INSTRUMENTATION
Advisory Panel Jonathan W. Amy Jack W . Frazer G. Phillip Hicks
Donald R. Johnson Charles E. Klopfenstein Marvin Margoshes
Harry L. Pardue Ralph E. Thiers William F. Ulrich
The Hall Effect Devices and Applications E. D. SISSON F. W. Bell, Inc., 4 9 4 9 Freeway Dr., East Columbus, Ohio 43229
Modern semiconductor technology has produced Hall effect devices capable of very accurately measuring magnetic field flux densities and gradients. Applications of the Hall effect include field monitoring in spectrometers, beam deflection coils, cyclotron or linear accelerator magnets, and magnetic resonance measurements.
ADVANCES in semiconductor technol-
ogy have produced an amazing variety of new devices. Transistors, di odes, silicon-controlled rectifiers, and many more components obtain their special properties as a result of "junc tions"—regions where dissimilar ma terials are joined together. The elec trical properties of the junctions de termine the device characteristics. A smaller class of devices utilize only the properties of the bulk semiconductor material itself, and have no junctions. The Hall effect device is an example in which the galvanomagnetic properties of the material provide a sensitive elec trical response to an applied magnetic field.
where VH is the Hall voltage, k is a con stant of proportionality, Ie is the strip current, and Β is the magnetic field strength. Hall published his work in the American Journal of Mathematics in 1879 in a paper entitled "On a NewAction of the Magnet on Electric Cur rents." The angle at which the magnetic flux lines intersect the Hall plate affected the Hall voltage such that only the component of field perpendicular to the plate was effective. Thus, the expres sion for the Hall voltage, including the
angle, Θ, to the perpendicular, is the following : VH = kIcB cos θ
(2)
Figure 1 shows these relationships. In addition, Hall theorized that the re sistance of the conducting strip should increase in a magnetic field because of the modified flow of the current car riers. This effect is now called trans verse magnetoresistance. Unfortunately, the Hall voltages ob tained with the simple metals were so extremely small that the Hall effect re-
Background
Discovery of the Hall effect is at tributed to Dr. Edwin II. Hall, who, in 1879, made the first experimental dem onstration of the action of a magnetic field upon the current flowing in a con ductor. He showed that the field acted directly on the current, tending to crowd the charges to one side of the conductor, and that a measurable po tential, therefore, was generated across the conductor width. Using strips of gold foil, Hall determined that the volt age developed across the strip was pro portional to the current flowing and to the magnetic field strength, as shown in Equation 1 : VH = kLB 1
New affiliation to be announced.
(1)
Figure 1. The Hall Plate Magnetic field density vector, B, is shown entering the Hall plate at angle Gto the perpendicular
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971 • 67 A
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mained merely a scientific curiosity for many years. It was not until the de velopment of semiconductor compounds with high mobilities that Hall devices gained sufficient output to be practical ( ί ) . As an example, the compound in dium antimonide can produce Hall volt ages 100,000 times greater than those obtainable from the pure metals. The constant of proportionality used in the expression for Vu is referred to as the sensitivity constant and is rep resented by the symbol y1]t- This is the product sensitivity and is given in units of volts per ampere-kilogauss. One kilogauss is equal to 1/10 tesla, or weber per square meter. Strictly speaking, yIB is not a true constant be cause VH is not in exact linear relation ship to Β because of temperature, magnetoresistance, and other effects. Very nearly linear proportionality can be ob tained by proper fabrication. Figure 1 depicts a typical Hall plate, showing a conducting band across each end of the semiconductor plate to help obtain uniform current flow through the plate. Hall connections are centrally positioned along each edge and aligned as accurately as possible on an equipotential line. High-alumina ceramic is often used as a mounting substrate be cause of the excellent strength and the thermal and dimensional stability of the material. A precision miniature circuit pattern, metallized directly on the substrate, serves to bring the Hall voltage out with a minimum of stray coupling. The final package will vary in size typically from less than 0.01 in. to 1/16 in. in thickness and from 0.1 to 3/4 in. in width or length.
