InxGai_xN quantum dots

Phase separation and In segregation effects

Quantum dots in the InGaN material system are achieved in numerous ways, since the instability of the material enables several possibilities for the growth. This section starts with highlighting several issues of the InGaN compound which are important for the understanding of InGaN quantum dot growth. Generally speaking, issues are due to the large differences of the atomic radii of the elemental constituents indium and gallium. In numbers, the Ga-N bond length of 1.95 A is about 10% smaller than the In-N bond length of 2.15 A which leads to micro-strains in the unit cell when indium atoms are incorporated on Ga sites. Consequently, the system’s energy is increased when In atoms are incorporated on Ga sites. The unit cell reacts by stretching and bending of bonds around In atoms in order to minimize the potential energy of the crystal [38]. Another option for the compound to restore its minimum energy is phase separation by spinodal and binodal decomposition. By calculating the enthalpy of mixing alloy decomposition is expected for temperatures below 1400° C. At a typical growth temperature of 800° C immiscibility of InN and GaN is predicted for 0 < x_In < 0.88 (see Fig. 5.10). Due to compressive strain exacerbated by GaN barriers onto InGaN the immiscibility region is, however, narrowed and shifted

Fig. 5.10. Spinodal and binodal curves within the calculated phase diagram of In_KGai__KN. The alloy is unstable within the binodal curve (solid line). (Reprinted with permission from [38], © 1999 by the American Physical Society.) towards high-In containing layers, and the critical temperature is lowered below about 700° C [39]. One should also recall that those calculations refer to thermodynamic equilibrium conditions which are not established during epitaxial growth methods like MBE or MOVPE. However, growth interruptions and very low growth rates, which are part of quantum dot formation in the SK regime, are likely to promote equilibration processes.

Important for In incorporation into the growing crystal is also the In-N bond energy (1.89 eV) which is only 80% of the Ga-N bond energy (2.34 eV). Moving an indium atom from one lattice site to another is therefore much more favored than for a gallium atom. Indium atoms sitting on a crystal’s surface also make fewer bonds with nitrogen atoms than for the four-fold coordinated group-III lattice sites in the bulk. In addition, indium atoms at crystal surfaces accommodate strain more efficiently by rearranging their bonding to next-neighbors. For these reasons, segregation of In atoms towards the surface is very likely to occur, as the total energy of the system becomes reduced thereby. Segregation phenomena are investigated by Monte Carlo simulation of In0.10Ga0.90N layer growth. Figure 5.11 shows that the surface In coverage exceeds by large amounts (>50%) the nominal bulk value, and less than 5% of indium is found in the bulk [40]. Through such a surface layer the chemical potential of In atoms is raised close to the value where In droplet formation starts. Northrup et al. also calculated that In incorporation is favored on {1122} surfaces because of In-In bilayer formation promoting In incorporation on such surfaces [41]. They identified the cores of threading dislocations on GaN(0001) as centers for In agglomeration.

Under such circumstances, controlling the self-organized growth of quantum dots in the Stranski-Krastanow regime may deviate from the binary GaN/AlN

Fig. 5.11. Composition profile near the surface of 15-ML thick In₀₁₀Ga_{0 90}N(0001) films for temperatures of 520°C (triangles) and 800°C (squares) as calculated by the Monte Carlo simulation method. (Reprinted with permission from [40].) system. Otherwise, miscellaneous techniques are developed for realizing InGaN quantum dots which take advantage of phase separation and In segregation effects.