Using the Ramp Rate Method for Making
Quasistatic C-V Measurements with the4200A-SCS Parameter Analyzer––APPLICATION NOTE

Using the Ramp Rate Method for Making Quasistatic C-V
Measurements with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

Introduction

Capacitor

I

Capacitance-voltage (C-V) measurements are generally
made using an AC measurement technique. However,Force HI

Force HIsome capacitance measurement applications require a DC
measurement technique. These are called quasistatic C-V (orA

QSCV) measurements because they are performed at a very
low test frequency, that is, almost DC. These measurements

Vusually involve stepping a DC voltage and measuring theresulting current or charge. Some of the techniques used
for quasistatic C-V measurements include the feedback
charge method and the linear ramp method. The 4200A-SCS

Force LO
internally connected

Parameter Analyzer uses a new method, the ramp rate
method, which employs two 4200-SMUs Source-Measure

SMU1
ForceSMU

Units (SMUs) with two 4200-PA Preamps. The optional 4200-SMU2
MeasureSMU

PA Preamps are required because this test involves sourcing
and measuring current in the picoamp range. The SMUs areused to source current to charge the capacitor, and then tomeasure the voltage, time, and discharge current.
The software calculates the capacitance as a function ofvoltage from the measured parameters and shows thecurve on the 4200A-SCS’s display. This application note
describes how to implement and optimize quasistatic C-V
measurements using the 4200A-SCS and the ramp rate

Figure 1. Connections for Capacitance Measurements UsingRamp Rate Method		dQ
C = ____		dV
Q = ∫Idt
The ramp rate method included with the 4200A-SCS follows
these steps when making QSCV measurements:
1.

Charge the Device: A precharge current of 100pA ismethod. It assumes the reader is familiar with making I-Vapplied to the DUT by an SMU, called ForceSMU, until

measurements with the Keithley 4200A-SCS at the level

the compliance voltage is reached. The complianceoutlined in the 4200A-SCS Reference Manual.

voltage is user specified and is called VStart. The polarityof the precharge current is the same as the polarity of theRamp Rate Method

VStart voltage. If the precharge current is not sufficient
to force the device to VStart, then a timeout error will be

Figure 1 illustrates the basic connection diagram for thegenerated.

ramp rate method. This configuration requires two 4200SMUs with 4200-PAs connected to either side of the device

2.

Bias the Device for Specified Time Prior to Sweep:

under test. Because the ramp rate method works over aThe device is biased at the VStart voltage for a user

limited range, the capacitance of the device under test should

specified time (PreSoakTime) prior to the sweep.

be in the range of 1pF to about 400pF.
3.

Apply Ramp Current to Discharge Device: Once

Basically, the ramp rate method works by charging up thethe device is biased for a specified time, a ramp rate

device under test to a specific DC voltage using an SMU as

current is applied to the device to discharge the device.

a current source. Once the device is charged up, a current

The ramp rate current is of the opposite polarity as theof the opposite polarity is forced to discharge the device as

precharge current. The value of the ramp current is:

the SMU measures voltage as a function of time. A second
SMU measures the discharge current. From the measured
voltage (V), current (I) and time (t) values, the capacitance (C)is derived as a function of voltage and time:

2 | WWW.TEK.COM

Iramp = CVal × RampRate
where:

Using the Ramp Rate Method for Making Quasistatic C-V
Measurements with the 4200A-SCS Parameter Analyzer

CVal = the estimated capacitance value input by the user

APPLICATION NOTE

Table 1. List of Adjustable Parameters in meas_qscv User Modulein farads (F).

Parameter

RampRate = user input slope of stimulus voltage

Range

Description

ForceSMU

1–8

SMU number that will force current
through capacitive load. This SMU
must have a preamp.

MeasureSMU

1–8

SMU number that will measure
current. This SMU must have apreamp.

(dV/dt) in V/s.
4.

