Patent Publication Number: US-9423471-B2

Title: Low offset vertical hall device and current spinning method

Description:
REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation of U.S. application Ser. No. 14/538,042 filed on Nov. 11, 2014, which claims priority to U.S. Divisional application Ser. No. 13/488,709 filed on Jun. 27, 2012, which claims priority to U.S. application Ser. No. 13/022,844 filed on Feb. 8, 2011. The present application claims priority to each of these three above applications, and the contents of the three above-referenced applications are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND 
     Hall-effect devices are often used in sensor applications for contactless sensing of magnetic fields.  FIG. 1  shows a conventional Hall plate  100 . The Hall plate  100  is operated by providing a predetermined current  104  along a first axis  106  between first and second supply terminals S 1 , S 2 . According to the Hall principle (and Lorentz&#39;s right hand rule as shown by  108 ), the presence of a magnetic field B causes positively charged particles (e.g., holes  110 ) which are traveling with velocity v during flow of current  104 , to be “steered” or deflected in the F direction along second axis  112 , thereby inducing a voltage differential between Hall effect terminals H 1  and H 2 . The amount of “steering” or deflection of these charged particles depends on the magnitude of the magnetic field B, such that the magnitude of voltage differential between H 1  and H 2  is proportional to the magnitude of magnetic field B. Hence, in the presence of predetermined current  104 , measuring the voltage across Hall effect terminals H 1  and H 2  provides an accurate measurement of the magnetic field B. 
     As will be appreciated in greater detail below, the present disclosure relates to improved Hall-effect measurement techniques. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates an operating principle of a conventional Hall plate. 
         FIGS. 2-3  illustrate a vertical Hall-effect device that suffers from some shortcomings. 
         FIG. 4  illustrates an equivalent circuit of  FIGS. 2-3 , including contact resistances which lead to offset errors. 
         FIG. 5  illustrates an equivalent circuit for contact resistance of Hall-effect sensors in accordance with some embodiments. 
         FIG. 6  illustrates a top view of a vertical Hall-effect device in accordance with some embodiments. 
         FIGS. 7A-7D  illustrate a series of applied biases and measured currents for the vertical Hall-effect device of  FIG. 6 . 
         FIG. 8  illustrates a top view of a vertical Hall-effect device in accordance with some embodiments. 
         FIGS. 9A-9D  illustrate a series of applied biases and measured currents for the vertical Hall-effect device of  FIG. 8 . 
         FIG. 10  illustrates a top view of another vertical Hall-effect device in accordance with some embodiments. 
         FIG. 11  illustrates an embodiment of a vertical Hall-effect device divided across two tubs, rather than a single tub. 
         FIGS. 12A-12B  illustrate another embodiment of a vertical Hall-effect device divided across two tubs. 
         FIG. 13  illustrates another embodiment of a vertical Hall-effect device divided across two tubs. 
         FIG. 14  shows a feedback circuit in accordance with some embodiments. 
         FIG. 15  shows a differential feedback circuit in accordance with some embodiments. 
         FIGS. 16A-16C  show a vertical Hall-effect device that makes use of FIG.  15 &#39;s differential feedback circuit. 
         FIG. 17  shows another embodiment of a vertical Hall effect device. 
         FIG. 18  shows another embodiment of a vertical Hall effect device. 
         FIG. 19  shows another embodiment of a vertical Hall effect device. 
     
    
    
     DETAILED DESCRIPTION 
     The present invention will now be described with reference to the attached drawing figures, wherein like reference numerals are used to refer to like elements throughout, and wherein the illustrated structures and devices are not necessarily drawn to scale. 
     In contrast to  FIG. 1 , which explained the Hall-effect in the context of a relatively flat Hall plate, the present disclosure deals with accurate measurement techniques for vertical Hall-effect devices.  FIGS. 2 and 3  show a perspective view and a cross-sectional view, respectively, for a vertical Hall-effect device  200  that suffers from some shortcomings. Vertical Hall-effect device  200  includes a hall sensing region  202  (e.g., lightly doped n− region), which is coupled to supply contacts S 1 , S 2  and Hall signal contact H. 
     The vertical Hall-effect device  200  is operated in a “voltage input—current output” mode. To this end, a voltage source  204  applies an input voltage Vin across the supply contacts S 1 , S 2 . For example, supply contact S 1  can be held at Vin while supply contact S 2  can be held at ground. In accordance with Ohm&#39;s law (V=IR), this input voltage Vin induces a corresponding current flow between supply contacts S 1 , S 2 . 
     Assuming the Hall signal contact H is centered between the supply contacts S 1 , S 2  and assuming that there is a uniform resistance over the Hall region  202 , then the Hall signal contact H will experience a voltage of Vin/2 at zero magnetic field. Hence, if Hall signal contact H was held at Vin/2 in the presence of zero magnetic field, this would constitute an equilibrium condition and no current would flow into the Hall signal contact H. 
