Electrical Characterization of Photovoltaic
Materials and Solar Cells with the 4200A-SCS
Parameter Analyzer
I‑V, C‑V, C-f, DLCP, Pulsed I-V, Resistivity, andHall Voltage Measurements––
APPLICATION NOTEElectrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

Introduction

APPLICATION NOTE

The increasing demand for clean energy and the largely

Making Electrical Measurements withthe 4200A-SCS

untapped potential of the sun as an energy source is making

To simplify testing photovoltaic materials and cells, thesolar energy conversion technology increasingly important.

4200A-SCS is supported with tests and a project for making

As a result, the demand for solar cells, which convert sunlightmany of the mostly commonly used measurements easily.

directly into electricity, is growing. Solar or photovoltaic (PV)

These tests, which include I‑V, capacitance, and resistivity

cells are made up of semiconductor materials that absorb

measurements, also include formulas for extracting common

photons from sunlight and then release electrons, causing an

parameters such as the maximum power, short circuit

electric current to flow when the cell is connected to a load.

current, defect density, etc. The SolarCell project (Figure 1) is

A variety of measurements are used to characterize a solar

included with all 4200A-SCS systems and can be found in thecell’s performance, including its output and its efficiency. This

Project Library if you use the PV cell filter. Most of the tests inelectrical characterization is performed as part of research

this project can also be found in the Test Library.

and development of photovoltaic cells and materials, as wellas during the manufacturing process.
Some of the electrical tests commonly performed on solar
cells involve measuring current and capacitance as a function

Table 1. Tests in the SolarCell projectMeasurement
DC I-V

of an applied DC voltage. Capacitance measurements are

Name

Description

fwd-ivsweep

Performs I‑V sweep and calculates
Isc, Voc, Pmax, Imax, Vmax, FF

rev-ivsweep

Performs reversed bias I‑V sweep

sometimes made as a function of frequency or AC voltage.

solarcell-cvsweep Generates C‑V sweep

Some tests require pulsed current-voltage measurements.

solarcell-c-2vsv

Generates C‑V sweep and calculates
1/C2

cfsweep

Sweeps the frequency and measurescapacitance

dlcp

Measures capacitance as AC voltage
is swept. DC voltage is applied so
as to keep the total applied voltage
constant. The defect density is
calculated.

solarcell-pulseiv-sweep

Performs pulse I-V sweep using one
channel of PMU

hir

Uses 3 or 4 SMUs to source current
and measure voltage difference
for high resistance semiconductormaterials. Calculates sheet resistivity.

lor

Uses 1 or 2 SMUs to source current
and measure voltage using remotesense. Calculates sheet resistivity.
Uses current reversal method tocompensate for thermoelectric
voltage offsets.

i1-v23First of 4 tests that are used tomeasure the van der Pauw resistivity.
This test sources current between
terminals 1 and 4 and measures thevoltage difference between terminals
2 and 3.

i2-v34

Sources current between terminals
2 and 1 and measures the voltage
difference between terminals 3 and 4.

i3-v41

Sources current between terminals
3 and 2 and measures the voltage
difference between terminals 4 and 1.

i4-v12

Sources current between terminals
4 and 1 and measures the voltage
difference between terminals 1 and 2.

These measurements are usually performed at different
light intensities and under different temperature conditions.

Capacitance

A variety of important device parameters can be extracted
from the DC and pulsed current-voltage (I‑V) andcapacitance‑voltage (C‑V) measurements, including output
current, conversion efficiency, maximum power output,
doping density, resistivity, etc. Electrical characterization isPulse-IV

important in determining how to make the cells as efficient as
possible with minimal losses.
Instrumentation such as the 4200A-SCS Parameter Analyzer
can simplify testing and analysis when making these critical

4-ProbeResistivity

electrical measurements. The 4200A-SCS is an integrated
system that includes instruments for making DC and ultra
fast I‑V and C‑V measurements, as well as control software,graphics, and mathematical analysis capability. The
4200A-SCS is well-suited for performing a wide range ofmeasurements, including DC and pulsed current-voltage (I‑V),
capacitance-voltage (C‑V), capacitance-frequency (C-f), drive
level capacitance profiling (DLCP), four-probe resistivity (ρ,σ), and Hall voltage (VH) measurements. This application note
describes how to use the 4200A-SCS to make these electricalmeasurements on PV cells.

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vdp Resistivity

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Figure 1. Screenshot of Solar Cell project for the 4200A-SCS

DC Current-Voltage (I‑V) Measurements

Parameters Derived from I‑V Measurements

As described previously, many solar cell parameters canA solar cell may be represented by the equivalent circuit

be derived from current-voltage (I‑V) measurements of thecell. These I‑V characteristics can be measured using the4200A-SCS’s Source-Measure Units (SMUs), which cansource and measure both current and voltage. Because these
SMUs have four-quadrant source capability, they can sink thecell current as a function of the applied voltage. Two types of
SMUs are available for the 4200A-SCS: the 4200-SMU, which
can source/sink up to 100mA, and the 4210-SMU, which
can source/sink up to 1A. If the output current of the cellexceeds these current levels, it may be necessary to reduceit, possibly by reducing the area of the cell itself. However,if this is not possible, Keithley’s SourceMeter ® instruments,

model shown in Figure 2, which consists of a light-induced
current source (IL ), a diode that generates a saturation current[IS(eqV/kT –1)], series resistance (rs), and shunt resistance(rsh). The series resistance is due to the resistance of themetal contacts, ohmic losses in the front surface of the cell,
impurity concentrations, and junction depth. The series
resistance is an important parameter because it reduces boththe cell’s short-circuit current and its maximum power output.
Ideally, the series resistance should be 0Ω (rs = 0). The shunt
resistance represents the loss due to surface leakage along
the edge of the cell or to crystal defects. Ideally, the shunt
resistance should be infinite (rsh = ∞).

which are capable of sourcing/sinking higher currents, offer
possible alternative solutions.

rs

PV Cell
Photon hυILrsh

Load RL

Figure 2. Idealized equivalent circuit of a photovoltaic cell

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

If a load resistor (RL ) is connected to an illuminated solar cell,

As defined, the fill factor is the ratio of the maximum power

then the total current becomes:(Pmax = ImaxVmax) to the product of the short circuit current (Isc)and the open circuit voltage (Voc). The ideal solar cell has a

I = IS(eqV/kT – 1) – IL

fill factor equal to one (1) but losses from series and shunt

where:

resistance decrease the efficiency.

