Strain of GaAs/GaAsP Superlattices Used as Spin-Polarized Electron Photocathodes, Determined by X-Ray Diﬀraction

The strains in GaAs/GaAsP superlattices used in spin-polarized photocathodes grown on GaAs and GaP (001) substrates were determined by X-ray diﬀraction. The thicknesses of the GaAs wells and GaAsP barrier layers were also determined. The band structures of the superlattices were calculated on the basis of these experimentally determined strains and layer thicknesses. The thicknesses and band structures were in good agreement with those observed by transmission electron microscopy and photoluminescence, respectively. The strains induced in the GaAs well layers were approximately linearly dependent upon the phosphorous fraction in the GaAsP layer, and the splitting between the heavy hole band and the light hole band of the superlattices grown on GaP substrates was larger than that of superlattices grown on GaAs substrates. In photocathodes grown on GaP substrates, low polarizations were observed, not due to a lack of band splitting, but to depolarization scattering caused by crystal defects, which were diﬀerent from that induced in superlattices grown on GaAs substrates.


I. INTRODUCTION
Spin-polarized electron photocathodes have primarily been applied in the field of high energy physics [1,2]. Spin-polarized beams are obtainable by irradiating mate-  9.0 GaP #7 12 9.0 GaP cathodes were irradiated by the laser. From the various structures developed, a high polarization and a high efficiency were realized using strained GaAs/GaAsP SLs grown on GaAs substrates [10].
To apply spin-polarized electron beams to the field of materials science, it is necessary to realize a high brightness. Therefore, electrons should be excited by a finely focused laser beam. For this purpose, a transmissiontype photocathode with a strained GaAs/GaAsP SL was developed, in which the cathode is irradiated from the rear. In a transmission-type photocathode, a transparent substrate for the excitation laser is required. Photocathodes with the same structure as that grown on the GaAs substrates were grown on GaP substrates. Photocathode growth on GaAs substrates resulted in high polarization, with a maximum value as high as 92% [10]. In contrast, the maximum polarization was as low as 64% when using GaP substrates, for reasons discussed in another paper [11]. The polarization was improved by inserting a 500-nm-thick GaAs layer between the GaP substrate and GaAsP layer [12,13]. A high polarization was realized, but no precise structural analysis of the SLs grown on GaAs and GaP substrates was performed. In the present paper, strains in the SLs were determined using X-ray diffraction, and the band structures were calculated on the basis of the experimentally determined parameters. The correlation between strain and polarization was examined.

A. Specimens
Seven spin-polarized electron photocathode specimens were prepared. These photocathodes were fabricated by metal organic vapor-phase epitaxy on GaAs and GaP substrates. Both the GaAs and GaP substrates were p-type and (001)-oriented. Specimens #1-3 were grown on GaAs substrates, and the others were grown on GaP substrates. The photocathodes consisted of stacks of a 1-to 2-µmthick GaAsP layer (called the buffer layer) and 12 or 16 pairs of GaAs-GaAsP strained SL. In specimen #5, an intermediate layer, with a phosphorous fraction changed stepwise from one to that of the GaAsP buffer layer, was inserted between the GaP substrate and the buffer layer. For specimens #6 and #7, a 500-nm-thick GaAs layer was inserted (referred to as the inserted layer) between the GaP substrate and the GaAsP layer. Finally, the SL was coated with a highly doped 5-nm GaAs layer. The important parameters are tabulated in Table I. Specimen #1 was grown at Daido Steel Co., and all other specimens were grown at Nagoya University. References [9,10] detail the respective source materials and growth conditions.

