33]. Here, E₀₀ < kT; thus, TFE is essentially absent. The high E₀₀ value of Fig. 3(b) reflects a locally enhanced electric field near the MS interface, associated with a local reduction of the Schottky barrier [28]. The electric field enhancement near the semiconductor surface may be attributable to interfacial nonuniformities, surface roughness near the periphery of the electrode, locally piled dopants and impurities, or an insulating interfacial layer [34]. Current conduction through a relatively small portion of an MS junction with a high E₀₀ (i.e., a low barrier) may govern the current transport over the entire junction [35].

An ideality factor larger than unity may also be attributable to certain interface states. The interface state density (D_it) distribution was calculated using the forward current characteristics; D_it is [36–39]:

  

\begin{equation} D_{it}(V,T) = \frac{1}{q}\left[\frac{\varepsilon_{i}\varepsilon_{0}}{\delta}\{n(V) - 1\} - \frac{\varepsilon_{S}\varepsilon_{0}}{W}\right] \end{equation} (6)

where ε_i and ε₀ are the permittivities of the interfacial layer and vacuum, respectively; ε_S the semiconductor dielectric constant; and W the depletion layer width. The ideality factor n(V) is then:

  

\begin{equation} n(V) = \frac{qV}{kT\ln (J/J_{0})} \end{equation} (7)

The value of ε_iε₀/δ can be extracted from [39]

  

\begin{equation} \frac{\varepsilon_{i}\varepsilon_{0}}{\delta} = \left[\frac{\varepsilon_{S}\varepsilon_{0}}{W}\left(\frac{1}{\beta_{r}} - 1\right)\right] \end{equation} (8)

where β_r = (kT/q)[d(ln I)/dV] is the slope of the reverse I–V data. When the probability of transmission between the metal electrode and the interface states is very low, the effective SBH (qϕ_e) of an n-type semiconductor may be bias-dependent, thus [40]:

  

\begin{equation} q\phi_{e} = q\phi_{B} + q\left(1 - \frac{1}{n(V)}\right)(V - IR_{s}) \end{equation} (9)

The energy level is then E_C–E_t = q(ϕ_e − V). As shown in Fig. 4, D_it decreased from the bottom of the conduction band (E_C) toward the mid-gap. For example, the D_it values at 100 K varied from 2.51 × 10¹³ eV⁻¹ cm⁻² at E_C–0.06 eV to 5.06 × 10¹² eV⁻¹ cm⁻² at E_C–0.27 eV and those at 300 K from 5.51 × 10¹² eV⁻¹ cm⁻² at E_C–0.52 eV to 5.25 × 10¹¹ eV⁻¹ cm⁻² at E_C–0.83 eV. This D_it distribution is similar to that of an earlier work [41]. Moreover, D_it varied by temperature (Fig. 4), perhaps attributable to atomic reordering/restructuring of the MS interface [42]. As the temperature decreased, the Fermi level moved toward a low E_C–E_t region with a higher D_it. The bias voltage-dependent variation in surface potential could then become (partially or completely) pinned, associated with a higher ideality factor [43]. An elevated D_it increases the metal tunneling probability, lowering the SBH. At high temperatures, the Fermi level moves toward a high E_C–E_t region with a lower D_it. The surface potential then readily changes, associated with a lower ideality factor and a higher SBH [43]. Consequently, the interface states behave as an interfacial layer through which electrons tunnel to the metal; the temperature-dependencies of SBH and the ideality factor then vary.

Fig. 4

The distributions of D_it values at each temperature obtained using the forward current characteristics. (online color)

The temperature dependence of D_it may also reflect barrier inhomogeneity [44–46]. Figure 2(b) shows the relationship between SBH and the ideality factor. At low temperatures, electrons cannot climb the high energy barrier and thus mainly tunnel through low-barrier regions; the ideality factor is then large. With increasing temperature, electrons can vault the high barrier; the SBH is then high and the ideality factor low [47]. The high SBH at elevated temperatures increases E_C–E_t; the plot of D_it versus E_C–E_t then shifts toward the mid-gap [48].