IS = current due to diode saturation

Another important parameter is the conversion efficiency (η),
which is defined as the ratio of the maximum power output to

IL = current due to optical generation

the power input to the cell:

Several parameters are used to characterize the efficiency ofthe solar cell, including the maximum power point (Pmax), the		Pmaxη = ______
		Pinenergy conversion efficiency (η), and the fill factor (FF). These

where:

points are illustrated in Figure 3, which shows a typicalforward bias I‑V curve of an illuminated PV cell. The maximum

Pmax = the maximum power output (W)power point (Pmax) is the product of the maximum cell current

Pin = the power input to the cell defined as the total radiant(Imax) and the voltage (Vmax) where the power output of the cell

energy incident on the surface of the cell (W)is greatest. This point is located at the “knee” of the curve.

Isc

Pmax

Figure 4 illustrates a solar cell connected to the 4200A-SCS

200

Cell Current (mA)Imax

Making Connections to the Solar Cell for
I‑V Measurements
for I‑V measurements. One side of the solar cell is connected

150

to the Force and Sense terminals of SMU1; the other side is100connected to the Force and Sense terminals of either SMU2

Maximum Power Area
Pmax = ImaxVmax

or the ground unit (GNDU) as shown.

50

0

SMU1
0.0

0.2

0.4

0.6

Cell Voltage (V)A

0.8

Vmax Voc

Figure 3. Typical forward bias I‑V characteristics of a PV cell

Force HI
Sense HI

V-Source

V
Solar Cell

The fill factor (FF) is a measure of how far the I‑V
Sense LO

characteristics of an actual PV cell differ from those of an
ideal cell. The fill factor is defined as:		I__________
maxVmax
FF =		IscVoc

Force LOSMU2 or GNDU

where:
Imax = the current at the maximum power output (A)Figure 4. Connection of 4200A-SCS to a solar cell for
I‑V measurements

Vmax = the voltage at the maximum power output (V)Using a four-wire connection eliminates the lead resistanceIsc = the short-circuit current (A)that would otherwise affect this measurement’s accuracy.

Voc = the open-circuit voltage (V)solar cell using one pair of test leads (between Force HI andWith the four-wire method, a voltage is sourced across theForce LO), and the voltage drop across the cell is measured
across a second set of leads (across Sense HI and Sense

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Figure 5. Results of calculated parameters shown in the Sheet in the Analyze pane.

LO). The sense leads ensure that the voltage developed

shows some of the derived parameters in the Sheet. These

across the cell is the programmed output value andparameters include the short-circuit current (ISC), the open

compensate for the lead resistance.

Forward-Biased I‑V Measurements
Forward-biased I‑V measurements of the solar cell are
made under controlled illumination. The SMU is set up to
output a voltage sweep and measure the resulting current.
This forward bias sweep can be performed using the Solar
Cell Forward I-V Sweep or “fwd-ivsweep” test, whichallows adjusting the sweep voltage to the desired values.
As previously illustrated in Figure 3, the voltage source isswept from V1 = 0 to V2 = VOC. When the voltage source is 0

circuit voltage (VOC), the maximum power point (Pmax), themaximum cell current (Imax), the maximum cell voltage (Vmax),
and the fill factor (FF).
The user can easily add other formulas depending on therequired parameters that need to be determined.
Using the Formulator, the conversion efficiency (η) can also
be calculated if the user knows the power input to the cell andinputs the formula. The current density (J) can also be derived
by using the Formulator and inputting the area of the cell.

(V1 = 0), the current is equal to the source-circuit current (I1

Figure 6 shows an actual I‑V sweep of an illuminated silicon= ISC). When the voltage source is an open circuit (V2 = VOC)

PV cell generated with the 4200A-SCS using the “fwd-then the current is equal to zero (I2 = 0). The parameters,

ivsweep” test. Because the system’s SMUs can sink current,

VOC and ISC can be derived easily from the sweep data using

the curve passes through the fourth quadrant and allows

the 4200A-SCS’s built-in mathematical analysis tool, thepower to be extracted from the device (I–, V+). If the current

Formulator. For convenience, the Solar Cell Forward I-V

output spans several decades as a function of the applied

Sweep test has the commonly derived parameters alreadyvoltage, it may be desirable to generate a semilog plot of I vs.

calculated, so the values automatically appear in the Sheet

V. The Graph supports an easy transition between displaying

in the Analyze pane every time the test is executed. Figure 5

data graphically on either a linear or a log scale.

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

By using additional light intensities, this technique can beextended using multiple points located near the knee of thecurves. As illustrated in Figure 8, a line is generated fromwhich the series resistance can be calculated from the slope.
When considered as ammeters, one important feature of
the SMUs is their very low voltage burden. The voltage
burden is the voltage drop across the ammeter during
the measurement. Most conventional digital multimeters(DMMs) will have a voltage burden of at least 200mV atfull scale. Given that only millivolts may be sourced to thesample in solar cell testing, this can cause large errors.
The 4200A-SCS’s SMUs don’t produce more than a few
hundred microvolts of voltage burden, or voltage drop, in the
Figure 6. I‑V sweep of silicon PV cell generated with the 4200-SMU

measurement circuit.

