Hall effect measurements have been valuable tools for material characterization since Edwin Hall discovered the phenomenon in 1879. Essentially, the Hall effect can be observed when the combination of a magnetic field through a sample and a current along the length of the sample creates an electrical current perpendicular to both the magnetic field and the current, which in turn creates a transverse voltage that is perpendicular to both the magnetic field and the current (see figure 1).
The underlying principle is the Lorentz force, that is, the force on a point charge due to electromagnetic fields. The “right hand rule” we all learned in our introductory physics classes allows us to determine the direction of the force on a charge carrier based on its direction of motion and the direction of the applied magnetic field.
Fig 1: Illustration of Hall effect.
This white paper addresses how Hall effect measurements are used in materials characterization, trends in the semiconductor industry that drive the need for making these measurements, and factors to consider when selecting measurement instrumentation.
Who needs to measure Hall effect?
Hall effect measurements are used in many phases of the electronics industry, from basic materials research and device development to device manufacturing. Users include integrated circuit producers, particularly their technology and their process development groups. Crystal manufacturers also use this measurement technique, as do researchers in university- and industry-based labs. For example, nanotechnology researchers studying graphene, a single-atom-thick, crystalline form of carbon, determined recently that the material demonstrated the quantum Hall effect; therefore, the electrons flowed through the crystal with relatavistic effects.
A Hall effect measurement system can actually be used to determine quite a few material parameters, but the primary one is the Hall voltage (VH
). Other important parameters such as carrier mobility, carrier concentration (n), Hall coefficient (RH
), resistivity, magnetoresistance (R ), and the conductivity type (N or P) are all derived from the Hall voltage measurement. With the addition of some other instruments, I-V characterization curves can be created with a similar test setup.
Hall effect measurements are useful for characterizing virtually every material used in producing semiconductors, such as silicon (Si) and germanium (Ge), as well as most compound semiconductor materials, including silicon-germanium (SiGe), silicon-carbide (SiC), gallium arsenide (GaAs), aluminum gallium arsenide (AlGaAs), indium arsenide (InAs), indium gallium arsenide (InGaAs), indium phosphide (InP), cadmium telluride (CdTe), and mercury cadmium telluride (HgCdTe). They’re often used in characterizing thin films of these materials for solar cells/photovoltaics, as well as organic semiconductors and nano-materials like graphene.
They are equally useful for characterizing both low resistance materials (metals, transparent oxides, highly doped semiconductor materials, high temperature superconductors, dilute magnetic semiconductors, and GMR/TMR materials used in disk drives) and high resistance semiconductor materials, including semi-insulating GaAs, gallium nitride (GaN), and cadmium telluride (CdTe).
Growing interest in the use of Hall effect measurements
Hall effect measurements were first routinely used in the semiconductor industry more than two decades ago, when scientists and researchers needed tools for characterizing bulk silicon materials. However, once the bulk mobility of silicon was well understood, Hall effect measurements were no longer considered critical. But today’s semiconductor materials are not just silicon—manufacturers often add germanium to silicon in the strain lattice to get higher mobility.
Moreover, modern semiconductor materials are no longer bulk materials—they’re often in the form of thin films, such as those used in copper indium gallium diselenide (CIGS) and CdTe solar cells. As a result, IC manufacturers now have to go back to determining carrier concentration and carrier mobility independently, applications for which Hall effect measurements are ideal. Hall effect measurements can also be used for characterizing novel storage devices that employ quantized Hall effect, magnetoresistance profiling, etc.
Another factor driving the growing interest in the Hall effect is related to how much current a device can handle. If device designers can maximize current flow, the devices they create can operate at lower power levels, switch faster, and have higher bandwidth. Several factors affect the magnitude of this current. The current is directly proportional to the carrier concentration, carrier mobility, the applied voltage and the cross-sectional area; it is inversely proportional to the sample length.
Fig 2: Parameters that affect current in a semiconductor.
Theoretically, there are several alternative approaches to increasing the level of current flow through a device, but all but one of them has significant disadvantages:
- Increasing voltage (V): Increasing the voltage through a device involves consuming additional power and generating heat. Today, however, the trend is heavily in the direction of mobile devices like smartphones, netbooks, tablet computers, and e-readers, in which long battery life is highly desirable, which makes increasing the voltage counterproductive.
- Increasing the number of electrons (n): There’s a limit to how much a semiconductor can be doped before it saturates or reaches its solid solubility limit, so materials scientists can only go so far in increasing the number of electrons.
- Increasing the cross-sectional area of the sample (A): Again, increasing device area conflicts with the consumer demand for light, compact handheld devices. Increasing the mobility of electrons or carriers: This is the optimum approach to maximizing current flow through a device. For materials scientists and solid-state physicists, Hall effect measurements are key to characterizing combinations of materials with high carrier mobilities.