Lecture 7

1 / 17

# Lecture 7 - PowerPoint PPT Presentation

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)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Lecture 7' - ezekiel-acevedo

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
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

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
• 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, 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: 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: 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: 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 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
• FBntends to increase with increasing metal work function

EE130/230M Spring 2013

Lecture 7, Slide 11

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 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
• Poisson’s equation:
• The solution is:

EE130/230M Spring 2013

Lecture 7, Slide 14

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)

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)

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