though sensitivity is somewhat lower. Other materials, including germanium, silicon, and gallium arsenide, have been used to advantage in specific applica tions. Hall Generator Characteristics
The Hall generator (Figure 2) enjoys several features which distinguish it from semiconductor devices such as transistors, which use junctions as a basis for their operation. Every pre caution is taken to assure purely ohmic contacts throughout fabrication. Hall characteristics result from the galvanomagnetic properties of the bulk semi conductor material, and majority car riers determine the primary character istics. The geometry of the Hall plate and the method of lead connections play secondary roles. Thus, many of the qualities peculiar to junction de vices and minority carriers are absent in a Hall generator. For example, junc tion threshold voltage, with its accom panying nonlinear voltage-current char acteristic, is eliminated. Reverse volt age breakdown, junction temperature drift, capacity effects, leakage, and noise associated with minority carriers are absent. Hall generators have inher ently linear response through zero field. The active part of the Hall generator, the Hall plate, must be made quite thin (1 to 5 mils in thickness), and it is, therefore, fragile and strain sensitive. However, when properly supported on its substrate and encapsulated, the Hall generator package can be extremely rugged and reliable. The ability of the Hall generator to directly convert magnetic flux density to output voltage is unique. A typical
bulk material InAs unit will produce about 10 mV output per kilogauss of flux density with 100 mA of current flowing. The 10 mV per kG figure is called the magnetic sensitivity and its value depends on the current. In creased current, within the limits of self-heating, will result in correspond ingly higher output voltage. Pulsedcurrent operation can allow consider able increase in output, as can good heat sinking. Devices using InSb ma terial have about three times higher output, but suffer from greater temper ature influence. The linearity of output voltage with flux density is affected by the dimen sional accuracy of the Hall plate, by length-width ratio, doping levels, con tacts and other factors, all of which can be well controlled in a modern manu facturing process. Various trimming and circuit resistance adjustments can be made, if needed to reduce further any remaining errors. One percent of reading errors are not uncommon over the range of ±20,000 gauss. Hall gen erators are now available having only one part in 1000 error over a range of ±30,000 gauss. Elevated temperatures generally re duce mobility, with a consequent reduc tion in sensitivity. The loss in output is usually stated as a percentage of error which is a mean value over a specified temperature range. Typically, the er ror is one percent per °C (—40° to +80° C range) for indium antimonide. Indium arsenide has less than 0.1 per cent per °C error for the same range. Figure 3 shows a typical temperature plot for indium arsenide units. Re cently, Hall generators have become
Hall Materials
The most commonly used materials for Hall generators are indium antimo nide (InSb) and indium arsenide (InAs). Such materials are made by com bining atoms of indium (group III of the periodic table) and antimony or ar senic (group V), and they are termed binary intermetallic compounds. They are not alloys, but true chemical com pounds with a 1:1 ratio between group III and group V atoms which occupy alternate sites in the crystal lattice. Their special properties are high elec tron mobility and small energy gap. The electron mobility of InSb, for ex ample, can be 50 times higher than that of silicon, the material used in junction transistors. Doping, which is the intentional but controlled addition of selected impurities, is used to stabil ize carrier concentration and improve thermal stability. Indium arsenide is often preferred over indium antimonide because of lower temperature influence, even
Figure 2. Transverse Hall generator (rectangular) and axial Hall generator
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available with special material formulation having less than 50 ppm per °C (0.005% per °C) error over the range of - 4 0 ° to +100°C. No thermal compensation or correcting circuits are used. Probes for cryogenic insertion are also available with typically one percent error at 4.2° K. Temperature also influences the zero field stability, an important factor when reading low Hall voltages. The effect is usually less than one microvolt per °C for the better bulk material InAs Hall generators. A small dc thermal voltage is also present, usually of even smaller magnitude. To obtain direct readout of magnetic flux density, the Hall voltage must be calibrated using a known field. Once calibrated, a modern Hall generator will retain calibration almost indefinitely if not abused. In a room-temperature continuous-operation test over a five-year period, test points fell within the limits of confidence of measurement accuracy, using a nuclear magnetic resonance measurement for comparison. Factors that might cause calibration change are mechanical strain, excessive temperature, or thermal shock. Each Hall generator must be individually calibrated because of variations in the Hall coefficient of the semiconductor material. A characteristic of Hall generators is that they do not possess a true zero, that is, the output may not be zero volts with zero magnetic field. This is because of extremely small positioning errors on the Hall contacts and a resulting voltage offset when current is applied. This residual offset usually measures in the microvolt range and can be
Figure 3. (InAs)
easily "zeroed" out by a simple external resistance adjustment. Similarly, small inductive residuals that may appear in high-sensitivity measurements can be balanced out without difficulty. Bulk material Hall generators have extremely low electrical noise output when properly fabricated, and the limits of sensitivity are usually set by amplifier noise or thermal drift. Noise is essentially Johnson (thermal) (£) in the material resistance. Current noise has not been isolated in InAs or InSb units of this type. The resistance of these units ranges from one ohm to 10 ohms in value. Thin-film Hall generators have additional noise arising within the film structure and resistance values are higher, typically 30 to 1000 ohms. The frequency bandwidth of the Hall generator is not generally limited by the semiconductor material itself, but by the connecting lead wires which have inductive impedance at very high frequencies. The semiconductor material, limited by carrier relaxation time, is usable into the gigahertz range, whereas an upper limit of one megahertz is more typical for the Hall package, including leads. A valuable feature of Hall generators is that they are made entirely from nonmagnetic materials and do not disturb the field being measured. This is in contrast to other types of probes which are made of magnetic metals. Another characteristic which is unique to the Hall generator is that its size can be reduced with no loss in sensitivity. This is in contrast to a coil pickup in which output is related directly to coil area. The small sensing area can be an
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Temperature characteristic of V,i for typical bulk material Hall generator F. W. Bell, Inc., Type JB-802 CIRCLE 5 ON READER SERVICE CARD
ANALYTICAL CHEMISTRY, VOL. 43, NO. 7, JUNE 1971
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advantage, since it provides better di mensional resolution and improved accuracj r in field gradient measurements. Hall output is a measure of the aver age flux density over the active area. Typical units have active areas of 1/16-in. diam, but have been made as small as 5 X 1CH cm2, and much smaller in thin-film units. A feature of the Hall generator is that Hall output does not depend on rate-of-change of flux as in a coil, but only on instantaneous flux value. In mechanical sensing applications it pro vides an output independent of speed, acceleration, frequency, or rate, and works equally well in a static or dy namic field, and down to zero speed. This feature is of particular advantage in the measurement and plotting of static fields, since no probe motion is required.
