magnetic-field-sensitive multicollector n-p-n transistors

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 1 , JANUARY 1982 83

Magnetic-Field-Sensitive Multicollector n-p-n Transistors

VICTOR ZIEREN AND BART P.M. DWNDAM

Abstract-A recently introduced type of magnetic-field-sensitive silicon microtransducer is described. These devices consist of a multicollector n-p-n transistor fabricated with standard integration techniques. The dependence of output signals on bias conditions, which influence the emitter and collector-current distribution, is analyzed theoretically for both two- and four-collector structures. These one- and two-dmen- sional vector sensors have been fabricated and tested. The experimental results are compared qualitatively with the theory.

Theory and measurements indicate that the two-collector structure gives a differential collector-output current, which is linearly proportional to a magnetic induction, applied along one axis only. Theory and measurements also indicate that the vector sensor gives output signals, which are a linear function of the two components of an in-plane magnetic-induction vector. Consequently, this device is capable of measuring the magnitude and direction of such a vector. .

B FL IC indices NA, s

NDepi 3 wepi a R Arc PH P B Pepi a, O

NOMENCLATURE = (B,, BY) flux-density vector. Lorentz force. Sum of collector currents = ~ Z E B(ase), C(ollector), E(mitter), S(ubstrate). Substrate doping (p-type). Epi-layer doping (n-type) and thickness. Common-base current gain. Relative output current per tesla, sensitivity. Current difference per collector pair. Electron Hall mobility. Average intririsic base resistivity. Epi-layer re,sistivity. Direction of B(O = @ t (7r/4), see Fig, 3).

I . INTRODUCTION

U P TO THE PRESENT, the ideal silicon magnetic-field sensor has not yet been made. Most problems encoun-

tered with silicon Hall 1C's deal with temperature instability, low dynamic range, or nonlinearity. An extensive review of the physics of the Ball effect and related phenomena is given in [ l ] . Basically, one can use the Lorentz force on moving charge carriers in two different ways, The first way is to use the Hall voltage generated in a semiconductor in crossed electric and magnetic fields, making the Hall coefficient the material property of interest. It depends on the concentration of free carriers and is magnetic-field dependent itself. The second way is to shortcircuit the Hall voltage and make use of the deflection of charge carriers, making the carrier mobility the

Manuscript received' April 2 1, 198 1. The authors are with the Department of Electrical Engineering, Delft

University of Technology, 2600 GA Delft, The Netherlands.

important factor. A well-known magnetoresistor like the Cor- bin0 disk uses this geometrical effect. However, it cannot be used in silicon because resistance changes with 0'. Even in strong fields this factor is too small.

This paper deals with a new type of magnetic sensor [2], 131, which makes use of the deflection effect by detecting current-flow changes in the collector region of a bipolar transistor. These magnetic-induction-sensitive transistors (so-called magnistors) were first described by Hudson 141, and their feasibility later proved by others [SI -[11]. All the devices described by these authors have two collectors. A magnetic induction causes an imbalance in the two collector currents. A drift-aided lateral p-n-p [ 6 ] , [ l l ] with the base merged in an n-type Hall plate uses the deflection of minority carriers injected into the base. It has a reasonable nonlinearity (NL) of 5 percent up to 0.3 T [6]. The sensitivities (71 in A/A * T = T-') are 0.07 [6] and 0.31 [ l l ] with a temperature coefficient (TC in percent per degree centigrade) of - 0.7 [6] and - 0.5 [ l l ] . A Hall element in [ l l ] gave -0.8 percent/'C. The DAMS [8] incorporates a Hall plate and a differential p-n-p stage, where a Hall voltage is directly converted into a difference in injection level between both emitters. It has a high y~ (0.50 T-') and a high NL (10 percent up to 0.2 T) due to the ex- ponential relationship between UBE and Zc. It is not made in a standard bipolar process. Another lateral p-n-p [ lo ] makes use of the Suhl or magneto-concentration effect and has a sensitivity of 0.018 T-' along an in-plane field axis. This axis is also used by Flynn [ 7 ] , who makes use of the deflection of majority carriers in the collector region of a vertical n-p-n transistor. Two bottom collector contacts are separated by a back- side groove, which makes this linear device essentially non- planar. Its 71 is 0.10 T-' . Thus the operating principle is not based upon Hall or Suhl effects nor upon current-gain variations.

