modelling of split-drain magnetic field-effect transistor (magfet)

Sensors and Actuators A 49 ( 1595) 155-l 62

Modelling of split-drain magnetic field-effect transistor (MAGFET)

Jack Lau, Ping K. Ko, Philip C.H. Chan Department of Electrical and Electronic Enginerring, The Hong Kong University of Science & Technology, Clear Water Bay, Hong Kong

Received I1 January 1995: accepted 17 May 1995

Abstract

By simply splitting the drain of a conventional MOS transistor into two, we can convert the transistor into a magnetic sensor. The ease of integrating split-drain magnetic field-effect transistprs (MAGFETs) in conventional CMOS technology and the potential of sensing small magnetic fields have fascinated many researchers. Yet many parameters, such as the maximum sensitivity and biasing dependence of the device, are not yet known. In this paper, we describe a model for the split-drain MAGNET. The model shows that the sensitivity of the sensor is primarily a function of the roll-off of the induced Hall potential in the channel and that the contribution due to channel inversion charge redistribution is very minor. The model also shows that the magnetic-field signal in terms of A&/Z,, is insensitive to geometry, linear to magnetic-field strength and affected by the gap between the two drains. Furthermore, we show that the sensitivity is typically limited by the Hall mobility, insensitive to operating regions and attributed to saturation voltage shifts in the saturation region. A maximum sensitivity of less than 5.8% T- ’ is predicted. The development of the model is assisted by computer simulations and verified by experimental results.

Keywords: Magaetic-field sensors; Mcdelling; Split-drain MAGFBTs

1. Introduction

When the drain of a MOS transistor is split into two, the transistor can act as a magnetic-field sensor. Application of a magnetic field perpendicular to the device causes an imbalance of current between the two drains (Fig. 1). The acronym MAGFET, which stands for magnetic field-effect transistor, is often used to refer to this kind of MOS magnetic sensor [I]. The sensitivity of the split-drain MAGFET has been shown to be limited by the 1 lfnoise of the MOS transistor, making it suitable for sensing low magnetic fields [2]. At this level of sensitivity, the split-drain MAGFET is suited for applications such as non-contact switching, current measure- ment and magnetic memory readout [ 31. The MAGFET is made more attractive for the applications mentioned above because integrating the MAGFET on a chip with complex signal-processing circuitry requires no modification of the standard MOS fabrication process. Experimental results showed that the sensitivity of the MAGFET is highly linear. Recently, Kub and Scott have shown a modified split-dram MAGFET with a sensitivity as high as 18.5% T- ’ [ 41. A split-drain MAGFET has also been demonstrated in a CMOS integrated duty-cycle oscillator [ 51.

Until now, no complete analytical model has been developed to describe the operation in both linear and saturation regions. The important questions about the maximum theo-

09244247/95/$09.50 Q 1995 Elwier Science. S.A. All rights reserved SYDfO924-4247(95)01025-V

retical sensitivity and how it depends on the device structure, dimensions and biasing conditions remain unanswered. In this paper a complete model is described. lbe maximum attainable sensitivity is also assessed. The development of the model is assisted by computer simulations and verified by experimental results.

2. Linear region

2.1. Definition

The sensitivity of the split-drain MAGFET can be char- acterized by the fraction of drain current changed under the influence of a magnetic field. The sensitivity of a split-dram MAGFET is normally defined as

S=AZ,l(z& (1)

where AZ, is the difference between the two drain currents, Z, is the total drain current andB is the strength of the magnetic field.

2.2. Model development

When a magnetic field is applied to the MAGFET, a Lor- entz force perturbs the distribution of inversion charges along

156 J. Lou et al. /Sensors and Actuators A 49 (1995) 155-162

A A A h h

When B >o, V V V v ”

Id1 > Id2

I Drain2 / I/ . I /

Fig. 1. Split-drain MOS transistor as a MAGFET.

the channel. Charges are swept across to the side, building up a Hall voltage. Equilibrium is achieved when the Lorentz force is balanced by the Hall voltage. Near the source and the drain regions, however, the source/dram contacts force an equipotential surface, short-circuiting the Hall voltage to zero at both ends. As a result, while no deflection occurs in the middle of the channel, deflection is possible at the drain where the effectiveness of the Hall voltage to balance the Lorentz force is lessened. In addition, the lowering of the Hall voltage from a maximum value near the middle of the channel to zero at the drain helps create a new electric field that increases the carrier velocity. Therefore, the imbalance of current observed at the split drain can occur due to an imbalance of charges, a change in carrier velocity or a combination of both effects. The quest for a model hinges on determining which effects are responsible for the sensitivity.

