Piotr Borowik

Monte Carlo based microscopic description of electron transport in GaAs/Al0.45Ga0.55As quantum-cascade laser structure

Results of multiparticle Monte Carlo simulations of midinfrared quantum cascade lasers structure initially fabricated by Page et al. are presented. The main aim of this paper is to discuss in details how electric current flows through the structure and which subbands are involved in this process. Monte Carlo method allows to predict the electron population inversion between the lasing levels and gives microscopic insight into processes leading to such behavior. Importance of a subband belonging to the laser injector region, with energy slightly below the upper lasing level, is demonstrated. The electron–electron Coulomb interactions influence the shapes of electron distribution functions; the values of average electron energies and effective subbands’ temperatures are calculated.

Monte Carlo study of electron transport in monolayer silicene

Electron mobility and diffusion coefficients in monolayer silicene are calculated by Monte Carlo simulations using simplified band structure with linear energy bands. Results demonstrate reasonable agreement with the full-band Monte Carlo method in low applied electric field conditions. Negative differential resistivity is observed and an explanation of the origin of this effect is proposed. Electron mobility and diffusion coefficients are studied in low applied electric field conditions. We demonstrate that a comparison of these parameter values can provide a good check that the calculation is correct. Low-field mobility in silicene exhibits temperature dependence for nondegenerate electron gas conditions and for higher electron concentrations, when degenerate conditions are imposed. It is demonstrated that to explain the relation between mobility and temperature in nondegenerate electron gas the linearity of the band structure has to be taken into account. It is also found that electron–electron scattering only slightly modifies low-field electron mobility in degenerate electron gas conditions.

Monte Carlo method for the investigation of electron diffusion in degenerate semiconductors

We propose an efficient Monte Carlo method for calculating diffusion coefficients in degenerate semiconductors by simulating two populations of particles: one obeying the nonlinear Boltzmann equation and the other obeying the linearized Boltzmann equation. The required numbers of particles and observation times are very different for the two populations. With the aim of improving computing efficiency, we have developed a rejection technique in order to account for the coupling between the two populations. We apply this method to the study of highly degenerate GaAs. We compare diffusivity and noise spectral density in order to investigate the noise reduction induced by degeneracy. We find that the magnitude of this effect is strongly sensitive to the applied field. We also suggest a possible application of our method to the accurate determination of low-field mobility.

Modified Monte Carlo method for study of electron transport in degenerate electron gas in the presence of electron–electron interactions, application to graphene

Standard computational methods used to take account of the Pauli Exclusion Principle into Monte Carlo (MC) simulations of electron transport in semiconductors may give unphysical results in low field regime, where obtained electron distribution function takes values exceeding unity. Modified algorithms were already proposed and allow to correctly account for electron scattering on phonons or impurities. Present paper extends this approach and proposes improved simulation scheme allowing including Pauli exclusion principle for electronelectron (ee) scattering into MC simulations. Simulations with significantly reduced computational cost recreate correct values of the electron distribution function. Proposed algorithm is applied to study transport properties of degenerate electrons in graphene with ee interactions. This required adapting the treatment of ee scattering in the case of linear band dispersion relation. Hence, this part of the simulation algorithm is described in details.

Combined rate equation and Monte Carlo studies of electron transport in a GaAs/Al0.45Ga0.55As quantum-cascade laser

Comparison of the Monte Carlo and rate equation methods as applied to the study of electron transport in a mid-infrared quantum cascade laser structure initially proposed by Page et al (2001 Appl. Phys. Lett. 78 3529) is presented for a range of realistic injector doping levels. An analysis of the difference between these two methods is given. It is suggested that justified approximations of the rate equation method, originated by imposing Fermi–Dirac statistics and the same electron effective temperature for each of the energy sub-bands, can be interpreted as partial inclusion of electron–electron interactions. Results of the rate equation method may be used as good initial conditions for a more precise Monte Carlo simulation. An algorithm combining rate equation and Monte Carlo simulations is examined. A reasonable agreement between the introduced method and a fully self-consistent resolution of Monte Carlo and Schr¨ odinger coupled with Poisson equations is demonstrated. The computation time may be reduced when the combined algorithm is used. (Some figures may appear in colour only in the online journal)

Optical Fourier transform diffractometry for kinoform technology

This paper presents a simple technique of phase retardation measurement applied to phase object manufacturing. This method is based on computer aided analysis of diffraction pattern generated by phase object. Application of this method to known intensity distribution in Fourier spectrum allows to find phase distribution in an object. The method is especially aligned for techniques where an unknown phase modulation is gained by the exposure of a photosensitive media. The described method can help to predict the desired phase shift from exposure. The phase retardation measurement technique presented in this paper is especially aligned to the problem of Holographic Optical Elements (HOE) manufacturing.