Electronic devices themselves have a variety of different noise sources, including thermal noise, shot noise, white (broadband) noise, and 1/f (flicker effect) noise. 1/f noise is low frequency electronic noise where the current (ISD) or power (PSD) spectral density is inversely proportional to frequency. Many component types can have 1/f noise, including semiconductor devices, some types of resistors, 2D materials like graphene, and even chemical batteries. To determine the 1/f noise of a device, we typically measure current versus time and convert the data to the frequency domain. The Fast Fourier Transform (FFT) is a popular method of converting time-domain data to frequency-domain data.

In a measurement setup, noise comes from different sources, one of which is the measurement instrument itself. To characterize the noise of the device under test (DUT), the instrument noise must be less than the DUT noise.

The Source Measure Unit (SMU) and Pulse Measure Unit (PMU) are two modules of the Keithley 4200A-SCS Parameter Analyzer that measure and source current and voltage in the time domain. The SMU and PMU can acquire measurement data at a constant rate, which can then be converted into parameters in the frequency domain using the FFT function, which is built into the Formulator of the Clarius software. The 4200A-SCS has a comprehensive test library including sample tests and AC parameter calculations to generate 1/f noise, current spectral density, and AC-based measurements.

This article describes how to make 1/f noise measurements using the SMU and PMU with the 4200A-SCS. In particular, the figures below describe 1/f noise basics, measure MOSFET drain current 1/f noise by deriving the current spectral density (ISD) over a specific range, configure 1/f noise measurements on 2-terminal devices, to determine the noise floor of the instrument, and we also describe the built-in FFT function.

**Measuring the 1/f noise of a device**

Flicker effect noise, or 1/f noise, covers many frequencies, but is usually observed at

Figure 1. Typical current noise spectrum of a device.

1/f noise can be determined in a number of ways, one of which is shown in Figure 2, using DC test equipment. In this example, a voltage is applied to both the gate and drain of the MOSFET, and the ammeter measures the drain current at a given sampling rate. Using FFT calculations, we convert the time-based current measurement data obtained by the ammeter into current noise spectral density (ISD) and frequency. Using the FFT function requires that the current and time measurements are evenly spaced.

Figure 2. Circuit used to measure the 1/f drain current noise of a MOSFET.

As shown in Figure 3, there are two power supplies in the circuit that can be replaced by two SMU (or PMU channels), which can both provide voltage, measure current, and determine the IV characteristics of the MOSFET. In this example, SMU1 is connected to the gate terminal, the gate voltage is applied; SMU2 is connected to the drain terminal, the drain voltage is output, and the drain current is measured.

Figure 3. Measurement of 1/f drain current noise using two SMUs.

The 4200A’s SMU has a 6½-bit resolution and typically has lower DC noise than the PMU. However, the current measurement of the SMU is obtained at a slower rate than the PMU, so the bandwidth is lower. The PMU can obtain high-speed current measurements, but at the expense of noise. The noise of the instrument used must be sufficiently lower than the expected device noise. The best way to determine this is to derive the noise of the instrument using an open circuit (described in the next section).

**Determining SMU and PMU Noise Using Open Circuits**

The instrument noise of the SMU or PMU can be derived using an open circuit. To determine its noise, place a metal cap on each of the Force HI terminal and the Sense HI terminal and allow the instrument to warm up for one hour. If the instrument is connected to a probe station, raise the probe before starting the test. Clarius software is used to control the instrument during noise testing.

The SMU Current Spectral Density (smu-isd) test in the Clarius Library derives ISD versus frequency from current and time measurements taken by the SMU. This test can be added to the project tree by searching for smu-isd in the Test Library and adding it to the project tree. This test measures open circuits on three different current ranges using Normal speed mode. In the Formulator, the FFT formulas derive the real and imaginary parts of the current, power, frequency, bandwidth, and ISD, as shown in the screenshot in Figure 4.

Figure 4. The formula used for the smu-isd test.

Since the current is measured using an open circuit, this test can be used to determine the noise floor of the SMU. The frequency will vary depending on the timing settings. The current noise density, expressed in A/sqrt(Hz), is calculated by deriving this from the noise of a single DC measurement, which is expressed in amperes. If expressed in digital fast Fourier transform, the formula for the current spectral density is:

ISD = sqrt((2*PWR)/(PTS*BW))

where: PWR is the square of the current magnitude, or PWR = Im(I)^2 + Re(I)^2

Bandwidth (BW) is defined as 1/dt, where dt is the time step between two measurement points, assuming a constant time step between all measurements. From this test, we can also derive the power spectral density (PSD) by adding the following formula to the Formulator:

PSD = (2*PWR)/(PTS*BW)

Figure 5 shows a graph of open-circuit current noise generation at 0 V measured using this test, which includes four different ranges: 100 mA, 1 mA, 1 mA, and 1 nA. In this test, instead of using the default normal speed mode, we used the Custom Speed custom speed mode. By customizing the speed mode, the user can further define the time parameters.

