Electric conduction in semiconductors: a pedagogical model based on the Monte Carlo method

Abstract

We present a pedagogic approach aimed at modelling electric conduction in semiconductors in order to describe and explain some macroscopic properties, such as the characteristic behaviour of resistance as a function of temperature. A simple model of the band structure is adopted for the generation of electron–hole pairs as well as for the carrier transport in moderate electric fields. The semiconductor behaviour is described by substituting the traditional statistical approach (requiring a deep mathematical background) with microscopic models, based on the Monte Carlo method, in which simple rules applied to microscopic particles and quasi-particles determine the macroscopic properties. We compare measurements of electric properties of matter with ‘virtual experiments’ built by using some models where the physical concepts can be presented at different formalization levels.

Uma introdução aos métodos computacionais em física a partir do problema do decaimento radioativo

“…Os próprios currículos de física mais recentes têm procurado incorporar cada vez mais a física computacional [4,[7][8][9]. Diante dessa crescente incorporação, torna-se então cada vez mais necessário colocar o estudante de física em contato com a física computacional, tendo em vista * Endereço de correspondência: migueljbf@gmail.com que essa possui diferentes abordagens em física [10][11][12][13][14][15][16][17][18][19]. Neste trabalho apresentamos uma introdução a duas importantes ferramentas da física computacional: o método de Runge-Kutta -para a resolução numérica de equações diferenciais de primeira ordem; e o método de Monte Carlo -para simulações estocásticas.…”

Elucidating the electron transport in semiconductors via Monte Carlo simulations: an inquiry-driven learning path for engineering undergraduates

“…In this paper we present and discuss an inquiry-based learning path for science or engineering undergraduates studying the electron transport dynamics via MC simulations in InP semiconductor bulks. This work is new with respect to others presenting semiconductor models based on MC simulations [22], because here the main focus is not on the model itself, which is considered to be a well-established starting point, but the sequence of reasoned explorations, carried out within a scaffolding environment aimed at stimulating an effective understanding of the physics concepts underlying the complex world of semiconductor electronics. Nevertheless, this learning path represents a powerful instrument for educators introducing young undergraduates to the efficacy of MC simulations for inquiry into a physical system where the theoretical processes are well understood, but analytical investigation methods still only provide approximate results.…”