If desired, the graph settings functions make it easy to create
an inverted version of the graph about the voltage axis.
select the Y1 Axis tab, and click on the Invert checkbox. The
inverse of the graph will appear as shown in Figure 7.

Current (mA)

Simply go to the Graph Settings tab, select Axis Properties,
rS =

∆V
∆I

Voltage (V)Figure 8. Slope method used to calculate the series resistance

Reverse-Biased I‑V Measurements
The leakage current and shunt resistance (rsh) can bederived from the reverse-biased I‑V data. Typically, the test
is performed in the dark. The voltage is sourced from 0V toa voltage level where the device begins to break down. The
Figure 7. Inversion of the forward-biased I‑V curve about thevoltage axis

The series resistance (rs) can be determined from the forward
I‑V sweep at two or more light intensities. First, make I‑V
curves at two different intensities (the magnitudes of theintensities are not important). Measure the slope of this curvefrom the far forward characteristics where the curve becomeslinear. The inverse of this slope yields the series resistance:		∆V
rs = ____
		∆I

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resulting current is measured and plotted as a function of
the voltage. Depending on the size of the cell, the leakage
current can be as small as picoamps. The 4200-SMU has apreamp option that allows making accurate measurements
well below a picoamp. When making very sensitive low
current measurements (nanoamps or less), use low noise
cables and place the device in a shielded enclosure to shield
it electrostatically. This conductive shield is connected to theForce LO terminal of the 4200A-SCS. The Force LO terminal
connection can be made from the outside shell of the triax

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

connectors, the black binding post on the ground unit
(GNDU), or from the Force LO triax connector on the GNDU.

APPLICATION NOTE

Capacitance Measurements
Capacitance-voltage measurements are useful in deriving

One method for determining the shunt resistance of the PV

particular parameters about PV devices. Depending on thecell is from the slope of the reverse-biased I‑V curve, as

type of solar cell, capacitance-voltage (C‑V) measurements

shown in Figure 9. From the linear region of this curve, thecan be used to derive parameters such as the doping

shunt resistance can be calculated as:concentration and the built-in voltage of the junction. A

		∆VReverse Biasrsh = _______________
		∆IReverse Bias

capacitance-frequency (C-f) sweep can be used to provide
information on the existence of traps in the depletion region.
The 4210-CVU, the 4200A-SCS’s optional capacitance meter,
can measure the capacitance as a function of an applied DC

VReverse Bias
timate rsh

to esLinear region used

∆VReverse Biasrsh ≈∆VReverse Bias
∆IReverse Bias

∆IReverse Bias

voltage (C‑V), a function of frequency (C-f), a function of time(C-t), or a function of the AC voltage. The 4210-CVU can alsomeasure conductance and impedance.
To make capacitance measurements, a solar cell is

log IReverse Bias

Figure 9. Typical reverse-biased characteristics of a PV cellconnected to the 4210-CVU as shown in Figure 11. Like
I‑V measurements made with the SMU, the capacitancemeasurements also involve a four-wire connection tocompensate for lead resistance. The HPOT/HCUR terminals
are connected to the anode and the LPOT/LCUR terminals

Figure 10 shows an actual curve of a reverse-biased solar

are connected to the cathode. This connects the high DC

cell, generated using the Solar Cell Reverse I-V Sweep orvoltage source terminal of the 4210-CVU to the anode.

“rev-ivsweep” test. In this semi-log graph, the absolute valueof the current is plotted as a function of the reverse-biased
voltage that is on an inverted x-axis.

4210-CVU

HCUR

AC
SourceHPOT
AC
Voltmeter

Solar
Cell
LPOT

ABB
Feedback

AC
Ammeter

LCUR

Figure 11. Connecting the solar cell to the 4210-CVU
capacitance meter

Figure 11 shows the shields of the four coax cables coming
Figure 10. Reverse-biased I‑V measurement of silicon solar cell using
the 4200‑SMU

from the four terminals of the capacitance meter. The shields
from the coax cables must be connected together as close
as possible to the solar cell to obtain the highest accuracy
because this reduces the effects of the inductance in themeasure circuit. This is especially important for capacitancemeasurements made at higher test frequencies.

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Performing an Open and Short Connection Compensation(N) can be derived from the slope of this curve because N iswill reduce the effects of cable capacitance on measurement

related to the capacitance by:accuracy. This simple procedure is described in the		2
N(a) = ______________________
2
		qESA [d(1/C2)/dV]

4200A-SCS Reference Manual.
Given that the capacitance of the cell is directly related to thearea of the device, it may be necessary to reduce the area ofthe cell itself, if possible, to avoid capacitances that may be
too high to measure. Also, setting the 4210-CVU to measure

where:
N(a) = the doping density (1/cm3)
q = the electron charge (1.60219 × 10 –19C)

capacitance at a lower test frequency and/or lower AC drive

ES = semiconductor permittivity (1.034 × 10 –12F/cm for silicon)

voltage will allow measuring higher capacitances.

A = area (cm2)

C‑V Sweep

C = measured capacitance (F)C‑V measurements can be made either forward-biased orV = applied DC voltage (V)reverse-biased. However, when the cell is forward-biased,
the applied DC voltage must be limited; otherwise, theconductance may get too high for the capacitance meter tomeasure. The maximum DC current cannot be greater than
10mA; otherwise, the instrument’s DC voltage source will go
into compliance and the DC voltage output will not be at thedesired level.

