This paper discusses properties of Hall effect sensors with only three terminals and compares them to conventional four-terminal devices. It covers both Horizontal and Vertical Hall effect devices. Their Hall-geometry factor is computed analytically. Several modes of operation are proposed and their signal-to-noise ratio is compared. A six-phase offset cancellation scheme is developed. All theoretical results are checked by measurements. The residual offset of Vertical Hall effect devices with three contacts is found to be smaller than the offset of conventional Vertical Hall effect devices with five contacts.

Traditionally, Hall plates have four contacts and two orthogonal planes of mirror symmetry: two opposite contacts are used to supply the device with electrical energy while the other two opposite contacts are used to tap the output signal. The Hall plate can be supplied by a voltage or a current source and the output signal can be sensed by a voltmeter or an amperemeter. The combination of these possibilities gives four operating modes. For such devices spinning current schemes are known: they swap the two pairs of contacts—inputs and outputs—in consecutive operating phases. Combining the outputs of so-called orthogonal phases cancels out offset errors while keeping the magnetic sensitivity high. The output in each phase has a raw or initial offset, whereas the combination of phases according to the spinning scheme gives a much smaller offset, which is called residual offset. Offset error is stochastic so that one has to measure its standard deviation in order to quantify it. The standard deviation of a Gaussian distributed quantity is equal to its root mean square value, which we denote by rms. Moreover, if we compare different technologies and different types of devices, it is pretty meaningless to specify the offset in microvolts. Instead one should divide the output signal by the magnetic sensitivity in order to get the so-called equivalent offset in microtesla. In silicon technology the raw offset of state-of-the-art packaged Hall plates is roughly 7.5 mTrms and the residual offset of a good spinning current circuit may be as low as 15

With the advent of Vertical Hall effect devices the spatial spinning of current during the “spinning” scheme became obsolete; however, up to now all published dynamic offset cancellation schemes still seem to work with exactly two inputs and two outputs, which are continuously swapped. We call Vertical Hall effect devices VHalls in contrast to Hall plates, which we also call Horizontal Hall effect devices or HHalls. The terms “horizontal” and “vertical” denote the orientation of the plate-like geometry of the devices with respect to the main surface of the semiconductor die. It is a misconception that VHalls need to have current flowing in vertical direction into the depth of the die. In fact the predecessors of VHalls with

A Hall plate with five contacts after [

We specify the number of contact diffusions per Hall effect region: for example, the well known original VHall device of [

A Vertical Hall effect device with five contacts and four terminals in BiCMOS technology with deep trench isolation. The contacts comprise shallow^{+}S/D-diffusions and slightly deeper

Obviously, the degree of symmetry in VHalls is smaller than that in HHalls, because the accessible contacts of VHalls are only on the top face of the Hall effect region, whereas the contacts of HHalls can be arranged symmetrically along the entire perimeter of the Hall plate. Thus, there must be two outmost contacts as long as the Hall effect region has the shape of a straight tub, and these outmost contacts break the symmetry. This might also contribute to the roughly ten times larger equivalent residual offset error of VHalls compared to HHalls. So several people have tried to improve the symmetry. Here we name just a few:

One may apply the principle of forced symmetrization as it is used by HHalls since the 1980s: instead of a single device with four terminals one uses four devices and connects each terminal to a different contact of a different device as shown in Figure

No matter how asymmetric a single device was, the complete network of four devices is symmetric in an electric sense: the resistance between terminals

One can avoid the two ends of the Hall tub by using a ring-shaped Hall effect region with eight or more contacts [

Another strategy is to use several disjunct Hall tubs and connect them with wires in a ring topology like in Figure

Four 5C-VHalls connected in a forced symmetrization pattern.

Examples of VHalls comprising several disjunct Hall tubs.

In fact, electrical symmetry is not the main problem for spinning schemes. Even if a four-terminal device would lack any kind of electrical symmetry the spinning scheme would cancel out the offset error perfectly well, as long as the device has linear electrical properties and if we disregard thermoelectric effects [

It is known for a while that large contacts reduce the Hall output signal, because on the one hand the output contacts draw current away from the Hall effect region (current likes to flow over the low ohmic contacts instead of flowing through the high ohmic Hall effect region) so that it is not available for the Hall effect any more, and on the other hand the input contacts short a part of the Hall electric field. For these reasons one is inclined to use as few contacts as possible, namely, three.

VHalls in BiCMOS technologies can benefit from the low

In the following we start with Hall plates having only three contacts, derive their equivalent circuit diagram, and discuss various operating modes and their signal-to-noise ratios (SNR). Then we derive a linear theory on spinning schemes for Hall effect devices with three contacts. In the measurement sections we check our theories with 3C-HHall and 3C-VHall and compare them to 4C-HHalls and 5C-VHalls.

Figure

A symmetrical 3C-HHall device (a), an asymmetrical 3C-VHall device (b), and an equivalent circuit diagram for general 3C-Hall devices (c).

If current flows between two supply contacts, the potential at the third sense contact depends on the symmetry: in the symmetric case it is close to half of the supply voltage at zero magnetic field; in the asymmetric case it is somewhat closer to that supply potential, whose contact is nearer. When a magnetic field is applied perpendicularly to the plate the potential at the third contact rises or decreases, depending on whether the contact is left or right to the current streamlines. This holds also for asymmetric operation: for example, if current flows from left to center contact of the VHall in Figure

Figures

Differential operating mode (a) and equivalent circuit model of its left half. (b) Operating mode (b) and equivalent circuit model. (c) Operating mode (c) has inverted current flow polarities of operating mode (b). (d) Operating mode (d) and its equivalent circuit diagram. (e) Operating mode (e) has inverted polarity of supply current from operating mode (d).