Simultaneously Trigger SMUs to Take
Measurements: The SMU that is the ForceSMU
measures voltage (V1, V2, V3 … Vn) and time (T1, T2, T3… Tn). The SMU that is the MeasureSMU measures thecurrent (I1, I2, I3 … In). The voltage, time, and current
measurements are made until the opposite polarity of theVStart voltage is reached.

5.

Calculate Voltage, Time, and Capacitance Output
Values: In real time, parameters are extracted from theVStart–200 to 200

Starting and ending voltages (V) for
C-V sweep.

CVal

1E–12 to 400E–12

Approximate capacitance of device
under test in Farads (F).

RampRate

0.1 to 1

Slope of stimulus voltage (dV/dt)
in V/s.

PreSoakTime

0 to 60

Additional time delay in seconds
to allow DUT, fixture, and cables tocharge up.

TimeOut

10 to 60

Time allowed in seconds to charge up
prior to time out.

measurements and will appear in the Sheet or Graph.
These parameters are Vout = voltage, Tout = time, and Cout= capacitance, and are calculated as follows:(V2 + V1)
Vout = ____________ (the average of two measured voltages)
2Here’s a more detailed description of the input parameters:
ForceSMU:

under test and measure the voltage as afunction of time. This SMU must have aTout = T2 (the time when the second measurement

preamp because it will be sourcing current inis made)I2
Cout = ________(dV/dt)

The SMU that will force current to the device

the picoamp range.
MeasureSMU: The SMU that will measure the current flowin the circuit. This SMU must have a preamp

where dV = V2 – V1 and dT = T2 – T1.

because it will be measuring current in theHow to Make QSCV Measurements
Using the Clarius Software

picoamp range.
VStart:This is both the starting and ending voltage

The system’s Clarius software includes a user moduleof the C-V sweep because the C-V sweep isto make quasistatic C-V measurements using the ramp

always symmetrical about 0V.

rate method. This user module, meas_qscv, located in theQSCVulib user library, can be opened up as a custom test

CVal:capacitance value of the device under test.

from within a project.

Setting up the Parameters in the meas_qscv
User Module

Enter at least the approximate maximumThis value is used to determine the magnitudeof the source current to charge the device.

RampRate:

The slope of the stimulus voltage in V/s. If theOnce you’ve created a test using the user module, you needramp rate is too fast, there will not be enoughto input a few parameters. The adjustable parameters for thedata points in the sweep. If the ramp rate it

meas_qscv user module are listed in Table 1.

too slow, the readings may be noisy. Someexperimentation may be needed to find theoptimal setting for a particular device.
PreSoakTime: The length of time in seconds to apply theVStart voltage to the device prior to the start ofWWW.TEK.COM | 3

Using the Ramp Rate Method for Making Quasistatic C-VMeasurements with the 4200A-SCS Parameter Analyzer

TimeOut:

APPLICATION NOTE

the C-V sweep. Specify sufficient time for themeasurements using the meas_qscv user module. Choose

device to charge up and reach equilibrium.

Select in the top left corner of the screen and then from either

The amount of time allowed to charge thedevice to the VStart voltage until the test
module times out. In some cases, such as

the Test or Project Library, enter qscv in the search bar andselect Search. The qscv Test or Project will automaticallyappear in the center pane.

when a device is shorted, the device may

The project tree for the Quasistatic C-V Using Ramp Ratenot reach the VStart voltage; this parameter

Project (ramprate-cvsweep) is shown in Figure 2.

enables the module to stop automatically andgenerate an error message. By default, this is
set to 10 seconds.

