Lecture 1 - University of California, Berkeley

Lecture 1 - University of California, Berkeley

Lecture 7 OUTLINE Poissons 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 Poissons Equation area A Gauss Law: s ( x x) A s ( x) A xA E(x) E(x+x) x

( x x) ( x) x s d dx s EE130/230M Spring 2013 Lecture 7, Slide 2 s : permittivity (F/cm) : charge density (C/cm3) Charge Density in a Semiconductor Assuming the dopants are completely ionized:

= q (p n + ND NA) EE130/230M Spring 2013 Lecture 7, Slide 3 Work Function 0: vacuum energy level M: metal work function EE130/230M Spring 2013 S: semiconductor work function 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: M > S, n-type Band diagram instantly after contact formation: Equilibrium band diagram: qVbi = Bn (Ec EF)FB n Schottky Barrier Height: Bn M W EE130/230M Spring 2013

Lecture 7, Slide 6 Ideal M-S Contact: M < S, n-type Band diagram instantly after contact formation: Equilibrium band diagram: EE130/230M Spring 2013 Lecture 7, Slide 7 Ideal M-S Contact: M < S, p-type p-type semiconductor Band diagram instantly after contact formation: Equilibrium band diagram:

Schottky Barrier Height: Bp qVbi = Bp (EF Ev)FB Bp EG M W EE130/230M Spring 2013 Lecture 7, Slide 8 Ideal M-S Contact: M > S, p-type p-type semiconductor Band diagram instantly after contact formation: Equilibrium band diagram: EE130/230M Spring 2013

Lecture 7, Slide 9 Effect of Interface States on Bn Ideal M-S contact: Bn =M Real M-S contacts: A high density of allowed energy states in the band gap at the M-S interface pins EF to be within the range 0.4 eV to 0.9 eV below Ec M Bn EE130/230M Spring 2013 Lecture 7, Slide 10

Schottky Barrier Heights: Metal on Si Metal M (eV) Bn (eV) Er 3.12 Ti 4.3 Ni 4.7 W 4.6 Mo 4.6 Pt

5.6 0.44 0.5 0.61 0.67 0.68 0.73 Bp (eV) 0.68 0.61 0.51

0.45 0.42 0.39 Bn tends to increase with increasing metal work function EE130/230M Spring 2013 Lecture 7, Slide 11 Schottky Barrier Heights: Silicide on Si Silicide ErSi1.7 TiSi2 CoSi2 NiSi WSi2

PtSi M (eV) 3.78 4.18 Bn (eV) 0.3 Bp (eV) 0.8 4.6 4.65 4.7 5 0.6 0.64 0.65 0.65 0.84 0.52 0.48 0.47 0.47 0.28 Silicide-Si interfaces are more stable than metal-silicon interfaces and hence are much more prevalent in ICs. 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. EE130/230M Spring 2013 Lecture 7, Slide 12

The Depletion Approximation The semiconductor is depleted of mobile carriers to a depth W In the depleted region (0 x W ): = q (ND NA) Beyond the depleted region (x > W ): =0 EE130/230M Spring 2013 Lecture 7, Slide 13 Electrostatics Poissons equation: The solution is:

qN D x s s x qN W x D s V x ( x)dx EE130/230M Spring 2013 Lecture 7, Slide 14 Depletion Width, W qN D W x 2 V x

2K S 0 At x = 0, V = -Vbi 2 sVbi W qN D W decreases with increasing ND EE130/230M Spring 2013 Lecture 7, Slide 15 Summary: Schottky Diode (n-type Si) metal M >S

n-type Si Eo Si M qVbi = Bn (Ec EFS)FB Bn Ec EF Depletion width Ev W EE130/230M Spring 2013 Lecture 7, Slide 16

2 sVbi W qN D Summary: Schottky Diode (p-type Si) metal M

EF Ev Bp qVbi = Bp (EF Ev)FB W EE130/230M Spring 2013 Lecture 7, Slide 17 Depletion width 2 sVbi W qN A

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