The concept of this Flynn device was implemented in our planar device (Fig. 1) in which one can use standard bipolar technology to fabricate an n-p-n transistor with two (or four) collector contacts. These contacts are formed by buried n+ layers which have a "gap" just underneath a narrow emitter area. When electrons move in a direction perpendicular to the in-plane magnetic field, they will be forced sideways. Thus when this field points in the y-direction (Fig. l), the collector- current beam will be deflected to the left under the so-called Hall angle-that angle between the electric-field and current- density vectors. The deflection of electrons gives rise to a small collector-current difference. It will be shown later that this current difference is very linearly proportional to BY. The

0018-9383/82/0100-0083$00.75 0 1982 IEEE

84 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 1 , JANUARY 1982

4 A .

wBN i * J

! LC p - SUBSTRATE

~

c

Fig. 1. Cross section of a two-collector n-p-n transistor used to detect the magnetic-flux density B,,.

gap in the butied-layer diffusion is necessary to avoid shortcircuiting the contacts. It was found experimentally that a device with a continuous buried layer had a strongly reduced S/N ratio [3], Because the sensor has a magnetic-field-sensitive axis lying in the plane of the chip it is possible to combine two pairs of collectors around a central emitter. The resulting vector sensor has two output currents which are linearly dependent on the two components of a magnetic-field vector. Possible device applications include ignition control, current detection, position and angle detection, magnetometry, and electronic compasses (after increasing the S/N ratio). Combining the vector sensor with a Hall plate wbuld lead to a one-chip, three- dimensional sensor, which might be used in narrow gaps, etc. Because of the small active ardh the spatial resolution is better than that of Hall plates. This would facilitate small-distance gradient measurements.

A theoretical analysis is offered next, which describes the current-distribution phenomeha in the collector region under the following assumptions:

1) There is an infinitesimally small isolation between the buried collector layers. ,

2 ) There is no current spreading in the collector region. This means we treat collector current as a “beam.”

3) The emitter-current-density distribution can be nonuniform across the width of an emitter stripe or an emitter circle, due to current crowding caused by the high intrinsic base resistivity., Base-width modulation may change the crowding profile and the magnistor output signal(s).

4) Nonisothermal conditions will not be considered. In the experimental section to follow results will be given for

both two- and four-collector transistors in flux densities ranging from up to 1 T (= io4 G). Also included are noise, drift, and temperature-dependency measurements.

11. THEORY This section describes a theoretical model of the collector-

current distribution, and is based on the assumption that a magnetic-flux density B causes a linear displacement in the direction of the Lorentz force FL of a current “beam,” in the collector region.

Under the assumptions of an infinitesimally narrow isolation between the collector contacts and no collector-current spreading, the collector-curreht difference may be calculated by integration of the emitter-current density in a small zone. The width of that area is equal to the displacement of the beam at the contacts on the bottom.

EPILAYER

Fig. 2. Cross section of the collector-region model. The top electrode represents the emitter (-base) region, The two bottom collector contacts are separated by an infinitesimally small isolation. The current path is deflected in a magnetic field. The deflection length L is defined as the distance between the top and bottom electrodes.

A. Two-Collector Model/Stripe Geometry Fig. 2 shows the schematic cross section of the epitaxial

region of a two-collector transistor. It is assumed that the emitter, which is represented by the top electrode, has a stripe geometry. Stripe width and length are WE and L E , respectively. The nonuniform current-density distribution along this electrode is Jc = Jc(x). This distribution will be shifted in a magnetic induction B y by rotatidn with the Hall angle OH, which is defined by tan OH = ~ H B ~ , where p~ is the electron Hall mobility.

Only the shaded part of IC in Fig. 2 will reach collector 1, where it should flow toward collector 2 in the absence of By. The width of that shaded part is equal to the Hall displacement at the electrodes on the bottom: Ax = LphB,, where L is the distance between the top and bottom electrodes. It follows easily that

AI, = Z C ~ - IC* = 2LE &(X) dX. loAx (1)

1x1 the case of a uniform current distribution &(x) = Ic/W‘LE wt obtain

AI, = KIc ( 1 4

where K is the Hall displacement, normalized to wE/2

K = 2LpHBy (0 < K < 1). WE

Obviously, the current difference in a magnetic field is linear up to very high fields where K approaches 1 (By 2 W’/2 L ~ H implies saturation, AI, =IC). In our sensor it turns out that K < 0.1 when B y < 1 T. Equation (1) can also be used in the case of a nonuniform current-density distribution (under iso- thermal conditions), Such a distribution may be caused by emitter-crowding effects, like those described by Hauser [12], for the stripe-emitter geometry, The following assumptions are made in his model:

1) parallel and planar junctions, 2) no voltage drops in emitter region, 3) no surface recombination, 4) no base cofiductivity modulation (low injection), 5) a(CB current gain) is constant across the base.