The reverse current characteristics were initially explored using the Schottky emission (SE) model (i.e., TE with image force-lowering); the reverse current density was then [10, 49]:

  

\begin{align} J &= A^{*}T^{2}\exp \left(-\frac{q\phi_{B}}{kT}\right)\exp \left(\frac{q\sqrt{qE/4\pi\varepsilon_{\infty}\varepsilon_{0}}}{kT}\right),\\ \beta_{\textit{SE}}& = \sqrt{\frac{q}{4\pi \varepsilon_{\infty}\varepsilon_{0}}} \end{align} (10)

where E is the electric field at the MS interface, ε_∞ the high-frequency dielectric constant (3.7 for ZnO [50]), and β_SE the SE coefficient. The plots of ln(J/T²) versus E^1/2 [Fig. 5(a)] yielded the slopes at each temperature. Next, linear fitting to the plot of Fig. 5(b) showed that the dielectric constant was 0.71, about five-fold less than the theoretical value.

Fig. 5

(a) Schottky emission (SE) plots of ln(J/T²) versus E^1/2 and (b) the slopes calculated using the SE model for each temperature. (online color)

When the Poole–Frenkel emission (PFE) predominates, the Coulombic potential energy of electrons trapped in defect states is reduced by an applied voltage. Thus, the probability that electrons are thermally emitted from the defect level to the conduction band or to a continuum of defect states increases. The current density associated with PFE exhibits an exponential dependence on the trap activation energy [49, 51]:

  

\begin{equation} J = CE\exp \left[-\frac{q(\phi_{t} - \sqrt{qE/\pi \varepsilon_{\infty}\varepsilon_{0}})}{kT}\right],\quad \beta_{\textit{PF}} = \sqrt{\frac{q}{\pi \varepsilon_{\infty}\varepsilon_{0}}} \end{equation} (11)

where C is a constant, qϕ_t is the energy barrier of electron emission from the trap, and β_PF is the PFE coefficient. Equation (11) can be written:

  

\begin{align} \ln(J/E) &= \frac{q}{kT}\beta_{\textit{PF}}E^{1/2} - \frac{q\phi_{t}}{kT} + \ln(C) \\ &\equiv S(T)E^{1/2} + R(T) \end{align} (12)

Linear fitting to the plots of ln(J/E) versus E^1/2 [Fig. 6(a)] yielded S(T) and R(T) [Figs. 6(b) and (c), respectively]. Linear fitting to the plot of Fig. 6(b) yielded β_PF = 4.46 × 10⁻⁴ eV cm^−1/2 V^−1/2 and a dielectric constant of 2.90. Compared to the dielectric constant from the SE model, 2.90 is closer to the theoretical ZnO value, indicating that the PFE model best explains the reverse I–V characteristics.

Fig. 6

(a) Poole–Frenkel emission (PFE) plots of ln(J/E) versus E^1/2 and (b) the calculated S(T) and (c) R(T) values. (online color)

The linear fitting of Fig. 6(c) yielded a qϕ_t of 0.15 eV. The principal ZnO defects are Zn interstitials (Zn_i) and oxygen vacancies (V_O). However, the prime, undoped ZnO defect remains debatable [52]. V_O are very deep donors (certainly not shallow) and barely contribute to n-type electrical conductivity [53]. In contrast, Zn_i are known to lie at E_C–0.15 eV [52] or E_C–0.20 eV [54]. Hence, Zn_i-related defects might explain the observed PFE process. As shown in Fig. 7, the calculated current densities using the S(T) and R(T) values at each temperature matched the experimental data. The inset of Fig. 7 is a schematic of the band diagram. When reverse bias was applied, electrons were injected from the electrode into ZnO and became trapped in ZnO defects. As the reverse bias increased further, the trapped electrons acquired energy that allowed them to exit the traps to the conduction band. Thus, current conduction is PFE-like.