     In the presence of a non-zero magnetic field B, however, the case is slightly different. Now charged carriers in the flow of current are “steered” or deflected according to the right hand rule  108  in an attempt to raise or lower the potential on the Hall signal contact H. For example, consider the illustrated case where B-field is directed in the negative x-direction and positively charged holes flow in the negative y-direction, such that the holes experience a Hall force that drives the holes downward from substrate surface  209  in an attempt to lower potential on Hall signal contact H. If the Hall signal contact H is still clamped to Vin/2, the charges “steered” by the Hall-effect are unable to raise or lower the potential at the Hall signal contact H. Therefore, a Hall current I Hall  will be injected into or sunk from the Hall signal contact H to maintain equilibrium, wherein amount of Hall current injected or sunk is proportional to the magnitude of the magnetic field B. Thus, the Hall current I Hall  on Hall signal contact H is indicative of the magnitude of the magnetic field B. 
     Referring to  FIG. 3 , one can see a cross-section of the vertical Hall-effect sensor  200  taken along axis  106 . First supply contact S 1  is implemented as a first well region  205  (e.g., n-well doped n) with one or more contacts  206  (e.g., shallow doped source/drain n+). Hall signal contact H is implemented as a second well region  207  (e.g., n-well doped n) with one or more respective contacts  210  (e.g., shallow doped source/drain n+). Second supply contact S 2  is implemented as a third well region  212  (e.g., n-well doped n) with one or more contacts  214  (e.g., doped n+). An isolation structure  215  surrounds Hall region  202 . 
     Ignoring the Hall signal contact H for the moment, let&#39;s briefly consider the case where voltage Vin is applied to first supply contact S 1 , and ground potential (0V) is applied to second supply contact S 2 . The voltage Vin is applied to a metal 1 wire  216 , so current flows over this wire, traverses contact plugs  218 , flows into highly doped source-drain diffusion region  206  (n+), spreads out in n-well  205  (n, which is more lightly doped than n+ source/drain regions but more highly doped than n-Hall region  202 ), until it finally enters the n-Hall region  202 . The same sequence in reverse order happens at for the second supply contact S 2 . 
     Unfortunately, the contact resistances of the metal 1 wire  216 , the contact plugs  218 , the n+ source/drain  206  and nwell  205  cause a voltage drop, such that the potential Vin does not actually reach the Hall-region  202 . Although these contact resistances are low, they may still cause a voltage drop of a few millivolts which can be significant given the fact that Hall-region  202  typically has a small resistance. Further, in the presence of a zero magnetic field, asymmetries in the geometry of the Hall device can lead to non-zero Hall-effect signals—so called raw offsets. Current spinning schemes combine signals of several spinning cycles, such that this total (combined) signal tends to have a much smaller raw offset than the individual current signals. This combined raw offset can be referred to as a residual offset. 
     The reason for this residual offset can be appreciated from  FIG. 4 , which shows an equivalent circuit diagram including the “true” Hall device  202  (that is the part of the Hall device which is made only of n-Hall region, where the Hall-effect predominantly develops), plus additional contact resistances (r 1 , r 2 , rH). Because these contact resistances are not precisely known (and can vary somewhat over the manufacturing process and show mismatch even within one device), these contact resistances cause inaccuracies in the applied voltage potential. For example, consider a hypothetical case where a voltage bias of 5V is applied between S 1  and S 2 , and where the contact resistances r 1  and r 2  are unknown to the user, but are each actually 10% of the resistance of the Hall region  202 , for example. In such a situation, an user might expect that the full 5V bias is applied to the Hall region, but in fact, only 0.8*5V=4V (i.e., 80% of the full bias) is applied over the Hall region, due to a 0.5V voltage drop over each contact resistance (r 1 , r 2 ). Thus, the potential at the positive supply S 1  of the Hall region  202  is 4.5V (instead of 5V) and at the negative supply S 2  of the Hall region  202  is 0.5V (instead of 0V). 
     These inaccurate potentials lead to residual offset errors for spinning current techniques, particularly if the device has an electrical nonlinearity, such as when the resistance level of the resistors r 1  and r 2  depends on the potential applied. For example, in the real world, the resistance value of r 1  is ever-so-slightly larger if 5V is applied S 1  and is ever-so-slightly smaller if 4.5V is applied to S 1 . In the same way, the resistance value of r 2  is smaller when 0V is applied to S 2 , compared to when 0.5V is applied to S 2 . This leads to the residual offset. 
     Therefore, it is desirable to apply well defined potentials to the resistors to avoid these residual offset errors. Unfortunately, however, the resistors in  FIGS. 2-4  are not directly accessible because of the small contact resistances for each contact. To circumvent the unknown voltage drop along these contact resistances, the invention splits each contact (e.g., supply contacts S 1 , S 2  and Hall signal contact H from  FIGS. 2-3 ) into two parts—a force contact (F) used to carry current and a sense contact (S) used to measure a voltage potential that develops at the ‘true’ Hall device in the active Hall region. These force-sense contacts achieve well defined potentials at all resistors of the equivalent circuit diagram in all operating phases of the spinning current scheme, thereby limiting or avoiding residual offset errors. 
       FIG. 6  shows an example of a vertical Hall-effect device  600  that makes use of “split” contacts in accordance with some embodiments. Within an n-type tub conductive tub  602  (which is surrounded by an isolation structure  606 , such as a deep trench isolation region or a p-type region) three pairs of “split” contacts are arranged (e.g., first contact pair  610 , second contact pair  612 , third contact pair  614 ). Each contact pair includes a first contact (e.g.,  610   a ,  612   a ,  614   a ) as well as a second contact (e.g.,  610   b ,  612   b ,  614   b ). As will be appreciated in more detail below, feedback circuits  626 ,  628 ,  630  clamp the contact pairs to respective voltage potentials (e.g., U 1 , U 2 , U 3 ) and measure a Hall-effect current from the biased device to accurately measure magnetic field. 
