1. Introduction

Germanium wafer has been widely used in the manufacture of solar cells (both for space and terrestrial concentrator systems) as a key-substrate material for building-up multi-junction solar cells made of various Ⅲ-V compound layers. The main reason for this success is that germanium shows only a small lattice mismatch to gallium arsenide and it offers clear advantages over conventional gallium arsenide substrates including high crystallographic perfection (especially for dislocation free wafers), high mechanical strength (used for thinner wafers), slightly higher thermal conductance, it is environmentally friendly and has a lower cost^[1]. By stacking multiple solar cells in order of their bandgaps, with the cell having the largest bandgaps at the top, the efficiency of a solar cell can be increased due to capturing a large fraction of the solar spectrum and having small thermal losses^[2]. Previous studies of multi-junction solar cells have reported the leading results of conversion efficiencies approaching 30% and more than 42% under concentrator system^[3-8]. The bottom cell made of germanium substrate not only plays a role in the current matching, but also dominates the epi-layer quality and the entire multi-junction cell. The dislocations generated due to the thermal or mechanical strain during the manufacturing of germanium substrate can propagate into the epi-layer as a severe carrier lifetime killer, which has a negative influence. Thus germanium crystals with an extremely low density of grow-in dislocation are desirable. Much of the research works have concerned the new techniques that can be introduced into the manufacture of germanium single crystal such as the cover of B₂O₃ and the traveling magnetic field^[9-15]. However, despite the dislocation-free epi-ready germanium substrates are claimed to have a nominally high and identical quality, the epi-layer quality and the multi-junction solar cell performance indicate that detection of the difference of substrates from different vendors is important for both industry and scientific research needs^[16].

In this work we investigate two groups of dislocation-free germanium single crystal epi-ready substrates from different vendors. Both samples are grown by the vertical gradient freeze (VGF) method and sliced from a similar portion of the ingots. Hall effect measurement and glow discharge mass spectrometry (GDMS) are used to analyze the electronic properties and impurity concentration. To reveal the etch pit density (EPD) distribution, the samples are etched in preferential etchant [HNO₃:HF:Cu(NO₃)₂] solution with a ratio of 2:0.5:1 for 5 min. Various techniques are used to estimate the residual stress and crystalline quality. Among them, X-ray diffraction (XRD) provides measurement of the lattice parameter, thereby giving the most fundamental measurement of the stress. Raman scattering was used to characterize residual stress in the wafer by checking the Raman peak splits and shifts.

2. Experimental

The samples used are Ga doped p-type 4 inch germanium single crystal substrates with thickness around 175 μm supplied by different vendors. The samples are sliced from the top portion of the ingots grown by the VGF method in [100] orientation and are claimed to be dislocation-free with an EPD under 500 cm^-2. The characterization of carrier concentration and minority carrier lifetime were made by Hall effect measurement and microwave photoconductivity decay (μ-PCD) at room temperature. To check the uniformity and distribution of the carrier concentration, we took ten points along the diameter on each sample wafer for Hall measurement. The preferential etching to measure the EPD distribution was taken at 30 ℃ for 5 min, using the etchant [HNO₃: HF: Cu(NO₃)₂] solution with a ratio of 2:0.5:1. After etching two samples were observed and pictured in a metallographic microscope. Impurity concentration was characterized by glow discharge mass spectrometry (GDMS) in Evans Analytical Group. Raman scattering spectra were obtained at room temperature via exciting the samples with an Ar⁺ laser at 514 nm in a Horiba LabRAM HR800 spectrometer. XRD diffraction measurement was operated by a Bede-Di system at room temperature. The identification of the diffraction plane and Bragg angle was made using the ICDD/JCPDS PDF database. A reference Ga doped p-type 4 inch Ge wafer sample with low dislocation density and good uniformity grown by the Cz method is also measured for comparison.

