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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. area A. Gauss’ Law:. E ( x ). E ( x + D x ). D x.  s : permittivity (F/cm)

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lecture 7
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
Poisson’s Equation

area A

Gauss’ Law:

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
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
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
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 f m f s p type
Ideal M-S Contact: FM <FS, p-type

p-type

semiconductor

Band diagram instantly

after contact formation:

Equilibrium band diagram:

Schottky Barrier Height:

FBp

qVbi = FBp– (EF – Ev)FB

W

EE130/230M Spring 2013

Lecture 7, Slide 6

ideal m s contact f m f s p type1
Ideal M-S Contact: FM >FS, p-type

p-type

semiconductor

Band diagram instantly

after contact formation:

Equilibrium band diagram:

EE130/230M Spring 2013

Lecture 7, Slide 7

ideal m s contact f m f s n type
Ideal M-S Contact: FM <FS, n-type

Band diagram instantly

after contact formation:

Equilibrium band diagram:

EE130/230M Spring 2013

Lecture 7, Slide 8

ideal m s contact f m f s n type1
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 9

effect of interface states on f bn
Effect of Interface States on FBn
  • Ideal M-S contact:

FBn=FM– c

  • 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

FM

FBn

EE130/230M Spring 2013

Lecture 7, Slide 10

schottky barrier heights metal on si
Schottky Barrier Heights: Metal on Si
  • FBntends to increase with increasing metal work function

EE130/230M Spring 2013

Lecture 7, Slide 11

schottky barrier heights silicide on si
Schottky Barrier Heights: Silicide on Si

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 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

EE130/230M Spring 2013

Lecture 7, Slide 13

electrostatics
Electrostatics
  • Poisson’s equation:
  • The solution is:

EE130/230M Spring 2013

Lecture 7, Slide 14

depletion width w
Depletion Width, W

At x = 0, V = -Vbi

  • W decreases with increasing ND

EE130/230M Spring 2013

Lecture 7, Slide 15

summary schottky diode n type si
Summary: Schottky Diode (n-type Si)

FM >FS

metal

n-type Si

Eo

cSi

FM

qVbi = FBn – (Ec – EFS)FB

FBn

Ec

EF

Depletion width

Ev

W

EE130/230M Spring 2013

Lecture 7, Slide 16

summary schottky diode p type si
Summary: Schottky Diode (p-type Si)

FM <FS

metal

p-type Si

Eo

cSi

Ec

FM

EF

Depletion width

Ev

FBp

qVbi = FBp– (EF – Ev)FB

W

EE130/230M Spring 2013

Lecture 7, Slide 17