In developing the model, we shall first assume that the gap between the two drains, A W, as defined in Fig. 1, is zero. We shall amend the model for non-zero drain gap later. We also assume that the device is N-channel. A P-channel device can be formulated in a similar manner. We consider the case of small V,, only. When there is no magnetic held (B = O), the drain current can be expressed as

WI2

IdI= Cm(Vg-V,-&b)~O~ I

(2)

0

where Id, is the current flowing into drain 1 (Fig. 1 ), C,, is the gate oxide capacitance, V, is the gate voltage, V, is the threshold voltage at the source, a is the body-effect coefficient as described in the BSIM model, & is the channel potential and u,, is the carrier drift velocity [ 63. When a magnetic field is applied to the device, the Hall voltage, V,, helps accumulate electrons on tbe side of drain 1 (Fig. l), lowering the channel potential on that side of the device at the same time. Due to short-circuit effects at the source and the drain, V,, reaches a maximum somewhere along the channel and is at a minimum at both source and drain. V,, changes the channel potential and induces a lateral field, which helps increase the carrier

velocity for I,,. The current in drain 1 under magnetic field can be expressed as

WI2

IdI'= Co,[Vg-V,-a(c&-V,)] uo+p2 dx

I c 1 (3)

0

where Id,’ is the drain current under the magnetic field. On the side of dram 1, V,, not only increases the amount of inversion charges but also the drift velocity. Expanding Eq.

(3), we have

WI2

Id]'= C,x(V,-Vt-a~O)uOdr I 0

WI2

+ C,,(V,-V,-a4,)cL(dV,/dy) dx I 0

WI2

(4)

While the first term represents the drain current when B = 0, the second term accounts for the extra current due to the additional lateral field. The third term accounts for a change in total current due to an increase in mobile charge, C,,uV,,. Using the symmetry argument to deduce I2 and 12’ and substituting Eqs. (3) and (4) into Eq. (I), we obtain

S=Sl+S2+S3

where

(5)

s1 = 21,w’2C,xWB- V,-a4)~(WJdy) dx 2#‘2C,,( vs - v, - a&) ug dX

(6)

(7)

l:‘2C,&,jGdVJdy) h

S3= 2@‘2C,,(Vs-V,-al#&J,d.x (8)

To determine the sensitivity, we are mostly interested in the current flow near the drain. After all, it is at the drain that we are about to detect the current difference. Because of the short-circuit effect, V, quickly ramps down from a maximum of typically a few millivolts to zero at the dram. V,, is small near the drain, especially when compared to Vs - V, - a&,. Therefore, the mobile charges represented can be assumed insignificant; S2 and S3 are ignored. Then

S=Sl (9)

2.3. Numerical simulations

The model hinges on how rapidly the Hall voltage rolls off near the drain, namely the value of dV,/dy. An insight with regard to dVJdy can be gained through computer simulation.

1. Lau t-t al. /Semors and Actuators A 49 (1995) 155-162 157

Since no commercially available device simulator considers magnetic field, we develop a finite-difference simulator using both symbolic and numerical tools similar to that developed by Nathan and Baltes [ 21. We discretize the device into 2500 nodes. The governing simulation equations are derived from basic semiconductor physics:

J.=q(/.&nE+DVn) -rCln(JnXB) (10)

Here p” denotes the drift mobility, n the carrier density, E the electric field, D, the diffusion constant and r the Hall scattering factor. Diffusion is of lesser significance in MOS operation and is neglected. Furthermore, in our context, the magnetic field is applied externally perpendicular to the surface of the device. We can solve Eq. (10) and get

(11)

