Fundamentos da teoria dos semicondutores

Apresentação em tema: "Fundamentos da teoria dos semicondutores"— Transcrição da apresentação:

1 Fundamentos da teoria dos semicondutores
Estatística de portadores em equilíbrio. Transporte de portadores. Processos de geração e recombinação de portadores.

2 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.

3 Dependência da largura da banda proibida com a temperatura

4

5 Densidade de estados

6 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.

7 densidade de estados

8 Distribuição de Fermi-Dirac

9 Other distribution functions and comparison
Bose-Einstein Maxwell-Boltzmann

10 Carrier densities

11 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.

12

13

14

15 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.

16 Effective densities of states

17 Densidade de portadores de carga intrínsecos
Mass action law Nível de Fermi intrinseco

18

19 Doped semiconductors

20

21

22

23 Non-equilibrium carrier densities
1. Injeção de portadores 2. Quase nível de Fermi

24 Condutividade

25

26

27 Geração e recombinação de portadores

28 Exemplos e Exercícios

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43