Self-Assembled InAs/GaAs Quantum Dot Solar Cells

Our work focuses on experimental and theoretical studies aimed at establishing a fundamental understanding of the principal electrical and optical processes governing the operation of quantum dot solar cells (QDSC) and their feasibility for the realization of intermediate band solar cell (IBSC). Uniform performance QD solar cells with high conversion efficiency have been fabricated using carefully calibrated process recipes as the basis of all reliable experimental characterization. The origin for the enhancement of the short circuit current density (Jsc) in QD solar cells was carefully investigated. External quantum efficiency (EQE) measurements were performed as a measure of the below bandgap distribution of transition states. In this work, we found that the incorporation of self-assembled quantum dots (QDs) interrupts the lattice periodicity and introduce a greatly broadened tailing density of states extending from the bandedge towards mid-gap. A below-bandgap density of states (DOS) model with an extended Urbach tail has been developed. In particular, the below-bandgap photocurrent generation has been attributed to transitions via confined energy states and background continuum tailing states. Photoluminescence measurement is used to measure the energy level of the lowest available state and the coupling effect between QD states and background tailing states because it results from a non-equilibrium process. A basic I-V measurement reveals a degradation of the open circuit voltage (Voc) of QD solar cells, which is related to a one sub-bandgap photon absorption process followed by a direct collection of the generated carriers by the external circuit. We have proposed a modified Shockley-Queisser (SQ) model that predicts the degradation of Voc compared with a reference bulk device. Whenever an energy state within the forbidden gap can facilitate additional absorption, it can facilitate recombination as well. If the recombination is non-radiative, it is detrimental to solar cell performance. We have also investigated the QD trapping effects as deep level energy states. Without an efficient carrier extraction pathway, the QDs can indeed function as mobile carriers traps. Since hole energy levels are mostly connected with hole collection under room temperature, the trapping effect is more severe for electrons. We have tried to electron-dope the QDs to exert a repulsive Coulomb force to help improve the carrier collection efficiency. We have experimentally observed a 30% improvement of Jsc for 4e/dot devices compared with 0e/dot devices. Electron-doping helps with better carrier collection efficiency, however, we have also measured a smaller transition probability from valance band to QD states as a direct manifestation of the Pauli Exclusion Principle. The non-linear performance is of particular interest. With the availability of laser with on-resonance and off-resonance excitation energy, we have explored the photocurrent enhancement by a sequential two-photon absorption (2PA) process via the intermediate states. For the first time, we are able to distinguish the nonlinearity effect by 1PA and 2PA process. The observed 2PA current under off-resonant and on-resonant excitation comes from a two-step transition via the tailing states instead of the QD states. However, given the existence of an extended Urbach tail and the small number of photons available for the intermediate states to conduction band transition, the experimental results suggest that with the current material system, the intensity requirement for an observable enhancement of photocurrent via a 2PA process is much higher than what is available from concentrated sun light. In order to realize the IBSC model, a matching transition strength needs to be achieved between valance band to QD states and QD states to conduction band. However, we have experimentally shown that only a negligible amount of signal can be observed at cryogenic temperature via the transition from QD states to conduction band under a broadband IR source excitation. Based on the understanding we have achieved, we found that the existence of the extended tailing density of states together with the large mismatch of the transition strength from VB to QD and from QD to CB, has systematically put into question the feasibility of the IBSC model with QDs.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.