Mechanism of twin-reduced III-V epitaxy on As-modified vicinal Si(111)

Rotational twins are fundamental defects in III-V epitaxy, in particular for the growth on nonpolar (111) surfaces. Based on density functional theory (DFT) calculations, we develop a general model for III-V nucleation on vicinal nonpolar (111)-oriented substrates and focus on the important differences in the atomic step configuration of different miscut directions. We verify this model by a relevant materials system when growing GaP epilayers on As-terminated Si(111): Scanning tunneling microscopy measurements reveal the formation of straight double bilayer steps after As passivation of the Si(111) surface, which persist after III-V growth, as we display when measuring the buried heterointerface with cross-sectional high-resolution transmission electron microscopy. A twin amount in the GaP epilayers is observed in dependence on the misorientation and our nucleation model explains the underlying mechanisms: The number of back bonds at the step edges determines the nucleation site. Accordingly, the substrate misorientation towards $\left[11\overline{2}\right]$ yields twin suppression, which is in full agreement with experiment. Finally, we use DFT input for kinetic Monte Carlo calculations to explain the formation of GaP rotational twins on Si(111):As in order to explain their volume fraction observed by high-resolution x-ray diffraction measurements. We thus derive a complete picture of the formation and suppression of rotational twins relevant for low-defect III-V–on–Si integration.

Figure 1

Schematic cross section of GaP/Si(111):As with twin domains forming at the interface. Regular untwinned GaP is shown as a stacking of red (111) planes following the ABC sequence of the vicinal substrate (green planes). Twinned GaP domains are depicted as a stacking of blue planes following a CBA sequence. Three types of boundaries occur: Coherent $\mathrm{\Sigma }3$ boundaries are separating the twinned GaP from the substrate lattice at the interface, incoherent $\mathrm{\Sigma }3$ boundaries $\left(\alpha |\beta \right)$ are separating the twinned GaP domains from the untwinned crystallites, and incoherent stacking boundaries appear between twinned domains. The latter occurs due to a stacking shift when nucleation starts at different plateaus.

Figure 2

Segments of the considered GaP/Si(111):As interfaces and their interface energies $\mathrm{\Delta }{\gamma }_{\mathrm{tot}}$ (definition in main text) compared to the reference structure $I_{\alpha }$. The following color coding is used throughout this paper: Si atoms are blue, As is red, Ga is green, and P is yellow. The difference between $I_{\alpha }$ and $I_{\beta }$ is the position of the P: $\alpha$ continues the normal stacking from the Si below, while $\beta$ contains P in cis configuration, starting a stacking change. For the remaining structures $I{I}_{\alpha }$–$I{V}_{\alpha }$ as described in the text, we only show the $\alpha$ configuration, as all $\beta$ configurations only differ in the topmost P positions and differences in $\mathrm{\Delta }\gamma$ are negligible. Note that for clarity, we only show the interface region of the calculated structures. The actual unit cell contains additional vacuum, Si, and hydrogen passivation layers.

Figure 3

Step structures of MOVPE-prepared Si(111) surfaces. (a) STM measurement of As-free Si(111):H interface with $3^{\circ }$ miscut in $\left[11\overline{2}\right]$ shows the formation of a step-bunched surface with mixed step heights after thermal deoxidation under $H_2$ (bias voltage: +1.25 V for samples without As; +1.44 V for samples with As). With thermal treatment under TBAs, a regularly stepped surface with double bilayer steps is observed. Also after GaP growth, HR-TEM measurements show the same stable, regularly arranged double bilayer steps. Here a GaP twin domain (lattice orientation marked in green) is observed above the step edge (TBBS type). (b) The Si(111):H surface with $3^{\circ }$ miscut in $\left[\overline{1}\overline{1}2\right]$ shows regularly arranged bilayer steps (STM), which rearrange during As termination to double bilayer steps. HR-TEM measurements of the GaP/Si(111):As interface confirm the presence of double bilayer steps (2x bl) after GaP growth also for this DBBS step type. Here no twin formation close to step edges is observed. For ease of comparison, all STM images have the same lateral dimensions.

Figure 4

HR-XRD analysis: RTD fraction $R_{\beta }$ depending on miscut angle for different nucleation temperatures and nucleation times given in the key. The red diamond marks a nominally flat surface. Orange and blue symbols mark the $\left[\overline{1}\overline{1}2\right]$ and $\left[11\overline{2}\right]$ direction, respectively. The darker arrows show the influence of increased miscut angle. The lighter arrows highlight the effect of a lower nucleation temperature $T_{\mathrm{nuc}}$ combined with shorter nucleation time $t_{\mathrm{nuc}}$.

