Outline
PSPICE: device non-uniformity
modeling and other examples
• PSpice for study of device non-uniformity
• Other applications
– Propagation of signal in PV cell
– FET system for cancer drug studies
• Hands-on session
Lecture 10
– Editing PSPICE models
– Modeling mini-module example file
Special Topics:
Device Modeling
Introduction
PV device performance
• Semiconductor device modeling in 2-D
and 3-D through equivalent circuits
• Applicable to modeling of any other
problems involving electro-magnetic
signals
• Basic approach: draw equivalent circuit,
vary part models, parameters, etc.
J
Voc
Jsc
Rsc
FF
Jsc
Rsc
Voc
V
Roc
FF
Roc
Voc is the open-circuit voltage
Isc is the short-circuit current
FF is the fill factor
Pmax is the maximum power
η is the efficiency
Pmax  V OC I SC FF
 
V OC I SC FF
Pin
Study of PV device non-uniformity
J
Voc
V
Roc
The input power for efficiency
calculations is 1 kW/m2 or 100 mW/cm2
PV device performance
J
FF
•
•
•
•
•
V
Jsc
Rsc
• Example of the shunt (RSC=>0) effect on IV curve
and major PV parameters
• Device is represented by equivalent circuits
for 2D or 3D connections
• Applicable at a cell, cell-on-a-substrate,
module, or PV field levels
• Device optimization, influence of
component parameters, and various other
phenomena can be studied
1
PV non-uniformity: Equivalent
circuit for module
Study of PV device non-uniformity
• Introduced distributions of PV parameters (Voc,
Jsc, Rser, Rsh), both statistical and spatial
• Calculated resulting device efficiency dependent
on changes in:
V
bus
bar
cell
.. .
.. .
.. .
.. .
PV non-uniformity: Procedure
...
R s e r3 1
R s e r3 2
R s e r3 3
13
13
13
13
R sh 3 0
9999 9
I3 0
20.5mA d c
R sh 3 1
9999 9
I3 1
D 30
20.5mA d c
R sh 3 2
9999 9
I3 2
D 31
R r1
0 .5
20.5mA d c
R sh 3 3
9999 9
I3 3
D 32
R r2
0 .5
2. Model J-V curve of non-uniform module, calculate relative
efficiency:
D 33
R r3
0 .5
...
R s e r1
R s e r2
13
20.5mA d c
13
R sh 1
9999 9
I1
20.5mA d c
D 1
V1
R s e r3
20.5mA d c
D 2
13
R sh 3
9999 9
I3
 rel   non
R s e r4
13
R sh 2
9999 9
I2
20.5mA d c
Equivalent circuit
3 by 4 sub-cells, lump
parameters
1. Generate parameter distributions:
statistics – by first three moments (average, SD, and skewness );
geometry – assign values to sub-cells
R r3 2
0 .5
R s e r3 0
V
Integrated module –
3 linear cells in-series
through metallized scribes
PV non-uniformity: PSPICE
Schematics
20.5mA d c
bus
bar
substrate
Diana Shvydka and V. G. Karpov, Power generation in random diode arrays,
Phys. Rev. B 71, 2005, pp. 115314-1-5.
Diana Shvydka and V. G. Karpov, Modeling of nonuniformity losses in integrated
large area solar cell modules, Proc. 31st IEEE PVSC, Florida, 2005, pp 359-362.
R r3 1
0 .5
Rr
electrodes
– Module size and disorder amplitude
– Series and interconnect resistances
– Shunting-like phenomena
R r3 0
0 .5
Rsh
Rs
 unif
/  uniform
R sh 4
9999 9
I4
D 3
or relative mismatch loss:
D 4
R o u t1
...
0 .0 1
m  Pnon
• Represents 2x1 ft module with 1
cells
• 58 linear cells in series, 29 sub-cells in parallel, total 1682 sub-cells
• Parameters: Voc, Jsc, Rs, Rsh, Rr (one fluctuating)
cm2
PV non-uniformity: Module
size dependence
C o n tin u o u s
d is o r d e r
d is o r d e r
)
sc
0 .0 1
500
50
650
300
800
B i-m o d a l
L o g ( C o u n ts )
oc
re l
S D (
50
J
0 .1
100
1000
14
V
Geometry
(Voc maps)
First three moments: <Voc>=755mV,
SD=100mV, =-1.3
500
40
1 E -3
40
/ Puniform
3. Study dependence on module size, degree of disorder
PV non-uniformity: Parameter
distributions
Statistics
 unif
R e l. M is m a tc h L o s s ( m ) , %
0Vd c
V
12
J
d is o r d e r
oc
sc
d is o r d e r
10
8
6
4
2
0
100
700
30
10
 rel  0 . 923
900
30
20
20
10
10
 rel  0 . 919
10
Scaling law:
SD  N

 Voc  0 . 74
1
150
300
450
600
V oc, m V
750
900
5
10 15 20 25
Continuous
100
N u m b e r o f s u b - c e lls
5
10 15 20 25
Bi-modal