The built-in voltage of the cell junction can be derived fromthe intersection of the 1/C2 curve and the horizontal axis.
This plot should be a fairly straight line. An actual curve takenwith the 4210-CVU, generated using the Solar Cell I/C2 C-V
Sweep or “solarcell-c-2vsv” test, is shown in Figure 13. The
Formulator function is used to derive both the doping density(N) and the built-in voltage on the x-axis (x-intercept). The

Figure 12 illustrates a C‑V curve of a silicon solar cell

doping density is calculated as a function of voltage in thegenerated by the 4210-CVU using the Solar Cell C-V Sweep

Formulator and appears in the Sheet in the Analyze pane. Theor “solarcell-cvsweep” test. This test was performed in theuser must input the area of the cell in the Constants area ofdark while the cell was reversed-biased.

the Formulator. The built-in voltage source value is derived
both in the Formulator and by using a Linear Line Fit option
in the Graph settings. Notice the value of the x-intercept
appears in the lower left corner of the graph.

Figure 12. C‑V sweep of a silicon solar cell

Rather than plotting dC/dV, it is sometimes desirable to viewthe data as 1/C2 vs. voltage because some parameters are
related to the 1/C2 data. For example, the doping density

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Figure 13. 1/C2 vs. voltage of a silicon solar cellElectrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

C-f Sweepthat the only charge density changes occur at the end of the

The 4210-CVU option can also measure capacitance,

depletion region.1

conductance, or impedance as a function of the test
frequency. The range of frequency is from 1kHz to 10MHz.
The curve in Figure 14 was generated by using the Solar
Cell C-f Sweep or “cfsweep” test. Both the range of sweep
frequency and the bias voltage can be adjusted. The desired
parameters, such as the trap densities, can be extracted fromthe capacitance vs. frequency data. The measurements canbe repeated at various temperatures.

Thus, in DLCP, the position (xe) can be varied by adjusting theDC voltage bias to the sample. This also allows determining
the defect density as a function of the distance, or special
profiling. The test frequency and temperature of themeasurement can also be varied to show a profile that isenergy dependent.
Once the measurements are taken, a quadratic fit of the C‑V
data is related to the impurity density at a given depletion
depth as follows for a p-type semiconductor:

NDL ≡E V + Eeρ
C03
= e = p + ∫ 0 g ( E, xe ) dE
2EF
2q ε A C1
qwhere:

NDL = defect density (cm –3)
C1, C0 = coefficients of quadratic fit of C‑V dataq = electron charge (1.60 × 10 –19C)
ε = permittivity (F/cm)
A = area of solar cell (cm2)ρe = charge density (C/cm3)
Figure 14. C-f Sweep of Solar Cell

Drive Level Capacitance Profiling (DLCP)

p = hole density (cm –3)
xe = distance from interface where EF – E v = Ee

Drive Level Capacitance Profiling (DLCP) is a technique for

The coefficients C0 and C1 are determined via a full least-

determining the defect density (NDL) as a function of depth

squares best fit of the data to a quadratic equation:of a photovoltaic cell1. During the DLCP measurement, theapplied AC voltage (peak-to-peak) is swept and the DC
voltage is varied while the capacitance is measured. This is incontrast to the conventional C‑V profiling technique, in which

dQ/dV = C2 (dV)2 + C1* (dV) + C0
However, only the C0 and C1 coefficients are used in
the analysis.

the AC rms voltage is fixed and the DC voltage is swept.
The Solar Cell DLCP or “dlcp” test allows making C‑V
In DLCP, the DC voltage is automatically adjusted to keep themeasurements for drive level capacitance profiling. During

total applied voltage (AC + DC) constant while the AC voltage

these measurements, the total applied voltage remains

is swept. By maintaining a constant total bias, the exposedconstant as the DC voltage bias is automatically adjusted as

charge density (ρe) inside the material stays constant up to

the AC voltage drive level amplitude varies. The AC amplitude

a fixed location (xe), which is defined as the distance fromof the 4210-CVU can vary from 10mVrms to 100mVrms

the interface where EF – E v = Ee. This is also in contrast to(14.14mV to 141.4mVp-p). The range of frequency can also be

conventional C‑V profiling, the analysis of which assumes

set from 1kHz to 10MHz. The capacitance is measured as the
AC voltage is sweeping.

1 J. T. Heath, J. D. Cohen, W. N. Shafarman, “Bulk and metastable defects in
CuIn1–xGaxSe2 thin films using drive-level capacitance profiling,” Journal ofApplied Physics, vol. 95, no. 3, p. 1000, 2004

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Table 2 lists the input parameters used in the test, thethe temperature of the measurement, the user can add anallowed range of input values, and descriptions. This

Action to the project to control a temperature controller via

test was created from the DLCP User Library and thethe 4200A-SCS’s GPIB interface. The 4200A-SCS is provided

ACSweep User Module. The user inputs the total appliedwith user libraries for operating the Temptronics, Lakeshore,voltage (VmaxTotal), the AC start, stop, and step voltages

and Triotek temperature controllers.

(VacppStart, VacppStop, and VacppStep), the time between
voltage steps (SweepDelay), the test frequency (Frequency),
the measurement speed (Speed), the measurement
range (CVRange), and offset compensation (OpenComp,
ShortComp, LoadComp, and LoadVal).
Table 2. Adjustable parameters for the dlcp test (ACSweep
User Module)
Parameter

Range

Description

VmaxTotal–10 to 10 volts

Applied DC Volts and ½ AC Volts p-p

VacppStart.01414 to .1414

Start Vac p-p

VacppStop.02828 to .1414

Stop Vac p-p

VacppStep.0007070 to .1414

Step Vac p-p

SweepDelay 0 to 100

Sweep delay time in seconds

Frequency

1E+3 to 10E+6

Test Frequency in Hertz

Speed0, 1, 20=Fast, 1=Normal, 2=Quiet

CVRange

0, 1E–6, 30E–6, 1E–3 0=autorange, 1µA, 30µA, 1mA

OpenComp

1, 0Enables/disables open compensation
for CVU

Pulsed I-V Measurements

ShortComp1, 0

Enables/disables short compensation
for CVU

Pulsed I-V measurements can be useful for studying

LoadComp

1, 0Enables/disables load compensation
for CVU

LoadVal1 to 1E+9

Load value

Figure 15. Capacitance vs. AC voltage p-p of a solar cellparameters of solar cells. In particular, pulsed I-V
measurements have been used to determine the conversion
efficiency, minimum carrier lifetime, and the effects of cell
capacitance. The 4225-PMU, the 4200A-SCS’s optional

