Fundamentos da teoria dos semicondutores

• Faixas de energia no cristal semicondutor.• Estatística de portadores em equilíbrio.• Transporte de portadores.• Processos de geração e recombinação de

portadores.

Faixas de energia no cristal semicondutor

Periodic potentials

Modelo de Kronig-Penney

Zonas de Brillouin

superfícies de energia constante

Massa efetiva

Superfícies de energia constante e massa efetiva

Simple energy band diagram of a semiconductor

Figure : A simplified energy band diagram used to describe semiconductors. Shown are the valence and conduction band as indicated by the valence band edge, Ev, and the conduction band edge, Ec. The vacuum level, Evacuum, and the electron affinity, c, are also indicated on the figure.

Dependência da largura da banda proibida com a temperatura

Densidade de estados

densidade de estados

The density of states in a semiconductor equals the density per unit volume and energy of the number of solutions to Schrödinger's equation. We will assume that the semiconductor can be modeled as an infinite quantum well in which electrons with effective mass, m*, are free to move.

densidade de estados

Distribuição de Fermi-Dirac

Other distribution functions and comparison

Maxwell-Boltzmann Bose-Einstein

Carrier densities

The carrier density in a semiconductor, is obtained by integrating the product of the density of states and the probability density function over all possible states. For electrons in the conduction band the integral is taken from the bottom of the conduction band, labeled, Ec, to the top of the conduction band:

The actual location of the top of the conduction band does not need to be known as the Fermi function goes to zero at higher energies. The upper limit can therefore be replaced by infinity. We also relabeled the carrier density as no to indicate that the carrier density is the carrier density in thermal equilibrium.

Semicondutor não degenerado

Non-degenerate semiconductors are defined as semiconductors for which the Fermi energy is at least 3kT away from either band edge. The reason we restrict ourselves to non-degenerate semiconductors is that this definition allows the Fermi function to be replaced with a simple exponential function, i.e. the Maxwell-Boltzmann distribution function.

Effective densities of states

Mass action law

Nível de Fermi intrinseco

Densidade de portadores de carga intrínsecos

Doped semiconductors

Non-equilibrium carrier densities

1. Injeção de portadores

2. Quase nível de Fermi

Condutividade

Geração e recombinação de portadores

Exemplos e Exercícios