# Measuring the Capacitance vs Voltage of a Reverse Biased PN Junction Increasing the reverse bias voltage VJ on the PN junction causes a redistribution of charge at the junction, forming a depletion region or depletion layer (W in Figure 1). This depletion layer acts as an insulator between the two conductive plates of the capacitor. The thickness of this W layer is a function of the applied electric field and doping concentration. PN junction capacitance is divided into two parts: barrier capacitance and diffusion capacitance. Under reverse bias conditions, free carrier injection does not occur; therefore, the diffusion capacitance is equal to zero. For reverse and forward bias voltages less than the diode turn-on voltage (0.6 V for silicon), the barrier capacitance is the dominant capacitance.

Target

The purpose of this lab activity is to measure the capacitance versus voltage of a reverse biased PN junction.

background knowledge

PN junction capacitance

Increasing the reverse bias voltage VJ on the PN junction causes a redistribution of charge at the junction, forming a depletion region or depletion layer (W in Figure 1). This depletion layer acts as an insulator between the two conductive plates of the capacitor. The thickness of this W layer is a function of the applied electric field and doping concentration. PN junction capacitance is divided into two parts: barrier capacitance and diffusion capacitance. Under reverse bias conditions, free carrier injection does not occur; therefore, the diffusion capacitance is equal to zero. For reverse and forward bias voltages less than the diode turn-on voltage (0.6 V for silicon), the barrier capacitance is the dominant capacitance. In practical applications, depending on the junction area and doping concentration, the barrier capacitance can be as small as a few tenths of pF or as high as several hundred pF. The dependence between the junction capacitance and the applied bias voltage is called the capacitance-voltage (CV) characteristic of the junction. In this lab, you will measure the value of this characteristic for each PN junction (diode) and plot the value.

Figure 1. PN junction depletion region. A 10 kΩ resistor
A 39 pF capacitor
A 1N4001 diode
A 1N3064 diode
A 1N914 diode

Red, yellow and green LEDs

A 2N3904 NPN transistor
A 2N3906 PNP transistor

step 1

On a solderless breadboard, build the test setup as shown in Figures 2 and 3. The first step is to measure the unknown capacitance Cm with the known capacitance C1 connected between the AWG output and the oscilloscope input. Both oscilloscope negative inputs 1C and 2C are grounded. The oscilloscope channel 1+ input is connected to the same row on the breadboard along with the AWG1 output W1. Insert the oscilloscope channel 2+ into the breadboard, and ensure that it is separated from the inserted AWG output by 8 to 10 lines. Connect the line adjacent to the oscilloscope channel 2+ that is biased towards AWG1 to ground to ensure any unnecessary noise between AWG1 and oscilloscope channel 2. Scatter coupling. Since there is no shielded flying lead, try to keep the W1 and 1+ connection wires away from the 2+ connection wire. Figure 2. Step 1 setup for measuring Cm

hardware setup

Use the network analyzer tool in the Scopy software to obtain a plot of gain (attenuation) versus frequency (5 kHz to 10 MHz). Oscilloscope channel 1 is the filter input, and oscilloscope channel 2 is the filter output. Set the AWG offset to 1 V and the amplitude to 200 mV. When measuring a simple real capacitor, the bias value is not important, but will be used as the reverse bias voltage when measuring diodes in subsequent steps. The ordinate range is set from +1 dB (starting point) to C50 dB. Run a single scan and export the data to a .csv file. You will find that there is a high pass characteristic, i.e. high attenuation at very low frequencies, where the impedance of the capacitor is very large compared to R1. In the high frequency region of the frequency sweep, there should be a relatively flat region. At this time, the impedance of the capacitive voltage divider of C1 and Cm is much lower than that of R1. Figure 3. Step 1 setup for measuring Cm

step 1

Figure 4. Scopy screenshot.

We choose to make C1 much larger than Cstray, so that Cstray can be ignored in the calculation, but the calculated value is still close to the unknown Cm.

Open the saved data file in a spreadsheet program and scroll to near the end of the high frequency (>1 MHz) data, where the attenuation level is essentially flat. The recorded amplitude value is GHF1 (unit: dB). With GHF1 and C1 known, we can calculate Cm using the following formula. Write down the Cm value, we will need this value in the next step to measure the capacitance of the various diode PN junctions.

Step 2

We will now measure the capacitance of various diodes in the ADALM2000 simulation kit under various reverse bias conditions. On a solderless breadboard, build the test setup as shown in Figures 4 and 5. Just replace C1 with D1 (1N4001). Insert the diode, making sure the polarity is correct so that the forward bias in AWG1 will reverse bias the diode. Figure 5. Step 2 setup for measuring diode capacitance.

hardware setup Figure 6. Step 2 setup for measuring diode capacitance.

Use the network analyzer tool in the Scopy software to obtain a plot of gain (attenuation) versus frequency (5 kHz to 10 MHz) for each AWG 1 DC offset value in Table 1. Export data from each scan to a different .csv file.

procedural steps

In the remainder of Table 1, fill in the GHF value for each bias voltage value, then use the Cm value and the formula in Step 1 to calculate the value of Cdiode. Table 1. Capacitance vs. Voltage Data

Figure 7. Scopy screenshot with 0 V bias.

Replace the 1N4001 diode with the 1N3064 diode from the ADALM2000 kit and repeat the scan steps performed for each diode. Fill another table with measured data and calculated Cdiode values. How is the value of the 1N3064 different compared to the value of the 1N4001 diode? You should attach a graph of your measured capacitance versus reverse bias voltage for each diode.

Then, replace the 1N3064 diode with one of the 1N914 diodes from the ADALM2000 kit. Then, repeat the same scan steps you just did for the other diodes. Fill another table with measured data and calculated Cdiode values. How is the value of the 1N914 different compared to the value of the 1N4001 and 1N3064 diodes?

The capacitance of the 1N914 diode you measured should be much smaller than the capacitance of the other two diodes. This value can be very small, almost comparable to the value of Cstray.

Measurements for extra points

Light emitting diodes or LEDs are also PN junctions. They are made of materials other than silicon, so their turn-on voltages are quite different from normal diodes. However, they still have depletion layers and capacitance. For extra points, measure the red, yellow, and green LEDs in the ADALM2000 simulator kit as you would a normal diode. Insert the LEDs in the test setup, making sure the polarity is correct for reverse biasing. The LED may sometimes light up if done incorrectly.

question

Using the formula in Step 1, the value of C1, and the graph in Figure 4, calculate the oscilloscope input capacitance, Cm.