B. Measurements
To enable strain analysis, the lattice constants of the respective layers should first be determined. For this purpose, reciprocal maps were measured using 004 symmetric reflections, as well as asymmetric 113 reflections. Asymmetric 113 reflection measurements were performed in which the glancing angle was either smaller or larger than the Bragg angle. These conditions are specified as 113S and 113L reflections, respectively. Furthermore, for some specimens, asymmetric 224 reflections were also measured, but only with a glancing angle smaller than the Bragg angle. All reciprocal maps were measured using the "ω step and radial (2θ − ω) scan" method [14]. The measurements were repeated by rotating the specimens stepwise in 90 • increments around the [001] direction. This rotation is referred to as φ rotation, in which the zero position of φ was defined as the position at which the incident beam was perpendicular to the [110] direction, and X-rays impinged upon the specimens from the (110) surface in the direction of the flat orientation cut on the (110) surface. The φ rotation was performed counter-clockwise. An X-ray diffractometer, ATX-G (RIGAKU), was used. The accelerating voltage was 50 kV, the beam current was 300 mA, and the target was Cu. A triple axis diffractometer was used, and the incident X-rays were monochromated and collimated by two channel-cut monochromators employing the Ge 220 reflection. The diffracted Xrays were analyzed by a channel-cut monochromator, using the Ge 220 reflection. To compare the X-ray diffraction results, the band gap energy was observed by a photoluminescence method, and the thicknesses of the SL layers were observed by transmission electron microscopy.

