MATERIALS I RESEARCH
M
easuring the Hall effect in a material using a DC magnetic field is a tried and true method of characterizing the electronic transport properties of semiconductor materials. Specifically, it is used to determine carrier type, carrier concentration, the Hall coefficient and mobility of the materials. DC field techniques are limited, however, in characterizing materials with low mobility, including many important in solar cell technology, thermoelectric technology, and organic electronics.
Now, interest is growing in a Hall effect measurement method that uses an AC magnetic field rather than the more traditional method that uses DC fields. Developed by Toyo Corporation in Japan,and used successfully there for more than 15 years, the AC Hall effect measurement provides better solutions for researchers exploring the properties of low mobility materials. The technique can measure mobilities as low as 10-3centimeters squared per volt per second (cm2/(V s)), whereas DC field techniques are generally limited to measuring mobilities of about 1 cm2/(Vs) in DC magnetic fields produced by conventional laboratory electromagnets.
DC field Hall effect measurement basics The Hall effect is the production of a voltage, transverse to an electric current in a conductor, caused by a magnetic field applied perpendicular to the current. The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field, divided by the sample thickness. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitute the current.
Measuring the Hall effect over a range of temperatures provides insight into the material’s charge transport mechanisms. And, by measuring the Hall effect in samples of a material that were produced using different methods, researchers can gather information to assess material performance in an electronic device and help optimize production methods. Hall mobility, the Hall coefficient divided by the resistivity of the material, is one of a material’s most important electronic properties. The traditional method for measuring the Hall effect and resistivity uses DC magnetic fields. The Hall voltage is proportional to the applied magnetic field, current, the Hall coefficient of the material, and the inverse of the thickness of the material sample. In an ideal system, the measured Hall voltage is zero when zero field is applied. However, in practice, the measured voltage also includes contributions arising from misalignment voltages and thermoelectric voltages.
The misalignment voltage is proportional to the resistivity of the material and the current, and is dependent on the sample geometry. The thermoelectric voltage arises from contacts between two different materials and is independent of the current, although it does depend on the thermal gradients present. In a DC field measurement, field reversal is used to remove the misalignment voltage, and current reversal is used to remove the thermoelectric voltage.
Image 1: Illustration of the Hall effect
Disadvantages of the DC method In low mobility materials the misalignment and thermoelectric voltages can be large compared to the Hall voltage, which limits the dynamic range of the DC voltmeter that is used to measure the voltage. Additionally, the misalignment and thermoelectric voltages can change in time producing systematic errors in the Hall voltage measured using field reversal. These effects make it difficult to precisely extract the small Hall voltage from the measured voltage, which in turn limits the Hall mobility that can be measured.
In practice, DC field measurement techniques employing conventional laboratory electromagnets work well when measuring materials with mobilities as low as approximately 1 cm2/(Vs). The emerging classes of photovoltaic, thermoelectric, and organic electronic materials are characterized by much lower mobilities, making them difficult, if not impossible, to measure using this method. It is challenging to extract the relatively small Hall voltage from the misalignment and thermoelectric voltages that are produced by such materials using DC field techniques.
AC field Hall effect measurement advantages For more than 15 years, Japanese scientists and materials researchers have been using an AC Hall effect measurement method. The method, while known in the U.S. and elsewhere, was not widely adopted, primarily because it offered few advantages for measuring materials for which DC measurements provided good results. Now, however, materials researchers are turning to AC field techniques to measure the Hall effect in low mobility materials.
Since the Hall voltage is proportional to the magnetic field, when an AC field is applied the Hall voltage signal will be an AC signal as well. The misalignment and thermoelectric voltages, however, areDC voltages that are easily separated from the AC Hall voltage signal. The method uses a lock-in amplifier that can separate the desired AC from the undesired DC voltages with a high degree of precision. As mentioned previously, this allows researchers to reliably measure much lower mobilities than is possible using the DC field technique.
Those interested in the scientific underpinnings behind the differences between AC and DC measurement can find more information in Hall measurements on low-mobility materials and high resistivity materials, by Jeffrey Lindemuth and Shin-Ichiro Mizuta.[1]
Issue II 2012 I
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