Nonequilibrium Green's function picture of nonradiative recombination of the Shockley-Read-Hall type

A quantum-kinetic picture of Shockley-Read-Hall-type (SRH) defect-mediated recombination is derived within the nonequilibrium Green's function formalism for an optoelectronic device with selectively contacted, current-carrying extended states and a localized deep defect state in the energy gap. The theory is first tested for recombination from bulk band states and then implemented for defective bipolar homo- and heterojunction thin-film devices with realistic spatial variation of the band edge profile. While the quantum-kinetic treatment reproduces the semiclassical characteristics for a bulk absorber in flat-band and quasiequilibrium conditions, for which the conventional SRH picture is valid, it reveals nonclassical features such as recombination enhancement by tunneling into field-induced subgap states in the presence of large fields, or the complex recombination current flow at heterointerfaces. Being fully compatible with the rigorous treatment of electron-photon and electron-phonon scattering in the nonequilibrium Green's function (NEGF) formalism, the approach enables a consistent inclusion of defect-mediated nonradiative recombination in comprehensive NEGF simulations of nanostructure-based quantum optoelectronic devices such as quantum well lasers, LEDs and solar cells.

Figure 1

Self-consistent computation of Green's functions and scattering self-energies enabling the description of nonradiative transitions via midgap defect states in a fully interacting quantum transport picture, where the band states are renormalized due to inter- and intraband scattering as well as coupling to contacts.

Figure 2

(a) Schematic representation of nonradiative carrier recombination via coupling of the contacted states to defects states in the band gap through multiphonon relaxation. (b) Volume recombination rate for bulk GaAs as obtained from the semiclassical approach in Ref. [37] and from the NEGF treatment, for a single iteration of the self-consistency iteration (one shot $\to$ Born approximation) and the full scheme. The bulk band and defect parameters used are given in Table 1, and a defect concentration ${\rho }_d={10}^{14}{\mathrm{cm}}^{-3}$ is assumed.

Figure 3

(a) Band profile and schematic recombination process in a 100-nm-thick GaAs $p\text{−}i\text{−}n$ diode with a single defect state located in the center of the intrinsic region ($z_0=50$ nm), displayed for a doping density of $N_{\mathrm{dop}}={10}^{18}{\mathrm{cm}}^{-3}$ and at 0.6 V forward bias. Electron and hole effective masses were set to $m_c^{*}=0.067m_0$ and $m_v^{*}=0.22m_0$, respectively. (b) Recombination characteristics for ${\varepsilon }_d=0.75$, ${\rho }_d={10}^{14}{\mathrm{cm}}^{-3}$, and ${\sigma }_n={\sigma }_p={10}^{-14}{\mathrm{cm}}^{-2}$. For $N_{\mathrm{dop}}={10}^{18}{\mathrm{cm}}^{-3}$ (filled squares), the large built-in electrostatic field leads to deviations from the semiclassical characteristics (triangles) due to the enhancement of recombination by tunneling into field-induced band tails. At reduced doping of $N_{\mathrm{dop}}={10}^{17}{\mathrm{cm}}^{-3}$ (filled circles), the lower field moves the characteristics closer to the ideality factor of 2 (dashed line) observed in the semiclassical result.

Figure 4

(a) Spectral recombination current flow at a defective AlGaAs-GaAs heterointerface (band edge profiles indicated as gray lines). While electrons tunnel to the defect location unhindered, the holes have to overcome an injection barrier, and a reverse flow at lower energies is generated. (b) The current density as obtained from integrating the spectral current flow over energy perfectly obeys current conservation in the digital form as expected from semiclassical simulations.

Figure 5

(a) Spectral current flow at the heterojunction in the absence of recombination, but under illumination with monochromatic photons of energy $E_{\gamma }=1.45$ eV and at an intensity $I_{\gamma }=10$ kW/${\mathrm{m}}^2$. (b) Integrated electron, hole, and total current; the latter is again conserved over the entire structure.

Figure 6

Current flow at the heterointerface in the presence of both defect-mediated recombination and photocurrent generation: (a) The spectral current flow shows complex patterns due to the superposition of generation and recombination components. (b) The integrated current reflects in the electron and hole components the competing processes of carrier injection and extraction, while the total current is again perfectly conserved.