Once the test is executed, the capacitance, AC voltage,
DC voltage, time stamp, frequency, and the defect density(NDL) are determined and their values are listed in the Sheet.
The defect density is calculated in the Formulator using aquadratic line fit of the C‑V data. The coefficients (C0 and C1)of the quadratic equation are also listed in the Sheet. The
user inputs the area and permittivity of the solar cell to betested into the Constants/Values/Units area of the Formulator.
Figure 15 shows the measurement results in the graph of
capacitance vs. AC voltage p-p. Notice the coefficients of thederived quadratic line fit and the defect density are displayedon the graph.
The capacitance measurements can be repeated atvarious applied total voltages in order to vary the positionof xe. The energy (Ee) can be varied by changing the test
frequency (1kHz to 10MHz) or the temperature. To change

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Ultra-Fast I-V Module, can output pulsed voltage andmeasure current, and can capture ultra-high-speed current or
voltage waveforms in the time domain. In addition to sourcing
a pulsed voltage, the PMU can sink current so it can measurea solar cell’s current output.
To make pulsed I-V measurements on a solar cell, the 4225PMU is connected to the cell as shown in Figure 16. EachPMU has two channels so the solar cell can be connectedusing either one or two channels. In the one-channel caseshown, one end of the cell is connected to the HI terminal of
PMU CH1 and the other side of the cell is connected to theshield of the coax cable, which is the LO terminal of the PMU.
Unlike the DC I-V and C-V measurements, the 4225-PMU
uses a two-wire technique. The Short Compensation feature
can be used to “zero out” the voltage drops due to the cables
so that a 4-wire measurement technique isn’t necessary.

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Solar Cell

Connection tocommon terminal

SMA Coax
Cable

A

A
V

50W

CH1

V

50W

4225-PMU

CH2

Figure 16. Connecting the solar cell to the 4225-PMU Ultra-Fast
I-V Module

Because solar cells are fairly capacitive, it is important toensure the pulse width is long enough for the pulsed I-V
sweep. The waveform capture mode should be used to verify
the pulse width prior to generating the pulsed I-V sweep. The
waveform capture mode enables a time-based current and/or
voltage measurement that is typically the capture of a pulsed
waveform. This can be used to perform a dynamic test on thecell or used as a diagnostic tool for choosing the appropriate
pulse settings in the pulsed I-V mode. Given that larger
solar cells have larger capacitances, it may be necessary to
reduce the area of the cell itself to avoid a long settling time in
the measurement.
The results of generating a pulsed I-V measurement sweep
on a silicon solar cell are shown in Figure 17. Note that the

Figure 17. Pulsed I-V measurement on solar cell using 4225-PMU

Resistivity and Hall Voltage
Measurements
Determining the resistivity of a solar cell material is a common
electrical measurement given that the magnitude of theresistivity directly affects the cell’s performance. Resistivity
measurements of semiconductor materials are usually
performed using a four-terminal technique. Using four probes
eliminates errors due to the probe resistance, spreading
resistance under each probe, and the contact resistance
between each metal contact and the semiconductor material.
Two common techniques for determining the resistivity of asolar cell material are the four-point collinear probe method
and the van der Pauw method. The SolarCell project contains
several tests for making both types of measurements.

current is in the fourth quadrant of the curve. This indicates

Four-Point Collinear Probe Measurement Methodthat the PMU is sinking current; in other words, the current is

The four-point collinear probe technique involves bringing

flowing out of the solar cell and into the PMU.

four equally spaced probes in contact with a material of
unknown resistance. The probe array is placed in the centerof the material as shown in Figure 18. The two outer probes
are used to source current and the two inner probes are used
to measure the resulting voltage difference across the surfaceof the material.

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Using the Four-Point Probe Tests
Current
SourceThe Solar Cell High Resistance or "hir" test or the Solar
Cell Low Resistance or "lor" tests are both used for making
four-point collinear probe measurements. The “hir” test can

Voltmeter

be used for materials over a wide resistance range, ~1mΩ
to 1TΩ. The 4200-PA preamps are required for making highresistance measurements (>1MΩ). The “lor” test is intended
for measurements of lower resistance materials (~1mΩ–1kΩ).
A screenshot of the “hir” test for measuring four-probe
resistivity is shown in Figure 19.

Figure 18. Four-point collinear probe resistivity configuration

From the sourced current and the measured voltage, thesurface or sheet resistivity is calculated by:		p		V
σ = ____× ___		ln2		 Iwhere:The Solar Cell High Resistance test (hir) uses either threeor four SMUs to make the resistivity measurements. One
SMU (SMU1) and the ground unit (GNDU) are used to source
current between the outer two probes. Two other SMUs
(SMU2 and SMU3) are used to measure the voltage drop
between the two inner probes. The Force HI terminal of each
SMU is connected to each of the four probes. The SMUσ= surface resistivity (Ω/ )V= the measured voltage (V)I= the source current (A)Note that the units for sheet resistivity are expressed as ohms
per square (Ω/ ) in order to distinguish this number fromthe measured resistance (V/I), which is simply expressed inohms. Correction factors to the resistivity calculation may berequired for extremely thin or thick samples or if the diameterof the sample is small relative to the probe spacing.
If the thickness of the sample is known, the volume resistivity
can be calculated as follows:		p		Vρ = ____
× ___ × t × k
		ln2		 Iwhere:

