InGaN ternary alloys have been extensively investigated as possible materials for the optoelectronic devices such as light emitting diodes (LEDs) and laser diodes (LDs), and multi-junction solar cells with extremely high efficiency. Recently, non-polar and semi-polar surfaces are intensively attracted much attention for the growth of InGaN quantum wells suitable for true green lasers [1]. These surfaces are expected not only to reduce the spontaneous polarization in InGaN quantum wells but also to enhance the In-incorporation due to the surface structural properties [2]. Our group has reported on the growth of InGaN by hydride vapor phase epitaxy (HVPE) using InCl₃ and GaCl₃ as precursors by thermodynamic analyses [3]. Actually, we succeeded in the growth of thick InGaN ternary alloy by HVPE system constructed based on the thermodynamic analyses. However, thermochemical data such as Gibbs’ free energy change, which are available from the database, do not take the surface orientation of crystal into consideration. Therefore, it is difficult to consider the behavior of vapor-solid relationship including the information of surface orientation by conventional thermodynamic analysis. Yayama et al. investigated the dependence of In solid composition on surface orientation for metalorganic vapor phase epitaxy (MOVPE) by the combination of first principles calculation and statistical thermodynamics [4]. In this study, we will report the influence of surface orientation on the In solid composition of HVPE-grown InGaN by taking the surface orientation into consideration.

     In the calculation, the values of Gibbs’ free energy change for InN deposition and GaN deposition were estimated by first principles calculation combined with statistical thermodynamics. We constructed the slab models of 8ML (before deposition) and 10ML (after deposition), and performed the vibration analysis to obtain the values such as entropy and heat capacity. And finally, Gibbs’ free energy change DG (equilibrium constant K_i) was estimated. In order to predict the In-incorporation on each crystal surface, solid composition index normalized by c-plane was calculated through [K_InN/(K_InN+K_GaN)]_{each-orientation}/[K_InN/(K_InN+K_GaN)]_c-plane.

     Figure 1 shows the values of Gibbs’ free energy change for InN deposition at various temperatures and various surface orientations. From this figure, the order of deposition superiority for InN was revealed as (10-1-1)>(000-1)>(10-10)>(10-1-3)>(10-12)>(0001). Thus, solid composition index of HVPE-grown InGaN was estimated from the equilibrium constants of InN deposition and GaN deposition calculated by above mentioned method (Fig. 2). Growth temperature was selected at 1000K. Although it is not accurate to consider the In solid composition in InGaN by equilibrium constant, it is possible to grasp the tendency of In-incorporation when we change the only surface orientation as the growth condition is fixed. Figure 2 shows the solid composition index of InGaN normalized by the value of (0001) plane. The order of superiority for In-incorporation was revealed. Wernicke et al. [2] reported the high In-incorporation for (10-11) surface orientation and that was consistent with our calculated value. We believe that it is possible to expect the suitable surface orientation by theoretical calculations and feed it back to growth experiments.

Figure 1 Dependence of Gibbs’ free energy change for InN deposition on various temperatures for each surface orientation.

Figure 2 Normalized solid composition index of InGaN for each surface orientation. Growth temperature was set to 1000K.

References

[1] S. Takagi et al., Appl. Phys. Express 5 (2012) 082102.

[2] T. Wernicke et al., Semicond. Sci. Tech. 27 (2012) 024014.

[3] K. Hanaoka et al., J. Cryst. Growth, 318 (2012) 441.

[4] T. Yayama et al., Jpn. J. Appl. Phys. in press.

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1. Growth of thick InGaN by Hydride Vapor Phase Epitaxy