1. Introduction

In the last decade, metamorphic growth has shown progressive potential in fabricating specific devices with high performance on conventional substrates. By using metamorphic growth, so-called "virtual substrates" or "metamorphic templates" are formed on conventional substrates. Consequently, the lack of large and high-quality commercial substrates with desired lattice constants can be partly overcome, which significantly favors the design of device structures. However, the quality of virtual substrates is still critical, as the generation of dislocations and the degradation of crystalline are always accompanied with the metamorphic growth. Accordingly, a suitable buffer layer between the substrate and the active layers is required. An appropriate buffer layer should relax the strain sufficiently, prevent the propagation of threading dislocations (TDs) formed during the relaxation process into the active layers, and generate a moderate smooth surface morphology suitable for further device processing. In$_{x}$Ga$_{1-x}$As (generally x < 0.5) metamorphic layers on GaAs substrates have been widely studied for the demonstration of GaAs-based 1.3-1.55 $\mu$m quantum wells^[1-6] or quantum dot lasers^[7-9], and high electron mobility transistors (HEMTs)^{[10, 11]}, where different growth technologies have been applied, such as solid source molecular beam epitaxy (SSMBE)^{[1-4, 7-11]} and metalorganic vapor epitaxy (MOVPE)^{[5, 6]}. On the other hand, In$_{x}$Ga$_{1-x}$As (0.53 < x < 1) metamorphic layers on InP substrates are attractive for the research of short wavelength infrared photodetectors^[12-14] and mid-infrared quantum well lasers^[15] using gas source molecular beam epitaxy (GSMBE). As there is higher indium composition in the InP-based InGaAs metamorphic structures and the segregation of indium is easy to occur, control of lattice integrity, alloy composition, and uniformity are more difficult than in GaAs-based structures.

Generally, the buffer layer should be thick enough to help the isolation of the dislocation and the relaxation of the buffer lattice. In vapor phase epitaxy, the high growth rate makes the growth of a buffer with thickness exceeding 10 $\mu$m ordinary. However, the buffer layer is optically and electrically inactive in the device, and the growth of a thick buffer is impractical, especially for molecular beam epitaxy where the actual growth rate is limited around 1 $\mu$m/h. Therefore, from a practical point of view, a thin buffer should be more preferable. Considering the convenience of practical operation during the growth, and the reliability and reproducibility of the devices, the linearly graded In$_{x}$Ga$_{1-x}$As buffer is an easy and effective approach for high quality InGaAs metamorphic layers grown on InP substrates. In addition, thick InGaAs epitaxy layers on an In$_{x}$Ga$_{1-x}$As graded buffer may affect the relaxation process and confuse analysis of the results. In this work, relatively thin In$_{0.80}$Ga$_{0.20}$As metamorphic layers on InP-based linearly graded In$_{x}$Ga$_{1-x}$As buffers with different mismatch grading rates have been grown by GSMBE. The effects of mismatch grading rate on the surface, structural and optical properties of the In$_{x}$Ga$_{1-x}$As graded buffer were investigated in detail.

2. Experimental details

The samples grown in this work were performed on the (001)-oriented InP epi-ready substrates by using a VG Semicon V80H GSMBE system. The elemental indium and gallium sources were used as group Ⅲ sources, and their fluxes were controlled by changing the temperatures of cells. Arsine and phosphine cracking cells were used as group V sources, and the fluxes were controlled by adjusting the pressure. The cracking temperature was about 1000 ℃ measured by thermocouple. The surface oxide desorption of the InP substrate was carried out under P₂ flux, including a slow ramp-up of the substrate temperature until the reflection high energy electron diffraction (RHEED) pattern showed an abrupt transformation to 2 × 4 surface reconstruction.

The growth of the samples began with an In$_{x}$Ga$_{1-x}$As graded buffer on the InP substrate directly. In the In$_{x}$Ga$_{1-x}$As buffer, the indium cell temperature was increased by a variation of $\Delta T$ at a slow rate during the growth, and the gallium cell temperature was decreased by a variation of 2$\Delta T$ simultaneously^[12]. The starting temperatures of the indium and gallium cell were based on the growth parameters of lattice matched In$_{0.53}$Ga$_{0.47}$As, and the ending temperatures were calculated to match the target indium composition value of the In$_{x}$Ga$_{1-x}$As metamorphic layers. Two samples with different compositional graded rates in the buffer layer were grown. As shown in Fig. 1, the target value of indium composition was 0.80 for both samples A and B, corresponding to the lattice mismatch between the InGaAs layer and InP substrate of about +1.86%. The thickness of the buffer layers were 1.6 μm and 0.6 μm for samples A and B, respectively, corresponding to the mismatch grading rates of around 1.2 % $\mu$m^-1 and 3.1 % $\mu$m^-1, respectively. The mismatch grading rate is defined as the variation of mismatch per unit thickness. Finally, the cell temperatures were kept at the ending temperatures for the buffer to grow a 100 nm thin In$_{0.80}$Ga$_{0.20}$As layer of fixed composition for both samples, and other growth parameters were the same for those two samples.