designation for this configuration is shown in Figure 20.
In the Formulator, the voltage difference between SMU2 andSMU3 is calculated and the resistance and sheet resistivity
are derived from the voltage difference. The results appear in
the Sheet in the Analyze pane of the test.
When making high resistance measurements, potential
sources of error need to be considered in order to make
optimal measurements. Use a probe head that has a level ofinsulation resistance between the probes that is sufficiently
higher than the resistance of the material to be measured.
This will help prevent errors due to leakage current throughthe probe head. Ensure that the measurement circuit iselectrostatically shielded by enclosing the circuit in a metalshield. The shield is connected to the LO terminal of the4200A. The LO terminal is located on the GNDU or on theρ = volume resistivity (Ω-cm)

outside shell of the triax connectors. Use triax cables tot = the sample thickness (cm)produce a guarded measurement circuit. This will preventk = a correction factor* based on the ratio of the probespacing to wafer diameter and on the ratio of wafer thickness
to probe spacing* The correction factors can be found in a standard fourpoint probe resistivity test procedure such as Semi MF84:
Standard Test Method for Measuring Resistivity of Silicon
Wafers With an In-Line Four-Point Probe. This standard was
originally published by ASTM International as ASTM F 84.

12 | WWW.TEK.COM

errors due to leakage current and significantly reduce the test
time. Finally, the 4200-PA preamp option is required to sourcevery small currents (nanoamp and picoamp range) and toprovide high input impedance (>1E16 ohms) to avoid loading
errors when measuring the voltage difference.
The Solar Cell Low Resistance (lor) test is only used for lower
resistance materials and requires only one or two SMUs. In
this case, the Force and Sense terminals of the SMUs areconnected to the four-point probe as shown in Figure 20.

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Figure 19. “hir” test module for measuring resistivity

Using the Formulator,
calculate the voltage
difference between
SMU2 and SMU3.
SMU1: Set to Current
Bias (VMU) – Set
current level to haveabout a 10mV drop
between SMU2 andSMU3.

SMU2: Set to Current
Bias (VMU) – Use as
high impedance voltmeter, and set
current to 0A on 1nA
range.

SMU3: Set to Current
Bias (VMU) – Use as
high impedance voltmeter, and set
current to 0A on 1nA
range.

GNDU: Common
connection for all
SMUs. Or, this can be
SMU4 set toCommon.

Force HI

Force HI

Force HI

Force HI

Figure 20. SMU designation for four-point collinear probe measurements

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

SMU2 or GNDU

Measuring Resistivity with the van der Pauw
MethodSense HI

Sense HIThe van der Pauw (vdp) technique for measuring resistivity

Force HI

Force HIuses four isolated contacts on the boundary of a flat,

SMU1

arbitrarily shaped sample. The resistivity is derived fromeight measurements made around the sample as shown in
Figure 22.
123Once all the voltage measurements have been taken, two4values of resistivity, ρA and ρB, are derived as follows:
		 ____p		(V2 + V4 – V1 – V3)
fAts _______________________
ρA =4I
		ln2		Figure 21. Connecting two SMUs for four-point probe measurements

In the configuration shown in Figure 21, the Force HI terminal

		 ____p		(V
6 + V8 – V5 – V 7 )fBts _______________________
ρB =
2
4I
		ln 		

SMU1 sources the current through Probe 1. The voltage

where:

difference between Probes 2 and 3 is measured through theρA and ρB are volume resistivities in ohm-cm;

Sense terminals of the two SMUs.

ts is the sample thickness in cm;

To compensate for thermoelectric offset voltages, twovoltage measurements are made with currents of opposite
polarity. The two measurements are combined andV1–V8 represent the voltages measured by the voltmeter;
I is the current through the sample in amperes;

averaged to cancel the thermoelectric EMFs. The Solar CellfA and fB are geometrical factors based on sample symmetry,

Low Resistance (lor) test performs this offset correction

and are related to the two resistance ratios QA and QB as

automatically by sourcing the two current values in the List

shown in the following equations (fA = fB = 1 for perfect

Sweep and then mathematically correcting for the offsets insymmetry).

the Formulator. The corrected resistance and sheet resistivity
are displayed in the Sheet.

V5
1

2

4

3

V3

1

2

1

2

1

2

4

3

4

3

4

3

V7

V1
V6
1

2

4

3

V4

1

2

1

2

1

2

4

3

4

3

4

3

V2

Figure 22. van der Pauw resistivity measurement conventions

14 | WWW.TEK.COM

V8

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

QA and QB are calculated using the measured voltages

APPLICATION NOTE

1.0

as follows:

0.9

		V
2 – V1
QA = __________
		V4 – V3

0.8

		V
6 – V5
QB = __________
		V8 – V7

fAlso, Q and f are related as follows:

(

0.7
0.6

Q – 1		 _______f		e_______=
arc cosh _______
2
Q + 1		 0.693		
0.693/f)

A plot of this function is shown in Figure 23. The value of “f”

0.5
0.4

1

be determined as follows:		ρA + ρB
ρAVG = __________
		 2

100

Q

can be found from this plot once Q has been calculated.
Once ρA and ρB are known, the average resistivity (ρAVG) can

10

Figure 23. Plot of f vs. Q

Using the vdp-resistivity subsite andvdp method tests
To automate the vdp resistivity measurements, the solarcell
project has a vdp-resistivity subsite with four tests: “i1-v23”,“i2-v34”, “i3-v41”, and “i4-v12.” A screenshot of the test is
shown in Figure 24.