     Before delving into the detailed functionality of vertical Hall-effect device  600 , reference is made to  FIG. 14 , which illustrates an exemplary feedback circuit  1400  (e.g., feedback circuit  626  in  FIG. 6 ). The feedback circuit  1400  comprises a transconductance input stage TC 1  and Current Controlled Current Source CCCS 1 . The transconductance input stage TC 1  comprises a positive non-inverting input (+) and a negative inverting input (−). The transconductance input stage TC 1  is configured to output a current I TC  that is proportional to the voltage between its non-inverting (+) and inverting (−) inputs. If the voltage at the non-inverting input is positive against the inverting input, the output current I TC  is positive. If the voltage at the non-inverting input is negative against the inverting input, the output current I TC  is negative. 
     The output current I TC  of the transconductance stage TC 1  is provided to CCCS 1 , which outputs a feedback current I 1  to a force contact F 1  to drive the voltage potential at an associated sense contact to the reference voltage potential U 1  (e.g., feedback current I 1  is provided to F 1  to drives the voltage potentials at S 1  to be equal to U 1 ). If TC 1  comprises a large factor of proportionality, a small voltage difference between the inverting inputs can provide a large output current to CCCS 1 , since I 1  is proportional to current I TC  and is independent of the contact resistance to which the current is supplied. In order to suppress the effect of contact resistances efficiently, the magnitude of current I 1  must be much larger than the magnitude of the current flowing in or out of the inverting input of TC 1 . In an idealized case the inverting input draws no current at all. 
     Therefore, during operation, if the voltage potential at a sense contact (e.g., S 1 ) is lower than the reference or target voltage potential of the feedback circuit (e.g., U 1 ), the feedback circuit (e.g., FB 1 ) injects a large positive current (e.g., I 1 ) into a force contact (e.g., F 1 ) of the Hall-effect device to raise the potential at the sense contact (e.g., S 1 ) until it is equal to the reference voltage (e.g., U 1 ). Similarly, if the voltage potential at a sense contact (e.g., S 1 ) is higher than the reference or target voltage potential of the feedback circuit (e.g., U 1 ), the feedback circuit (e.g., FB 1 ) reduces its output current supplied to a force contact (e.g., F 1 ) of the Hall-effect device, thereby lowering the potential at the sense contact (e.g., S 1 ) until it is equal to the reference voltage (e.g., U 1 ). 
     Referring now to  FIGS. 7A-7D , one can see operation of the Hall-effect device  600 . In  FIG. 7A , at a first time, controller  624  sets switching network  636  to couple respective feedback circuits ( 626 ,  628 ,  630 , respectively, having reference voltages +1V, +0.5V, and 0V, respectively) to contact pairs  610 ,  612 ,  614 , respectively. 
     More particularly, in the illustrated example, the first feedback circuit  626  is coupled to first contact pair  610  for  FIG. 7A . The first feedback circuit  626  changes the amount of current I 1  delivered to force contact F 1  until sense contact S 1  measures a voltage of U 1  (here 1V). In this way, first and second contacts  610   a ,  610   b  are clamped at 1V during first time in  FIG. 7A . In this way, first contact  610   a  is clamped at 1V. Similarly, second contact  612   a  is clamped to 0.5V, and third contact  614   a  is clamped to 0V ( 612   b  will have a potential close to 0.5V, may be slightly smaller or larger than 0.5V depending on its contact resistance and applied magnetic field, whereas  614   b  will have a potential slightly lower than 0V depending on its contact resistance). This voltage bias induces a current between force contact  610   b  and force contact  614   b  (due to V=IR), and magnetic field B drives the charged carriers of this induced current upward or downward with respect to the upper planar surface of substrate depending on the direction of the magnetic field B. Because the voltage potential on sense contact S 2  ( 612   a ) is clamped at 0.5V and because feedback circuit FB 2  does not allow current to be drawn into/from S 2  (S 2  is only used for voltage measurement), any Hall current I hall  will be sunk into or injected from force contact F 2   612   b  depending on the direction and magnitude of B. FB 2  (or an ammeter elsewhere) can measure the Hall current injected into or sunk from F 2   612   b , and thereby determine the corresponding magnetic field. 
     In  FIG. 7B , at a second time, the controller  624  changes the state of the switching network  636  to “flip” the currents/voltages for the first and third contact pairs  610 ,  614  while leaving the second contact pair  612  clamped at 0.5V (e.g., FB 1   626  is coupled to F 3 /S 3   614  and FB 3   630  is coupled to F 1 /S 1   610 ). This “flip” causes a new current I Hall ′ to be sunk into or injected from F 2 . The new current I Hall ′ is again proportional to the magnetic field B, but will flow in the opposite direction of I Hall  because of the switched voltage bias. If the device were perfectly symmetrical, the currents measured in  FIGS. 7A and 7B  would completely cancel one another, but in reality,  FIG. 7B &#39;s Hall current I Hall′  differs slightly from  FIG. 7A &#39;s Hall current I Hall  due to slight imperfections in the geometries of the device and other non-linearities. Assuming that magnetic field B is constant between  FIG. 7A  and  FIG. 7B , taking the difference between I Hall  ( FIG. 7A ) and I Hall ′ ( FIG. 7B ) provides a greatly reduced offset (as any errors between the two contacts, due to manufacturing imperfections and the like, tend to cancel each other). Thus, the magnetic field B is measured with greater precision. 
