Lecture #12
OUTLINE
• Metal-semiconductor contacts (cont.)
– I-V characteristics
Reading: Finish 14.2
Spring 2007
EE130 Lecture 12, Slide 1
Current Flow in a Schottky Diode
FORWARD BIAS
REVERSE BIAS
Spring 2007
• Current is determined by
majority-carrier flow across
the MS junction:
– Under forward bias,
majority-carrier diffusion
from the semiconductor
into the metal dominates
– Under reverse bias,
majority-carrier diffusion
from the metal into the
semiconductor dominates
EE130 Lecture 12, Slide 2
Voltage Drop across the MS Diode
• Under equilibrium conditions
(VA = 0), the voltage drop
across the semiconductor
depletion region is the built-in
voltage Vbi.
• If VA  0, the voltage drop
across the semiconductor
depletion region is Vbi - VA.
Spring 2007
EE130 Lecture 12, Slide 3
Depleted Layer Width, W, for VA  0
Last time, we found that
V x  
 qN D
W  x 2
2K S 0
At x = 0, V = - (Vbi - VA)
2 s (Vbi  VA )
 W
qN D
• W increases with increasing –VA
• W decreases with increasing ND
- (Vbi - VA)
Spring 2007
EE130 Lecture 12, Slide 4
W for p-type Semiconductor
V x  
qN A
W  x 2
2 K S 0
At x = 0, V = Vbi + VA
2 s (VA  Vbi )
 W
qN A
• W increases with increasing VA
• W decreases with increasing NA
Spring 2007
EE130 Lecture 12, Slide 5
Thermionic Emission Theory
• Electrons can cross the junction into the metal if
1
2
K.E. x  mvx  qVbi  VA 
2
2q
Vbi  VA 
vx  vmin 
*
mn
• Thus the current for electrons at a given velocity is:
I s   M , v x  qAvx n(vx )
• So, the total current over the barrier is:
 v min
I s  M  qA
 v n(v )dv
x

Spring 2007
EE130 Lecture 12, Slide 6
x
x
Schottky Diode I - V
• For a nondegenerate semiconductor, it can be shown
that
 4kTm*2 
*
2
nv x   

n
h3
 EF  Ec  / kT mn / 2 kT v x
e
e


• We can then obtain
4qmn* k 2
2  F B / kT qVA / kT
I S  M 
AT
e
e
3
h
*
m
 AJ S e qVA / kT , where J S  120 n T 2 e F B / kT A/cm 2
m0
• In the reverse direction, the electrons always see the
same barrier FB, so I M  S   I S  M VA  0
• Therefore
Spring 2007
I  I S (e qVA / kT  1) where I S  AJ S
EE130 Lecture 12, Slide 7
Applications of Schottky Diodes
•
IS of a Schottky diode is 103 to 108 times larger than
that of a pn junction diode, depending on FB .
 Schottky diodes are preferred rectifiers for lowvoltage, high-current applications.
Spring 2007
EE130 Lecture 12, Slide 8
Summary
• In a Schottky contact, charge is stored
on either side of the MS junction
– The applied bias VA modulates this
charge and thus the voltage drop
across the semiconductor depletion
region
 Flow of majority carriers into the
metal varies exponentially with VA
J  J S (e qVA / kT  1)
mn* 2 qF B / kT
where J S  120 T e
A/cm 2
m0
Spring 2007
EE130 Lecture 12, Slide 9