III. RESULTS AND DISCUSSION
As typical examples, the reciprocal maps for 113S reflections from specimens #1, #2, #4, and #7 at φ = 0 • are shown in Figs. 1(a), (b), (c), and (d), respectively. In Figs. 1(a)-(d), the main satellite peak and peaks due to the GaAs or GaP substrate and the GaAsP buffer layer are observed, while in Figs. 1(c) and (d), two sub-peaks of the SL of the 1st order are observed in addition to the main peak. The main satellite peak of the SL is denoted as ST0 and the sub-peaks are denoted as ST±1. In Fig. 1(d), a peak due to the inserted GaAs layer is also observed. These maps were plotted on a logarithmic scale. In the present paper, the results of the reciprocal maps are presented using scales of the ω scan (abscissa) and the 2θ − ω scan (ordinate), instead of the conventional reciprocal scales. Because the angular width of 2θ for the 2θ − ω scan was set to equal twice the value of the ω step, the lines parallel to the diagonal line from the Values of 2θ and ω for the respective peaks were determined by the method of least squares, using the numerical data from the maps. Then, the coordinates of the peaks in reciprocal space were calculated. In this process, we assumed that the GaAs or GaP substrates were located at their perfect crystal positions. The observed positions of the substrates deviated from those of the perfect crystals, due to uncertainty of the zero-positions of 2θ and ω in specimen setup, so that the calculated positions of all peaks deviated by the same amount from the observed positions, and the deviations were modified.
The lattice constants of the GaAsP buffer layers were determined for all specimens. For specimens #6 and 7, the lattice constants of the inserted GaAs layers were also    Figs. 2(a) and (b), respectively. It should be noted that the lattice constants c determined from the 004 reflection and from the asymmetric reflections were almost identical for all specimens, supporting the reliability of the present analysis. Therefore, the following analysis was performed using only 113S reflections, in which the clearest peaks were observed among the asymmetric reflections.  For specimen #4, the lattice constants a and c were nearly equal, indicating that the layer was unstrained. However, for specimen #7, the c-values were smaller than the a-values, indicating that the layer was under tensile strain along the crystal surface. The implicit lattice constants of the buffer layers, a 0,GaAsP , which would exist when the layer was strain-free, were determined by assuming that the layers were distorted into a tetragonal form. The implicit lattice constants are given by, where C 11 and C 12 are elastic constants, and are given by [15] C 11 = 11.88 + 2.24x(N/m 2 ) and (2) where x is the P fraction of the GaAsP buffer layer. Although the elastic constants depend on the P fraction, both C11 C11+2C12 and 2C12 C11+2C12 are almost independent of this fraction. Therefore, a 0,GaAsP could be determined, even though the exact fraction was unknown. The P fraction was determined from the obtained implicit lattice constants using the following equation, a 0,GaAsP (nm) = 0.5654 − 0.0203x, (4) and the results are tabulated in Table II. Secondly, the strains of the GaAs well layers and GaAsP barrier layers of the SLs are obtainable if we assume that  the layers are tetragonally distorted, and further assume that the P fraction of the GaAsP barrier layer is identical to that of the buffer layer. Furthermore, it was also assumed that the lattice constants along the , where a 0,GaAs is the lattice constant of perfect GaAs, 0.5654 nm. Here, the average lattice constant of the SL along the [001] direction was also determined from the reciprocal position. The results are shown in Table II, and are compared with the P fraction. The relationship between x and ε 0,GaAs was approximately linear with respect to the phosphorous fraction of the GaAsP layer, as shown in Fig. 3.
Finally, the thicknesses of the layers were determined. The strains along the [001] direction are given by ε zz = −2 C12 C11 ε xx , where C 11 and 12 are the elastic constants for the respective layers, and ε xx are the strains of the respective layers. As the strains of both layers and the P fraction of the barrier layer were obtained, the lattice constants for the layers along the [001] direction were determined, as shown in the Appendix. The periods of the SLs were experimentally determined from the satellite peaks for specimens from which these peaks were observable, and the design values were used for specimens from which only the main satellite peak was observable. The results are tabulated in Table III. The obtained thicknesses differed from their design values for some specimens. Therefore, the thicknesses of the SL layers were measured by transmission electron microscopy, and the results for specimen #3 are shown in Fig. 4. The image indicates that the ratio of the thickness of the well layer to that of the barrier layer was almost 1:2, in agreement with the present X-ray diffraction results. These results support the reliability of the present analysis.
Once the strains and thicknesses of the well and barrier layers were known, the band structures of the SLs were calculated on the basis of model solid theory [16]. In Table IV, the band gap energy (E th ) and the splitting between the heavy hole band and the light hole band (∆ s ) are tabulated. Figure 5 shows a comparison of E th with the peak energies of photoluminescence (E ph ), demonstrating good agreement. The splitting amounts were important to realizing high polarization, and the relationship between the band splitting (∆ s ) and the maximum polarization were compared, with the results shown in Fig. 6. Figure 6 indicates that the polarization from photocathodes grown directly on GaP substrates was low, despite significant band splitting. In contrast, for photocathodes grown on a GaAs layer or a GaAs substrate, high polarizations were realized. The strains and lattice constants determined by X-ray diffraction gave average values over a wide area, so local fluctuations may exist, and would appear as a spreading of the intensity regions in the reciprocal maps. In the present experiments, the intense regions in the maps of the GaAsP layer and the SL were much wider than those of the GaAs substrate and GaP substrate, as shown in Fig. 1. The same behavior was observed for all specimens. However, the local fluctuations of specimens #4 and #5 were rather small compared to those of the other specimens. Further investigation is necessary to conclusively explain the reasons for the low polarization from these specimens. However, it can be concluded that the lower polarizations from photocathodes grown directly on GaP substrates were not due to a lack of band splitting. One possible explanation is that before polarized photoelectrons are extracted into vacuum, they become depolarized due to scattering by lattice defects induced by compressive strain, which are different from those induced by tensile strain. The present results support previous results, in which the insertion of a GaAs layer between the GaP substrate and the superlattice effectively yielded 90% polarization [13].

IV. CONCLUSIONS
The strains and thicknesses of GaAs/GaAsP superlattices used in spin-polarized photocathodes grown on GaAs and GaP (001) substrates were determined by Xray diffraction, and the band structures were calculated. The splitting between the heavy hole band and the light hole band of superlattices grown on GaP substrates was large compared to that of superlattices grown on GaAs substrates. The reason for the low polarization of photocathodes with a GaP substrate was not the lack of band splitting, but depolarization scattering caused by crystal defects, which were different from those present in the superlattices grown on GaAs substrates. and the thicknesses of the barrier and well layers, t B and t W , are given by t B = n B c B , and (11) t W = n W c W . (12)