Microscopic nonequilibrium theory of quantum well solar cells

U. Aeberhard and R. H. Morf

Phys. Rev. B 77, 125343 – Published 28 March 2008

Abstract

We present a microscopic theory of bipolar quantum well structures in the photovoltaic regime, based on the nonequilibrium Green’s function formalism for a multiband tight-binding Hamiltonian. The quantum kinetic equations for the single particle Green’s functions of electrons and holes are self-consistently coupled to Poisson’s equation, including intercarrier scattering on the Hartree level. Relaxation and broadening mechanisms are considered by the inclusion of acoustic and optical electron-phonon interaction in a self-consistent Born approximation of the scattering self-energies. Photogeneration of carriers is described on the same level in terms of a self-energy derived from the standard dipole approximation of the electron-photon interaction. Results from a simple two-band model are shown for the local density of states, spectral response, current spectrum, and current-voltage characteristics for generic single quantum well systems.

Received 10 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.125343

Authors & Affiliations

U. Aeberhard^* and R. H. Morf

Condensed Matter Theory, Paul Scherrer Institute, CH-5232 Villigen, Switzerland

^*urs.aeberhard@psi.ch

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Issue

Vol. 77, Iss. 12 — 15 March 2008

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Images

Figure 1
(Color online) Characterizing structure and processes of a pin-QWSC. Generation and recombination: 1. Photogeneration of electon-hole pairs; 2. Radiative recombination; 3. Nonradiative recombination (Auger, trap). Transport: 4. Resonant and nonresonant tunneling; 5. Thermal escape and sweep-out by built-in field; 6. Relaxation by inelastic scattering (optical phonons).Reuse & Permissions
Figure 2
(Color online) Computational scheme for the calculation of physical quantities from Green’s functions and self-energies. The inner self-consistency loop connects the equations for the Green’s functions and the self-energies, while the outer loop provides the update of the Hartree potential from the solution of Poisson’s equation.Reuse & Permissions
Figure 3
(Color online) (a) Local density of states (LDOS) at $k = 0$ for a 25 ML SQW pin diode at $V_{bias} = - 0.01 V$ : quantum confinement leads to the formation of quasibound states and higher transmission resonances in the well region, in addition to the stripelike interference pattern due to the built-in field (strong band bending); (b) LDOS at the well center and optical transitions between confinement levels: the quasibound states near the well edge show the characteristic broadening associated with shorter carrier dwell time, as compared to the sharp deep and strongly bound states; (c) photocurrent response (pcr) and absorptivity (abs): steplike and square-root-like dependence on the photon energy below and above the higher band gap value, reflecting the density of the states participating in the corresponding optical transitions, i.e., confinement level to confinement level, confinement level to quasicontinuum, and quasicontinuum transitions, respectively.Reuse & Permissions
Figure 4
(Color online) (a) Spatially resolved photocurrent spectrum (at zero bias voltage) in the QW region and (b) at the interface to the $n$ contact (electrons) and to the $p$ contact (holes): the spectrum reflects the joint density of states for the contributing transitions between the confinement levels, modified by the probability for escape, which is suppressed in the case of the deep electronic level. (c) Electron and hole components of the photocurrent grow toward the respective contacts, while the total current is conserved. In the dark, the bands are uncoupled, and current is conserved for the two carrier species separately.Reuse & Permissions
Figure 5
(Color online) (a) $I V$ characteristics for a 25 ML SQW structure and the current spectrum at the lead-device interface for (b) $0 V$ (short circuit conditions), (c) $- 0.26 V$ (near the maximum power point), and (d) $- 0.32 V$ (near the open circuit voltage). The spectrum of the exponentially increasing diode current reflects the density of states and the distribution of the carriers in the bulk contacts, modified by the effects of relaxation due to inelastic scattering in the active region, which leads to the formation of phonon satellites (weakly recognizable near the band edge).Reuse & Permissions
Figure 6
Tight-binding elements for a zinc-blende lattice in (001) direction.Reuse & Permissions

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