In the case of two base contacts, one on each side of the

ZIEREN AND DUYNDAM: MULTICOLLECTOR n-p-n TRANSISTORS 85

emitter (see Fig. l), he obtained an emitter-current-density profile JE(x) =&(x, WE, LE, IE, Z ) , where x is defined in Fig. 2. The crowding parameter Z (0 d Z < n/2) is defined by

where VT = kT/e, p~ is the average base resistivity, WB is the intrinsic base width (between depletion layers), and ZE is the dc emitter current, applied in a common base configuration. His expression may be used with (1) and (2) to calculate AI,, where & ( x ) = cvJ' (x) . The result is given by

In the absence of crowding (2 * 0) (4) reduces to (la). The nonlinearity (NL) will be defined as the relative difference between

r 1 1

From (4) it follows that

For a fixed magnetic field (K) , NL increases rapidly for increased crowding (2). At K = 0.1 (B * 1 T) and 2 tan Z = 4, NL will be 0.53 percent.

Finally, the sensitivity of the two-collector/stripe-emitter geometry is obtained from (4) as the relative output current per tesla for small fields

It may be noted that this figure of merit for the two-collector transistor is strongly affected by heavily crowding, when 2 =$

1712. This means that under heavy crowding conditions the emitter injects at the edges only, thereby reducing the current (in the center of the emitter finger) that could be urged by a Lorentz force to pass on to another contact. Consequently, the sensitivity will be deteriorated. Further, it follows from ( 6 ) that it is favorable to have a thick epi-layer (large L ) and a narrow emitter.

As the crowding parameter Z is a function of the intrinsic base sheet resistance ~ B / W B , it is expected that the base-width modulation (Early effect) will influence the crowding. Hence, the sensitivity will decrease at higher collector-base voltages. A higher collector-substrate reverse-bias voltage will increase the depletion-layer thickness, which in the real device (Fig. 1) will decrease the effective deflection length in the epi-layer (Leff), thereby also decreasing the sensitivity.

B. Four-Collector ModelICircular-Emitter Geometry

When measuring two-dimensional fields, four buried n* layers are used in combination with a circular emitter-base geometry. The four layers have the shape of a circle sector and are shifted apart to avoid shortcircuiting, as is shown in Fig. 3, along with

Fig. 3. Schematic layout of the buried-layer pattern of a four-collector transistor used to detect two-dimensional in-plane magneticdux densities E. Also shown is the circular-emitter region.

Fig. 4. Normalized emitter circle (center point 0) and displaced collector-current profile (center point 0') projected to the same plane. Dis- tance between top and bottom electrodes is L . The horizontal and vertical axes through 0 represent the buried-layer separations.

the projection of the emitter. The positive direction of the applied magnetic flux-density vector B is referred to as 0, with 0 = @ t (n/4), where Q, is the angle between the x axis and B in Fig. 3 . In order to analyze the two-dimensional collector- current distribution, again under the assumptions mentioned earlier regarding gap and current spreading, we now have to deal with a vectorial shift in the direction of the Lorentz force FL. Fig. 4 schematically shows the emitter circle (with center 0) and the displaced collector-beam (center O'), both projected to the same plane. The distance between top and bottom electrodes is again L (see Pig. 2) . The vertical and horizontal axes (center 0) now form the separations between the four collector sectors, and 0 is still the same B direction as in Fig. 3. The Hall displacement is now 3 vector. All dimensions in Fig. 4 are normalized to the emitter radius RE and the absolute value of the relative-Hall-displacement vector K is (compare (2) )

In a way similar to the one-dimensional case the collector- current differences for both pairs of opposite collectors may be found 10 be

Arcx = IC, - I c ~ = 2 (Y( IH~ -t I H ~ )

Arcy = Icl - I c ~ = 2ff(IHA - 1 ~ ~ ) . (8)