Eq. (9) is solved throughout the device. At the source and the dual drains, the equal potential condition is imposed due to ohmic contacts. Based on the relationship in Eq. ( 1 l), we can solve for the current-density equation at all nodes. The result is a set of 2500 non-linear equations:

A-v=0 (12)

where A is a 2500 X 2500 matrix and Y is the voltage at all nodes. Eq. (12) is solved by applying the Newton-Raphson iteration, which states that v can be solved by linearization and iteration:

$Al.n%+,-v.)_ -AIvnv, (13)

where v, and v,, + , are nodal voltages of present and subse- quent iteration steps. Rather than using a numerical tool to solve the Jacobian equation, dAldv, we compute the Jacobian matrix using a symbolic computation tool. By using a symbolic computation tool, we are able to preserve precision during linearization. The symbolic output is then translated into standard programming language for numerical compu- tations. b is taken to be 670 cm2 V-’ s-l, a is 1.92 and V, is 0.7 V. These numbers are consistent with the 2 pm N-well Orbit Foresight [ 71 process with which we ultimately fabricated our device. TCL,B is set to be 0.2, to be consistent with the low-field requirement in order for relation ( 10) to hold [ I]. A typical value of r is between 1 and 2 [ 1,2,9]. Simu- lation results indicate convergence down to 5.67 nV [ 81.

The Hall potential profile of a 100 pm X 100 pm MAGFET is shown in Fig. 2. The device is simulated using V, = 2.5 V and V,,= 1 V. In Fig. 2, the Hall potential of the device is plotted with respect to the left edge of the channel. A four- point piecewise linear model can be applied to model the profile as shown in Fig. 2. Because of the short-circuit effect, the Hall voltage is kept at zero at the source. It reaches a value that is proportional to the carrier velocity as it is further away from the source (point B). From this point, it increases grad- ually since the carrier velocity itself increases. The rise con-

Fig. 2. Computer simulation of a channel profile. Here, the potential of a unity ratio device is plotted with respect to the left edge of the channel under the influence of a magnetic field. A four-paint linear model cau be applied to approximate the profile. a, the Hall voltage roll-off distance, is shown.

tinues until it reaches an overall maximum (point C) , Due to the short-circuit effect again, the Hall voltage beings to roll off until it reaches zero at the drain. The distance between point C and the drain is denoted by a new parameter a. The piecewise linear model overestimates the Hall profile, which is actually parabolic. A correction factor is introduced to compensate the overestimation.

With this simplification, we realize that V, is a function of both x and y:

v x dv,,,hmnx_ dy WCX (14)

where V,,, is the maximum Hall voltage attainable, W is the channel width, a is the roll-off distance and m is a constant compensating for the overestimation due to the linear model. For a simple Hall plate, it can be shown that

V ,,_ = rWv$G (15)

where r, the Hall coefficient, is added to take the Hall scattering effect into account and G is a geometric factor that depends on the length, L and the width, W. Substituting Eqs. (14) and (15) into Eq. (9), we obtain the sensitivity as

s= ‘Cc??!!!-__ G

4 L (CYlL) (16)

2.4. Maximum sensitivity

One important question about a sensor is its maximum sensitivity. With r and p being intrinsic physical constants, Wand G being geometrically dependent, the maximum sensitivity can be calculated if a is determined.

An insight into a is sought by using the simulator developed in Section 2.3. The Hall profiles for several devices with variable aspect ratios are shown in Fig. 3. The maximum Hall voltage is increased either by reducing the channel lengths or by increasing the channel widths. As the length of the device is reduced, the carrier velocity increases, raising the Hall voltage. Because of a lesser inversion charge density near the drain than the source, the short-circuit effect is less severe

158 1. Lau et al. /Smors ad Actuators A 49 (1995) 155-162

Fig. 3. Computer simulation of Hall voltage for different aspect ratios but the same length.

Table 1 Summary of computer simulation results

W/L Cdl. G G(W/L) - EN

Cdl,

101200 0.02 1 2.5 20/200 0.04 1 2.5 40/200 0.08 1 2.4

200/200 0.17 0.42 2.4 400/200 0.20 0.31 3.0 8001200 0.22 0.20 3.6

near the drain. Therefore, the peak of the Hall profile appears closer to the drain than to the source. As the maximum Hall voltage is increased by either increasing the channel width or reducing the channel length, the distance between the drain and the peak Hall voltage increases. This is consistent with intuition, since a reduction of channel length or an increase in channel width worsens the short-circuit effect.