Jsc
 0 . 64
1000
10
100
1000
N u m b e r o f s u b - c e lls
• SD of relative efficiency changes by 2 orders
• Module size changes from 3x3 to 35x35 sub-cells
• For large module mismatch loss converges
• Each point obtained on 20 simulations
2
PV non-uniformity: Disorder
Dependence
V
oc
1 .0 0
= 0 .3
scribe lines
V
25
20
V
oc
oc
re l
30
= 0 .2 5
R e l. E ffic ie n c y , 
R e l. M is m a tc h L o s s (m ), %
35
PV non-uniformity: Series and
scribe resistances
= 0 .2
15
V
10
oc
= 0 .1 3
0 .9 5
Rr
0 .9 0
S c r ib e ( r o w ) r e s is t a n c e :
R r= 2 5
R r= 5
0 .8 5
R r= 0 .5
5
Rs
0 .8 0
0
-1 .5
-1 .0
-0 .5
0 .0
S kew ness
0 .5
1 .0
1 .5
2 .0
S h u n ts
R e l. E ffic ie n c y , 
re l
" H o le s "
Shunt:
Rsh=0
0 .7
0 .6
‘Hole’:
Rs=0 and low Voc
0 .4
0 .3
0 .0 0
0 .0 5
0 .1 0
0 .1 5
15
20
25
30
s
0 .8
0 .5
10
S e r ie s r e s is t a n c e R , O h m
PV non-uniformity: Shunting-like
phenomena
0 .9
5
 (V o c )
Voc disorder:
m ~ 8% for moderate disorder Voc ~ 13%
m ~ 30% for higher degree of disorder Voc ~ 30%
1 .0
0
0 .2 0
F r a c tio n o f d a m a g e d e le m e n ts
Large module 29x56 sub-cells, disorder in Voc (Voc ~ 13%)
Large module 29x56 sub-cells, disorder in Voc (Voc ~ 13%)
Low resistance promotes non-uniformity losses
PV non-uniformity: Conclusions
• Parameter distribution statistics plays the dominant
role in resulting module efficiency; geometry has a
minor effect
• Mismatch loss is almost independent of the module
size; depends on degree of disorder
• Module series and scribe resistances interfere with
non-uniformity effects
• Shunting entities close to scribes and bus bars can be
a significant efficiency loss factor
Effect of shunts and “holes” is comparable at fraction < 0.1
Propagating electric impulses
in thin film photovoltaics
• Modeled a new physical phenomenon: solitons
traveling in the lateral directions of thin-film PV
• A small signal perturbation decays while pulses of
certain shape and amplitude propagate
• Soliton velocity depends on specific resistance,
capacitance, and nonuniformity screening length
• Verified with experiment
Propagating electric impulses
• Equivalent circuit
j
J
• Experimental setup
G
T. K. Wilson, Diana Shvydka, and V. G. Karpov, Propagating
electric impulses in thin film photovoltaics, Proc. 4th IEEE PV
World Conference, Waikoloa, HI, 2006, pp 471 - 474.
O
TCO
CdS/CdTe
3
Propagating electric impulses:
Edge effect
Propagating electric impulses:
Parameters
0.6
0.6
Propagating electric impulses
• The predicted phenomenon of soliton propagation
could develop into a future non-destructive
diagnostic technique sensitive to device
imperfections
• Applicable to the problem of electric pulse
propagation in living tissues, particularly, nerves
(axon of a giant squid system)
– Ion channels of biological membranes typically exhibit
the diode-like IV characteristics
Analysis of anti-cancer drug action
R=0.5 
R=0.1 
0.2
0.4
Voltage, V
0.4
Voltage, V
• Considered circuits of 20 – 100 diodes with the
parameters chosen to allow for pulse propagation
trough the entire system
• Typical parameters: Voc = 520 mV, j0 =0.1515mA, R=0.01 – 10 Ohm, C=5-2500 nF
• Rectangular pulses with varying amplitudes in the
range of +/- 700 mV and durations 10-1000 ms
0.0
5 nF
0.2
25 nF
0.0
250 nF
R=0.02 
-0.2
-0.2
0
10
20
30
40
50
Diode #
Voltage on different diodes rescaled according
to y=(Diode #)/L with L inversely proportional
to the lateral resistance R. Higher resistances
show good scaling, since L is considerably
shorter than the system dimension. For low
R=0.05 Ohm, L becomes comparable to the
system dimension thus violating the scaling
2500 nF
0.00
0.02
0.04
0.06
0.08
0.10
Time, s
Pulse shape on a given diode for systems
with different capacitors measured at
different instances and scaled as Q=t/t. The
scaling fails for small C when velocity v
becomes large enough for the pulse to span
across the entire system and experience
edge effects
Impedance spectroscopy with field-effect transistor
arrays for the analysis of anti-cancer drug action on
individual cells
A. Susloparova, D. Koppenhofer, X.T. Vu, M. Weil, S. Ingebrandt
• Impedance spectroscopy measurements of silicon-based
open-gate field-effect transistor (FET) devices were
utilized to study the adhesion status of cancer cells at a
single cell level
• A well-known chemotherapeutic drug, topotecan
hydrochloride, was used to investigate the effect of this
drug to tumor cells cultured on the FET devices
• Real-time impedance measurements were performed to
verify the design
Analysis of anti-cancer drug action
• The developed method could be applied
for the analysis of the specificity and
efficacy of novel anti-cancer drugs in
cancer therapy research on a single cell
level in parallelized measurements
4
Summary
• Semiconductor device modeling in 2-D and
3-D through equivalent circuits
• Basic approach: draw equivalent circuit,
vary part models, parameters, etc.
• Applicable to modeling of any other
problems involving electro-magnetic signals
References
• OrCAD Capture user manual
• OrCAD PSpice user manual
• Additional references are given within slides
5