       FIG. 7C  shows the Hall sensor  600  at a third time, wherein the controller  624  has changed the state of the switching network  636  such that the force contacts and sense contacts have been “flipped”. Thus, the upper row of contacts (e.g., first contacts  610   a ,  612   a ,  614   a ) now act as force contacts, and the lower row of contacts (e.g., second contacts  610   b ,  612   b ,  614   b ) now act as sense contacts.  FIG. 7D  shows the Hall sensors at a fourth time wherein the biases are flipped horizontally. Again, because the offsets inherent in these measured currents tend to cancel one another, by iteratively measuring the currents and subtracting them, the offset can be finely turned and the magnetic field can be measured with high accuracy. 
     It is also possible to start with a slight variation of  FIG. 7A  where only S 2 /F 2  are flipped for a first clock phase, and in a second clock phase use a slight variation of  FIG. 7B  where S 2 /F 2  are flipped. In general, the force/sense contacts can be changed in any permutation (e.g., checker board). While there are countless versions of these permutations, the important aspect is how to apply well defined potentials to the Hall region and how to extract output current from the Hall device, which is accomplishing using the “split” contacts and corresponding feedback circuits. 
     Note that in other (slightly more complicated) cases, the controller can apply Vin to S 1  and concurrently drive S 2  to ground. In the absence of magnetic field, the potential at S 3  is no longer Vin/2, because S 3  is not positioned halfway between the sense contacts S 1 , S 2 . The exact potential at S 3  depends on the geometry (lateral and vertical) of the Hall-effect device features. The potential at S 3  will be roughly at 0.3V for many kinds of devices, but can vary widely. To find the potential, it can be measured in an end-of-line test at zero B-field. Then the controller can be programmed to apply exactly this potential (e.g., 0.3V) to S 3  during actual operation. Subsequently, during actual operation, a magnetic field would again like to raise or lower the voltage potential on sense contact S 3 . However, because S 3  is clamped to 0.3V for example, a current will be injected to or sunk from S 3  instead, wherein the amount of current provided is proportional to B-field. 
     Regardless of the particular biasing sequencing applied, the respective “first” and “second” contacts in contact pairs  610 ,  612 ,  614  are switched between acting as so-called “force contacts” (current flows through them) and so-called “sense contacts” (no current flows through them and they are used to measure the potential). Thus, the terms “force contact” and “sense contact” may be interchangeable in this respect, as currents and voltages may be measured and/or injected/applied from the various contacts depending on the time involved. 
     Referring back to  FIG. 6 , one will note that the first contacts  610   a ,  612   a ,  614   a  are arranged along a first line  616  extending in parallel with a first axis  618 , while the second contacts  610   b ,  612   b ,  614   b  are arranged along a second line  620  extending in parallel with the first axis  618 . The first and second lines  616 ,  620  are spaced equally apart from the first axis  618  by a distance D 1 , such that the respective first and second contacts are spaced symmetrically about opposite sides of the first axis  618 . A second axis  622 , which is perpendicular to the first axis  618 , passes through second contact pair  612  such that the first and third contact pairs  610 ,  614  are spaced equally apart from the second axis  622  by distance D 2 . 
     In some embodiments, each first and second contact has outer dimensions that can range from approximately 0.2 μm on a side to approximately 10 μm on a side. Contacts can be square, rectangular, polygonal, or even rounded geometries; and multiple vias and/or multiple contact plugs can be coupled to each first or second contact (e.g.,  610   a ). For example, for an illustrated rectangular contact  610   a , a shorter side  632  could have a width of approximately 1 μm to about 0.2 μm, while a longer side  634  could have a length of approximately 3 μm to approximately 10 μm. The length and width can depend on the depth of the Hall region. For example, relatively shallow hall region of approximately 1 μm might correspond to a length of approximately 3 μm; while a deeper hall region of approximately 5 μm might correspond to a width of approximately 10 μm. 
       FIG. 5  illustrates a schematic depiction of a vertical Hall-effect device  500  having “split contacts”. Relative to  FIG. 4 &#39;s circuit diagram, each supply contact S 1 , S 2  in  FIG. 5 &#39;s Hall-effect device has been split into two contacts—a force contact (F) and a sense contact (S). Similarly, the Hall-effect contact H has been split into a force contact (F) and a sense contact (S). Each force contact its own contact resistance (e.g., rF 1 ) as does each sense contact (e.g., rS 1 ), which are connected to a corresponding feedback circuit (e.g., FB 1 ). During operation, the feedback circuit FB 1  pushes current I 1  into F 1 , causing a corresponding voltage drop over rF 1 . However, little or no current is drawn into port S 1  of FB 1 , such that little or no voltage drop occurs over rS 1 . Therefore, the potential on S 1  is an extremely accurate representation of the potential at terminal Hall region terminal  202   a . Therefore, FB 1  can adjust I 1  until the potential at the Hall region  202  is exactly the one we want, namely Vin, which helps provide extremely accurate magnetic field measurements. 