Executing the Test
The meas_qscv user module can be opened up in a projectby selecting a new Custom Test in the Test Library. Then
select Configure in the top left corner of the screen and in
the right hand pane select the QSCVulib user library and themeas_qscv user module. You can then enter the appropriate
values based on your application.
However, Keithley has already created a test and a projectthat comes in the Library that makes quasistatic C-V

Figure 3. Configuration pane for ramprate-cvsweep test

4 | WWW.TEK.COM

Figure 2. Project Tree for Quasistatic C-V Using Ramp Rate
Project (qscv)

This project contains a test called ramprate-cvsweep
for making measurements on a MOSFET device. The
configuration pane for setting up the test parameters isshown in Figure 3.

Using the Ramp Rate Method for Making Quasistatic C-V
Measurements with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

In this test, SMU1 (ForceSMU) and SMU2 (MeasureSMU)

techniques must be implemented. Use the triax cables thatare used to make the C-V measurements. The VStart value

come with the 4200A-SCS, which are shielded and will allow

is set to 4V, so this will generate a voltage sweep from –4V tomaking a guarded measurement. To reduce noise due to4V. The approximate capacitance value is 10pF, so this waselectrostatic interference, make sure the device is shielded

entered as the CVal parameter. This CVal capacitance valueby placing it in a metal enclosure with the shield connected towill be used to determine the ramp rate current. If this number

the Force LO terminal of the 4200A-SCS. Detailed information

is too low (for example, 1E–12 instead of 10E–12), then theon low current measurement techniques can be found incapacitance measurements will appear noisy. The RampRate

Keithley’s Low Level Measurements Handbook.

value was set to 0.7V/s. In this case, a RampRate that islarger (1V/s) will produce a somewhat quieter curve but will

The parameter settings in the meas_qscv module that will

have fewer data points. A RampRate that is smaller (0.1V/s)

most affect the measurements are CVal and RampRate. CValwill produce a much noisier curve with lots of data points.

is the approximate value of the device under test. If you input

You will need to experiment in order to determine the optimala value that is larger than that of the actual device, then thesettings for a particular device under test.

RampRate will be larger and there will be fewer data points.
Conversely, if the capacitance value entered is smaller thanOnce the device is connected to the two SMUs and the test

the actual device capacitance, the RampRate will be lower

is created with the desired input parameters, the C-V sweep

and there will be more data points in the curve. Use thecan be executed. The results of such a sweep are shownlargest RampRate possible, but ensure the device curvein Figure 4.

appears settled. However, if the RampRate is too fast, theremay not be enough points in the sweep.

Quasistatic C-V Curve of MOSFET
5.3E–12To reduce the noise level of the curve, the moving average

5.2E–12
5.1E–12(MAVG) function in the Formulator can be used. Try using a

5.0E–12

moving average of three readings to see if this helps. Do not

Capacitance (F)4.9E–12
4.8E–12

set the moving average number so large so that you lose the

4.7E–12

shape of your C-V curve.

4.6E–12
4.5E–12
4.4E–12

To subtract the offset due to the cables and probe station,

4.3E–124.2E–12

generate a C-V sweep using the meas_qscv module with the4.1E–12
4.0E–12

–4

–3

–2–1

0

12

3

4Voltage (V)probes up or with an open circuit in the test fixture. Using theFormulator, take an average of the readings. Subtract thisaverage offset value from capacitance measurements taken

Figure 4. Quasistatic C-V Sweep of MOSFET device

Optimizing Measurements
When making quasistatic C-V measurements using theramp rate method, various techniques must be used tooptimize measurement accuracy. These techniques include
implementing low current measurement practices andchoosing the appropriate settings in the software.

on the device under test.

Conclusion
Quasistatic C-V measurements can be made with the4200-SMUs with pre-amps using the ramp rate method.
This technique is implemented in software in the meas_qscv
module of the QSCV_uslib user library of the Clarius software.
Using low level measurement techniques and choosing theBecause using the ramp rate method involves sourcing andappropriate parameter settings in the software will ensure

measuring picoamp-level current, low current measurement

optimal results.

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Using the Ramp Rate Method for Making Quasistatic C-V
Measurements with the 4200A-SCS Parameter Analyzer

APPLICATION NOTE

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