Role of excited states in Shockley-Read-Hall recombination in wide-band-gap semiconductors

Defect-assisted recombination is an important limitation on efficiency of optoelectronic devices. However, since nonradiative capture rates decrease exponentially with the energy of the transition, the mechanisms by which such recombination can take place in wide-band-gap materials are unclear. Using electronic structure calculations we uncover the crucial role of electronic excited states in nonradiative recombination processes. The impact is elucidated with examples for the group-III nitrides, for which accumulating experimental evidence indicates that defect-assisted recombination limits efficiency. Our work provides insights into the physics of nonradiative recombination, and the mechanisms are suggested to be ubiquitous in wide-band-gap semiconductors.

Figure 1

Shockley-Read-Hall recombination at a defect with a level at energy $\mathrm{\Delta }E$ above the valence-band maximum (VBM), in two different representations: (a) energy level diagram; (b) configuration coordinate diagram. Electron and hole capture rates $R_n$ and $R_p$ are expressed as a function of capture coefficients $C_n$ and $C_p$, carrier densities $n$ and $p$, and defect concentrations in charge states $N^0$ and $N^{-}$.

Figure 2

Formation energy of the $V_{\text{Ga}}\text{−}{\mathrm{O}}_{\text{N}}$ complex in bulk GaN in different charge states as a function of Fermi energy, under Ga-rich conditions. Blue solid lines correspond to the lowest-energy configuration for each charge state; the black lines highlight the charge state with the lowest ground-state energy for a specific Fermi-level position. Red (dashed) and green (dashed-dotted) lines correspond to excited states of the neutral and negatively charged state, respectively. $\mathrm{\Delta }{E}_0$ and $\mathrm{\Delta }{E}_{-1}$ are intradefect excitation energies for the neutral and the negatively charged defect. Charge-state transition levels that involve excited states and that are important for SRH recombination are explicitly marked.

Figure 3

Single-particle states of the VO defect for charge states (a) $q=-1$ and (b) $q=0$. Intradefect excitation occurs by promoting an electron from the $a_1$ state to the $e$ state.

Figure 4

Calculated total capture coefficient $C_{\text{tot}}$ (left vertical axis) and SRH coefficient $A=N{C}_{\text{tot}}$ (right vertical axis) as a function of band gap for gallium-vacancy complexes with oxygen. We assumed a defect concentration $N={10}^{16}{\mathrm{cm}}^{-3}$.