Using a new variable K to denote G( W/L) / (a/L), we rewrite the sensitivity Eq. (16) as

mw S=TK (17)

The sensitivity reaches a maximum when K reaches a maximum. The results from computer simulations assert that a/L

is related to the aspect ratio, W/L, of the MAGFET. For a long-channel device, G is equal to one, and the ratio between a/L and W/L is constant (Table 1). As the channel length begins to decrease, W/L increases faster than a/L. Yet, at the same time, G decreases due to the short-circuit effect. There- fore, while an increase in aspect ratio increases W/L, G is reduced. Maximum sensitivity occurs when the two factors are balanced. G( W/L) becomes a constant of about 0.7 after W/L becomes two or more [ lo]. At W/L = 2, K is 3.6. Sub- stituting this value into Eq. ( 15)) we predict that the maximum sensitivity achievable by the split-drain MAGFBT is

L = 0.9mq.k (18)

Fig. 4. The introduction of a drain gap distolts the potential profile: (a) potential profile of a 100 pm/ 100 pm MAGFET without any drain gap; (b) pmfile of the same device but with a 60% drain gap.

2.5. Drain-gap effect ana’ model refinement

In the above derivation, we have assumed that the gap between the two drains is zero. Using the same simulator we have developed, we observe how the drain gap affects the Hall voltage profile. Fig. 4(b) shows a three-dimensional simulation plot of channel profile with a 60% drain gap. By pulling down the potential near the gap, the drain gap has an overall effect of lowering the Hall voltage as well. Simulation results indicated that Eq. (16) should be appropriately modified to include the drain-gap effect. The drain-gap effect can be seen as affecting the geometric factor [ I 11. A curve-fitting parameter, d, is used to denote the drain-gap degradation:

+~!I!!! 4 L ?iY++%q (19)

where d is the drain-gap degradation factor, A W is the size of the drain gap and W is the device width.

3. Saturation region

As V,, increases, the device comes close to saturation. Unlike operation in the linear region, the carrier velocity

J. Lau et al. / Stmors and Actuators A 49 (195’5) 155-162 159

reaches saturation when the charges approach the drain and remains unchanged afterwards. Thus, the Hall voltage also remains unchanged beyond the saturation point [ 11. At the saturation point, when the device is in saturation and under no magnetic field, based on the Sodini, Ko and Moll model [ 121 we get

Id, = v,, !! 2 C”X ( V, - v, - V&a,) (20)

where v,, is the saturation velocity and V,, is the saturation voltage. When the device is placed under magnetic field, the Hall voltage adjusts the entire channel potential. The current at drain 1 becomes

Id,‘=v/ 2 C,X( V, - V, - Vds,l) (21)

While a total Hall voltage of V,, spans across the channel width from + VJ2 at one end to - Vi,/2 at the other end, the average Hall voltage each side experiences is T&, where 1) is between 0 and 0.5. The point at which the channel potential reaches the saturation voltage on the side of drain 1 becomes

V &at) = V&at - ~Vllsat (22)

where V,,,,, is the Hall voltage near the saturation point. Sub stituting Eq. (22) into Eq. (21), we get

Id,‘= %I ; C.X( v, - v, - vd,at) + vs~ 4 cox?lvh,, (231

The first term in Eq. (23) is just the saturation drain current when no magnetic field is applied. The second part is the additional current. Therefore, applying the definition of sensitivity as in Eq. (1) and based on symmetry, we derive

s= 17VllUll

v, - v, - vd,,

V,,,, is (see Appendix A)

vhs, = V~,rcLG ;

Including the drain-gap effect, we obtain

(24)

w

c+ WctatvGWL) ( vg - K - vdm>

(26)

