1

MSE 510

Knowlton 1

- Applications -Using Band Diagrams and Fermi Energy Level

Applications to Devices – PhysicsHomojunctions

Heterojunctions

junctionsp-n

junctions

p-n-p junction

Metal-oxide-semiconductorjunction

diodes

p-n-pBipolar

transistors

MOS capacitorsMOS transistors

NVM

LightEmittingDevices

&

junctionsmetal-s/cjunctions

metal-metaljunctions

Thermocouples

&

MSE 510

Knowlton 2

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

(M

o) =

4.2

0 eV

Electrons

Fermi level

(Pt) - (Mo) = 1.16 eV = eV

Vacuum

Vacuum

Fermi level

Pt MoVacuum

Fermi level

Vacuum

Electrons

(b) 5.36

eV

4.20

eV

(a)

Fig. 4.28: When two metals are brought together, there is a contactpotential, V. (a) Electrons are more energetic in Mo so they tunnelto the surface of Pt. (b) Equilibrium is reached when the Fermi levelsare lined up.

(P

t) =

5.3

6 eV

Part 1: Metal-Metal Contacts

- Workfunction Differences -

Evac’s aligned

Ef’s aligned

Flat band

Equilibrium

2

MSE 510

Knowlton 3

Workfunctions of Various Metals

Mehrotra & Mahanty, Free electron contribution to the workfunction of metals, J. Phys. C: Solid State Phys., Vol. 11, 1978.

Workfunction Equation asDetermined by

Mehrotra & Mahanty

ao = Bohr radiusp = plasmon frequency= numerical value for integral = (1/3)0.5 vf

vf = Fermi velocityro = radius of equilibrium density distribution of free electrons

MSE 510

Knowlton 4

Image PE

0

EF +

x

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

x

Net PE

x

EF +

Applied PE

EF + eff

(a) (b) (c)

Fig. 4.36: (a) PE of the electron near the surface of a conductor, (b)Electron PE due to an applied field e.g. between cathode and anode(c) The overall PE is the sum.

Image Potential = Schottky Effect

2

( )16image vacuum

eV r E

r

p. 287-288

2

( )16image

eV r

r

Image ForcePotential Energy:an e- a distance r from a metal surface that has a potential energy, Vimage.

work vacuum FE E

vacuumE

( )appliedV r er

2

( )16Total vacuum

eV r E er

r

To find eff:Need to find maximum:•Take derivative and set = 0•Find rmin.•Substitute rmin back into equation and solve for eff.

electric field

min

( )0Total

r r

V r

r

Ef

max effV e

Ng, p. 608-609

3

MSE 510

Knowlton 5

From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

PE(x)

x

EF + eff

xF

Metal Vacuum

EF

00

Vo

e-

x = 0 x = xF

EF

(a)

(b)

Fig. 4.37 (a) Field emission is the tunneling of an electron at anenergy EF through the narrow PE barrier induced by a large appliedfield. (b) For simplicity we take the barrier to be rectangular. (c) Asharp point cathode has the maximumfield at the tip where the field-emission of electrons occurs.

E

Cathode

Grid or Anode

HV V

(c)

Field Emission & Image Force

max effV e

max

3

where:

4

electric field

eff

V

kT

e

kT

effo

J e

e

ee e

Field-Assisted Thermionic Emission

MSE 510

Knowlton 6

Metal-Metal Contacts – Seebeck Effect

Seebeck effect (thermoelectric power)

Built-in potential difference, ΔV, across a material due to a temperature difference, ΔT, across it

Kasap, Electronic Materials & Devices (McGraw-Hill, 2006) Ch. 4

T

VS

Sign of S: potential of the cold side with respect to the hot side; Thus, neg. if e-’s have accumulated in the cold side.

4

MSE 510

Knowlton

++++

----

Fig 4.61From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Density of States = Low at Ef

Phonon Scattering will have a greater effect on electrons

Lhot < Lcold (L = e- mean free path)

Density of States = High at Ef

Phonon Scattering will have a lesser effect on electrons

Lhot > Lcold (L = e- mean free path)

++++

----

e.g.: Ni, Pt, Al, Pd

e.g.: Cu, Li, Au

Seebeck Effect

7

MSE 510

Knowlton

Fig 4.32

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

(a) If same metal wires are used to measure the Seebeck voltage across themetal rod, then the net emf is zero. (b)The thermocouple from two differentmetals, type A and B. The cold end is maintained at 0 ¡C which is thereference temperature. The other junction is used to sense the temperature. Inthis example it is heated to 100 ¡C.

Metal

100oC

ColdHot

V

0

Metal

Metal

0oC

(a)

ColdHot

V

0Metaltype B

Metaltype B

Metaltype A

(b)

100oC 0oC

T

T AB

T

T BAABoo

dTSdTSSV

Number of Carriers Diffusing to Hot Region will differ in each metal, thus voltage difference occurs

Metal-Metal Contacts – Seebeck Effect Application = Thermocouple

5

MSE 510

Knowlton 9

Metal-S/C Contacts: Schottky & Ohmic Contacts

R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14

Flat band

MSE 510

Knowlton 10

Metal-S/C Contacts: Schottky & Ohmic Contacts

R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14

Flat band

Equilibrium

Flat band

Equilibrium

6

MSE 510

Knowlton 11

Band-BendingWhere does it come from?

R.F. Pierret, Semiconductor Device Fundamentals(Addison-Wesley, 1996) Ch. 14

Metal-S/C Contacts: Schottky & Ohmic

Contacts

D Aq p N n N

where

o R

d

dx

2

2

d V d

dx dx

Poisson's Equation

MSE 510

Knowlton 12

Biasing Effects

R.F. Pierret, Semiconductor Device Fundamentals(Addison-Wesley, 1996) Ch. 14

Metal-S/C Contacts: Schottky & Ohmic Contacts

7

MSE 510

Knowlton 13

Metal-S/C Contacts: Schottky & Ohmic Contacts

Doping Effects

R.F. Pierret, Semiconductor Device Fundamentals (Addison-Wesley, 1996) Ch. 14

Equilibrium

MSE 510

Knowlton 14

Metal-S/C Contacts: Schottky & Ohmic Contacts

Overview

Muller & Kamins, Device Electronics for Integrated Circuits, 3rd Ed. (Wiley, 1996) Ch. 3

Note: Blocking = Schottky

Equilibrium