Examining the transport properties of electrons in delta doped semiconductors with the Monte Carlo method

Electrons trapped in the well formed by delta doping of a semiconductor material form a quasi-two-dimensional electron gas (2BEG). In this thesis study, the transport properties and carrier (electron) mobility of this two-dimensional electron gas were found for different temperatures, doping ratio, doping geometry and material parameters using the Monte Carlo method. For the specified structure, Schrödinger and Poisson equations were first solved self-consistently. In this solution, the potential energy profile in which the electrons are trapped, the energy levels, the electron density at each level, and the wave functions corresponding to each level are solved within the framework of Hatree and effective mass approaches. Using the found wave functions, the scattering rates of two-dimensional electrons within and between energy bands corresponding to energy levels resulting from acoustic and polar optical phonons were calculated by using Fermi's golden rule. Using the found scattering rates in Monte Carlo calculations, the transport properties of electrons under an electric field applied parallel to the material plane were calculated for different temperatures. The average velocity of electrons as a function of time and their average steady state velocities, and the variation of the average steady state velocities of carriers as a function of the applied field, have been found by numerical methods. Finally, mobility calculation was made using the speed-applied field curves.