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