Lecture 10 OUTLINE Poissons Equation Work function MetalSemiconductor

Lecture #10 OUTLINE • Poisson’s Equation • Work function • Metal-Semiconductor Contacts – equilibrium energy-band diagram – depletion-layer width Read: Chapter 5. 1. 2, 14. 1, 14. 2 Spring 2007 EE 130 Lecture 10, Slide 1

Poisson’s Equation Gauss’s Law: area A s : permittivity (F/cm) : charge density (C/cm 3) E(x+Dx) Dx Spring 2007 EE 130 Lecture 10, Slide 2

Charge Density in a Semiconductor • Assuming the dopants are completely ionized: = q (p – n + ND – NA) Spring 2007 EE 130 Lecture 10, Slide 3

Work Function E 0: vacuum energy level FM: metal work function Spring 2007 FS: semiconductor work function EE 130 Lecture 10, Slide 4

Metal-Semiconductor Contacts There are 2 kinds of metal-semiconductor contacts: • rectifying “Schottky diode” • non-rectifying “ohmic contact” Spring 2007 EE 130 Lecture 10, Slide 5

Ideal MS Contact: FM > FS, n-type Band diagram instantly after contact formation: Schottky Barrier : Equilibrium band diagram: Spring 2007 EE 130 Lecture 10, Slide 6

Ideal MS Contact: FM < FS, n-type Band diagram instantly after contact formation: Equilibrium band diagram: Spring 2007 EE 130 Lecture 10, Slide 7

Ideal MS Contact: FM < FS, p-type metal p-type Si Eo c. Si Ec FM EF Ev FBp q. Vbi = FBp– (EF – Ev)FB W Spring 2007 EE 130 Lecture 10, Slide 8 FBp = c + EG - FM

Effect of Interface States on FBn metal FM > FS n-type Si • Ideal MS contact: FBn = FM – c • Real MS contacts: § A high density of allowed energy states in the band gap at the MS interface pins EF to the range 0. 4 e. V to 0. 9 e. V below Ec Eo c. Si FM q. Vbi = FB – (Ec – EF)FB FBn Ec EF Ev W Spring 2007 EE 130 Lecture 10, Slide 9

Schottky Barrier Heights: Metal on Si · FBn tends to increase with increasing metal work function Spring 2007 EE 130 Lecture 10, Slide 10

Schottky Barrier Heights: Silicide on Si Silicide-Si interfaces are more stable than metal-silicon interfaces. After metal is deposited on Si, a thermal annealing step is applied to form a silicide-Si contact. The term metal-silicon contact includes silicide-Si contacts. Spring 2007 EE 130 Lecture 10, Slide 11

The Depletion Approximation The semiconductor is depleted of mobile carriers to a depth W Þ In the depleted region (0 x W ): = q (ND – NA) Beyond the depleted region (x > W ): =0 Spring 2007 EE 130 Lecture 10, Slide 12

Electrostatics • Poisson’s equation: E • The solution is: E E Spring 2007 EE 130 Lecture 10, Slide 13

Depleted Layer Width, W At x = 0, V = -Vbi • W decreases with increasing ND Spring 2007 EE 130 Lecture 10, Slide 14

Summary: Schottky Diode (n-type Si) metal FM > FS n-type Si Depletion width: Eo c. Si FM q. Vbi = FBn – (Ec – EF)FB FBn Ec EF Ev W Spring 2007 EE 130 Lecture 10, Slide 15 Equilibrium (VA = 0) -> EF continuous, constant § FBn = FM – c

Summary: Schottky Diode (p-type Si) metal FM < FS p-type Si Eo Depletion width: c. Si Ec FM EF Ev FBp q. Vbi = FBp– (EF – Ev)FB W Spring 2007 EE 130 Lecture 10, Slide 16 Equilibrium (VA = 0) -> EF continuous, constant FBp = c + EG - FM