4. Experimental results

Experimental devices were fabricated in a 2 w CMOS N-well process using the Orbit Foresight process [7]. The packaged devices are placed under a large electromagnet. Magnetic field is monitored with a hand-held Hall probe capable of sensing down to 1 G. These devices consist of three groups: unity ratio (W/L= l), same length and same width. To minimize the geometric factor due to the shortening of the Hall voltage at the drain and source electrodes, the

25

I(a)

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

W&c FM ma

0.i 0.1 0.2 hia@&d&)

03 0.6

Fig. 5. Linearity of the Hall sensitivity operating under (a) linear region (V~=lV.Vs=5V),aad(b)saturationregion(V,=5V.V,=5V).

devices with the same length and same width were made very long. In addition, these non-unity devices maintain ratios of l/5,1 / 10 and l/20 for meaningful comparison. All devices have a drain gap of 4 pm. Fig. 5 shows the sensitivity in both linear and saturation regions. The measured result is shown in Table 2.

4.1. Linear region

Experimental results show that the devices with W/L of 20/100,20/200 and 20/400 have a sensitivity of 2.85,2.91 and 2.862, respectively, in the linear region. As predicted by Eq. ( 19) and the numerical simulation. long devices with the same width suffer from the same drain-gap degradation and have similar values of K. Thus, these devices should have a similar sensitivity, as shown experimentally. The drain-gap effect is more visible among the unity devices (W/L= lO/ 10,5O/SO and lOO/ 100). With the same K, the difference in degradation is attributed to the drain-gap factor, d. From these

160 J. Luu et al. /Sentort and Actuators A 49 (1995) 155-162

Table 2 Table 3 F!xperimeotal results (Vd,=l V, V,=5 V and V&=5 V, V,=S V) and model predictions

Maximum sensitivity achieved by other xsearchers

W/L S (linear) (a0 T-‘)

S (saturation) (% T-‘)

S (our model) (% T-‘)

IO/10 1.8 1.7 1.8 50150 3.1 3.2 3.5

loO/lc+l 3.1 3.8 3.1 20/100 2.9 3.0 3.0 201200 2.9 3.1 3.0 20/4&I 2.9 3.0 3.0 10/200 1.2 1.1 1.7 20/200 2.1 3.0 3.0 40/200 3.5 3.8 3.6

lP04 , a

14 (b)

:

-41 I , , , 1 2 2.2 2A 2.6 2.8 3.0 3.2 3.4 3.6 3.8 40

V&

0.01 , , I I 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 40 45 5.0

Vds

Fig. 6. (a) I-V curve for one of the drains of a 20/ 100 device under the influence of magnetic field. As the magwic field increases, the drain current decrwses. (b) Output resistance vs. V, plot for deducing VW V,, is shown to increase as a magnetic field is applied. The increase in V, corresponds to the decrease in drain current.

experimental devices, d is found to be 1.2. The drain-gap degradation also has an important effect for devices with W/L of 40/200,20/200 and 101200. The sensitivity of the 40/200 device is almost twice that of the lo/200 device. m is found to be 0.5.

Reference S V, V, W L

(a) (run) (lun)

[I31 4 3 3 loo 100

[ 141 4.5 3.5 3 100 100

1151 1.51 1 1.5 4 16

1161 4 NA’ NA’ 25 50 ourdata 3.8 1 5 100 100

’ NA: not available.

4.2. Saturation region

The experimental results indicate that the sensitivity does not vary with respect to the operating region. While the sensitivity in the linear region is mainly attributed to the change in drift velocity, the sensitivity in the saturation region is attributed to the change in saturation voltage. Using Eq. ( 19) with Eq. (26)) we prove in Appendix B that the sensitivities in the two regions are the same as long as V, - V, e V,, which is true for long devices (large L) . Experimental results also indicate that V,, is shifted by the magnetic field, as predicted by Eiq. (22). Fig. 6 shows plots of Zd versus V, and Rml versus V,, which indicate that V,, increases as the magnetic field increases. Experimental data indicate that V&, is shifted by roughly 2% T-’ on each side of the device.

4.3. Maximum sensitivity

Maximum sensitivity can be predicted using Eq. (18). Withm=0.5,r=1.92and~=670cm2V-‘s-’,amaximum sensitivity of 5.8% is predicted. A summary of previous experimental results performed by others is shown in Table 3. Except for Ref. [ 141, where arathernarrow device as used, the maximum sensitivities achieved by most others are very close together.