Figure 5. Current spectral density versus frequency for open-circuit current data measured from the SMU.

SMU measurement speed is controlled in the Test Settings window. By adjusting parameters in custom speed mode, the sample rate changes, which determines the bandwidth. Although the measurement time cannot be set directly for the SMU, we can measure the computation time, bandwidth, and test frequency and return the Sheet. By increasing the sample rate, the noise remains nearly constant, but the ISD curve shifts left or right on the frequency axis, depending on whether the sample rate is increased or decreased.

When setting the speed mode, there is usually a compromise between speed and noise for each measurement. The faster the measurement, the higher the noise. Therefore, the slower the sampling rate, the smaller the bandwidth and the lower the noise during measurement. The readings in this test are taken on a fixed current range. Using fixed range instead of auto range is important to keep the measurement time constant for each reading, which is also a requirement for FFT calculations.

**PMU Current Spectral Density vs. Frequency**

Like the SMU, we can also derive the PMU’s ISD from current and time measurements and FFT calculations. The pmu-isd test uses open circuits to calculate the PMU current spectral density, which can be found in the Test Library and added to the project tree. This test was generated using the PMU_sampleRate user module in the PMU_freq_time_ulib user library. However, the PMU_SMU_sampleRate user module from the same user library can also be used for this test. With this test, the user can simultaneously input a voltage bias for CH1 and CH2, select a current range for CH2, specify the test time and sampling rate. Figure 6 shows a screenshot of the Configure view for the pmu-isd test.

Figure 6. Configuration view for pmu-isd test.

As with the SMU current spectral density test, the Formulator has multiple formulas to derive bandwidth, real and imaginary parts of the test current, power, frequency, and current spectral density. Table 2 lists these formulas and descriptions used for the pmu-isd test. Information about timing, range, number of points, and other equipment is similar to that described when deriving the SMU current spectral density.

The screenshots in Figure 7 show the current spectral density versus frequency for the PMU at 100 nA, 100 mA, and 10 mA. Since we are using data obtained with an open circuit, this graph shows the calculated PMU noise for a fixed current range obtained at a specified sample rate (SampRate) and total test time (SampTime).

Figure 7. PMU current spectral density.

For the pmu-isd test, the voltages on both CH1 and CH2 are set to 0 V. In the Configure view, the user enters the total test time and sample rate. The number of points is equal to the sample rate multiplied by the total test time. Choose the input parameters so that the total number of points is a power of 2, since we will be performing FFT calculations on the data. For best results, use a minimum of 512 points and a maximum of 4096 points. For the curves generated in the example, we use a sampling time of 1 second and a sampling rate of 2048 samples/second. These numbers can be adjusted to change the frequency.

When using the PMU_sampleRate or PMU_SMU_sampleRate user modules, multiple rounds of tests can be used to expand the frequency range on the graph, as each test has its own sample rate. For example, the data plotted in Figure 8 combines data from 5 different open-circuit measurement tests obtained on the 100 nA PMU range. Each test has 1024 points, but tests are performed with different test times and sampling rates. The frequency range on the graph can be extended by adjusting timing parameters and checking multiple runs in the Run History.

Figure 8. Examine multiple rounds of testing, expanding frequencies on the graph.

**Determining the 1/f Noise of MOSFET Drain Current**

The Clarius library includes a test to determine the 1/f noise of the MOSFET drain current. This test, mosfet-isd, uses the SMU to bias the gate and the PMU to bias the drain, and measures the resulting drain current. The voltage source of the SMU is less noisy than the PMU, but the PMU measures current faster than the SMU. Remember that the noise on the gate will be amplified and detected by the ammeter on the drain. Figure 9 shows the circuit diagram tested using the mosfet-isd. The SMU is connected to the gate and the PMU is connected to the drain. The source and substrate bias potential terminals are connected to GNDU, which outputs 0 V.

Figure 9. Apply gate voltage using SMU and measure drain current using PMU.

To implement these measurements, the mosfet-isd tests can be copied from the Test Library into the project tree. This test was created using the PMU_SMU_sampRate user module in the PMU_ freq_time_ulib user library.

In this test, both the SMU and PMU output a constant voltage, and the PMU measures the current for a specified time period at a configured sampling rate. The resulting current and time are returned to the Sheet, and the formula in the Formulator converts the time-based measurement to a frequency-based measurement using the FFT formula. In particular it calculates the current spectral density (ISD) and frequency. Figure 11 shows the results of measuring the drain current noise on a MOSFET.

Figure 11. MOSFET drain current ISD versus frequency.

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