     As can be appreciated from  FIG. 8 , the present disclosure is not limited to three contact pairs as previously discussed with regards to  FIG. 6 . Rather, the concept can be applied to any number of contact pairs.  FIG. 8  shows one such example with four contact pairs, although additional contact pairs could also be used. The contacts of the contact pairs are again arranged on first and second lines  802 ,  804  that are spaced apart from a first axis  806 , and are symmetrically arranged about a second axis  808  which is perpendicular to the first axis  806 . 
       FIG. 9A-9D  show one manner of successively applying biases (e.g., currents and voltages) to the contact pairs of  FIG. 8  in a manner analogous to previously described  FIGS. 7A-7D . In a first clock phase ( FIG. 9A ), respective feedback circuits (not shown) are coupled to contact pairs F 1 -S 1 , F 2 -S 2 , F 3 -S 3 , F 4 -S 4 , respectively, to establish potentials Vin, k 1 *Vin, 0V, and k 2 *Vin (with k 1  preferable close to 0.5, yet it may range from 0.2 . . . 0.8; and k 2  closer to 0V) on S 1 , S 2 , S 3 , S 4 , respectively. The difference of currents I 2 −I 4  is proportional to the B-field. 
     In a second clock phase ( FIG. 9B ), the respective feedback circuits are coupled to contact pairs F 1 -S 1 , F 2 -S 2 , F 3 -S 3 , F 4 -S 4 , respectively to establish potentials k*Vin, Vin, k*Vin, and 0V (with k preferable close to 0.5, yet it may range from 0.2 . . . 0.8) on S 1 , S 2 , S 3 , S 4 , respectively. The difference of currents I 1 −I 3  is proportional to the B-field. The combination I 1 −I 3 −(I 2 −I 4 ) is proportional to B-field and has greatly suppressed offset error. 
     In a third clock phase ( FIG. 9C ) the measurement performed in the first clock phase is re-taken, albeit with the force-contacts and sense-contacts interchanged. The Hall signal is I 2 ′−I 4 ′, which is proportional to magnetic field. 
     In a fourth clock phase ( FIG. 9D ) the measurement performed in the second clock phase is re-taken, albeit with the force-contacts and sense-contacts interchanged. The Hall signal is I 1 ′−I 3 ′. The combination [I 1 −I 3 −(I 2 −I 4 )]+[(I 1 ′−I 3 ′)−(I 2 ′−I 4 ′)] is proportional to B-field and shows even smaller offset error than above. 
     This spinning current scheme can be further improved by swapping the positive and negative supply terminals in all clock phases and repeating the measurements. For example, in a fifth clock phase (not shown), we can swap the supply terminals relative the illustrated first clock phase ( FIG. 9B ), such that the difference of currents I 2 ″−I 4 ″ is proportional to the B-field. If we, in a sixth clock phase, swap the supply terminals relative to the second clock phase ( FIG. 9B ) the difference of currents I 1 ″−I 3 ″ is proportional to the B-field. If, in a seventh clock phase, we swap the supply terminals relative to the third clock phase ( FIG. 9C ) the difference of currents I 2 ′″−I 4 ′″ is proportional to the B-field. If, in an eighth clock phase, we swap the supply terminals relatively to the fourth clock phase ( FIG. 9D ) the difference of currents I 1 ′″−I 3 ′″ is proportional to the B-field. Lastly, we compute I 1 −I 2 −I 3 +I 4 +I 1 ′−I 2 ′−I 3 ′+I 4 ′−(I 1 ″−I 2 ″−I 3 ″+I 4 ″+I 1 ′″−I 2 ′″−I 3 ′″+I 4 ′″), which is proportional to B-field and shows even smaller offset error than above. Moreover, it is also possible to swap e.g. F 2  with S 2  and F 4  with S 4  in  FIG. 9A : then not all force contacts are in a single row any more—only the force contacts of the supply terminals are in a row with the sense contacts of the Hall effect terminals (=signal terminals). In principle it is also possible to additionally swap F 1  with S 1 : this gives an asymmetric arrangement of force and sense contacts that is likely not to provide very good residual offset, yet it may still give better results than prior art 
       FIG. 10  shows another embodiment of a vertical Hall-effect device  1000  where the contacts have a slightly different configuration. Like previous embodiments, the Hall-effect device  1000  includes a conductive tub  602  having a first conductivity type (e.g., n-type) disposed in a semiconductor substrate  604 , and surrounded by isolation structure  606 . The illustrated Hall-effect device  1000  again includes a three contact pairs  610 ,  612 ,  614 . In this example, the first and third contact pairs  610 ,  614 , however, are each split into two vertical contacts. The voltage biases applied to and currents measured from the various contacts can be flipped such that all contacts act as a force contact at one time and a sense contact at another time, as previously described in  FIGS. 7A-7D . Although it is generally advantageous to have force and sense contacts of equal size, the force and sense contacts may also differ in size (e.g. the force contact may be larger to have a smaller voltage drop—there is no voltage drop along the sense path, because little or no current flows there), as shown by first contact pair  610  and third contact pair  614 . 
       FIG. 11  illustrates an embodiment of a vertical Hall-effect device  1100  that includes two tubs, rather than a single tub. The Hall-effect device includes a first tub  1102 , which is surrounded by isolation structure  1104 , and has a first conductivity type and is disposed in a semiconductor substrate. A first group of contact pairs  1106  having respective first and second contacts  1108 ,  1110  are disposed in the first tub  1102 . First contacts  1108  are arranged along a first line  1112  and second contacts  1110  are arranged along a second line  1114 , wherein the first and second lines  1112 ,  1114  run in parallel with a first tub axis  1116  arranged between the first and second lines  1112 ,  1114 . 