86 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 1, JANUARY 1982

I H ~ and i H B are the emitter currents injected into the base within the two shaded areas, enclosed by the two coordinate systems as defined in Fig. 4 . The widths of these areas are KA = K sin 0 and KB = K cos 0, respectively. Assuming a circular symmetry of the current-density profile we only have to ac- count for the radial distribution: Jc = Jc(r) = aJE (Y), where Y is the radius normalized to RE. Using almost the same assumptions as Hauser [12], Rey [13] has given a solution to the emitter-current crowding effect in a transistor ofcircular geometry, for the case of a circumambient base contact. His base- current-density distribution can be used to calculate &(Y) = &(Y, RE, ZE, a). Here a is the crowding parameter, comparable to Z tan 2 in (3)

Note that a is independent of the emitter radius. The circular symmetry enables us to calculate the currents I H ~ and I H ~ in (8) as a general solution ( Z H ) for an area with width K . After- wards we substitute KA or K s for K .

where Y and cp are defined in Fig. 4 .

iE only Substituting JE(Y) in (10) we obtain a function of K , a, and

( K ) - - * 2n P G P + 4 (1 1)

with p = da(1 - K 2 ) t 4 , q = v'w. In the case of a saturation displacement K * 1 it appears that

IH(1, a) indeed has the upper limit IE/4, which means that all current from one sector is deflected to its counterpart.

Substituting KA and KB for K , we can calculateiHA andIHB. Thus

Arcx = ~ & ! ( I H ( K Sin 0, a) t IH(K COS 0, a))

Arc,, = ~ & ! ( I H ( K Sin 0, a) - IH(K COS 0, a)). (12)

This result describes the behavior of the collector-current distribution under crowding conditions and when a magnetic-field vector is applied, where its magnitude is represented in K (7) and its direction 0 is defined in Fig. 3.

In the absence of crowding (a * 0) and in case of small magnetic fields (K < 0.1) and when we substitute (a = 0 - (n /4) , (12) reduces to

where B, = ( B I cos Qi and By = IB I sin Qi (see (7)). Thus the output signals of the device are linearly proportional to the corresponding field-vector components. The sensitivity is defined in the field direction where one of the output currents

L - 41/2

CULAR GEOMETRY I L C O L L I

_____:

STRIPE GEOMETRY 12 C O L L I -

0 5 10 15 20

CROWDING PARAMETER a, ZfanZ-

Fig. 5. Normalized calculated sensitivities of circular and stripe geometries, plotted as function of the crowding parameters a and 2 tan Z, respectively.

has its maximum ((a = N (n /2) , N = 0, 1, * * *)

Note that the output current is now related to the total current per collector pair: Ic/2. Hence, with (1 1) and (12) the sensitivity for 0 = n/4((a = 0) is

with

The value of 7;" is lowered from 2 to 1 for value a increasing from 0 to 00.

For a * 0 it follows that the maximum obtainable sensitivity is

In Fig, 5, the normalized sensitivities of the circular and stripe geometries are plotted as a function of the crowding parameters a and Z tan 2, respectively. In the circular case, in (15) was normalized to p~ * (L /RE) , whereas in the stripe- emitter case, yI in (6) was normalized to pH * ( 2 L / w ~ ) . It is obvious that the four-collector structure compares favorably with the two-collector device (if WE = 2 RE), although the lat- ter might exhibit less crowding in a given technology and emitter current by possibly low WE/LE ratios (see (3 ) and (9)).

Due to nonlinearities in both Arcx and Arcy, deviations from ideal vector signal outputs will occur. For instance, when the sensor is used as a contactless angle detector, it is important to know the deviation angle A@, which is defined as the difference between the direction Qi of B and the direction of the electronic output-vector representation

A(a(K, (a, a ) = (a - arctan [:E: :::;I* Another important feature is the relative deviation of the


0 1 i 0 10 20 30 LO 50

J o

CROWDING PARAMETER a

Fig. 6 . Maxima of vector-output errors INLMoD~ and A@ calculated as a function of the crowding parameter a, with K = 0.1.

modulus of the electronic-output vector for the ideal (linear) sensor output. This type of nonlinearity is defined as

NLMoDW, a, a)

In Fig. 6, the maxima of (NLMoDI (in percentages) and A@ (in degrees) are plotted as a function of a, with K = 0.1. The minima occur for a = 2.6. When the calculated vector modulus is plotted as the radius of a polar diagram with @ as the angular coordinate, deviations from the ideal circle can clearly be seen. If a = 3, these deviations are negligible up to very high fields (= 10 T).

