## Measuring the I-V Characteristic of PN Junction Devices with HF2LI Lock-in Amplifier

**Co-author and main contributor: Dr. Antonio Braga**

**Introduction**

The p-n junction is the fundamental building block of semiconductor material electronics device such as transistors, diodes, sensors, laser, light emitting diodes, as well as solar cells. If one wants to know the fundamental functional properties of these devices, it is crucial to determine the current-voltage (I-V) characteristic. In fact, this method can be used as a measure of material quality in a device application, or as a standard characterization for improving the device fabrication.

The I–V characteristic is used to extract the parameters from the diode ideal current equations ^{[Sze 2007]}, giving an indirect measurement of physical properties of the p-n junction material. Commonly measured parameters for a single p-n junction are the built-in voltage (V_{bi}), the diode ideality factor (n) and the reverse breakdown voltage.

In photovoltaics (PV), the I–V characteristic is even more important. When a PV device (i.e. solar cell) is placed under (simulated) sunlight irradiation at 1 sun intensity, the I–V characteristic shows all the fundamental DC parameters one needs for evaluating the functional properties of the cell such as open circuit voltage V_{OC}, short circuit current I_{SC}, fill factor, maximum power point MPP, fill factor FF and efficiency.

HF2LI Lock-in Amplifiers can be used to measure this type of I-V characteristic. It should be noted that the impedance of junction device is dependent on the DC bias voltage applied on the device-under-test (DUT). Since the HF2LI Lock-in Amplifier does not have a potentiostat output (see related blog), the voltage drop across the sample cannot be kept at a given value. The actual voltage drop does not equal to the applied dc voltage which can lead to an inaccurate I-V curve. Therefore, one must measure the actual voltage drop across the sample with the second HF2LI input while measuring the current. In this blog, I-V characterization on two different components, a resistor and a solar cell, will be described. A procedure to properly measure and calibrate the DC voltage and DC current will be described as well.

## Experimental Setup

The experimental setup for p-n junction I–V measurement is actually the same as the 4-Term configuration (see the following picture) for impedance measurement.

As one can see, two channels are required to measure bolt voltage and current simultaneously. The current is converted to voltage with the HF2TA Transimpedance Amplifier externally.

## Measure and Save Data

The screenshot below shows the proper ziControl input settings. Two HF2LI demodulators referenced at 0 Hz (i.e. DC measurement) are required. It is not important that two channels have the same reference oscillator since we are only interested in DC amplitude (i.e. no phase information). Please ensure that the readout triggers are on for continuous recording. The trigger readout rate does not have to be so high. The output voltage should be set to 0 V since we will be supplying a DC bias by feeding one of the four auxiliary outputs to the Add connector.

**click to enlarge**

To save the measurement data, we now need to setup the Save tab as below. Note that we are going to save continuously in time the measurement data from both channels even though we will be doing a voltage sweep using the Sweeper tool. The reason is that the ziControl Sweeper does not allow saving two channels at once. Without doing a new Sweeper GUI, we will just extract the necessary values from the time domain save data with post-processing. Note that the Save button should be turned on before the sweep and stopped after the sweep to capture the entire sweep curve.

Now, we can start the I-V curve voltage sweep with the Sweeper tool. The screenshot below should be self explanatory. Note that we only need to do Single sweep which will also make the post processing straightforward.

## Data Analysis

The raw data are saved with the csv extension. These files can be easily imported, for instance, in MATLAB, and then processed. An example of this can be found in the first part of this Matlab code. The plot below is the measured differential voltage across the DUT. Each point on the x-axis is actually the trigger readout time step. It is labelled as arbitrary unit (a.u.) for simplicity. The rising steps in the stair curve are simply the result of the Sweeper changing the swept voltage values. The flat part is the actual measured voltage.

In the next figure, we can see the measured voltage zoomed in at Sweep START (left), as well as over the whole sweep time from 0 to 7000 a.u. (right). We can see that the measured voltage is not exactly 0 V, especially for the resistor which should have 0 V under normal circumstances. (One can argument that a solar cell might have significant DC offset at 0 V bias, but not a passive resistor). And this DC offset value is quite consistent before, during and after the sweep as shown on the right-side plot. This means the DC offset is time independent. The reason for the existence of the offset is the HF2LI input stage. The next section will show how to remove DC offsets from both input channels.

**click to enlarge**

## DC Offset Correction

After having imported the full data sets (from both demodulators), one for the current and the other for the voltage, each corrected data set must be calculated by subtracting the DC offsets must be subtracted. To get the DC offset values for both input channels, one simply has to perform a short circuit measurement as illustrated below. The measurement frequency should be at 0 Hz as before. The offset measurement from channel 1 and channel 2 should then be subtracted from the current and differential voltage measurement data, respectively. This measurement can be performed any time. Long demodulation time constant with many averaging in time may be needed to filter out low frequency noises. An example of post-processing correction can be found in the second part of the Matlab code here.

## Parameter Extractions

The I-V curve characterization does not end with the measurement and the correction. One needs to interpret the curve as well as extracting some useful parameters. Below is a plot of an offset-corrected J-V measurement of a solar cell sample. J (mA/cm^{2}) is used to normalize performance of solar cells to the standard impinging light intensity of 1 sun.

From this curve, the following data can be plotted and extracted. Based on the area of the sample, one can then re-plot a current density J-V curve as well as power density P-V curve. Then using known formulas, one can then extract or calculate parameters such as Power Conversion Efficient (PCE), fill factor (FF), and Maximum Power Point (MPP) etc. The actual extraction and calculation formulas can be found in the third part of the Matlab code here.

_{Note that PCE must be calculated under nominal simulated light irradiation of 1 sun. For this exercise, the PCE value is just an approximation since no real light source was used.}

**click to enlarge**

For example, the fill factor (FF) is the parameter describing how well the solar cell approach the theoretical maximum power the a solar cell can generate (Isc ∙ Voc) and it is calculated by the following formula: FF=P_{MPP}/( Isc ∙ Voc). It can be seen the FF is a dimensionless number. Shunt resistance (Rsh) and series resistance (Rs) are two interesting parameters describing the material quality of the solar cells. By definition, Rsh is calculated as the inverse of the current derivative versus voltage, calculated at Voc. Rs is calculated as the inverse of the current derivative versus voltage, calculated at Isc. The mathematical definition of both Rsh and Rs has no practical use. Therefore in order to achieve consistent values, one should identify a set of data point around the Voc (or Isc) and then make a linear interpolation. The inverse slope of the fitted line is the resistance values.

## Conclusion

In this blog, we demonstrated how to use HF2LI Lock-in Amplifier to characterize I-V curve of a p-n junction device, in particular a solar cell. The main challenge is to know how to remove the instrument dc offset from the real measurement data in order to obtain accurate I-V characteristics. The short-circuit dc calibration procedure turns out to be quite straightforward. Matlab scripts are also provided for the necessarily post-processing and data analysis. Once the corrected plots can be obtained, the relevant dc parameters of the device can then be derived easily.

If you have any comments regarding this type of measurement, we are always very happy to have your feedback.

## References

Sze, S. M., and Ng, K. K., Physics of Semiconductor Devices, 3rd ed. John Wiley & Sons, Inc., Hoboken, NJ, 2007

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