Alison B. Walker

Monte Carlo simulation of the transport of fast electrons and positrons in solids

Abstract We give a detailed description of a Monte Carlo simulation method for the transport of high energy (1–50 keV) positrons and electrons in solids using either the Penn dielectric loss function or the Lindhard dielectric function to model inelastic scattering and elastic scattering cross sections obtained from a partial wave expansion. Results for positron implantation and backscattering for Be, Al, Cu, Ag and Au are presented. Simulation results and experiments for positrons are found to be in very good agreement, which confirms the accuracy of the Penn model for describing inelastic scattering of positrons in solids. In the case of electrons agreement between simulated and experimental backscattering probabilities is reasonable but there are significant discrepancies which can be explained by the neglect of the indistinguishability of electrons in the Penn model.

Transient response of photodetectors

Calculations by drift diffusion and Monte Carlo methods and experimental data on the transient response of metal–semiconductor–metal photodetectors are reported. We have shown how the interplay of carrier and displacement currents, inhomogeneities in field and charge distributions, and hot electron effects determines observed structure in the transient response. In particular, we have demonstrated the role played by the regions under the contacts that are not illuminated in forming peaks in the transient response. We have also demonstrated that the peaks in the transient response need not be attributed to velocity overshoot and the scaling of detector response with contact separation has been studied.

Backscattering of slow positrons from semi-infinite aluminum

Monte Carlo simulation for 1–10 keV positron backscattering from semi-infinite aluminum with normal angle of incidence is reported. The elastic scattering cross sections have been obtained from the modified Rutherford differential cross section where the numerical coefficient in the atomic screening parameter is taken to be variable. To model inelastic scattering, we have investigated for the first time the effects of continuous slowing down through collisions with conduction electrons. Attention has also been paid to effects of changing the angle of incidence. Our simulated results and the available experimental data are found to be in reasonable agreement, and show that the energy dependence of the backscattered fractions can be fitted with a simple function: B(E)=0.0187997 ln E+0.102644. This suggests that both the transport model and the scattering cross sections used in the present work are reliable.

Modelling the influence of high currents on the cutoff frequency in Si/SiGe/Si heterojunction transistors

A one-dimensional self-consistent bipolar Monte Carlo simulation code has been used to model carrier mobilities in strained doped SiGe and the base-collector region of Si/SiGe/Si and SiC/Si heterojunction bipolar transistors (HBTs) with wide collectors, to study the variation of the cutoff frequency with collector current density . Our results show that while the presence of strain enhances the electron mobility, the scattering from alloy disorder and from ionized impurities reduces the electron mobility so much that it is less than that of Si at the same doping level, leading to larger base transit times and hence poorer performance for large for an Si/SiGe/Si HBT than for an SiC/Si HBT. At high values of , we demonstrate the formation of a parasitic electron barrier at the base-collector interface which causes a sharp increase in and hence a dramatic reduction in . Based on a comparison of the height of this parasitic barrier with estimates from an analytical model, we suggest a physical mechanism for base pushout after barrier formation that differs somewhat from that given for the analytical model.

Monte Carlo simulation of positron slowing down in aluminium

We have performed Monte Carlo simulations of positron slowing down in Al for incident positron energies in the range 1–10 keV. We present results for the backscattering probabilities and implantation profiles. The backscattering probabilities are significantly higher than the experimental values obtained at University of East Anglia (UEA) by Baker et al. However, the results for implantation profiles show good agreement with experimental results by the UEA group, and they indicate that the Makhov distribution, commonly employed in analysis of positron experiments, is not an accurate representation of the true profile. By comparing results obtained fo different models for the scattering cross sections we identify the transport cross section for elastic scattering and the stopping cross section for inelastic scattering as the parameters characterising the influence of the different scattering processes on the positron transport.