Clearly, it is favorable to have some crowding even though this means a lower sensitivity. Physically, the decrease in nonlinearity is caused by the fact that the emitter edge crosses the buried-layer gap between two neighboring collectors. Thus increased crowding will create a large edge contribution toIH (see Fig, 4), which compensates for the decrease of the current density in the emitter center. At even greater crowding an over-compensation will occur.

111. EXPERIMENTS In this section, some experimental characteristics will be

described of both one- and two-dimensional magnistors, which are fabricated with the parameters listed in Table 1. Fig. 7 shows the electronic-instrumentation circuitry, which (in its simplest form) consists of an adjustable dc emitter current sink and an op-amp current mirror connected to each collector pair. All collectors are kept at the same (reverse) bias voltage with respect to the base (UCB). The mirror provides, at its noninvert- ing input node, the differential current which is measured in the next stage. The vector sensor is connected to two similar circuits. Due to process tolerances (mask misalignments) offset output currents (when IBI = 0) are unavoidable. The most important cause is the shift which the buried-layer pattern undergoes on top of the epi-layer, as the emitter mask can only

Fig. 7 . Scheme of experimental one-dimensional detection circuitry. In the case of measuring two-dimensional magnetic fields, the four- collector sensor is used in combination with two similar current- mirrors and I/U converters.

TABLE I PARAMETERS OF FABRICATED TWW~OLLECTOR AND FOUR-COLLECTOR

SENSORS

w . = 9 . 5 UP. Xe = 1.9 L m ( e m i t t e r - end epl c o l l e c t o r - j m c t i o n

be aligned to the shifted pattern and not to the original mask. In order to restrict the shift, an SiH4 epi-layer was grown in- stead of our standard SiHC13 epi-layer. Nevertheless, an over- all misalignment of 1-3 pm was measured. For an emitter- stripe width of 20 pm, this results in an offset current of 10-30 percent of the emitter current.

However, a simple compensation of the offset is possible. The offset current is added to one of the collectors of a pair by means of an adjustable current sink. A problem related to the offset is the drifting o f the nulled output signal: larger off- sets result in larger drift. It is found that drift predominates over the noise when time periods of more than 5 min are considered. A typical short-term (2-min) disturbance level is 3 X

T, which would result in an SIN ratio of 60 dB for a signal of 30 mT. The equivalent rms noise is dependent on bias conditions and can be as low as 1 X IO-' T (between 0 and 2 Hz).

The temperature coefficient (TC) of the sensitivity (- 20 to 50°C) was measured to be - 0.62 percent/OC and is mainly due to mobility variation. This can be compensated on-chip by using an epi-layer resistor for the I /U conversion. The sensitivity variation of a Hall IC such as TL173 is given as + 5 percent (- 20 to 85OC), which is better, but already compensated. The NL of our devices was measured up to 1 T and is smaller than 0.5 percent. This compares very well with Hall IC's (1-2 percent in a smaller range) and other two-collector devices. The average value of y~ at low U& ranges from 0.03 to 0.05 T-l , which is less than y~ of the DAMS [8] and the p-n-p of [ l 11 (see Introduction).

88 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 1 , JANUARY 1982

I ‘w 15

1

I T = 3 0 0 K I I I

G I I 0 10 20 28

u,, IVl - Fig. 8 . Measured two-collector sensitivity versus UCB, at Ucs = 5 V,

for various emitter currents.

A. Two-Collector Magnistor The early devices of the two-collector magnistors have a

20-pm-wide emitter stripe (140 pm long) within a 30-pm-wide base region. Unlike Fig. 1, the base is contacted near both short emitter edges. Fig. 8 shows the measured sensitivity ( T ~ ) of this type as function of G B , with the emitter current as a parameter, whereas UCS equals 5 V. Typically, an increase in UcB causes a decrease in sensitivity. According to the theory, it is very likely that this is caused by an aggravation of the crowding, which is a consequence of the narrowing of the effective base width. When 1, exceeds 5 mA, a sensitivity falloff is measured if UCB is decreased below 1 V. Due to the high collector series resistance the collector-base junction becomes forward biased and an excess base current is injected into the collector. This might cause increased crowding and, consequently, the sensitivity would be deteriorated.