     A second tub  1118 , which is surrounded by isolation region  1120 , has the first conductivity type and is disposed in the semiconductor substrate. A second group of contact pairs  1122 , which include respective third and fourth contacts  1124 ,  1126 , are disposed in the second tub  1118 . The third contacts  1124  are arranged on a third line  1128  and fourth contacts  1126  are arranged on a fourth line  1130 , wherein the third and fourth lines  1128 ,  1130  run in parallel with a second tub axis  1132  arranged between the third and fourth lines. The tubs are not necessarily parallel, but can also be orthogonal or at any angle. 
     An interconnect layer  1134  couples a first contact pair F 1 /S 1  in the first tub  1104  with a second contact pair F 6 /S 6  in the second tub  1118 . The first and second contact pairs are spaced symmetrically about an axis  1136  passing between the first and second tubs. The first and second contact pairs are also spaced symmetrically with respect to a second axis that is perpendicular to the axis passing between the first and second tubs. For example, the interconnect structure couples F 1  to F 6  and S 1  to S 6 , all of which are driven by FB 1 . The interconnect structure also couples F 3  to F 4  and S 3  to S 4 , all of which are driven by FB 2 . Alternatively one may swap S 4  with F 4  and/or S 5  with S 5  and/or S 6  with F 6 . This gives a large number of possible configurations whereof the preferred ones are those with higher degree of geometrical, thermal, electrical, and/or magnetic symmetry and/or symmetry with respect to mechanical stress on the devices. 
     Another Hall-effect sensor is illustrated in  FIG. 12A-12B , wherein the Hall-effect sensor  1200  is divided across two tubs. Hall-effect sensor  1200  consists of two separate Hall regions, each one with three contacts, where the center contacts of both tubs (C 2 , C 5 ) are shorted. One of the other two contacts is used as a supply terminal and the other as a Hall-effect signal terminal. 
     As shown in  FIG. 12A  in a 1 st  clock phase, a positive supply voltage is applied to S 1 , and negative supply voltage is applied to S 4 . S 3  and S 6  are clamped to intermediate potentials and the difference I 3 −I 6  increases with increasing By-field. 
     Note that at vanishing magnetic field, I 3 −I 6  is usually not equal to zero: this is the systematic raw offset of the device. 
     In a second clock phase, S 3  is forced to the positive supply voltage and S 6  to the negative one. Then S 1  and S 4  are forced to intermediate potentials: ideally S 1  is forced to the same potential as S 3  was forced in the 1 st  clock cycle and S 6  is forced to the same potential as S 4  was forced in the 1 st  clock cycle. The difference I 4 −I 1  increases with increasing By-field, and its systematic raw offset is equal in magnitude and opposite in sign to the raw offset of clock phase  1 . 
     A total signal I 3 −I 6 +I 4 −I 1  has greatly reduced offset and large sensitivity to By-field. 
     Another two clock cycles #3 and #4 may be added, where the roles of positive and negative supply voltages are exchanged: this changes the sign of the respective signals I 3 ′−I 6 ′ and I 4 ′−I 1 ′ so that they have to be subtracted from I 3 −I 6 +I 4 −I 1 −(I 3 ′−I 6 ′+I 4 ′−I 1 ′). This gives in total 4 clock phases. 
     Another 4 clock phases #5, #6, #7, #8 may be added, where the roles of force and sense contacts are exchanged, as shown in  FIG. 12B . 
     In the clock phase #5 positive supply voltage is established on S 1   a , S 1   b  and negative supply voltage on S 4   a , S 4   b  and intermediate voltages are established on S 3   a , S 3   b  and S 6   a , S 6   b . Then the current difference I 3 ″−I 6 ″ is measured. 
     In the clock phase #6 positive supply voltage is established on S 3   a , S 3   b  and negative supply voltage on S 6   a , S 6   b  and intermediate voltages are established on S 1   a , S 1   b  and S 4   a , S 4   b . Then the current difference I 4 ″−I 1 ″ is measured. 
     In the clock phase #7 positive supply voltage is established on S 4   a , S 4   b  and negative supply voltage on S 1   a , S 1   b  and intermediate voltages are established on S 3   a , S 3   b  and S 6   a , S 6   b . Then the current difference I 6 ′″−I 3 ′″ is measured. 
     In the clock phase #8 positive supply voltage is established on S 6   a , S 6   b  and negative supply voltage on S 3   a , S 3   b  and intermediate voltages are established on S 1   a , S 1   b  and S 4   a , S 4   b . Then the current difference I 1 ′″−I 4 ′″ is measured. 
     The overall signal is computed: I 3 −I 6 +I 4 −I 1 −(I 3 ′−I 6 ′+I 4 ′−I 1 ′)+I 3 ″−I 6 ″+I 4 ″−I 1 ″−(I 3 ′″−I 6 ′″+I 4 ′″−I 1 ′″). It has very small residual offset error and strong sensitivity to magnetic field. 
     A drawback of the device is the large raw offset due to the systematic difference in potentials of both Hall-effect terminals in both tubs. 
