Hall Effect Measurement System

The Hall effect was discovered by Edwin Hall in 1879, but it was many years before technological developments made it possible for integrated circuits to take full advantage of this phenomenon. Today, Hall effect sensor ICs offer a convenient way to achieve accurate current measurements that maintain electrical isolation between the measured current path and the measurement circuit.

From Lorentz to Hall
The Hall effect is an extension of the Lorentz force, which describes the force exerted on a charged particle—such as an electron—moving through a magnetic field. If the magnetic field is oriented perpendicular to the direction of the electron's motion, the electron experiences a force that is perpendicular to both the direction of motion and the orientation of the magnetic field.

Harnessing the Hall Effect
The voltages generated via the Hall effect are small relative to the noise, offsets, and temperature effects that typically influence a circuit, and thus practical sensors based on the Hall effect were not widespread until advances in semiconductor technology allowed for highly integrated components that incorporate a Hall element and additional circuitry needed to amplify and condition the Hall voltage. Still, though, Hall effect sensors are limited in their ability to measure small currents. For example, the ACS712 from Allegro MicroSystems has a sensitivity of 185 mV/A. This means that a current of 10 mA would produce an output voltage of only 1.85 mV. This voltage may be acceptable if the circuit has a low noise floor, but if a 2 Ω resistor could be included in the current path, the resulting 20 mV output voltage would be a major improvement.

The Hall effect is relevant to a variety of sensor applications; devices based on this relatively simple relationship between current, magnetic field, and voltage can be used to measure position, speed, and magnetic field strength. In this article, however, we will focus on devices that measure current via the Hall voltage generated when a magnetic field induced by the measured current is concentrated toward an integrated Hall effect element.

Pros and Cons
Performance characteristics vary from one Hall effect current sensor to another, so it is difficult to precisely summarize the advantages and disadvantages of Hall effect sensing relative to the other common current-sense technique; namely, inserting a precision resistor into the current path and measuring the resulting voltage drop with a differential amplifier. In general, though, Hall effect sensors are valued for being "nonintrusive" and for providing electrical isolation between the current path and the measurement circuit. These devices are considered nonintrusive because no significant amount of resistance is inserted into the current path, and thus the circuit being measured behaves almost as if the sensor is not present. An additional benefit is that minimal power is dissipated by the sensor; this is particularly important when measuring large currents.

Regarding accuracy, currently available Hall effect sensors can achieve output error as low as 1%. A well-designed resistive current-sense circuit could surpass this, but 1% would generally be adequate in the high-current/high-voltage applications for which Hall effect devices are particularly suitable.

Isolation
One of the dominant benefits of Hall effect sensors is electrical isolation, which in a circuit- or system-design context is often referred to as galvanic isolation. The principle of galvanic isolation is involved whenever a design requires that two circuits communicate in a way that prevents any direct flow of electrical current. A simple example is when a digital signal is passed through an opto-isolator, which converts the voltage pulses to light pulses and thus transmits data optically rather than electrically. One of the primary reasons for implementing galvanic isolation is to prevent problems related to ground loops:

Basic circuit design principles assume that interconnected components share a common ground node, which is assumed to be at 0 V. In real life, however, the "ground node" is composed of conductors having nonzero resistance, and these conductors serve as a return path for current flowing from the circuit back to the power supply. Ohm's law reminds us that current and resistance make voltage, and these voltage drops in the return path mean that "ground" in one part of the circuit or system is not at the same potential as "ground" in another part. These differences in ground potential can lead to problems ranging from negligible to catastrophic.

By preventing direct current flow between two circuits, galvanic isolation enables circuits with different ground potentials to successfully communicate. This is particularly relevant to current-sense applications: a low-voltage sensor and processing circuit may need to monitor large, highly variable currents in, for example, a motor drive circuit. These large, rapidly changing currents will lead to considerable voltage fluctuations in the return path. A Hall effect sensor allows the system to both monitor the drive current and protect the high-precision sensor circuit from these detrimental ground fluctuations.

Common-Mode Voltage
Another important application for Hall effect sensors is current measurements involving high voltages. In a resistive current-sense circuit, a differential amplifier measures the difference in voltage between one side of a resistor and the other. A problem arises, though, when these voltages are large relative to the ground potential:

Real-life amplifiers have a limited "common-mode range," meaning the device will not function properly when the input voltages, though small relative to each other, are too large relative to ground. Common-mode ranges of current-sense amplifiers typically do not extend beyond 80 or 100 V. Hall effect sensors, on the other hand, can convert current to voltage without reference to the measured circuit's ground potential. Consequently, as long as the voltages are not large enough to cause physical damage, common-mode voltage does not affect the operation of a Hall effect device.

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 create an electrical current perpendicular to both the magnetic field and the current, which in turn creates a transverse voltage perpendicular to both. The underlying principle is the Lorentz force: the force on a point charge due to electromagnetic fields

Hall effect measurements are invaluable for characterizing semiconductor materials whether they are silicon-based, compound semiconductors, thin film materials for solar cells, or nanoscale materials like graphene. The measurements span low resistance (highly doped semiconductor materials, high temperature superconductors, dilute magnetic semiconductors, and GMR/TMR materials) and high resistance semiconductor materials, including semi-insulating GaAs, gallium nitride, and cadmium telluride.

A Hall effect measurement system is useful for determining various material parameters, but the primary one is the Hall voltage (VH). Carrier mobility, carrier concentration (n), Hall coefficient (RH), resistivity, magnetoresistance (RB), and the carrier conductivity type (N or P) are all derived from Hall voltage.

As researchers develop next-generation ICs and more efficient semiconductor materials, they're particularly interested in materials with high carrier mobility, which is what's sparked much of the interest in graphene. This one-atom-thick form of carbon exhibits the quantum Hall effect and, as a result, relativistic electron current flow. Researchers consider Hall effect measurements crucial to the future of the electronics industry

Materials with high carrier mobility allow creating devices that obtain maximized current flow at lower power levels with faster switching times and higher bandwidth. A manipulation of Ohm's Law shows the importance of carrier mobility in maximizing current. The current is directly proportional to carrier mobility

The options for maximizing current flow through a device include increasing voltage, charge carrier concentration, the cross-sectional area of the sample, or the mobility of the charge carriers. All but the last of these have serious disadvantages.

Measuring Mobility
The first step in determining carrier mobility is to measure the Hall voltage (VH) by forcing both a magnetic field perpendicular to the sample (B) and a current through the sample (I). This combination creates a transverse current. The resulting potential (VH) is measured across the device. Accurate measurements of both the sample thickness (t) and its resistivity (r) are also required. The resistivity can be determined using either a four-point probe or the van der Pauw measurement technique. With just these five parameters (B, I, VH, t,and resistivity), the Hall mobility can be calculated:
Both Hall voltages and the measured van der Pauw resistivity are typically quite small, so the right measurement and averaging techniques are critical for accurate mobility results.