An increase in UCS causes an additional decrease in sensitivity, which is ascribed to the expansion of the collector-substrate depletion layer into the epi-layer. This expansion causes a decrease in the deflection length L . For instance, at 1, = 5 mA, the sensitivity decreased by about 0.23 percent/T when U& was increased from 2.5 to 20 V. The decrease in the absolute differential output current after such a step in UCS was found to be independent of UCB. The measured nonlinearity was smaller than 0.5 percent in flux densities up to 1 T.

When the formulas of the theory section are used with the parameters of Table I, sensitivities about 2.5 times larger than the measured data are calculated. This discrepancy can be explained by comparing the buried collectors of the real device (Fig. 1) with the simplified construction of Fig. 2. Due to the wide gap, the collector-current beam will be spread. In addition, the buried layer will cause an autodoping ofthe epi-layer during the epitaxial growth. As a consequence, the deflection length L will, effectively, become shorter, resulting in Leff <L. Leff is the effective deflection length, and is a function of the effective gap between the buried layers, of U& and of the “updiffusion,” d ~ , during epitaxy. The effective gap width is smaller than WBN because of the lateral outdiffusion of the buried layers dl (see Fig. 1). Regardless of the factor 2.5, the

TABLE I1 MEASURED TWW~OLLECTOR SENSITIVITY VERSUS GAP WIDTH

e p i w .

epl TI ( 2 - c o l l . )

( u r n ) (ncm) (u rn ) ( % T - ’ )

0 (no gap) 0.85 9 . 5 .o .6

10 1.6 12 2.71

15 1.6 12 4 .a 20 1.0 12 3.93

30 1.8 12 3.73

40 0 .85 9.5 2.92

no buried 0.85 9 . 5 l a y e r

1.45

theory indeed predicts almost the same numerical sensitivity falloff as that which is measured.

The influence of WBN on L,ff, and hence, on the sensitivity, is investigated next. Table I1 gives the measured sensitivities yr for devices with different gap widths WBN, together with the epi-layer properties pepi and Wepi. Four devices (W’N = 10, 15, 20, and 30 ym) have a layout like that of Fig. 1 and are fabricated on a thicker epi-layer with a higher resistivity (larger Hall mobility) than the above-mentioned device, in order to increase the sensitivity. The data are measured at 1, = 5 mA, UCB = 5 V, and U& = 5 V. The effect of a continuous buried layer or its omission [3] is also listed. The optimum gap width is about 15 pm, where W’ equals 20 pm. If WBN < 15 pm, the contacts might be shortcircuited. Furthermore, Leff is reduced by the updiffusion. If WBN > 15 ym, Leff will decrease because of collector-current spreading.

B. Four-Collector Magnistor

The experiments with the four-collector vector sensor were performed with a rotatable pair of field coils, with the sensor centered on the axis of rotation. The maximum obtainable flux density is about 45 mT. In the higher field regions (up to 1 T) only one-dimensional measurements were done. The sensitivity, as defined in (14), was measured at UCS = 5 V at var- iable I, and UcB. The results are plotted in Fig. 9. At low currents ( 1 ~ < 10 mA), the sensitivity decreases just as in the two-collector device. In conformity with the theoretical pre- dictions, the vector sensor shows a higher output level. At current levels I‘ 2 3 mA the sensitivity falloff for low UcB can be explained, just as in the two-collector case, by a saturated forward-biased CB junction. Fig. 10 shows the measured curves of the base current 1, and substrate current 1s (definition in Fig. 1) versus U&, at UCS = 5 V. The curves labeled “a” are measured at I, = 5 mA and show that Is is nonzero (negative) only when UCB < 0.5 V, whereas IB increases with decreasing UCB. Apparently, the holes, injected from the base, are col- lected by the substrate. For U& increasing beyond 0.5 V, I, will drop, due to rising current gain. The “dip” in the 1, curve is yet to be explained. The curves labeled “b” are measured at IE = 20 mA. In the low voltage range we again encounter the same performance. However, the higher current level causes


Fig. 9. Measured four-collector sensitivity versus UCB, at Ucs = 5 V, for various emitter currents.