Figure 24. Screenshot of van der Pauw test

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Test Name:
i4-v12

Test Name:
i2-v34
CommonCurrent Bias (+)

SMU1

SMU2

CommonCurrent Bias (–)

SMU1

SMU2

Voltmeter

Voltmeter

Voltmeter

SMU1

SMU2

SMU1

V12

2

1

2

1

2

1

2

4

3

4

3

4

3

4

3

SMU4

SMU3

V34

Voltmeter

SMU4

SMU3

V34

Voltmeter

Voltmeter

SMU4

SMU3

Current Bias (+)

CommonVoltmeter

CommonVoltmeter

Common

SMU1

SMU2

SMU1

SMU2

1

SMU4

2

4

V41

3
SMU3

Current Bias (+)

SMU4

Voltmeter

SMU4

SMU3

Current Bias (–)

CommonTest Name:
i1-v23

Test Name:
i3-v41

Voltmeter

SMU2

V12

1

Voltmeter

V41

Voltmeter

Current Bias (+)

SMU2

1

2

1

4

3

4
SMU3

Current Bias (–)

Voltmeter

SMU1

SMU4

CommonCurrent Bias (–)

2
3

V23
SMU3

Voltmeter

Voltmeter

SMU1

SMU4

Common

SMU2
1

2

4

3

V23
SMU3

Voltmeter

Figure 25. SMU configurations for van der Pauw measurements

Each terminal of the sample is connected to the Force HI
terminal of an SMU, so a 4200A-SCS with four SMUs is
required. The four SMUs are configured differently in each of
the four tests – one SMU supplies the test current, two are
configured as voltmeters, and one is set to common. Thismeasurement setup is repeated around the sample, with eachof the four SMUs serving a different function in each of thefour tests. A diagram of the function of each SMU in each test
is shown in Figure 25.

Adjusting the Test Parameters
Before executing the test, some of the test parameters must
be adjusted based on the sample to be tested. In particular,
it’s necessary to specify the source current, the settling time,
and the thickness of the material.
Input Source Current: Before running the project, input
the current source values based on the expected sample
resistance. Adjust the current so that the voltage difference
will not exceed approximately 25mV to keep the sample
in thermal equilibrium. In each of the four tests, enter bothpolarities of the test current. The same magnitude must be
used for each test.

16 | WWW.TEK.COM

Input the Settling Time: For high resistance samples,it will be necessary to determine the settling time of themeasurements. This can be accomplished by creating a test
that sources current into two terminals of the samples andmeasures the voltage drop on the adjacent two terminals. The
settling time can be determined by taking multiple voltage
readings and then graphing the voltage difference as afunction of time.
This settling time test can be generated by copying and thenmodifying one of the existing vdp tests. Switch the source
function from the sweep mode to the sampling mode. Then,in the Test Settings pane, take a few hundred or so readings
with a delay time of one second. Make sure that the “Report
Timestamps” box is selected. After the readings are done,plot the voltage difference vs. time on the graph. The settling
time is determined by observing the graph and finding thetime when the reading is within the desired percentage of the
final value.
Input the Thickness of the Sample: Enter the thickness ofthe sample into the Calc sheet at the subsite level. Select thesubsite vdp_resistivity. Go to the Subsite Data vdp-device
tab. It contains the output values of the voltage differences
and test current. From the Calc tab, the thickness can be
adjusted. The default thickness is 1cm.

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Figure 26. vdp resistivity calculation

Input Correction Factor: The resistivity formula found in
the Calc sheet at the subsite level also allows inputting acorrection factor, if necessary. The resistivity is multipliedby this number, which may be based on the geometry or
uniformity of the sample. By default, the correction factor is 1.

Running the ProjectHall Voltage Measurements
Hall effect measurements are important to semiconductormaterial characterization because the conductivity type,
carrier density, and Hall mobility can be derived from the Hall
voltage. With an applied magnetic field, the Hall voltage canbe measured using the configuration shown in Figure 27.

The van der Pauw resistivity measurements must be run at
the subsite level. Make sure that all four checkboxes to theB+right of the vdp tests (“i1-v23,” “i2-v34,” “i3-v41,” and “i4-v12”)
are selected and then select vdp_resistivity. Execute theiproject by using the Run button. Each time the test is run, thesubsite data is updated. The voltage differences from each1of the four tests will appear in the Subsite Data vdp-device
Sheet tab. The resistivity will appear in the Subsite Data Calc
sheet as shown in Figure 26.

2

4

3
t
V2–4+

Figure 27. Hall voltage measurement

With a positive magnetic field (B+), apply a current between
Terminals 1 and 3 of the sample, and measure the voltage
drop (V2–4+) between Terminals 2 and 4. Reverse the current
and measure the voltage drop (V4–2+). Next, apply current

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Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

between Terminals 2 and 4, and measure the voltage drop(V1–3+) between Terminals 1 and 3. Reverse the current andmeasure the voltage drop (V3–1+) again.

B+
Current Bias (+)

Voltmeter

SMU1

Reverse the magnetic field (B–) and repeat the procedure,measuring the four voltages: (V2–4–), (V4–2–), (V1–3–), and (V3–1–).
Table 3 summarizes the Hall voltage measurements.

