Effect of Atomic-Scale Alloy Randomness on the Optical Polarization of Semiconductor Quantum Dots

Alloyed Ga$_{1-x}$In$_x$As system consists of different random assignments $\sigma$ of the Ga and In atoms to the cation sublattice sites; each configuration having, in principle, distinct physical properties. For self-assembled dots made of finite number of cations ($\leq$10$^5$), self-averaging of configurations may not be complete, so single-dot spectroscopy can observe the atomic-scale alloy randomness effects. We examine the effect of such atomic-scale randomness on the fine structure-splitting (FSS) of the exciton observed via the polarization anisotropy of its components. We find: (i) The FSS of the monoexciton X$^0$ changes by more than a factor of 7 with $\sigma$. Thus, finite nanostructure systems provide clear evidence for the effects of atomic-scale randomness on physical properties. (ii) The polarization anisotropy of two X$^0$ transitions is affected both by $\sigma$ variations and from possible QD base elongation. Thus, the polarization anisotropy cannot be used as a measure of geometrical anisotropy alone, (iii) Polarization directions of different multiexciton emission lines are determined by $\sigma$.