Charge-carrier statistics atInAs∕GaAsquantum dots

Abstract

The statistics of thermal electron emission from $\mathrm{InAs}∕\mathrm{GaAs}$ quantum dots with base/height dimensions of $20∕10\phantom{\rule{0.3em}{0ex}}(\mathrm{nm})$ are developed. The quantum dots considered are assumed to have two electron energy levels. For the electrons captured in the ground state, this gives the possibility of two different emission paths. Starting from a grand canonical ensemble and using an idea for ``truncated cascade capture,'' we derive ``effective thermal emission rates'' corresponding to experimental quantities. From experimental data of the capture cross sections, we demonstrate that the thermal emission path for electrons is shifted when the temperature is changed. In an Arrhenius plot for electron emission rates from the ground state, this is manifested as a transition region with varying slope which does not give any information about activation energies. The position on a temperature scale of this transition region depends on the internal relaxation time for electrons to go from the excited to the ground states. Due to limitations of experimental setups normally used for measuring activation energies, such measurements are done within a very limited temperature range. Erroneous interpretations of measured data therefore may occur if the possibility of a change in emission path is not taken into account. A method to avoid this problem in an experimental situation is pointed out in the discussion.