First-Principles Calculations of Luminescence Spectrum Line Shapes for Defects in Semiconductors: The Example of GaN and ZnO

We present a theoretical study of the broadening of defect luminescence bands due to vibronic coupling. Numerical proof is provided for the commonly used assumption that a multidimensional vibrational problem can be mapped onto an effective one-dimensional configuration coordinate diagram. Our approach is implemented based on density functional theory with a hybrid functional, resulting in luminescence line shapes for important defects in GaN and ZnO that show unprecedented agreement with experiment. We find clear trends concerning effective parameters that characterize luminescence bands of donor- and acceptor-type defects, thus facilitating their identification.

Figure 1

1D configuration coordinate diagram describing optical absorption and emission at a point defect. The minima of the ground-state and excited-state potential energy surfaces are displaced. $\Delta E_{\{e,g\}}$ are the relaxation energies and ${\Omega }_{\{e,g\}}$ the effective phonon frequencies. ZPL indicates the zero-phonon line, i.e., the transition between the zero-point vibrational states in excited- and ground-state configurations.

Figure 2

Normalized luminescence spectrum of the ${\mathrm{Mg}}_{\mathrm{Ga}}(0/-)$ transition, calculated by taking into account vibrational modes of only those atoms that relax most (labeled in the inset). Black solid line (and shaded area): Calculation including mode mixing; blue dashed line: parallel-mode approximation; red solid line: effective 1D vibrational problem.

Figure 3

Calculated (solid lines) and measured (symbols) luminescence line shapes for (a) ${\mathrm{Mg}}_{\mathrm{Ga}}$ in GaN, (b) ${\mathrm{C}}_{\mathrm{N}}$ in GaN, (c) $V_{\mathrm{N}}$ in GaN, and (d) ${\mathrm{N}}_{\mathrm{O}}$ in ZnO. The arrows indicate the ZPL, and the calculated spectra were shifted by $\sim 0.1\mathrm{eV}$, as discussed in the text. In (a), the experimental spectrum of Ref. 19 has been used as a reference in this procedure.