ECE 417517 Basic Semiconductor Devices

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ECE 417/517 Basic Semiconductor Devices

• Derivation of Schottky Diode
• I-V Characteristics

2
Schottky junctions
Metal Semiconductor
Vacuum level
cs
Fs
Fm
EC
EF
EF
EV
Fm work function of metal Fs work function of
semiconductor cs electron affinity of
semiconductor
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Schottky junctions
Vacuum level
Consider
cs
Fs
N-type semiconductor, Fm gt Fs
Fm
EC
EF
EF
EV
In thermal equilibrium Ef must line
up. Electrons move from semiconductor to metal
to reduce energy in semiconductor FB Fm-cs
barrier to electrons from metal
Vacuum level
cs
Fm
FB
EC
EF
EF
EV
4
Schottky junctions Electrostatics

• Depletion of electrons leaves
• bound donor ions, ND.
• Depletion region has electric field.
• No electric field in metal.
• Electrons accumulate on surface of metal

FB
EC
EF
EF
EV
r
ND
E
W
Emax
V
More generally
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Schottky junctions with bias
FB
EC
EF
EF
Equilibrium
EV
FB
EC
Forward bias Majority carriers in semiconductor
can spill into metal.
EF
EF
EV
FB
Reverse bias Large barrier to electrons
EC
EF
EF
EV
Expect
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Schottky junctions Thermionic Emission Theory
FB
EC
EF
EF
EV
General idea find number of electrons in
semiconductor with enough energy to get over
barrier.
We know distribution of electron energies
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Schottky junctions Thermionic Emission Theory
From previous page
or equivalently
Doping dep. constant
Excess energy above conduction band is kinetic
energy
Substituting
Integral over all electrons with velocity in x
greater than minimum required to get over barrier
constants
Plug into original integral
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Schottky junctions Thermionic Emission Theory
From previous page
problem
Minimum velocity to get over barrier
Need to express integral in terms of vx
All together
Maxwell Speed Distribution hyperphysics.phy-astr
.gsu.edu
constants
Gaussian integral
Integrate over vx
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Schottky junctions Thermionic Emission Theory
From previous page
FB
EC
EF
EF
EV
This is commonly expressed as
Richardson contant
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Schottky junctions Thermionic Emission Theory
From previous page
FB
EC
At equilibrium
EF
EF
EV
So, total current is
I
does not depend on VA
Schottky diode current
VA