Quantum-kinetic theory of steady-state photocurrent generation in thin films: Coherent versus incoherent coupling

The generation of photocurrents due to coupling of electrons to both classical and quantized electromagnetic fields in thin semiconductor films is described within the framework of the nonequilibrium Green's function formalism. For the coherent coupling to classical fields corresponding to single field operator averages, an effective two-time intraband self-energy is derived from a band decoupling procedure. The evaluation of coherent photogeneration is performed self-consistently with the propagation of the fields by using for the latter a transfer matrix formalism with an extinction coefficient derived from the electronic Green's functions. For the “incoherent” coupling to fluctuations of the quantized fields, which need to be considered for the inclusion of spontaneous emission, the first self-consistent Born self-energy is used, with full spatial resolution in the photon Green's functions. These are obtained from the numerical solution of Dyson and Keldysh equations including a nonlocal photon self-energy based on the same interband polarization function as used for the coherent case. A comparison of the spectral and integral photocurrent generation pattern reveals a close agreement between coherent and incoherent coupling for the case of an ultrathin, selectively contacted absorber layer at short circuit conditions.

Figure 1

Schematic band diagram representation of a flat band solar cell architecture with finite photocurrent flow enabled by carrier selective contacts: electrons ($e^{-}$) are blocked in the conduction band at $z=z_0$ via an infinite barrier potential in the conduction band energy $E_C$, while holes ($h^{+}$) are reflected at $z=z_{\max }$ due to a similar barrier potential in $E_V$. For closer resemblance to actual thin-film solar cell configurations, an additional back reflector layer is considered in the optical simulations.

Figure 2

Local electron generation rate as given by the energy integrand of (46) for the two-band effective mass model of a homogeneous (bulklike) GaAs slab under monochromatic illumination with $E_{\gamma }=1.48$ eV. The rate is normalized to the local photon flux and to the maximum value. Both the $k_{\parallel }=0$ component (a) and the momentum integrated rate (b) show a good agreement between the simulation based on the numerical solution of the NEGF transport problem at zero bias and the analytical evaluation of (46) using the exact GF expressions (A1) and (A2).

Figure 3

(a) Spatially averaged absorption coefficient of an electronically open 40-nm-thick GaAs slab, for consideration of different fractions of off-diagonals in the charge carrier Green's functions. (b) The absorption coefficient from the full matrix is in excellent agreement with the analytical result for bulk, while it is slightly reduced and shows additional oscillatory features for selective contacts. (c) Local absorption coefficient for open and selectively contacted slab systems, with interferences from reflections and zero magnitude minima from wave function nodes at closed contacts. (d) Comparison of the photocurrent as obtained from the absorptance with the terminal current from the full NEGF transport simulation based on the same illumination and extinction coefficient.

Figure 4

(a) Local generation rate spectrum for open and selectively contacted 40-nm GaAs slab with 100-nm Ag reflector and under monochromatic, normally incident light of 1 kW/m${}^2$ at $E_{\gamma }=1.48$ eV. (b) Integrated local carrier generation rate, which is identical for electrons and holes, with closed contacts resulting in reflection-induced interference effects and boundary nodes.

Figure 5

(a) Spatially resolved photocurrent spectrum for the open slab under monochromatic illumination of 1 kW/m${}^2$ with $E_{\gamma }=1.48$ eV; in the absence of carrier selective contacts, diffusion leads to inverse current flow towards the minority contacts, with the result of vanishing net current upon energy integration as displayed in (b). (c) For carrier selective contacts, reverse current components are small, and the net integral current (d) is strictly positive and perfectly conserved.

Figure 6

Photon energy flux in the selectively contacted slab as computed via TMM and NEGF methods, showing the close agreement of the two approaches for coherent light propagation, i.e., in absence of spontaneous emission.

Figure 7

(a) Local charge carrier generation rate spectrum, (b) local carrier generation rate and optical rate, (c) local charge carrier current spectrum, and (d) integral current for the selectively contacted slab system, as provided by the NEGF formalism using the coupling to the photon GF. The results are in close agreement with those from the coherent coupling approximation. The local charge carrier generation rate coincides exactly with the optical rate from photon self-energy and GF.