     To reduce this large raw offset the tubs and contacts can be arranged more symmetrically as shown in  FIG. 13 .  FIG. 13  illustrates an embodiment of a vertical Hall-effect device divided across four tubs  1302 ,  1304 ,  1306 ,  1308 . The wiring of individual contacts is such that two sense contacts (e.g. S 3  and S 7 ) and multiple force contacts (F 3   a , F 3   b , F 7   a , F 7   b ) are coupled to each feedback circuit (e.g., FB 3 ). For the sense contacts coupled to a given feedback circuit (e.g., which can be accomplished via a switching network (not shown)), one of them is placed in a tub with positive supply terminal (e.g. S 3  if F 1  is the positive supply) and the other one is placed in a tub with negative supply terminal (e.g. S 7  if F 9  is the negative supply). If these two sense contacts are shorted (i.e. their respective force-contacts F 3   a , F 3   b , F 7   a , F 7   b  are shorted and also their respective sense contacts S 3 , S 7  are shorted) a large difference current flows across these shorts in the absence of magnetic fields: this current corresponds to the raw offset of devices. This short pulls down the potential in S 3  and up in S 7  so that finally they are both at half of the supply voltage of the vertical Hall device. Then the feedback circuit FB 3  only has to supply a small current I 3  to the force contacts F 3   a , F 3   b , F 7   a , F 7   b  to account for statistical offset (=mismatch between the devices) and to the applied By-field. 
     Note that the above figure is a circuit diagram where only each tub with its contacts corresponds to the layout—it does not say anything about the orientation of the four tubs in the layout. In a real layout the four tubs may be aligned in a row on a single horizontal line, they may be aligned in a column on a single vertical line, or they may be aligned in a quadrangle (e.g., 2×2 matrix). 
     Note that in  FIG. 13  we may also skip two tubs in order to simplify the device.  FIG. 11  illustrated one such example. In this instance, the potentials are forced in such a way that the current flow in both tubs is in opposite directions: In the 1 st  clock phase FB 1  forces S 1 =S 6 =+1V and S 3 =S 4 =0V and S 2 =S 5 =0.5V. Then the difference in currents I 2 −I 5  is proportional to the magnetic field. In a 2 nd  clock phase FB 1  still forces S 1 =S 6 =+1V, yet this time FB 3  forces 0.5V (or some value between 0.2V and 0.7V) on S 3  and S 4  and FB 2  and FB 5  force S 2 =S 5 =0V. Then the difference in currents goes toward zero. 
     In some embodiments, a differential feedback circuit can be used, such as shown in  FIG. 15 . Differential feedback circuit  1500  has two voltage inputs U 1 , U 2  and two current outputs I 1 , I 2  and two reference voltages Ud, Ucm and it controls I 1  and I 2  in such a way that U 1 −U 2 =Ud and (U 1 +U 2 )/2=Ucm. The control loop might look like this, however, there are many modifications possible. The circuit subtracts U 1 −U 2 . A transconductance amplifier TCd with high open loop gain compares this value with Ud. If U 1 −U 2 &gt;Ud then TCd outputs a large current into the current controlled current source CCCSd, which also outputs a large current (symbolized by the arrow at the upper end of the CCCSd symbol). The circuit also computes the average of U 1  and U 2 (=(U 1 +U 2 )/2) and TCcm compares it with Ucm. If (U 1 +U 2 )/2&gt;Ucm then TCcm outputs a large current into both current controlled current sources CCCSm, which output a large current. The wiring ensures that I 1 =I(CCCScm)+I(CCCSd) and I 2 =I(CCCScm)−I(CCCSd). As shortcut: if Ud=0V or Ucm=0V we simply skip it in the symbol. 
       FIGS. 16A-16C  show one example of how the differential feedback circuit  1500  can be used. In a 1 st  clock phase illustrated in  FIG. 16A , dFB 1  forces the potential Usup on S 1  and S 6  and dFB 2  forces 0V (=ground) on S 3  and S 4 . dFB 3  forces k*Usup on S 2  and S 5 , with k=0 . . . 1 (preferably 0.5). The current flows in the upper device from F 1  to F 3  and in the lower device from F 6  to F 4 . Thus the current passes underneath F 2  and F 5  in opposite directions. Therefore if F 2  and F 5  would be floating a By-field would cause the potential at F 2  to decrease and the potential at F 5  to increase. In the absence of magnetic fields the potentials at F 2  and F 5  would be at Usup/2, if the devices are symmetric. Usually they are not symmetric, because the thickness of the depletion layer at the boundary of the device depends on the reverse bias voltage, which is a function of the spatial coordinate. Therefore even in the case of vanishing fields and perfect geometric symmetry of all tubs the potential at F 2  and F 5  is not exactly 0.5*Usup but rather 0.4*Usup. This is why we may use the k-factor to account for this. 
     Note that instead of 0V (=ground) it may be advantageous to force a slightly higher potential (e.g. 0.2 . . . 0.5V) on S 3 , S 4 , because this requires even lower potential at F 3 , F 4  and in most systems voltages below 0V are not available. If we denote the positive supply voltage by Vsupp and the negative one by Vsupn, then the Hall effect terminals should be forced at Vsupn+k*(Vsupp−Vsupn)/2: e.g. Vsupp=1V, Vsupn=0.25V, k=0.45. The output signal is I 2 ′−I 5 ′. 