Voltage
Designation

Magnetic
Flux

Current Forced
BetweenTerminals

Voltage Measured
BetweenTerminals

V2–4+

B+

1–3

2–4

V4–2+

B+

3–1

4–2

V1–3+

B+

2–4

1–3

V3–1+

B+

4–2

3–1

V2–4–

B–

1–3

2–4

V4–2–

B–

3–1

4–2

V1–3–

B–

2–4

1–3

V3–1–

B–

4–2

3–1

From the eight Hall voltage measurements, the average Hall
coefficient can be calculated as follows:		t(V
4–2+ – V2–4+ + V2–4– – V4–2–)
RHC = ___________________________________
		
4BI

Voltmeter

SMU1

SMU2

1

2

1

2

4

3

4

3

SMU4

SMU3

Voltmeter

Table 3. Summary of Hall Voltage Measurements

Current Bias (–)

SMU2

SMU4

CommonVoltmeter

Voltage Measured: V2–4+

SMU3

V34

CommonVoltage Measured: V4–2+
B+

Voltmeter

Current Bias (+)

V41

Voltmeter

SMU2

SMU1

1

2

4

3

SMU4

V41
SMU3

CommonCurrent Bias (–)
SMU2

SMU1

1

2

4

3

SMU4

Voltmeter

SMU3

CommonVoltage Measured: V1–3+

Voltmeter

Voltage Measured: V3–1+
B–

Current Bias (+)
SMU1
V12

Voltmeter
SMU2

Current Bias (–)
SMU1
V12

Voltmeter
SMU2

1

2

1

2

4

3

4

3

		t(V
3–1+ – V1–3+ + V1–3– – V3–1–)
RHD = ___________________________________
		
4BI

SMU4

SMU3

SMU4

SMU3

where:

Voltmeter

CommonVoltmeter

Common

RHC and RHD are Hall coefficients in cm3/C;
t is the sample thickness in cm;
V represents the voltages measured in V;

Voltage Measured: V2–4–

Voltage Measured: V4–2–
B–

Voltmeter
SMU1

Current Bias (+)
SMU2

Voltmeter
SMU1

Current Bias (–)
SMU2

I is the current through the sample in A;

1

2

1

2

B is the magnetic flux in Vs/cm2

4

3

4

3

Once RHC and RHD have been calculated, the average Hall
coefficient (RHAVG) can be determined as follows:		R
HC + RHDRHAVG = ______________
		
2
From the resistivity (ρAVG) and the Hall coefficient (RH), the Hall
mobility (µH) can be calculated:		______| RH |
µH =
		
ρAVG

18 | WWW.TEK.COM

SMU4

SMU3

SMU4

SMU3

CommonVoltmeter

CommonVoltmeter

Voltage Measured: V1–3+

Voltage Measured: V3–1–

Figure 28. SMU configurations for Hall voltage measurements

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Using the 4200A-SCS to Measure theHall Voltage

If a permanent magnet is used, an Action from the Actions

The SolarCell project does not include a specific test tothat will stop the test sequence in the project tree and instructmeasure the Hall voltage; however, four tests can be added tothe subsite for determining the Hall coefficient and mobility.
Given that the configuration for the Hall measurements is very
similar to the van der Pauw resistivity measurements, the vdp
tests can be copied and modified for making the Hall voltage
measurements. The modifications involve changing thefunctions of the SMUs. Figure 28 illustrates how to configure
the four SMUs in the tests to measure the Hall voltage. Use
the Output Value checkboxes on the Test Settings paneof each test to return the Hall voltages to the subsite-level
Calc sheet.

Library can be used to create a dialog box Project Prompt
the user to change the polarity of the magnetic field applied
to the sample. A Project Prompt is a dialog window thatpauses the project test sequence and prompts the user toperform some action. See the 4200A-SCS Reference Manual
for a description of how to use Dialog Box Actions.
Finally, the Hall coefficient and mobility can be derived in thesubsite-level Calc sheet. These math functions can be added
to the other equations for determining resistivity.

Conclusion
Measuring the electrical characteristics of a solar cell is

A custom test must be added to control the magnet. For

critical for determining the device’s output performancea GPIB-controlled electromagnet, users can write a userand efficiency. The 4200A-SCS simplifies cell testing

module using KULT (the Keithley User Library Tool) to

by automating the I‑V, C‑V, pulsed I-V, and resistivity

control the magnitude and polarity of the electromagnet. The

measurements and provides graphics and analysis capability.

code can be opened up in a custom test within the project.

For measurements of currents greater than 1A, Keithley offers

Information on writing code using KULT is provided in the

SourceMeter instruments that can be used for solar cell

4200A-SCS Reference Manual.

testing. Information on these models and further information
on making solar cell measurements can be found on
Keithley’s website: www.keithley.com.

WWW.TEK.COM | 19

Electrical Characterization of Photovoltaic Materials and Solar Cells
with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Contact Information:
Australia* 1 800 709 465
Austria 00800 2255 4835
Balkans, Israel, South Africa
and other ISE Countries +41 52 675 3777
Belgium* 00800 2255 4835
Brazil +55 (11) 3759 7627
Canada 1 800 833 9200
Central East Europe / Baltics +41 52 675 3777
Central Europe / Greece +41 52 675 3777
Denmark +45 80 88 1401
Finland +41 52 675 3777
France* 00800 2255 4835
Germany* 00800 2255 4835
Hong Kong 400 820 5835
India 000 800 650 1835
Indonesia 007 803 601 5249
Italy 00800 2255 4835
Japan 81 (3) 6714 3010
Luxembourg +41 52 675 3777
Malaysia 1 800 22 55835
Mexico, Central/South America
and Caribbean 52 (55) 56 04 50 90
Middle East, Asia, and North Africa +41 52 675 3777
The Netherlands* 00800 2255 4835
New Zealand 0800 800 238
Norway 800 16098
People’s Republic of China 400 820 5835
Philippines 1 800 1601 0077
Poland +41 52 675 3777
Portugal 80 08 12370
Republic of Korea +82 2 6917 5000
Russia / CIS +7 (495) 6647564
Singapore 800 6011 473
South Africa +41 52 675 3777
Spain* 00800 2255 4835
Sweden* 00800 2255 4835
Switzerland* 00800 2255 4835
Taiwan 886 (2) 2656 6688
Thailand 1 800 011 931
United Kingdom / Ireland* 00800 2255 4835
USA 1 800 833 9200
Vietnam 12060128* European toll-free number. If notaccessible, call: +41 52 675 3777

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