Reciprocal capacitance transients?
Tim Gfroerer and Peter Simov
Davidson College, Davidson, NC
with Mark Wanlass
National Renewable Energy Lab, CO
~ Supported by the American Chemical
Society – Petroleum Research Fund ~
Quick Outline
• Review diode capacitance and the DLTS
experiment
• Our measurements and an unusual result
• A possible explanation and a nice way to
test it …
Bias-Dependent Depletion
+
+
+
+ + +
+ + + +
+ + P+ +
+ + + +
+ + + +
+
+
-
+
-
+
+
+
Depletion Layer
-
+
-
N+ -
With
Bias
-
+
Diode Capacitance
d1
No
bias
Vbuilt-in
d2
Reverse
bias
C = DQ/DV
~ eA/d
Vbuilt-in+Vapplied
Reverse bias increases the separation between the layers where free
charge is added or taken away.
Defect characterization via DLTS
+
+
+
+ + + + + + + +
+ + P+ + + + + +
+
+
+ + +
+
+ -
+
+
+
-
+
-
-
+
-
N+ -
Depletion
Temporary
Layer With Bias
Reduced Bias
+
Typical DLTS Measurements
0
e
T = 200K
T = 180K
T = 160K
T = 140K
-1
Capacitance Change (a.u.)
e
-2
e
Pulse
toward
zero
bias
free carriers
-3
e
Return to steady-state reverse bias
-4
e
-5
e
trapped carriers
-6
e
0.0
0.1
0.2
0.3
Time (ms)
0.4
0.5
Peter Simov (Davidson ’08)
DLTS Experiment
Computer with LabVIEW
(5)
Digital Scope
(Tektronix)
Capacitance
meter (Boonton)
(4)
Cryostat with sample
(1)
(2)
77K
(3)
Oxford
Agilent
Temp Controller
Pulse Generator
Device Structure and Band Diagram
Ga0.65In0.35P (S)
Barrier
GaAs0.72P0.28 (S+)
N+
P
GaAs0.72P0.28 (Zn)
Ga0.65In0.35P (Zn)
Barrier
GaAsP step-grading
GaAs Substrate
{
N+ P Junction
Conduction band
Energy
Quasi EF,p
Quasi EF,n
+ + +
Valence band
---Position
Depletion
region
W
Exponential transient analysis
10
Steady-state Bias = -2V
Pulse height = +1V
400ms RF
400ms RS
Ea = 93meV
40ms RF
40ms RS
10
2
Ea = 91meV
-1
Rate (s )
Capacitance Change (pF)
5
1
0.5
0.0
155K
160K
165K
170K
175K
180K
0.1
Ea = 81meV
10
0.2
Time (s)
0.3
0.4
1
Ea = 91meV
60
65
70
75
-1
1/kT (eV )
Reciprocal Analysis
10
Steady-state Bias = -2V
Pulse height = +1V
Capacitance Change (pF)
5
Slope of 1/C(t) (a.u.)
10
155K
160K
165K
170K
175K
180K
1
0.0
0.1
3
Ea = 0.38eV
10
2
10
1
40 ms response
400 ms response
0.2
Time (s)
0.3
0.4
60
65
70
-1
1/kT (eV )
75
80
Conclusions
• Capacitance transients are non-exponential and
rates are incompatible with conventional
thermal activation analysis
• The reciprocal of the capacitance varies
linearly with time, and the slope yields a single
thermal activation energy of 0.38eV.
Future Work
• Thermally-activated reciprocal behavior is a
characteristic of hopping transport.
• Test dependence on transport distance by
varying magnitude of bias pulse.