     In the 2 nd  clock phase ( FIG. 16B ) the only difference to the 1 st  clock phase is that Ucm of dFB 3  and dFB 2  are swapped. The output signal is I 3 ′−I 4 ′. 
     In the 3 rd  clock phase ( FIG. 16C ) the only difference to the 2 nd  clock phase is that Ucm of dFB 1  and dFB 2  are swapped. The output signal is I 1 ′−I 6 ′. Note that in all 3 clock phases there is no systematic raw offset (which means that at zero magnetic field and if there is no statistic mismatch between the two Hall regions and its contacts the output signals vanish at each clock phase). Alternatively F 2  and S 2  can be swapped as well as F 5  and S 5 . 
     Although several examples have been shown above where the feedback control circuits establish respective predetermined reference potentials (e.g., U 1 , U 2 , U 3 =1V, 0.5V, 0V, respectively in  FIG. 7A ), it will be appreciated that it is not necessary that the reference potential be predetermined. In other embodiments discussed below with regards to  FIGS. 17-19 , the reference potential can correspond to a dynamic potential on a sense contact, for example. 
       FIG. 17  shows a 5-contact device including force and sense contacts in accordance with some embodiments. A lower row of sense contacts S 1 , S 2 , S 3 , S 4 , S 5 , and an upper row of force contacts F 1 , F 2 , F 3 , F 4 , F 5  are shown. For purposes of simplicity a switching network is not shown, although the force contacts and sense contacts can be swapped, for example as described in previous embodiments. Feedback circuits FB 2  and FB 3  are the same as in  FIG. 14 , and the feedback circuit FB 1  is the same, except the lower current terminal is now connected to F 4  rather than ground. 
     In this arrangement, S 3  is clamped to a predetermined reference potential of +1.5V; while S 1  and S 5  are clamped to a predetermined reference potential of +0.5V, such that current flows into F 3 . Approximately half of the current into F 3  flows from F 3  in an arc shape below F 2  into F 1 ; while the other half of the current into F 3  flows from F 3  below F 4  to F 5 . Rather than feedback circuit FB 1  forcing a common mode potential at S 2  and S 4 , feedback circuit FB 1  forces the difference in potentials S 2 −S 4  to be zero (or some other predetermined value). Hence, unlike previous embodiments, the feedback circuit FB 1  works differentially between contacts  2  and  4 . That is, FB 1  senses the potential difference between S 2  and S 4  and injects a current into F 2  while extracting the same current out of F 4  so that S 2 −S 4  is zero volts (or some other predetermined value). The current may also have opposite sign so that current is extracted out of F 2  and injected into F 4 , depending on the process deviations and magnetic field applied. Because sense contacts S 2  and S 4  (rather than predetermined reference voltages from dedicated reference circuits) are used to provide reference potentials to FB 1 , it will be appreciated that feedback circuits can use dynamic reference potentials rather than predetermined potentials. 
     In  FIG. 18 , feedback circuits FB 3 A and FB 3 B force the voltage between S 2  and S 4  to zero. FB 3 A, FB 3 B each sense the voltage between S 2  and S 4 —but only block FB 3 A forces current to or from F 4  (but not into or from F 2 ) and only block FB 3 B forces current into or from F 2  (but not into or from F 4 ). Notably, the reference potential of FB 3 A is the potential measured at S 2 , which is not predetermined and which can vary dynamically. Thus, rather than the reference voltage used for the feedback circuits being a predetermined reference voltage supplied by a dedicated reference circuit (e.g., a band-gap reference circuit or voltage divider) providing U 1  to FB 1  in  FIG. 6 , the reference potential may also be supplied by the Hall device itself (e.g., from a sense contact). 
     In  FIG. 19 , FB 1  clamps the sense contact S 3  to predetermined potential of 1.5V and FB 2  clamps S 1  and S 5  to 0.5V. A differential feedback circuit dFB 3  is used to force S 2 −S 4  to a predetermined differential potential U d  of zero volts and to force (S 2 +S 4 )/2 to a predetermined common mode potential U CM  of +1V. ((S 2 +S 4 )/2 is the common mode potential of S 2 , S 4 ). Thus,  FIG. 19 &#39;s circuit forces not only the difference but also the common mode, whereas  FIGS. 17-18  force only the difference voltage. Another aspect of  FIG. 19  is that it shows how to use differential feedback circuits with a Hall device that has only a single tub. In comparison,  FIGS. 16A-16C  disclosed how to use differential feedback circuits with two-tub devices. 
     Although the invention has been illustrated and described with respect to one or more implementations, alterations and/or modifications may be made to the illustrated examples without departing from the spirit and scope of the appended claims. In particular regard to the various functions performed by the above described components or structures (assemblies, devices, circuits, systems, etc.), the terms (including a reference to a “means”) used to describe such components are intended to correspond, unless otherwise indicated, to any component or structure which performs the specified function of the described component (e.g., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary implementations of the invention. In addition, while a particular feature of the invention may have been disclosed with respect to only one of several implementations, such feature may be combined with one or more other features of the other implementations as may be desired and advantageous for any given or particular application. Furthermore, to the extent that the terms “including”, “includes”, “having”, “has”, “with”, or variants thereof are used in either the detailed description and the claims, such terms are intended to be inclusive in a manner similar to the term “comprising”.