After growth, the surface morphology of the grown samples was observed by an atomic force microscope (AFM). X-ray diffraction (XRD) rocking curves and reciprocal space mappings (RSMs) were performed by using a Philips X-pert high-resolution diffractometer. The CuK$\alpha_{1}$ wavelength was selected by a Ge (220) fourfold monochrometer. The photoluminescence spectra of the samples were measured using a Nicolet Megna 860 Fourier transform infrared (FTIR) spectrometer under double modulation mode^[16], in which a liquid-nitrogen cooled InSb detector and a CaF₂ beam splitter were used.

3. Results and discussions

3.1 Surface morphology

Figure 2 shows the AFM images with a 60 × 60 $\mu$m² scan area measured in tapping mode, where the details of the morphology could be seen clearly. In AFM images, the cross-hatch pattern exists obviously on the surface of the two samples. This type of pattern could be attributed to the two types of $\alpha$ and $\beta$ misfit dislocations oriented along the [110] and [110] directions at compressively stressed (001) interfaces, corresponding to group V and Ⅲ atom-based cores, respectively. The morphology features along the [110] and [110] directions are quite different; the undulation along the [110] direction, which makes the main contribution to the roughness, is distinctly larger than that along the [110] direction. Along the [110] direction, the primary ridges are in parallel but not uniform in width. The nonuniformity of the morphology is probably caused by the different local growth rates on the surface after strain relaxation. When the epi-layers relax by generation of dislocations, the residual strain is not uniform over the surface. The regions with less strain have a lower elastic energy and thus a relatively higher local growth rate, which causes the nonuniformity of the morphology. It can be observed from Fig. 2 that the average width of the ridges in sample A looks slightly larger than that in sample B. Oval-like morphology popping out on the top of some ridges can be seen from sample A, while this morphology is not so obvious in sample B.

The root mean square (RMS) roughness is 6.4 nm and 4.9 nm for samples A and B, respectively. It means that sample A with a lower mismatch grading rate in the buffer has a rougher surface, which is coherent to the behavior of GaAs-based In$_{x}$Al$_{1-x}$As linearly graded buffers reported in Ref. [17]. This is caused by the increased accumulation of morphology nonuniformity as the layer thickness increases.

3.2 Optical characteristics

The room temperature photoluminescence (PL) spectra of the two samples are shown in Fig. 3, where the PL signals are excited from the top In$_{0.80}$Ga$_{0.20}$As layers. It is observed that the PL peak of sample A has stronger intensity as well as a narrower FWHM compared to those of sample B. This means that there are fewer defects or non-radiative combination centers in the In$_{0.80}$Ga$_{0.20}$As layer and the optical properties are improved for sample A, where a lower mismatch grading rate is used. The peak wavelengths of the PL are 2.42 $\mu$m for both samples, corresponding to the bandgap $E_{\rm g}$ of 0.51 eV.

3.3 Structural properties

To investigate the structural properties and strain relax process of the grown samples, X-ray diffraction measurements were applied. At first, $\omega$/2$\theta$ scans on the (004) reflection were performed and the rocking curves are shown in Fig. 4. It can be observed that for each sample there is a strong substrate peak and a weak and wide layer ridge, where the signals of In$_{x}$Ga$_{1-x}$As buffer and In$_{0.8}$Ga$_{0.2}$As layer are merged. The accurate positions of the layer peaks with maximum intensity are difficult to determine because the layer peaks are very flat in a large angle range. The substrate peak of sample B is stronger than that of sample A due to the thinner buffer. The XRD intensity of the In$_{0.8}$Ga$_{0.2}$As layer of sample B is weaker than that of sample A, which indicates an improved lattice quality of sample A. As shown in Fig. 4, the layer peak of sample A is closer to the substrate peak than that of sample B, which can be explained by the assumption that sample A has a larger degree of lattice relaxation and a smaller perpendicular lattice constant $a_{\bot }$, since the (004) diffraction peaks reflect the lattice constant in the growth direction. To confirm this assumption, XRD RSM measurements were further performed.

Figure 5 shows the RSMs from the symmetric (004) and asymmetric (224) reflections, the intensities are in logarithm scale. In all RSMs, the relative narrow and symmetric circular peaks at the upper part of each graph correspond to the InP substrate (denoted as S), and the wide and elliptical peaks at the lower part belong to the In$_{0.80}$Ga$_{0.20}$As top layers (denoted as L).