3. Results and discussion

3.1 Dislocation etching result

We took 9 positions into the analysis on each sample. After preferential etching for five minutes, we counted and pictured the specimens in a metallographic microscope. The EPD results of sample A are 331, sample B 203 and the reference sample 235. We choose three representative figures for each sample to show the difference. As is shown in Figure 1, the etch pits in Figures 1(a) to 1(c) are a little more than the other six figures. As is known the VGF method has a superiority in low crystal dislocation density because of the low temperature gradient and low growth rate used in the growth process. Although the etch pits density in both samples are quite low, sample A shows more dislocation and an inferior uniformity than sample B. Compared to the reference sample whose dislocation etching result is shown in Figures 1(d) to 1(f), it seems that the dislocation distribution is not uniform and a dislocation cluster or an aggregation region exist on the two wafers although their average dislocation density is low. This situation is apparent for sample wafer A. It is most likely the reason that there is a large difference of X-ray rocking FWHM across the wafer as shown by the following result.

3.2 Residual impurity and electronic property

The impurity content in the Ge wafers measured by GDMS is listed in Table 1. It shows that the concentration of most impurities in the germanium wafers is in the same level. Especially, although encapsulant B₂O₃ and pBN crucible are used in the VGF growth process of Ge single crystal, the boron concentration is quite low. This result suggests that boron contamination is negligible in the VGF growth process. In addition, the transition metal contents in two samples are all below the detection limit of GDMS, indicating the concentration of the conventional lifetime killer in the samples is very low. Indeed, the microwave photo conductivity decay (μ-pcd) measurement shows a small difference of the Ge wafers with the minority carrier lifetime ranging from 11 to 13 μs.

The difference in Ga concentration of the two samples is mainly because they came from different vendors with different standards of dopant concentration. The carrier concentration distribution along the diameter direction is shown in Figure 2. Samples A and B show the same shape of distribution plot^[16]. The inset figure is the statistics of the mean carrier concentration and standard deviation of two samples. Sample A has a smaller standard deviation of 0.14148, while sample B has a larger standard deviation of 0.16636. Although the standard of the Ga dopant concentration is different in the samples, the doping activation rate of the three samples seems to be at the same level by a comparison of the mean carrier concentration and the measured Ga concentration. This fact is most likely related to the low growth rate used in the growth process and that most Ga atoms occupy the lattice site which acts as a shallow acceptor in this case.

3.3 Lattice parameter analysis

The lattice parameter of each sample was measured by the precision X-ray method of Bond^[18]. This method consists of the accurate determination of the angle between two positions of the crystal when X-rays are being diffracted from the desired crystal plane. We took five points from each sample into characterization and took an average. Therefore, the accurate Bragg angle of plane (400) can be calculated. Bragg′s law is used to obtain the lattice spacing of a particular cubic system through the following relation:

$2d\sin q=nl,$

(1)

$d=\frac{a}{\sqrt {h^2+l^2+k^2}},$

(2)

where d is the lattice spacing of the cubic crystal, a is the lattice parameter and h, k, and l are the Miller indices of the Bragg plane, so that, the lattice parameters of the three samples can be calculated by using d-spacing values for plane (400) as shown in Table 2.

It is clear that the lattice parameter of sample A is smaller than sample B. The lattice parameter shown in the PDF card is 5.658 Å. Comparing the deviation from each sample to the PDF card, we can deduce that sample A has the largest lattice deformation which is most likely caused by the generation and aggregation dislocation. Combining with the EPD result sample A has an inferior crystallographic perfection and has released the residual stress through the formation of dislocation. During the epitaxial process, lattice imperfections, such as dislocations in substrate could extend into the epi-layer and propagate, which results in the formation of interface defects. The interface defects are non-radiative recombination centres, which act as the minority carrier lifetime killer and influence the open circuit voltage of the MJC.