Fig. 7

Fitting results of the reverse leakage current using the Poole–Frenkel emission (PFE) model. The inset shows a schematic of the band diagram under reverse bias. (online color)

A thin, surface barrier model has been used to simulate the high leakage current of GaN Schottky diodes. The high density of interface states increased the electric field at the MS interface, enhancing the tunneling current [55]. Wu et al. added an electric field enhancement coefficient to the Fowler–Nordheim model when investigating the reverse current characteristics of AlGaN/GaN Schottky diodes [56]. The forward current characteristics yielded a high E₀₀ value. Thus, the actual electric field might be stronger than the theoretical field. The average electric field in a ZnO film may be enhanced by localized electric fields (LEFs). Then, the PFE model can be modified as follows [57, 58]:

  

\begin{equation} J \propto \frac{kT}{\alpha \beta_{\textit{PF}}E^{1/2}}\exp\left(\frac{\alpha \beta_{\textit{PF}}}{kT}E^{1/2}\right) \end{equation} (13)

where α is the ratio of the experimental and theoretical PFE coefficients. From Fig. 6(b), α was found to be 1.133. Here, α² is an electric field enhancement factor given by α²E that increases the internal electric field by the factor α² = 1.285. LEFs may be induced by band-bending at the electrode-ZnO boundary, nonuniform crystallinity, or trap states [59].

To confirm that PFE dominated the reverse I–V characteristics, two other Ag Schottky diodes (D1 and D2) formed on the same ZnO surface were similarly analyzed. Figures 8(a) and 9(a) show the plots of ln(J/E) versus E^1/2 for D1 and D2, respectively. The linear fittings to the plots [Figs. 8(b) and 9(b)] yielded β_PF values of 8.93 × 10⁻⁴ and 4.77 × 10⁻⁴ eV cm^−1/2 V^−1/2, corresponding to dielectric constants of 0.72 and 2.53 for D1 and D2, respectively. Note that the D1 and D2 dielectric contacts based on the SE model were 0.17 and 0.89, respectively. The results confirm that (mainly) PFE controls the reverse current characteristics. Linear fittings to the plots of Figs. 8(c) and 9(c) yielded qϕ_t values of 0.24 and 0.16 eV for D1 and D2, respectively. The electric field enhancement factors (α²) were 5.131 and 1.463, respectively.

Fig. 8

(a) Poole–Frenkel emission (PFE) plots of ln(J/E) versus E^1/2 and (b) the calculated S(T) and (c) R(T) values for D1. (online color)

Fig. 9

(a) Poole–Frenkel emission (PFE) plots of ln(J/E) versus E^1/2 and (b) the calculated S(T) and (c) R(T) values for D2. (online color)

Reverse leakage currents may reflect electrode-limited conduction (Schottky emission, TFE, and Fowler–Nordheim tunneling) and semiconductor bulk-limited conduction (PFE, variable range hopping conduction, and space charge-limited current). Table 1 summarizes these current conduction mechanisms and how they are affected by the electric field and temperature [49, 60, 61]. In the real world, two transport mechanisms can simultaneously contribute to reverse currents. Within the same device, different mechanisms may be in play depending on the bias voltage at any time. The transport mechanisms may vary greatly by the device conditions.

Table 1 The various possible reverse current transport mechanisms [49, 60, 61].

In this work, the focus has been on temperature-dependent current transport properties below room temperature. Gür et al. [62] obtained the I–V characteristics of an Ag/ZnO Schottky diode from 200 to 500 K. The diode characteristics deviated from those of TE at high temperatures (above 440 K), associated with trap-assisted tunneling stimulated by deep states at E_C–0.62 eV [62]. Hence, new defects triggered by high temperatures may affect both the forward and reverse I–V characteristics. Oxidized metal contacts on a bulk ZnO planar diode exhibited stable forward and reverse current characteristics up to 180°C [13, 18, 63]; the reverse current was explained by Schottky emission. In the present context, such an approach might reduce D_it and change the dominant transport mechanism from a trap-involved PFE process to Schottky emission. Our future work will explore the current transport properties using such a metal scheme.

4. Conclusion

The current conduction mechanisms of Ag/ZnO Schottky diodes were explored after determination of the I–V characteristics from 100 to 300 K. The plot of the SBH versus the ideality factor exhibited two distinct linear regions, indicating the presence of two sets of Gaussian distributions. The experimental ideality factors were fitted using a tunneling-related characteristic energy E₀₀ = 31 meV. This reflects barrier inhomogeneity; locally enhanced electric fields were associated with local low-barrier regions that enhanced the probability of tunneling transmission [28, 64]. The reverse I–V characteristics were dominated by PFE, with involvement of Zn_i-related defects. LEFs increased the internal electric field approximately five-fold.

Acknowledgements

This study was supported by the Research Program funded by the Seoul National University of Science and Technology (Seoultech).

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