Figure 5

Fundamental atomic structure of As-terminated Si(111) with double bilayer step configuration in both crystallographic directions (TBBS related to $\left[11\overline{2}\right]$, DBBS to $\left[\overline{1}\overline{1}2\right])$. For DFT calculations of the GaP nucleation a large number of variations of atomic configurations was used (see Appendix pp1-s3).

Figure 6

Outcome of likely GaP nucleation scenarios: (a) Nucleation at a double bilayer step with DBBS configuration. At DBBS, only $\alpha$-GaP nuclei form. Hence, twin formation is only possible on a plateau. (b) Nucleation scenario at a double bilayer step with TBBS configuration. TBBS enforces $\alpha$-GaP “below” and potentially $\beta$-GaP “above” the step. Hence, twin formation is possible on a plateau as well as on upper step edges.

Figure 7

Our HR-XRD data [25] in an Arrhenius-like plot of the RTD fraction $R_{\beta }$ in the GaP layer depending on the nucleation temperature for the two miscut directions $\left[\overline{1}\overline{1}2\right]$ and $\left[11\overline{2}\right]$ with $3^{\circ }$ miscut, $t_{\mathrm{nuc}}=15\min$. Right and top axis labels show the value of $R_{\beta }$ and temperature in ${}^{\circ }\mathrm{C}$ for better orientation. Dashed lines represent the Boltzmann expression (A1) of Appendix pp1-s4 for different energy differences. Solid lines show Arrhenius fits.

Figure 8

SEM images of 3D GaP nuclei (SK or VW growth) on vicinal Si(111):As. The MOVPE process was stopped directly after the nucleation step. Even an additional heat-up step to the growth temperature of $T_{\mathrm{growth}}=660{}^{\circ }\mathrm{C}$ did not change the morphology noticeably. The average nuclei size increases with increasing $T_{\mathrm{nuc}}$ while the surface coverage decreases (due to lower nucleation density and Ostwald-like ripening). At $T_{\mathrm{nuc}}=500{}^{\circ }\mathrm{C}$, the nuclei show a triangular shape and have overgrown on average $\sim 10$ double bilayer steps. The nuclei arrangement is influenced by the substrate steps, which leads to different morphologies for both miscut directions (visible also by comparing the darker regions in which no GaP has nucleated). The images are reminiscent of Stranski-Krastanow and Volmer-Weber growth. Blue circles highlight the nuclei orientation. All four samples were grown with $t_{\mathrm{nuc}}=7.5\min$ and a nominal V/III ratio = 432.

Figure 9

Kinetic Monte Carlo results for miscut along (a) $\left[11\overline{2}\right]$ and (b) $\left[\overline{11}2\right]$. In the upper parts, red and blue mark phosphorous atoms two bilayers above substrate in $\alpha$ and $\beta$ positions, respectively. The lower parts show a projected cross section with the same color coding as in Fig. 6. See main text for discussion.

Figure 10

Schematic side view of GaP/Si(111):As along $\left[\overline{1}10\right]$: (a) shows the atomic lattice of untwinned GaP growth on Si(111) with DBBS. The drawn ABC stacking follows the substrate without defects, which is also true for grown untwinned GaP over a TBBS (b). For simplicity, the following panels indicate only the ABC stacking, leaving out atoms and bonds. (c) and (d) show situations in which twinned GaP nucleates below and above the step edge leading to the formation of an incoherent stacking (orange) somewhere near the step edge. To avoid such energetically unfavored defects, the twins can overgrow each other by forming a coherent, low-energy $\mathrm{\Sigma }3$ {111/111} boundary. The arrows (green + red) indicate that here such an overgrowth is only possible step-upwards. Panel (e) shows untwinned GaP nucleating below the step edge in contact with twinned GaP nucleating on the upper step plateau, while (f) represents a nucleation mechanism for twins at TBBS based on our model. In both cases the incoherent $\alpha |\beta$ twin boundary is not fixed close to the step edge. Every third layer, the stacking coincides again, allowing for growth of one domain over another.

Figure 11

The volume ratio of twins $R_{\beta }$ decreases slightly with increasing V/III ratio. Although lower nucleation temperature $T_{\mathrm{nuc}}$ reduces the P supply and thereby the effective V/III ratio, the XRD-measured $R_{\beta }$ cannot be explained solely by such an indirect effect of changed temperature: Even in the wide range of deliberate sixfold increase in the V/III ratio (plotted here), we do not see such a strong change in $R_{\beta }$ as we observe by changing $T_{\mathrm{nuc}}$; cf. Fig. 7. Thus, $T_{\mathrm{nuc}}$ must have an additional effect on the III-V growth, which is mainly a kinetic one as described in Sec. 6c.