3.4 XRD measurement

In this study we characterized four regions in each sample to analyze the uniformity of the crystalline quality using XRD measurement. XRD rocking curves of the two samples and the linewidth designating the full width at half maximum (FWHM) are shown in Figure 3 and Table 3. The results exhibit the clear difference in the shape of diffraction peaks. It is clear that we can ignore the FWHM caused by beam divergence and focus on the peak broadening owing to the crystal quality. In sample A, the value of FWHM changes from 20 to 200 arcsec, which means an inferior uniformity and the existence of lattice deformation such as polycrystalline or low angle grain boundary, which is usually caused by dislocation cluster or aggregation. The narrow diffraction peaks and good uniformity indicate that sample B has better crystalline quality. In contrast, the reference sample gives a very good result in the shape of diffraction peaks with FWHM in the range of 15-18 arcsec. This result gives further evidence that the dislocation cluster is a main factor that influences the lattice perfection and uniformity of the VGF wafer.

3.5 Raman spectra

The Raman spectra of the two samples are shown in Figure 4. While the Raman spectra peaks have a somewhat different intensity depending upon the surface roughness of the samples, we use the normalized intensity to focus on the frequency shift referring to stress and strain. The peak observed at around 300 cm^-1 is assigned to the longitudinal optical (LO) Ge-Ge phonon mode^[19]. Using Gaussian functions to fit Raman spectra peaks, we obtained the peak frequency and linewidth in full width at half maximum. The following equation we used to calculate the stress: s (dyne/cm²) = 3.4 × 10⁹ δΩ_s (cm^-1) is obtained from deducing the dynamics equations of optical photons in Ge and considering the Raman selection rule, as referenced in the pertinent literatures^[20]. The peak shift δΩ_s and calculated stress σ are summarized in Table 4, while the standard germanium single crystal peak frequency we used here is 300.5 cm^-1. As well as the XRD rocking curve, the full width at half maximum (FWHM) of, Raman spectra indicate the crystalline quality. Sample B has the minimum FWHM compared to sample A. Both of the two samples show a peak shift to the higher wavenumber signifying the compressive stress. The stress in sample A is smaller than that of sample B as calculated. Considering the crystalline quality and uniformity resultsgot from FWHM in the XRD rocking curve and the difference in lattice parameter we believe that the stress in sample A is released through lattice deformation.

3.6 Multi-junction photovoltaic cell performance

To further evaluate the quality of the substrates and their influence on the multi-junction photovoltaic cells, the statistical results of GaInP/GaAs/Ge three-junction photovoltaic cells manufactured on each sample with the same process are listed in Table 5. $V_{\rm mp}$ and $I_{\rm mp}$ mean the voltage and the electric current at the max power point. These results coincide well with the conclusion we made from the crystal quality and residual stress results, where the open circuit voltage of sample A is lower than sample B and the reference sample. It has been reported that the interface recombination velocity S_I for the InGaP/GaAs heteroepitaxial interface is semi-empirically proportional to lattice mismatch ( $\Delta a/{{a}_{0}}$ ) as: $S_{\rm I}(cm/s)$ =1.5 × 10⁸ \Delta a/a_{0} ^[21], and minority carrier diffusion length (L) in Ⅲ-V compounds is related with dislocation density (N_d) as: $1/L^{2} = 1/L_{0}^{2}+\pi ^{3}N_{\rm d}/4$ ^[22]. Thus, dislocation propagation from the substrate into the epitaxial layer (or diffusion layer) and interface defects generated act as non-radiative recombination centres, which results in the decrease of minority carrier diffusion length and inferiority of the cell manufactured. However, the performance of most cells manufactured by using sample wafer B, which has better lattice perfection, is very close to that of the reference sample wafer. It means that the VGF wafer B is basically satisfied for the requirement of cell manufacture and the growth condition for sample wafer A needing to be optimized.

4. Conclusion

VGF Ge wafer contains dislocation aggregation regions which influence its lattice perfection uniformity, residual stress and lattice parameters. After growth condition optimization, MTJ cells manufactured by using substrate Ge wafer with good lattice perfection and uniformity give good parameters across the whole wafer. Harmful impurity concentration in VGF-Ge is quite low and has a negligible influence on the material property.