Theoretical Studies of Bound Exciton Decay and of Transport across Semiconductor Interfaces

Author: Osbourn, Gordon Cecil

Year: 1979

Degree: Dissertation (Ph.D.)

Advisors: Smith, Darryl L.; McGill, Thomas C.

Committee Member: Unknown, Unknown

Option: Physics

DOI: 10.7907/78qm-hz56

Abstract

This thesis presents theoretical studies of three topics in solid state physics. Chapters 2 and 3 are concerned with the Auger and radiative decay properties of excitons bound to acceptors in indirect and direct band semiconductors, respectively. Chapter 4 deals with the transport properties of carriers across semiconductor heterojunctions. Chapter 5 treats the effect of a heterojunction on carrier impact ionization (the inverse of a free carrier Auger process).

In Chapter 2, we present calculations of the phononless Auger and radiative transition rates for excitons bound to the four common shallow acceptors (B, Al, Ga and In) in Si and Ge. The calculated Auger rates for the bound excitons in Si vary significantly for the different acceptors, increasing rapidly as the acceptor binding energy increases. This is in agreement with the rapid decrease with increasing acceptor binding energy of measured acceptor bound exciton lifetimes in Si. Numerically, the calculated Auger rates are within about a factor of three of the measured recombination rates for the different acceptors. The dependence of the Auger rates on acceptor binding energy is due to an increased spreading in momentum space of the bound exciton wavefunction. In Ge, the calculated Auger rates are orders of magnitude less than the measured free exciton recombination rate in undoped Ge, suggesting that the phononless Auger transition is not important for acceptor bound excitons in Ge. This is consistent with the experimental observation that light doping with shallow acceptors has little effect on the lifetimes of photoexcited carriers at low temperatures in Ge; whereas, in Si the carrier lifetimes can be decreased by orders of magnitude. The principle difference between Si and Ge is that the acceptor binding energies are much greater in Si than they are in Ge. The calculation of radiative transition rates is compared to estimates obtained from absorption experiments. Results of the calculation agree with experiment to within a factor of two.

In Chapter 3, we present calculations of the Auger and radiative recombination rates for acceptor bound excitons in the HgCdTe alloy system and in GaAs. The transition rates are computed as a function of band gap in the HgCdTe alloy and as a function of the acceptor binding energy. The Auger rate is found to increase and the radiative rate to decrease with increasing acceptor binding energy. The radiative recombination rate is found to increase with increasing band gap. The Auger rate decreases with increasing band gap except: when the band gap first exceeds the spin-orbit splitting in the valence band and for band gaps less than about 0.2 eV where the density of final hole states and the electron-hole overlap becomes small. We find that Auger recombination is dominant for hydrogenic acceptors in HgCdTe for materials with a band gap less than about 0.35 eV and radiative recombination is dominant for larger gap materials. For deeper acceptors, this crossover occurs at larger band gaps. For GaAs, we find that radiative recombination dominates for all reasonably shallow acceptors.

In Chapter 4, we present calculations of reflection and transmission coefficients for electrons and holes at abrupt and graded (100) interfaces for the GaAs-Ga1-xAlxAs system. We consider semi-infinite crystals of the two semiconductors joined at an abrupt or compositionally graded interface . The calculations are performed using the empirical tight binding approximation. The transport coefficients were computed as a function of the components of the incident carrier wavevector normal and parallel to the interface. We have investigated the transport coefficients for incident states near various band minima into different final state channels. The transmission into states with qualitatively similar character to the incident state is found to be much greater than transmission into states of different character. For example, an electron near the X minimum normal to the interface in GaAs-Ga1-xAlxAs transmits into the X valley of GaAs with much greater probability than it transmits into the r minimum of GaAs. The dependence of the transport coefficients on the alloy composition has been investigated. The effect of the distance over which the interface is graded on the transport coefficients has also been investigated.

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