From Ohm's law R=V/I so the slope of the V vs. I curve obtained in the measurement sweep is the resistance. To improve measurement precision by reciprocity ...
van der Pauw Measurement using Keithley 2400 and LabTracer LabTracer is a Keithley designed, LabView based application to enable simple test sequences using SourceMeter Products. Start Up 1.) Begin by plugging in the Keithley 2400 power cord and turning the machine on. 2.) Attach the KUSB-488B controller to the back of the Keithley (secure with the screws) and plug the USB end of the cable into the computer. 3.) Place your device on the Power Stage and use the micromanipulators to place four tungsten needles on your device contacts as shown in Figure 1.
Figure 1. Device on power stage with 4 point contacts for van der Pauw measurements.
4.) Connect the wires to the needles and attach the wires to the Keithley front panel inputs and outputs as shown in Figure 2. The Input/Output connections on the right source current to the device and the 4-Wire Sense connections on the left measure the voltage drop across the device. current
5.) The van der Pauw method measures the sheet resistance Rs of a film. The average resistivity ρ and conductivity σ can be calculated as follows.
4
2
3
voltage current
Where t is the film thickness as measured on a profilometer.
1
Figure 2. Schematic of wire connections for making 4 point van der Pauw measurements. Device contacts are labeled 1 through 4 counter-clockwise.
6.) To calculate Rs the van der Pauw method makes two measurements. First, it sources current along the horizontal edge of the film and measures the voltage drop across the opposite edge. Then it sources current along the vertical edge of the film and measures the voltage drop across the opposite edge. From Ohm’s law R=V/I so the slope of the V vs. I curve obtained in the measurement sweep is the resistance. To improve measurement precision by reciprocity, four total measurement sweeps are taken; sourcing current along each of the film edges. To cancel any offset voltages, four additional sweeps can be taken with the polarity of each measurement reversed. The average vertical and horizontal resistances are calculated:
Where R1243 indicates a sweep where current was sourced 12 and voltage was measured 34. A numerical method like Newton Raphson is then used to solve for the sheet resistance
7.) For our measurements, the following current sweeps will be made with the wire configurations illustrated.
Device Contact Position Front Panel Wire Position Output Hi Output Lo Sense Hi Sense Lo
Vertical 1 R1243 1 2 4 3
Vertical 2 R4312 4 3 1 2
Horizontal 1 R1423 1 4 2 3
Horizontal 2 R2314 2 3 1 4
4
1
1
4
2
1
1
2
3
2
2
3
3
4
4
3
Vertical 1
Vertical 2
Horizontal 1
Horizontal 2
Figure 3. Wire configurations in the Keithley front panel for 4 current sweeps. Right side sources current and left side measures voltage.
8.) For high conductivity samples like PEDOT:PSS, 4 sweeps are sufficient. For lower conductivity samples we want to take reverse polarity sweeps as well, for 8 total sweeps.
9.) Use the following wire configurations to take 8 total sweeps and calculate Rvertical and Rhorizontal using the following equations:
Device Contact Position Front Panel Wire Position Output Hi Output Lo Sense Hi Sense Lo
Vertical 1 R1243
Vertical 1 Reverse R2134
Vertical 2 R4312
Vertical 2 Reverse R3421
Horizontal 1 R1423
Horizontal 1 Reverse R4132
Horizontal 2 R2314
Horizontal 2 Reverse R3241
1
2
4
3
1
4
2
3
2
1
3
4
4
1
3
2
4
3
1
2
2
3
1
4
3
4
2
1
3
2
4
1
4
1
3
2
1
4
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3
2
4
1
2
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1
4
Vertical 1
Vertical 1R
Vertical 2
Vertical 2R
2
1
3
4
1
2
4
3
3
4
2
1
4
3
1
2
Horizontal 1
Horizontal 1R
Horizontal 2
Horizontal 2R
Figure 4. Wire configurations in the Keithley front panel for 8 current sweeps. Right side sources current and left side measures voltage.
Current Sweeps 1.) Open the LabTracer program under Start>>Keithley Instruments>>LabTracer 2.) In LabTracer go to File>>Open Test. When prompted “Would you like to save the project and data before opening a different project?” choose No. 3.) The program default is to sweep current from -10mA to 10mA and measure voltage with 4 wire sense mode. To edit the current sweeping range, click on Setup2400 below the picture of the Keithley and click on the ‘Source’ tab. There you can edit the stop and start current (unit is A) and the number of points to take in the sweep. The ‘Advanced’ tab has a selection for 2 wire or 4 wire mode. 4.) When the program is set and the device ready, click the ‘Run Test’ icon. When prompted to replace the existing project file select ‘Replace’. 5.) A progress bar will be shown and the Keithley will beep as it completes the test. 6.) The Data Center will then open where you can see the raw data and format a graph to visualize the sweep. Click on Define Graph and select voltage on the yaxis and current on the x-axis. You will have to rename the axis titles in the text boxes on the bottom left of the graph. 7.) To save the sweep data, go to the ‘Data Sheet’ tab and click on the ‘Save Data’ button. This will open a prompt for file location, select your desired location and hit save. Figure 5. LabTracer Channel Setup for 4 wire current sweep.
8.) Open a new Excel file and open the template of the van der Pauw measurement. Go to the ‘Data’ tab and select ‘From Text’ in the ‘Get External Data’ box. Click through the ‘Text Import Wizard’, making sure the column locations are correct, and add the data to the Excel sheet.
Figure 6. Screen shot of where to import data from text file in Excel.
To take the van der Pauw measurement, run a sweep with each of the four different wire configurations specified in the Start Up section. 9.) After sweeping Vertical 1, save the data in the ‘Data Sheet’ tab to a text file with the sample name and date, and add the data to the Excel spreadsheet template as specified in Step 8. 10.) Change the wire configuration to Vertical 2 11.) In the ‘Data Sheet’ tab in LabTracer select ‘Clear Data’. Then select the ‘Run Test’ icon. Do not use ‘Test Again’ as this will not properly log the data. 12.) Save the Vertical 2 data to the same text file as before, replacing the Vertical 1 data because it is already in the Excel file. 13.) In the open Excel file, insert the Vertical 2 data below the Vertical 1 data and make sure the data sets are labeled. 14.) Repeat Steps 11 to 14 for Horizontal 1 and Horizontal 2, making sure to save and import the data into the master Excel sheet. 15.) After the sweeps are complete, close LabTracer and analyze your data using the template to get a value for Rs. Use the profilometer to measure the film thickness and calculate conductivity to later calculate the device material’s power factor.
