#### Date of Award

1-1996

#### Degree Type

Thesis

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics

#### Supervisor

Dr. John S. Preston

#### Abstract

The escape of photogenerated carriers from semiconductor quantum wells is investigated theoretically and experimentally. Calculations of the tunnelling, thermionic emission, and thermally-assisted tunnelling escape times are given, where the thermionic emission process is split into low and high field regimes. At low fields, the escape rate is limited by the diffusion of the continuum carriers away from the well, while at high fields, the scattering rate from the confined to continuum states is the limiting process.

Barrier lowering effects are reviewed. The image force barrier lowering in a quantum well is calculated in the classical quasi-static approximation where the diffusion current is included for the first time. Both bipolar and unipolar wells are considered. In each case, the diffusion current inhibits the image charge formation, resulting in significant reductions in the barrier lowering; this is quantified by the concept of the effective image charge. At high carrier densities in the well (≥10¹² cmˉ²), it has a value approaching the electronic charge, while at low densities (≤10¹⁰ cmˉ²), it tends to zero. The only exception is in the case of majority carrier escape from a unipolar well, where at sufficiently high fields the barrier lowering is independent of the electric field.

Calculations of the 2D-to-3D scattering rate required for the high field description of thermionic emission are presented where the effects of a transverse electric field are explicitly included. Deformation potential and piezoelectric scattering by acoustic phonons are considered for the first time, as well as polar scattering by longitudinal optical (LO) phonons. It is found that polar LO phonon absorption dominates the thermionic emission rate at all temperatures despite its infinitesimal occupation factor at low temperatures. This is attributed to lowering of the effective barrier by an amount equal to the phonon energy. As the electric field is increased, the scattering function is smeared such that the rate is reduced just above the barrier, while a low energy tail extends to energies below the barrier. The scattering function does not shift with the potential barrier as expected, nor does the scattering rate rise abruptly at the barrier energy. As a result, it is expected that image charge lowering of the barrier will have only a minor effect on thermionic emission rates, particularly at higher temperatures. Calculations are presented for a range of well widths and depths. It is found that the emission rate oscillates as a function of the well width, with the jumps in emission rate corresponding to the confinement of a new upper subband.

Fits to the calculated scattering functions are presented as the basis for a simplified thermionic emission calculation. The step function approximation gives a simple analytic formula but performs well only in limited cases. A more complex approach, where the scattering function is approximated as a Fermi-Dirac function, reproduces the results of the full calculation to within 10% in most situations.

Calculated electron escape times are compared with reported experimental values from an asymmetric GaAs/AIGaAs quantum well (Cavaillès, 1992) with qualitative success. While the bias dependence was well reproduced, the calculated thermionic emission times were slow by factors of ~3-5. The principal causes of this discrepancy are believed to be band non-parabolicities and inaccuracies in the 3D density of states.

Measurements of hole escape times in an InGaAsP/InP multiple quantum well laser structure using time-resolved photoconductivity (PC) are presented as a function of temperature and bias. These are compared with calculated values which reproduce the qualitative behaviour but underestimate the thermionic emission time by one to two orders of magnitude. This is attributed primarily to the complexity of the valence and structure, further illustrating its impact on thermionic emission calculations.

#### Recommended Citation

Takasaki, Bruce Warren, "Carrier Escape from Semiconductor Quantum Wells" (1996). *Open Access Dissertations and Theses.* Paper 2385.

http://digitalcommons.mcmaster.ca/opendissertations/2385