Lecture 7 OUTLINE Poisson’s equation Work function

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Presentation transcript:

Lecture 7 OUTLINE Poisson’s equation Work function Metal-Semiconductor Contacts Equilibrium energy band diagrams Depletion-layer width Reading: Pierret 5.1.2, 14.1-14.2; Hu 4.16

Poisson’s Equation Gauss’ Law: E(x) E(x+Dx) s : permittivity (F/cm) area A E(x) E(x+Dx) Dx s : permittivity (F/cm)  : charge density (C/cm3) EE130/230M Spring 2013 Lecture 7, Slide 2

Charge Density in a Semiconductor Assuming the dopants are completely ionized: r = q (p – n + ND – NA) EE130/230M Spring 2013 Lecture 7, Slide 3

Work Function E0: vacuum energy level FM: metal work function FS: semiconductor work function EE130/230M Spring 2013 Lecture 7, Slide 4

Metal-Semiconductor Contacts There are 2 kinds of metal-semiconductor contacts: rectifying “Schottky diode” non-rectifying “ohmic contact” EE130/230M Spring 2013 Lecture 7, Slide 5

Ideal M-S Contact: FM > FS, n-type Band diagram instantly after contact formation: qVbi = FBn– (Ec – EF)FB Equilibrium band diagram: n Schottky Barrier Height: W EE130/230M Spring 2013 Lecture 7, Slide 6

Ideal M-S Contact: FM < FS, n-type Band diagram instantly after contact formation: Equilibrium band diagram: EE130/230M Spring 2013 Lecture 7, Slide 7