In the (224) reflections of Fig. 5, the fully relaxation line (solid line) and fully pseudomorphic line (dashed line) with respect to the substrate were drawn for reference. In the (224) reflections for the both samples, two slopes of the contour center exist as the indium composition of the graded In$_{x}$Ga$_{1-x}$As buffer increases. The contour center of the buffer layer is parallel to the relaxation line at first, and then is parallel to the pseudomorphic line. It reveals that the total relaxation process in the graded buffer evolves by two steps. At first the lattice is almost fully relaxed, whereas a nearly fully strained layer is formed in the second step. This can be explained by Tersoff's model, which predicts that there is a fully strained layer in the top part of linearly compositionally graded layer^[18]. In this fully strained layer, it is free of dislocation, whereas residual strain cannot be released. The thickness $Z_{\rm f}$ of the fully strained layers can be calculated by the formula $Z_{\rm f} = (2\lambda / bc \varepsilon^{\prime})^{1/2}$ ^[18], where $\varepsilon$$^{\prime }$ is the mismatch grading rate, $\lambda$ is the energy per unit length of the dislocation, b is the misfit component of the Burgers vector of the dislocation and c is the elastic constant for biaxial strain. For sample A and sample B the values of $Z_{\rm f}$ are calculated to be 0.38 $\mu$m and 0.24 $\mu$m respectively. In the calculation $\lambda$/$bc$ = 0.83 nm was used adopting the value from Ref. [19]. From the (224) reflections in Fig. 5, the thicknesses of this layers can be estimated to be 0.47 μm and 0.26 μm for sample A and sample B, respectively. The experimental and theoretical results match well if considering the errors of measurements and calculations.

From both (004) and (224) reflections, the peaks of the top In$_{0.80}$Ga$_{0.20}$As layer of sample A are stronger than that of sample B, which indicates the more preferable lattice quality of sample A. More detailed parameters were extracted from the RSM results and are listed in Table 1.

The definition of degree of relaxation R is the ratio of parallel lattice mismatch $\delta$$a_{/\!/}$ to the cubic lattice mismatch $\delta a_{\infty}$, i.e. $R=\delta a_{/\!/}$/$\delta a_{\infty}$. The cubic mismatch can be calculated from the perpendicular and parallel mismatch $\delta a_{/\!/}$ and $\delta a_{\bot }$ using $\delta a_{\infty }$ = ($\delta _{\bot }$ $+$ 2$\delta a_{/\!/}$ $c_{12}$/$c_{11})$/(1 $+$ 2$c_{12}$/$c_{11})$, where $c_{11}$ and $c_{12}$ are the elastic constants of the layer. The residual strain $\varepsilon$ can be calculated from the expression $\varepsilon$ = ($a_{/\!/}-a_{\infty})$/$a_{\infty}$. At room temperature the bandgap of In$_{x}$Ga$_{1-x}$As can be expressed as $E_{\rm g}$ = 1.424 -1.541x $+$ 0.477$x^{2}$ according to Vergard's rule, where x is the indium composition. Here, the bandgap value of $E_{\rm g}$ is calculated to be 0.52 eV for both samples A and B using the indium composition of 0.80, which matches well with the PL results considering the errors in the measurements and calculations. The degree of relaxation is 82.5% for sample A and 77.8% for sample B, respectively. The residual strain of sample A is smaller than that of sample B. Therefore, the use of lower mismatch grading rate in the buffer is beneficial for the lattice relaxation and the release of residual strain. However, it is still not sufficient to achieve a full relaxation even in the linearly compositionally graded In$_{x}$Ga$_{1-x}$As buffer with a mismatch grading rate of 1.2% $\mu$m^-1 in our experiments. To further increase the relaxation degree in the In$_{x}$Ga$_{1-x}$As graded buffer, two methods are suggested: one is to use a mismatch grading rate smaller than 1.2% $\mu$m^-1 in the buffer layer, the other is to increase the end indium composition in the In$_{x}$Ga$_{1-x}$As graded buffer and thus introduce an indium composition overshoot in the buffer layer^[18].

4. Conclusions

InP-based high indium composition In$_{0.80}$Ga$_{0.20}$As layers have been grown using compositionally graded In$_{x}$Ga$_{1-x}$As metamorphic buffers with different mismatch grading rates by GSMBE. Their properties have been evaluated by means of AFM, PL and XRD measurements. The results show that the sample with lower mismatch grading rate in the buffer has preferable optical properties, a larger relaxation degree, and less residual strain, although it causes a slightly rougher surface in the meantime. The relaxation procedure with two steps in the buffer layers has been observed by XRD RSM and compared to the calculation of Tersoff's model. To further increase the relaxation degree, an even lower mismatch grading rate and composition "overshoot" are suggested.