-. 0.5 I 1 5

‘i - 0 3 1

0 10 20 30

u,, IVl 7 Fig. 10. Measured substrate and base currents of the vector sensor,

versus UCB, at Ucs = 5 V and ( a ) IE = 5 mA (left axis), ( b ) 1~ = 20 mA (right axis).

the crossover point t o shift to a higher value: Is < 0 when U& < 4.5 V. When UcB is increased (>6 V), Is will become positive, The high epi-layer resistivity apparently causes a forward-biased substrate-collector junction when the BC depletion layer expands downwards. In turn, the base will collect the injected holes from the substrate, the net base current will decrease, and, finally, at UcB = 9 V even become negative! This reversed IB causes a reversed crowding, which implies that JE now has its peak value in the center of the emitter circle.

Returning to Fig. 9, this must be the explanation of why the sensitivity suddenly stops decreasing and rises rapidly with increasing UCB. In fact, we have, under these circumstances, an n-p-n-p structure with a complicated current flow. The current- density profile contracts itself into a “current filament” or “carrier domain” [ 141, [ 151. Although under these bias conditions, the sensitivity may even be blown up to 16 percent/T, the stability of the device gets worse, resulting in a nearly unaltered resolution.

Summarizing, there are three distinctive regions, namely the saturation, normal, and reversed-crowding regions for low,

moderate, and high UcB, respectively. At low I, the reversed- crowding region might be absent, just like the saturation region at still lower IE.

Vectorial measurements indicate a perfect behavior at least up to 45 mT. The rotation of a constant magnetic-flux density yields a regular circle on an XY plotter. The nonlinearity is smaller than 0.3 percent at 1 T.

IV. CONCLUSIONS Based upon the same operating principles as the device of

Flynn [7], a planar type of magnetic-field-sensitive transistor has been described which can be made sensitive to either one or two directions of a magnetic-induction vector. The one- dimensional as well as the two-dimensional device has been built and tested. The multicollector transistors provide output signals which are linearly proportional to the components of a magnetic-induction vector (NL < 0.5 percent when IB I < 1 T). This linearity is confirmed by a theoretical collector- region model, which incorporates a nonuniform current-density distribution. This nonuniform distribution is caused by emitter- current crowding and it is shown, that increased crowding may result in decreased magnetic sensitivity and linearity. Measure- ments indicate that an increase in UCB causes a base-width narrowing which, in turn, results in more crowding and, indeed, in lower sensitivity. In spite of the simplification of the collector structure, the model can be used to optimize most of the multicollector transistor parameters. The devices can be fabricated in standard, bipolar technology without critical steps.

ACKNOWLEDGMENT The authors wish to thank Prof. S. Middelhoek for his sug-

gestions and useful comments during this work, P. K. Nauta and E. Smit of the Delft University Integrated Circuit Work- shop for fabricating the devices and helpful discussions, and S. Kordic for performing the temperature-stability measurements.

REFERENCES [ 11 A. C. Beer, “The Hall effect and related phenomena,” Solid-State

Electron., vol. 9 , pp. 339-351, 1966. [2] V. Zieren, “A linear magnetic-field-sensitive silicon micro-trans-

ducer,” presented at the 10th ESSDERC, York, United Kingdom; also in Europhysics Con$ Abstr., vol. 4H, pp. 33-34, Sept. 1980.

[ 31 -, “A new silicon micro-transducer for the measurement of the magnitude and direction of a magnetic-field vector,” in IEDM Dig. Tech. Papers, (Washington, DC), pp. 669-672, Dec. 1980.

[4] E. C. Hudson, Jr., “Semiconductive magnetic transducer,” U.S. Patent 3 389 230, 1968.

[5 J R. H. Cushman, “Transistor responds to magnetic fields,” EDN, pp. 73-78, Feb. 1969.

[6] L. W. Davies and M. S. Wells, “Magneto-transistor incorporated in an integrated circuit,” Proc. IREE Australia, pp. 235-238, June 1971.

[7] J. B. Flynn, “Silicon depletion layer magnetometer,” J. Appl.

[8] S. Takamiya and K. Fujikawa, “Differential amplification magnetic sensor,” IEEE Trans. Electron Devices, vol. ED-19, no. 10,

[9] I. M. Vikulin et al., “Investigation of the characteristics of a two- collector magnetotransistor,” Sov. Phys.-Semicond., vol. 8, no. 3, pp. 369-370, Sept. 1974.

[ l o ] I . M. Mitnikova et al., “Investigation of the characteristics of silicon lateral magnetotransistors with two measuring collectors,” Sou. Phys.-Sembcond., vol. 12, no. 1, pp. 26-28, Jan. 1978.