Figure

A numerical simulation assumed a conductivity tensor

For the device in Figure

However, magnetic sensitivity is less important than signal-to-noise ratio, which we derive next. The equivalent resistor network in Figure

For the device in Figure

Figure

Figure

With the parameters from above a numerical simulation gives a voltage difference of

Figure

Figure

In this section we discuss an offset cancellation scheme for 3C-Halls: Iv-biasing. Thereby, the device is supplied with

(a) Operating phase 1 of Iv-biasing scheme of differential operating mode according to Figure

The Iv-biasing scheme applies to the differential operating mode of Figure

Figure

Basically, the two phases 1 and 3 are enough to cancel out the offset, if the origins of offset were fully described by the equivalent circuit. However, in reality offset also comes from thermoelectric voltages: the output voltage is tapped at a contact, where the

Figure

Obviously, the current does not spin around continuously in space like with conventional 4C-HHalls. So the term “spinning” is misleading and the term “contact commutation” is more correct. The essential feature is that each contact acts as positive supply terminal in two phases, as negative supply terminal in two phases, and as sense contact in two phases.

Figure ^{3} and the thickness was 0.7

Layout of three devices of type 3C-HHall connected in parallel.

The internal resistance versus supply voltage was measured (see Figure

Input resistance of the 3C-HHalls of Figure

The supply voltage related magnetic sensitivity is plotted versus supply voltage in Figure

Voltage related magnetic sensitivity

The following offset cancellation schemes were investigated: in mode (a) the devices were operated like in Figure _{1}-_{2},_{2}-_{3}, and_{3}-_{1}; then both current sources were swapped and the three phases were repeated; finally all six output voltages were summed up. The label “modes (b) + (c)” means that the phase signals of both schemes (b) and (c) were added up.

Figure

Residual offset of the 3C-HHalls of Figure

Measurements were carried out on test structures shown in Figure ^{3}, which is way smaller than the doping of the^{3}). The contacts were made of^{+}S/D diffusion and

Measured residual offset of 5C-VHalls of Figure

Measured residual offset of 3C-VHalls operated in Iv-biasing six-phase offset cancellation scheme. The devices were actually 5C-VHalls from Figure

Comparison of Figures

Standard deviation of the residual offsets of Figures

The paper discusses Hall plates (HHalls) and Vertical Hall effect devices (VHalls) with only three contacts. Various geometries with smaller or higher degree of symmetry were shown. Hall sensor devices with single tubs were shown as well as arrangements, where several tubs are connected into a ring circuit. Several operating modes of these devices were discussed and their signal-to-noise ratios were compared. Unfortunately, at given input resistance, the signal-to-noise ratio of 3C-Halls is generally smaller than the SNR of conventional 4C-Halls even though 3C-Halls achieve higher voltage related magnetic sensitivity. The equivalent circuit diagram of 3C-Hall comprises only three resistors and two current controlled voltage sources. Numerical simulations of several operating modes suggest that the equivalent circuit correctly predicts the output signals. An offset cancellation scheme for 3C-Halls was studied. The roles of orthogonal and inverse pairs of operating phases were elucidated. Measurement results on the residual offset of symmetric 3C-HHalls and asymmetric 3C-VHalls show that the offset cancellation schemes also work in practice. The residual offset of 3C-HHalls was found to be larger than that of conventional 4C-HHalls. However, the residual offset of 3C-VHalls was found to be smaller than that of conventional 5C-VHalls. A comparison with [

In general it was found that unconventional devices like the ones with three contacts shed new light on topics like spinning current schemes and signal-to-noise ratio. Further studies of these devices are likely to bring more aspects to our attention, both in theory and in practice; this paper could touch only on the basic topics of unconventional Hall effect devices.

Here we derive the input resistance and the Hall-geometry factor of a 3C-Hall with two arbitrarily large supply contacts and one point-sized sense contact. We apply the method of [

Series of conformal transformations that map a disc of radius 1 with two arbitrarily large supply contacts in the

The bilinear transformation

Since the length

Equations (

Hall potential along the right isolating boundary between the two supply contacts. Comparison of results from a finite element simulation and an analytical calculation after (

If both supply contacts become point-sized and the sense contact is in the symmetry plane between them we have

Here we show that conventional 4C-Hall plates have the highest signal-to-noise ratio at given input resistance, if they are 90° symmetric with

The ratio of Hall-geometry factor at small magnetic field over the square-root of product of input and output numbers of squares for all 4C-Halls with two orthogonal mirror symmetries plotted for input and output numbers of squares between 0 and 4. The maximum is in the diagonal

From Figure

Here we compute numerically the input resistance and the Hall-geometry factor for symmetrical 3C-Halls which have three contacts of arbitrarily large, equal size and which exhibit 120° symmetry. The finite element models comprised 0.5⋯1.3 million elements, whereby the large numbers of elements were used for small contacts. Lagrange multipliers were used. The parameters were

The Hall-geometry factor

The author declares that there are no competing interests.

All sensor layouts were done by Manfred Steiner, and all measurements were carried out by Michael Holliber. Their support is gratefully acknowledged.