ECE 4813
Semiconductor Device and Material
Characterization
Dr. Alan Doolittle
School of Electrical and Computer Engineering
Georgia Institute of Technology
As with all of these lecture slides, I am indebted to Dr. Dieter Schroder from Arizona State
University for his generous contributions and freely given resources. Most of (>80%) the
figures/slides in this lecture came from Dieter. Some of these figures are copyrighted and can be
found within the class text, Semiconductor Device and Materials Characterization. Every serious
microelectronics student should have a copy of this book!
ECE 4813 Dr. Alan Doolittle
Diodes
PN Junction Diodes
Current - Voltage
Series Resistance
Schottky Diodes
ECE 4813 Dr. Alan Doolittle
PN Junction Diodes

The current in a Si pn junction diode at room temperature
is due to recombination in the space-charge region, Iscr,
and the quasi-neutral regions, Iqnr

 q (V − Irs )  

 q (V − Irs )  

 − 1




+
−
1 Io ,qnr exp
I = Io ,scr  exp

 

 nscr kT  

 nqnr kT  

Current (A)
100
For V > 3kT/q and negligible rs:
10-2
∆V = Irs
10-4
 qV 
I = Io exp

 nkT 
qnr
10-6
log I = log Io + qV nkT ln 10
Slope = 1/2.3nkT/q
V = 0 intercept ⇒ I = Io
10-8 scr
Io,scr
Io,qnr
10-10
10-12
0
0.2
0.4
Slope =
0.6
0.8
1
1
d log I
=
ln 10 nkT q
dV
Voltage (V)
ECE 4813 Dr. Alan Doolittle
PN Junction Diode Resistance
Diode series resistance reduces the current

 qVd  
I = I0  exp
 − 1
 nkT  

V = Vd + Irs

 q (V − Irs )  
I = I0  exp
 − 1
nkT

 

I
+
rs
100
+
Vd
V
_
_
Current (A)

10-2
∆V = Irs
10-4
qnr
10-6
10-8 scr
10-10
10-12
0
0.2
0.4
0.6
0.8
1
Voltage (V)
ECE 4813 Dr. Alan Doolittle
Diode Resistance
Diode conductance
gd =
I (1 − rs gd )
nkT q
0.2
0
0
Slope = rs
Intercept = nkT/q
0.2
0.4
0.6
0.8
Current (A)
gd 1 − rs gd
=
I
nkT q
I
nkT
=
+ Irs
gd
q
0.3
0.1
40
gd/I (V-1)

I/gd (V)
 q (V − Irs ) 
I = Io exp

nkT


0.4
Intercept = q/nkT
30
Slope = qrs/nkT
20
10
Intercept = 1/rs
0
0
0.5
1
1.5
2
2.5
gd (S)
ECE 4813 Dr. Alan Doolittle
Schottky Barrier Diodes


Schottky barrier diodes have I-V curves very similar to pn
junction diodes
The turn-on voltage can be controlled more than that of pn
diodes because the barrier height can be controlled
somewhat
I = I s (e qV nkT − 1); I s = AA*T 2e −qφ kT
B
A* = 4πqk 2 mn* h 3 = 120(m0 mn* ) A / cm 2K 2
Richardson Constant
φB
Ec
Ec
EF
Ev
φB
EF
Ev
ECE 4813 Dr. Alan Doolittle
Schottky Barrier Diodes: I - V
I = I s (e qV
nkT
− 1); I s = AA*T 2e −qφ
B
kT
Want n, A* and φB
Current - Voltage
log I = log IS + qV nkT ln 10
V = 0 intercept ⇒ I = IS
1
d log I
=
Slope =
ln 10 nkT q
dV
10-5
Current (A)

10-7
Slope = 1/2.3nkT/q
10-9
Intercept = IS
kT  AA*T 2 

φB =
ln
q  IS 
10-11
0
0.1
0.2
0.3
0.4
Diode Voltage (V)
Need to know A*
For V ≥ 4 kT q ⇒ I = I se qV
nkT
ECE 4813 Dr. Alan Doolittle
Schottky Barrier Diodes: I - T
log(J/T2) versus 1/T
 To determine
φB and A*
J = A*T 2 exp(− q (φB − V n ) kT )
q (φB − V n )
ln (J T ) = ln A −
kT
2
*
1/T = 0 intercept = A*
10-6
J/T2 (A/cm2K2)

d log ( J T 2 )
q (φB − V n )
Slope =
=−
⇒ φB
d(1 T )
k ln( 10 )
Intercept = A*
10-7
Slope=
-q(φB-V/n)/2.3k
10-8
V = 0.3 V
10-9
2.5 10-3
2.9 10-3
3.3 10-3
1/T (K-1)
ECE 4813 Dr. Alan Doolittle
Schottky Barrier Diodes: I - V




Barrier height can be determined from I-V or I-T plots
Forward-biased current is very sensitive to barrier height
If barrier height non-uniform, the lowest barrier height
regions dominate
Series resistance is important
101
10-1
0.6 V
10-3
A/2, φB=0.6 V
A/2, φB=0.7 V
10-5
10-7
φB=0.7 V
rs=0
0
0.1 0.2 0.3 0.4 0.5 0.6
Diode Voltage (V)
Current (A)
Current (A)
101
10-1
0.6 V, rs=10 Ω
10-3
A/2, φB=0.6 V
A/2, φB=0.7 V
10-5
10-7
φB=0.7 V, rs=0.1 Ω
0
0.1 0.2 0.3 0.4 0.5 0.6
Diode Voltage (V)
ECE 4813 Dr. Alan Doolittle
Schottky Barrier Diodes: C - V

C-V measurements are less sensitive to φB variations
C
qK sε 0ND
=
A
2(Vbi − V )
φB
2(Vbi − V )
 A
  =
qK sε 0ND
C 
Vbi
2
Ei
Slope ⇒ ND
Slope =

EF
φF
−2
qK sε 0ND
Intercept ⇒ φB
φB = Vbi + Vo
Vo = EG q − E i / q − φF
1.5 1014
(A/C)2 (cm4/F2)

Ec
Vo
1 1014
Slope
5 1013
Intercept
0
-1
0
1
2
3
4
Diode Voltage (V)
ECE 4813 Dr. Alan Doolittle
Review Questions





Why is the I-V curve a straight line on a semilog
plot?
Why does a Si diode logI – V curve have two
slopes?
How does series resistance affect the diode
current?
How is the barrier height of Schottky diodes
determined?
Why can the Schottky diode barrier heights be
different when determined from I-V or C-V data?
ECE 4813 Dr. Alan Doolittle