G. Rupper

Effect of n-p-n heterostructures on interface recombination and semiconductor laser cooling

The design of doped n-p-n semiconductor heterostructures has a significant influence on the structures’ nonradiative decay and can also affect their photoluminescence characteristics. Such structures have recently been explored in the context of semiconductor laser cooling. We present a theoretical analysis of optically excited n-p-n structures, focusing mainly on the influence of the layer thicknesses and doping concentrations on nonradiative interface recombination. We find that high levels of n-doping (1019 cm−3) can reduce the minority-carrier density at the interface and increase the nonradiative lifetime. We calculate time-dependent luminescence decay and find them to be in good agreement with experiment for temperatures >120 K, which is the temperature range in which our model assumptions are expected to be valid. A theoretical analysis of the cooling characteristics of n-p-n structures elucidates the interplay of nonradiative, radiative, and Auger recombination processes. We show that at high opti...

Theory of Luminescence and Optical Refrigeration in p-doped Semiconductors

We present a microscopic many-body theory of optical refrigeration of p-doped semiconductors. Conceptually, the refrigeration mechanism is the upconversion of pump photons through absorption and subsequent luminescence by electron-hole pairs. The electron-hole pair can be an unbound pair, a pair bound by the attractive Coulomb interation (exciton), or a pair in which the hole is located at an acceptor site. Assuming the electron-hole pairs to be in quasi-thermal equilibrium, our theory calculates its absorption and luminescence spectra within a diagrammatic (real-time) Greens function approach at the self-consistent T-matrix level. The strong on-site Coulomb repulsion of holes at acceptor sites is taken into account via a truncation of the acceptor Fock space, which excludes states with higher than single-hole occupation. The resulting absorption and luminescence spectra are used in a cooling threshold analysis for GaAs that also takes into account other losses into heat. We compare the present results for p-doped GaAs with previous ones obtained for undoped GaAs.

Theory of semiconductor laser cooling at low temperatures

On the road toward experimental realization of laser-induced cooling of semiconductors, theoretical investigations are necessary for a detailed understanding of the microscopic phenomena underlying the cooling process, and for a prediction of optimal parameter regimes where efficient cooling could be expected. A recent realistic theory for cooling of bulk GaAs by Sheik-Bahae and Epstein has focused on the high-temperature regime, where the cooling process involves absorption of and luminescence from an electron-hole plasma. Using a microscopic many-particle theory, we extend the Sheik-Bahae Epstein approach to the low-temperature regime, where excitonic effects, i.e. effects of bound electron hole pairs in quasi-thermal equilibrium with correlated unbound pairs (i.e. the plasma) become important. We use a diagrammatic approach that is non-perturbative in the Coulomb interaction and contains effects of phase-space filling, single-particle renormalization in a partially ionized plasma, and screening. We ensure that our theory contains the relevant limiting cases for (partial) ionization in the low-density regime (Saha equation and Beth-Uhlenbeck formula) as well as the high density regime (Mott transition). Based on our microscopic theory for absorption and luminescence in the quasi-thermal equilibrium regime, we present a detailed study of cooling criteria at low temperature, focusing mainly on the temperature regime between 5K and 100K. In particular, we discuss the transition from the high temperature regime dominated by absorption in the e-h continuum to the low-temperature regime dominated by resonant exciton absorption.

Theory of time-resolved photo-luminescence and carrier lifetime measurements in GaAs/GaInP heterostructures

Recently, interest in optical refrigeration of semiconductors, which is based on photo-luminescence up-conversion, has drawn extensive attention both theoretically and experimentally. Theoretical descriptions often treat spatially homogeneous semiconductors, because of their conceptual simplicity. In typical experiments, however, semiconductors are usually heterostructures designed to reduce non-radiative recombination at the samples surface. In particular, GaAs/GaInP structures have been used in experiments. In these structures, the GaAs layers are usually unintentionally p-doped, while the surface layers of GaInP are n-doped. Recent measurements of the non-radiative recombiation lifetime yielded values in the desirable inverse microsecond regime, and it is believed that the non-radiative recombination processes occur mainly at the heterostructure interfaces and its surfaces. For this reason, it is important to know the spatial density distribution of the excited carriers. Furthermore, photo-luminescence and carrier lifetime measurements are not spatially resolved, and therefore it is desirable to have a theory that can simulate lifetime measurements using the spatially varying density profile as an input. We have developed such a theory, using the simplifying assumption of quasi-thermal equilibrium (at each time during the photo-luminescence decay process). Using this theory, we are able to relate measurable (i.e. spatially averaged) lifetime measurements to the underlying non-radiative decay processes that, in our simulations, occur predominantly at the GaAs/GaInP interface. From this, we find that spatial inhomogeneities in the carrier density, which are most pronounced at low optical excitation powers, can have appreciable effects on the interpretation of the lifetime measurements.

The role of finite spatial beam profiles on photo-luminescence and laser cooling in GaAs structures

We present a microscopic many-body theory of optical refrigeration of semiconductors with nite spatial beam prole extension. The theory is an extension of our previous theory of optical refrigeration of GaAs, which had been limited to spatially homogeneous systems. In it, optically excited electron-hole pairs can be an unbound pairs, or pairs bound by the attractive Coulomb interaction (excitons). Assuming the electron-hole pairs to be in quasi-thermal equilibrium, our theory calculates its absorption and luminescence spectra within a diagrammatic (real-time) Greens function approach at the self-consistent T-matrix level. The present extension to lateral spatial inhomogeneities due to nite beam spot size utilizes a photon transport equation which is based on a diagrammatic formulation of Maxwells equations for photon correlation functions. Assuming only radial ux for simplicity, and analytical solution for the pair density and power density rate equations is obtained, and numerical self-consistent solutions are presented. The results show that for typical beam waist parameters, lateral (radial) photon transport does not signicantly impede the theoretically predicted cooling process.

The relation between light absorption and luminescence in laser cooling of two-dimensional semiconductor systems

In efforts underway to achieve laser cooling of semiconductors, an electron-hole population is generated in the sample and maintained in a steady state. The analysis of light absorption by and luminescence from this population is basic to the understanding of feasibility and efficiency issues of the cooling process. It is commonly understood that, when this electron-hole plasma is in quasi-thermal equilibrium (equilibrium at a fixed density), the KMS (Kubo-Martin-Schwinger) relation holds between its luminescence and absorption spectra: their ratio is proportional to the Bose distribution function characterized by the temperature and chemical potential of the plasma. The proportionality factor, which affects the total luminescence rate, may generally depend on the dimensionality and geometry of the system. In this Contribution, as a preliminary step to extend our theoretical analysis of semiconductor cooling to quantum well systems, we discuss the application of the KMS relation to their spectra. In particular, we derive and discuss the geometrical proportionality factor in the KMS relation for quantum wells and compare it to its counterpart for bulk semiconductors.

Theory of optical refrigeration in p-doped semiconductors

We present a microscopic theory for luminescence of doped GaAs and its application to a study of optical refrigeration. We find that p-doping affects the temperature dependence of the cooling threshold in a complex way.