Hall voltages and van der Pauw voltages can be as low as millivolts, so the recommended test technique involves a combination of reversing source current polarity, sourcing on additional terminals, and reversing the direction of the magnetic field. Eight Hall effect and eight van der Pauw measurements are performed. If the voltage readings within each measurement differ substantially, always recheck the test setup for sources of error.
A basic Hall effect measurement configuration will likely include the following components and optional extras:
- A bipolar, constant-current source. For low-resistivity samples, it must be able to source from milliamps to amps. For high-resistivity samples (107 ohm·cm or higher), a sourcing range as low as 1nA will be needed.
- A high input impedance voltmeter. Depending on the resistivity under test, the voltmeter used must be able to measure voltages from 1 microvolt to 100V accurately. High-resistivity materials may require ultra-high input impedance or differential measurements.
- A permanent magnet or an electromagnet capable of generating field magnitudes from 500 to 5000 gauss.
- A sample holder.
- Optional equipment. A switch matrix helps to eliminate the need for manual connections/disconnections between probe contacts. A switch matrix is definitely required if the sample is in a liquid nitrogen dewar for temperature studies. Hall measurements are highly dependent on sample temperature, so it is often important to monitor this temperature. A prober chuck that can either heat or cool the sample and a temperature controller are generally necessary for on-wafer measurements when doing temperature studies.
The most appropriate Hall effect measurement instruments will be based on the total resistance of the sample and the resistance of its external contact points. The sample resistance is the sample’s intrinsic resistivity, expressed in units of ohm-centimeters (ohm·cm), divided by its thickness. The contact resistance to the sample can be orders of magnitude higher than the sample’s resistance. The measurement system might be designed to accommodate samples with a wide range of resistances, or optimized specifically for studying low-resistance (narrow bandgap) or high-resistance (wide bandgap) materials.
Wide Resistance Measurement System
Figure 5 shows a Hall effect/van der Pauw measurement system appropriate for sample resistances ranging from 1μΩ to 1TΩ. It employs Keithley’s Model 7065 matrix switching card optimized for Hall effect measurements housed in a Model 7001 Switch Mainframe. This card buffers test signals from the sample to the measurement instrumentation, and switches current from the current source to the sample. It offers the advantage of unity gain buffers that can be switched in and out to allow measuring high resistances by buffering the sample resistance from the meter.
The test setup also includes a Model 6485 picoammeter, Model 6220 DC current source, and Model 2182A nanovoltmeter. The picoammeter is included as an option for monitoring system leakage currents. The current source and nano-voltmeter work together using internal techniques to synchronize their operation, eliminate thermal offsets, and improve measurement accuracy. The nanovoltmeter’s second voltage measurement channel is useful for monitoring the sample temperature.