[ 111 L. Halbo and J. Haraldsen, “The magnetic field sensitive transis-

Phys., V O ~ . 41, pp. 2750-2751, 1970.

pp. 1085-1090, Oct. 1972.

90 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 1, JANUARY 1982

tor: A new sensor for crankshaft angle position,” presented at Soc. of Automotive Engineers, 1980 Congress and Exposition, Detroit, MI, Feb. 1980.

[12] J. R. Hauser, “The effects of distributed base potential on emitter-current injection density and effective base resistance for stripe transistor geometries,” ZEEE Trans. Electron Devices, voi.

[13] G. Rey, “Effets de la dhfocalisation (c.c. et c.a.) sur le comporte- ED-11, pp. 238-242, 1964.

ment des transistors i jonctions,” SoEidState Electron., vol. 12,

[14] G . Persky and D. J . Bartelink, “Controlled current filaments in PNIPN structures with application to magnetic field detection,” Bell Syst. Tech. J., vol. 53, no. 3, pp. 467-502, Mar. 1974.

[15] M. H. Manley and G. G. Bloodworth, “The carrier-domain magnetometer: A novel silicon magnetic field sensor,” Solid-state andElectron Devices, vol. 2, no. 6 , pp. 176-184, Nov. 1978.

pp. 645-659,1969,

An MOS Device for AC Measurement of Surface Impedance with Application to Moisture

Monitoring STEVEN L. GARVERICK AND STEPHEN D. SENTURIA, MEMBER, IEEE

Absrract-A surface impedance measurement (SIM) device fabricated using a metal-gate n-channel depletion-mode MOS process is reported. The device serves as the basis of an ac instrumentation system for the measurement of sheet resistances as high as 10l6 a/square in the frequency range 1 Hz t o 10 kHz. Results are presented illustrating the use of the device as a moisture monitor.

S I. INTRODUCTION

URFACE impedance measurements are employed in a variety of applications, such as moisture sensing [ l ] -[4].

Techniques for these measurements are typically based on sensing the current between an interdigitated electrode pair. The electrodes may be coated with a thin film whose electrical properties are to be measured, or the device may be left un-

Manuscript received May 27, 1981; revised August 18, 1981. This paper was supported by the MIT-Industry Polymer Processing Program. Devices were fabricated in the Microelectronics Laboratory of the MIT Center for Materials Science and Engineering, supported in part by the National Science Foundation under Contract DMR 78-24185. Poly- mers and facilities for the moisture measurements were provided under programs supported in part by the Office of Naval Research and by the National Science Foundation.

S. L. Garverick was with the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cam- bridge, MA, 02139. He is now with the MIT Lincoln Laboratory, Lexington, MA, 02173.

S. D. Senturia is with the Department of Electrical Engineering and

MA, 02139. Computer Science, Massachusetts Institute of Technology, Cambridge,

coated, in which case the surface of the substrate on which the electrodes are fabricated serves as the conducting path between electrodes. Since sheet resistances as high as 1Ol6 a/ square are often encountered [5], direct measurement of this current requires an electrometer and careful attention to guarding and shielding. Furthermore, the slow response times of typical electrometers limits the experiment to dc conditions, in which case electrode polarization and space-charge effects can become important.

The surface impedance measurement (SIM) device presented here allows ac measurement of sheet resistance at frequencies in the range 1 Hz to 10 kHz, and exhibits good sheet resistance sensitivity in the range lo9 to 10’6 a/square [ 6 ] .

The SIM device combines a guarded interdigitated electrode pair with a depletion-mode n-channel MOSFET (Figs. 1 and 2) . One electrode (the floating gate) is connected to the gate of the FET; the other electrode (the driven gate) is available externally. The device has four terminals: source, drain, driven gate, and substrate. A voltage signal applied to the driven gate results in current flow between driven and floating gates. Because the floating-gate-to-substrate capacitance is small, even small interelectrode currents can produce substan- tial changes in the floatinggate voltage. This voltage change is evidenced by a change in the channel conductance of the FET, which is monitored with the aid of an on-chip reference FET, as described in Section 111. Depletion-mode devices are used in this device so that no dc bias is required on the floating

0018-9383/82/0100-0090$00.75 0 1982 IEEE

magnetic-field-sensitive multicollector n-p-n transistors

Documents