Lucky Drift Research Articles

A test by Monte Carlo simulation of the lucky drift theory of impact ionisation for a model with energy-dependent parameters

The lucky drift theory of the impact ionisation coefficient is tested against a Monte Carlo simulation for a model semiconductor with a multi-valley band structure and energy-dependent parameters. The lucky drift formulation due to Burt (1985) is applied to this model to calculate the steady-state drift velocity, average electron energy, energy and momentum relaxation lengths and the impact ionisation coefficient. The lucky drift predictions for these quantities are compared with estimates derived from a Monte Carlo simulation over a range of values of the applied electric field. The agreement between the lucky drift predictions and Monte Carlo results is quite encouraging, given the extreme simplicity of the theory and the generality of the model.

"Soft" energy thresholds in impact ionization: A classical model

A new simplified approach to the problem of soft threshold energy in impact ionization in semiconductors is presented. The model used is entirely classical and leads to a simple exact formula for the ionization rate as a function of energy. This result is used as the basis for modifying the lucky drift model of impact ionization, as has been done previously for other models of the soft threshold. The final analytic relations show excellent agreement with the available experimental data for the ionization coefficients in GaAs but indicate that the impact ionization process may involve three (or more) incident particles rather than two as previously thought.

Soft-threshold lucky drift theory of impact ionisation in semiconductors

Arguments are presented for the existence of a soft threshold to impact ionisation in GaAs and other related semiconductors. A soft-threshold factor is introduced into the theory of lucky drift and the results are applied to some major semiconductors. Excellent fit of theory to experiment is obtained, which confirms that the thresholds are indeed soft. Soft-threshold factors and new mean free paths are obtained for Ge, Si, GaAs, InP and GaP. The mean free paths are shown to obey a simple law. The results for GaAs are applied to the case of multilayer APD. It is shown that excellent agreement with the results of Capasso et al. (1982) are obtained, even with a 60:40 division of band edge discontinuity.

Lucky drift models of multilayered structures and approximate forms of lucky drift expressions

An approximate form of the lucky drift expression for ionisation coefficients is presented. This simplified expression enables analytic calculation of the ionisation coefficients in staircase avalanche photodiode structures using some approximations. The ionisation coefficients in superlattice avalanche photodiodes are calculated in the same manner. The results for both these structures are compared with other theories and with experimental observations.

A lucky drift model, including a soft threshold energy, fitted to experimental measurements of ionization coefficients

We have fitted the lucky drift model of impact ionization due to Burt to experimental data for GaAs, InP, Si and In 0.53Ga 0.47As. The agreement is surprisingly good considering the simplicity of that model. The lucky drift model has been further extended to include the effects of a soft threshold energy where carriers do not necessarily ionize immediately on achieving the threshold energy. This new lucky drift model is found to fit the same experimental data better than the model due to Burt in all cases but one.

A new simple expression for the impact ionisation coefficient and its verification using Monte Carlo simulation

Abstract A new expression for the impact ionisation coefficient is derived without heuristic arguments from the basic assumptions of lucky drift theory. Monte Carlo simulation is used to test the new expression for a model semiconductor. The agreement is very impressive for such a simple approximate theory.

An alternative expression for the impact ionisation coefficient in a semiconductor derived using lucky drift theory

Lucky drift theory is used to derive an alternative expression for the impact ionisation coefficient in a semiconductor to that given by B.K. Ridley (1983). This alternative expression has a simple physical interpretation. It also agrees well with a Monte Carlo simulation for a model semiconductor.