Using AC Hall Effect Method for Low Mobility Materials

The measurement of the Hall effect using a DC magnetic field is a reliable technique for the characterization of the electronic transport properties of semiconductor materials.

Hall's effect is specially used for the determination of carrier concentration, carrier type and the Hall coefficient and mobility of the materials. There are only a very few DC field techniques which are currently used in characterizing materials with low mobility including those used in solar cell technology, thermoelectric technology, and organic electronics.

Presently, a Hall effect measurement method that makes use of an AC magnetic field, rather than the conventional DC, is attracting increasing interest. The method has been devised by Toyo in Japan and has been used successfully for over 15 years, offering better solutions for researchers studying the properties of low mobility materials. The technique can measure mobilities as low as 10^-3 centimeters squared per volt per second (cm²/(Vs)), whereas DC field techniques are normally 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’s effect occurs when a voltage is produced in a direction transverse to an electric current in a conductor due to the application of a magnetic field perpendicular to the current (Fig. 1). The ratio of the induced electric field to the product of the applied current density and the magnetic field divided by the sample thickness is termed as the Hall coefficient.

The Hall coefficient characterizes the material the conductor is made of, since its value may vary based on the type, number and properties of the charge carriers that constitute the current. Measuring the Hall effect over a range of temperatures offers insight into the material charge transport mechanisms. The measurement of the Hall effect in material samples produced using different methods, can be used to evaluate the performances of the material in an electronic device and help optimizing the production techniques. The Hall mobility is one of the most significant electronic properties of a material.

Figure 1. Illustration of the Hall effect

The conventional methods for Hall effect and resistivity measurement use 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. Ideally, the measured Hall voltage is zero when no field is applied. However, the measured voltage often includes contributions arising from misalignment 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 does not depend on the current, although it does depend on the presence of thermal gradients. In a DC field measurement, field reversal is used to eliminate the misalignment voltage and current reversal is used to remove the thermoelectric voltage.

Disadvantages of the DC Method

Some of the main disadvantages of the DC method are listed below:

• In low mobility materials, misalignment and thermoelectric voltages can be large compared to the Hall voltage, which limits the dynamic range of the DC voltmeter used to measure the voltage.
• Furthermore, 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 capability of measuring the Hall mobility.
• DC field measurement techniques using conventional laboratory electromagnets work well when measuring materials with mobilities as low as approximately 1 cm²/ Vs (Fig. 2). However, the evolving classes of thermoelectric, photovoltaic and organic electronic materials are characterized by much lower mobilities, which are therefore difficult to measure by this method. Using DC field techniques to extract the relatively small Hall voltage from the misalignment and thermoelectric voltages that are produced by such materials is a non-trivial task.

Figure 2. Mobility ranges for the AC and DC Field Hall

Advantages of the Proven AC field Hall Effect Measurement

For over 15 years, Japanese scientists and materials researchers have been using an AC Hall effect measurement method.

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 thermoelectric voltages and misalignment, however, are DC voltages and therefore easy to separate from the AC Hall voltage signal. Some of the advantages of this method are:

• The method uses a lock-in amplifier that can separate the desired AC from the undesired DC voltages with high-accuracy.
• Researchers can reliably measure mobilities much lower than those measurable by the DC field technique (Fig. 3).

Figure 3. In low mobility and moderate resistivity (< 1 GΩ) materials, the misalignment voltage - mainly a result of asymmetry in sample contacting - is frequently the predominant contributor to error in DC Hall measurement, limiting resolution of mobility measurement. AC field techniques eliminate this form of error, allowing for significantly lower mobility measurements.

Applications

The AC field method is being used successfully for a variety of applications, which include the following:

• Measurement of photovoltaic and thermoelectric materials for alternative energy applications, including amorphous silicon (a:Si), copper indium gallium selenide (CIGS) and other solar cell materials which typically have mobilities between 10^-3 and 10 cm²/(Vs).
• The method is also useful for new display technologies that use transparent conducting oxide (TCO) semiconductors like zinc oxide (ZnO), indium gallium zinc oxide (IGZO) and other TCO materials with mobilities between 16 and 300 cm²/(Vs). While the higher end is well handled by DC measurements, the low end would benefit greatly by using the higher precision AC measurement.
• Another class of materials that researchers can better understand by using AC Hall measurements is organic electronic materials, which are being studied for use in electronic devices and have very small mobilities ranging from below 10^-3 to 1 cm²/(Vs). These materials, including organic light-emitting diodes (OLEDs), organic field-effect transistors (OFETs) and organic thin-film transistors (OTFTs) are lighter, more flexible and more economical to manufacture than inorganic materials and have high potential in enabling advancement of the electronics market.

Instrumentation

The 8400 Series Hall effect measurement system utilizes the AC Hall effect to study the electronic and magneto-transport properties of electronic materials. This fully automated and integrated measurement system was developed by Lake Shore Cryotronics in partnership with Toyo Corporation of Japan, a company with several years of experience in AC field technology. The 8400 Series HMS features optional AC field measurement capability that enables measurement of Hall mobilities down to 10^-3 cm²/(Vs). It is also capable of measuring resistances ranging from 200 GΩ to as low as 10 μΩ over a range of temperatures extending from as low as 15 K to as high as 1273 K.

With the capability to measure low mobilities, the AC Hall effect method offers solutions to researchers working with novel materials that will be used for next-generation devices and technologies.

This information has been sourced, reviewed and adapted from materials provided by Lake Shore Cryotronics.

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