Generation of t h e inverse f u n c t i o n o u t p u t , using a high-gain a m p l i f i e r
ANALYTICAL CHEMISTRY, VOL. 4 3 , NO. 7, J U N E 1 9 7 1
P u t t i n g t h e H a l l Effect t o Work
Although a surprising variety of Hall effect applications exists, the most obvi ous is the sensing and measuring of magnetic fields. By holding current constant, usually at a value that will calibrate the Hall voltage, the Hall out put voltage is directly related to flux density in magnitude and direction. The simple arrangement of Figure 4 forms the basis for a gauss meter capa ble of reading fields from a few gauss to 10,000 gauss or more. Rotation of the Hall probe in the field will provide field direction information in space. Two Hall generators can measure field gradients by taking the difference output. Two Hall generators can also generate an H 2 output, useful in con nection with the mass spectrometer where mass number is related to the square of the field strength (3). This is illustrated in Figure 5 where two units, both mounted in the deflection field, are connected in tandem to ob tain an output of H multiplied by H. This permits plotting on a linear H 2 scale. In another interesting variation the Hall generator is placed in the feedback loop of a high-gain amplifier to obtain a reciprocal, or 1/H, output. An ap plication where the measured variable depends upon the inverse function of II is the recording of de Haas-van Alphen oscillations (4)- The arrange ment of Figure 6 will permit plotting directly on a linear 1/H scale. In this circuit the input current to the Hall generator is caused to vary inversely with H by the amplifier, which will maintain a fixed VH — Vr(1( condition required at. the input. The circuits of Figures 5 and 6 both illustrate the ability of the Hall gener ator to make analog computations by
Instrumentation
operating on the input flux signal to obtain a desired function of flux output. This ability results from the multiplying ability of the Hall effect; that is, output is proportional to current times flux. Many other applications take advantage of this capability. Since the Hall probe yields a continuous output reading as long as the field is present, it is useful for driving the H axis on an X-Y plotter in field plotting and in tests using laboratory electromagnets. Other uses include field monitoring in spectrometers, beam deflection coils, cyclotron or linear accelerator magnets, and magnetic resonance measurements. Field programming and control of electromagnets have been carried out using Hall probes. Hall instruments have advantages in the study of flux transients in solenoids, motors, relays, etc., since thin probes will fit into narrow gaps in confined spaces and can feed signals directly to an oscilloscope for display and analysis of the field waveforms. Magnetic fields within solid material cannot be directly measured with a Hall probe for obvious reasons, but a proportional field value can often be indicated if a suitable air gap is available. A Hall generator positioned to sense the tangential field alongside a fluxcarrying member can read the value of surface II and is used for this purpose in B-H plotters, permeameters, and coercimetcrs. Magnetic susceptibility and saturation magnetization (a) of small samples have been measured using Hall devices. Industrial applications include the control and adjustment of field strength in the manufacture of dc motors, relays, and similar devices, and in the nondestructive testing of parts by magnetization or by eddy current methods. Noncontacting measurement of electric current is accomplished using Hall generators to sense the field around the conductor. Electric power is measured by Hall multipliers designed for use in power circuits. A host of other applications exist beyond the scope of this article, many of which have become feasible as a result of recent advances in Hall device technology. References
(1) "The Hall Effect and Its Applications," F. W. Bell Inc., Columbus, Ohio, 1962. (2) M. Epstein, L. J. Greenstein, H. M. Sachs, Proc. Nat. Electron. Conf., 15, 241 (1959). (3) A. J. Monks, U. S. Patent 3,469,092 (September 23, 1969). (4) R. J. Higgins, Rev. Sci. Instrum., 36 (11), 1536 (1965). (5) W. Viehmann, ibid., 33 (5), 537 (1962).
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