Mechanism of impact ionization enhancement in GaAs p-i-n diodes under high illumination conditions

Recent experimental work on AlGaAs p-i-n photodiodes [Dudley R A and Vickers A J 1995 Proc. Hot Carriers in Semiconductors IX (New York: Plenum)] has generated evidence that the transient photocurrent produced by high-intensity pulsed laser illumination is larger than expected for any given value of the bias. It has been postulated that this enhancement is due to the modification of the internal electric field by the photogenerated charge. A similar effect has been seen in calculations for metal-semiconductor-metal semiconductors [Dunn G M, Rees G J and David J P R 1997 Semicond. Sci. Technol. 12 692-7], but we present here details of the first calculation of the effect in a p-i-n diode. A drift-diffusion model is used to calculate photocurrent versus reverse bias for several values of illumination intensity, illustrating the enhancement effect. The origin of the enhancement is then highlighted and explained.

Modelling of hole mobilities in heavily doped strained SiGe

Low-field hole mobilities have been calculated for heavily relaxed and strained doped SiGe alloy layers with Ge contents varying from 0 to 50%, using a novel semi-analytical bandstructure model which incorporates the effects of strain on the valence band of the alloy. We obtain poor results compared with experiment for mobilities in heavily doped Si, and attribute this to (i) a failure of the Born approximation at low carrier energies and (ii) the omission of additional effects associated with heavy doping and high carrier concentrations. For the strained doped and intrinsic alloy we observe that both the in-plane and out-of-plane hole drift mobilities increase with increasing Ge content relative to those for Si. These enhancements are due mainly to the effects of strain, and to a lesser extent due to alloying with Ge, but are offset by the presence of alloy scattering. Our results are sensitive to the details of the models used for scattering by ionized impurities; however, the large uncertainties and scatter of the experimental data preclude accurate estimates of the alloy potential. We find that an alloy potential of 2.0 eV gives an in-plane mobility consistent with experimental data for intrinsic material. Our calculations for heavily doped layers are affected by uncertainties in the value of the alloy potential and highlight a need for a better quantitative understanding of the scattering processes which are important in heavily doped alloy layers.

Calculation of hole mobilities in relaxed and strained SiGe by Monte Carlo simulation

Hole mobilities in relaxed and strained undoped SiGe layers have been calculated with a one-dimensional self-consistent bipolar Monte Carlo simulation code. We have adopted a novel bandstructure model that incorporates strain effects in the alloy valence band. Both alloying and strain enhance the hole mobility compared with bulk Si and we find that alloy scattering is the dominant scattering mechanism. An alloy potential of 1.4 eV was obtained by matching our Monte Carlo data on drift mobilities to experimental Hall mobility measurements. Uncertainties in this value arise from scatter in the experimental data and a lack of detailed knowledge of the Hall factor.

One- and two-dimensional models of the transient response of metal - semiconductor - metal photodetectors including diffraction

The response of metal - semiconductor - metal photodetectors to pulsed illumination was simulated for GaAs and low temperature grown LT-GaAs detectors, using a drift-diffusion model in one and two spatial dimensions. We found that the response predicted by the one-dimensional model could be made to agree closely with that of the two-dimensional model by using a single adjustable parameter representing the distance a carrier must travel in a nonilluminated region. In the two-dimensional model, diffraction of the light around the contacts has been shown to be important for a contact separation of one micron and to reduce the photocurrent significantly. LT-GaAs was modelled with the same two-dimensional model as for GaAs, but with a recombination lifetime of 5 ps and lower carrier mobilities. Our results show that the photocurrent decreases to zero in 40 ps, whereas in bulk GaAs, with a recombination lifetime of 1 ns, there is a long lived tail in the photocurrent after 100 ps. Diffraction was shown to have similar effects for LT-GaAs as for GaAs.

Scaling properties of metal - semiconductor - metal photodetectors

A drift-diffusion model was used to investigate the scaling behaviour of the terminal characteristics of metal - semiconductor - metal (MSM) photodiodes. A one-dimensional model with both constant and field-dependent carrier mobilities was used to study the steady-state response to optical illumination. The scaling behaviour with respect to changes in illumination intensity, nominal electric field, contact separation and recombination lifetime was investigated. It is shown that the scaling behaviour derived from a simple analytical photodetector model is inappropriate even under conditions where it is expected to be valid. The scaling behaviour that is derived may be used in the design of efficient MSM photodiodes and is an essential prerequisite to understanding their transient behaviour.