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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. Lecture #10. Poisson’s Equation. Gauss’s Law:. area A.  s : permittivity (F/cm)  : charge density (C/cm 3 ). E ( x ).

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Lecture #10

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  1. 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 Lecture #10 EE130 Lecture 10, Slide 1

  2. Poisson’s Equation Gauss’s Law: area A s :permittivity (F/cm)  :charge density (C/cm3) E(x) E(x+Dx) Dx EE130 Lecture 10, Slide 2

  3. Charge Density in a Semiconductor • Assuming the dopants are completely ionized: r = q (p – n + ND – NA) EE130 Lecture 10, Slide 3

  4. Work Function E0: vacuum energy level FM: metal work function FS: semiconductor work function EE130 Lecture 10, Slide 4

  5. Metal-Semiconductor Contacts There are 2 kinds of metal-semiconductor contacts: • rectifying “Schottky diode” • non-rectifying “ohmic contact” EE130 Lecture 10, Slide 5

  6. Ideal MS Contact: FM >FS, n-type Band diagram instantly after contact formation: Schottky Barrier : Equilibrium band diagram: EE130 Lecture 10, Slide 6

  7. Ideal MS Contact: FM <FS, n-type Band diagram instantly after contact formation: Equilibrium band diagram: EE130 Lecture 10, Slide 7

  8. Ideal MS Contact: FM <FS, p-type metal p-type Si Eo cSi Ec FM EF Ev FBp = c + EG -FM FBp qVbi = FBp– (EF – Ev)FB W EE130 Lecture 10, Slide 8

  9. Effect of Interface States on FBn FM >FS metal 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 eV to 0.9 eV below Ec Eo cSi FM qVbi = FB – (Ec – EF)FB FBn Ec EF Ev W EE130 Lecture 10, Slide 9

  10. Schottky Barrier Heights: Metal on Si • FBn tends to increase with increasing metal work function EE130 Lecture 10, Slide 10

  11. 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. EE130 Lecture 10, Slide 11

  12. The Depletion Approximation • The semiconductor is depleted of mobile carriers to a depth W • In the depleted region (0  x  W ): r = q (ND – NA) Beyond the depleted region (x > W ): r = 0 EE130 Lecture 10, Slide 12

  13. Electrostatics E • Poisson’s equation: • The solution is: E E EE130 Lecture 10, Slide 13

  14. Depleted Layer Width, W At x = 0, V = -Vbi • W decreases with increasing ND EE130 Lecture 10, Slide 14

  15. Summary: Schottky Diode (n-type Si) FM >FS metal n-type Si Equilibrium (VA = 0) -> EF continuous, constant • FBn =FM – c Depletion width: Eo cSi FM qVbi = FBn – (Ec – EF)FB FBn Ec EF Ev W EE130 Lecture 10, Slide 15

  16. Summary: Schottky Diode (p-type Si) FM <FS metal p-type Si Eo Depletion width: cSi Ec FM Equilibrium (VA = 0) -> EF continuous, constant FBp = c + EG -FM EF Ev FBp qVbi = FBp– (EF – Ev)FB W EE130 Lecture 10, Slide 16

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