5. Conclusions

We have investigated the split-drain MAGFET, and described a complete analytical model. The model is suitable for describing the device in both linear and saturation regions. It predicts that the maximum sensitivity attainable for the split-drain device is about 8.5%. In addition, it is found that fluctuation of inversion charges does not contribute to the sensitivity in the linear region. Instead, an increase in drift velocity arises as a result of the roll-off of the Hall voltage. In the saturation region, the shift of V,, is responsible for the sensitivity.

Acknowledgements

The authors would like to thank ILK. Tam for support in developing the simulator, KM. Fung for helping in data col- lection and R. Murch for discussing the simulation model.

1. Luu n al. /Sensors and Actrrnrors A 49 (1995) 155-162 161

Appendix A: Hall voltage in saturation region for long channel device

In deriving the Hall voltage for the linear region, we stated in Eq. (15) that the Hall voltage is proportional to the drift velocity. However, when a long-channel device operating in saturation is placed under a magnetic field, the Hall voltage does not reach a maximum proportional to the saturation velocity.

For long-channel devices [ 171,

v,-vt 1_ y -I’* EC(Y) = 2L ( 1 L

(AlI

where EC is the lateral electric field. The carrier velocity reaches saturation when E, reaches a saturation field of the order of lo4 V cm- ‘. For a 100 w long device, for instance, Eq. (Al) implies that the saturation point is 0.02 pm away from the drain. The carrier velocity remains rather stable until fairly close to the saturation point. Once near the saturation point, the velocity rises rapidly until it finally reaches saturation. A MEDIC1 simulation on a 100 v long device indi- cates that during the final micrometres to the drain, the electric field rises 23.5 dB’ [ 181. In the case of the linear region, we observe that the short-circuit effect forces the maximum Hall voltage to be micrometres away from the drain, a couple of orders of magnitude further away from the drain than the saturation point. While the lessened inversion charges near the drain alleviate the short-circuiteffect, the effect still forces the Hall voltage to reach a maximum much before the carrier velocity reaches saturation. The Hall voltage can track the carrier velocity till it reaches a maximum, before the velocity comes close to uSp. This is consistent with experimental results. Typical Hall voltages observed are in the millivolt range. For a long-channel device, the carrier velocity prior to reaching saturation is a few orders of magnitude smaller than IJ,,~ Had the relationship between Hall voltage and carrier velocity remained linear and in the absence of a short-circuit effect, a Hall voltage in the range of volts would have been observed. Instead, the Hall voltage remains unchanged after reaching a maximum when V, approaches V,, [ 11. V,,,, reaches a maximum when the drift velocity approaches p-

VdsmIL.

Appendix B: comparing sensitivity in saturation and linear regions

Experimentally, it is observed that the sensitivity is invar- iant with respect to operating regions. If this is true, the model for the linear region and that of the saturation must be the same. We can prove that conditions are met to uphold the relationship

if and only if, substituting Eqs. ( 19) and (26) into Eq. (B 1) ,

Simplifying, we hold that Eq. (B 1) is only true if

v,-v,=v,,, ( 1 1+ z

032)

(B3)

Eq. (B3) is held true. For long-channel devices, a/L is of the order of 0.02 and m is 0.5. Furthermore, 9 is between 0 and l/2. Therefore, the last term in Eq. (B3) can be ignored. Indeed, for a long-channel device, V, - V, = V,,.

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Biographies

Jack Luu received his B.S. and MS. degrees from the University of California at Berkeley, and aPh.D. degree from the Hong Kong University of Science and Technology. His research interests include silicon magnetic sensors and high- speed SOI devices. He is currently an assistant lecturer at the Hong Kong University of Science and Technology.

Ping K. Ko received the B.S. degree in physics with special honours from Hong Kong University in 1974, and M.S. and Ph.D. degrees in electrical engineering from the University of California at Berkeley, in 1978 and 1983, respectively. In 1982 and 1983, he was a member of technical staff at Bell Laboratories, Holmdel, NJ, and was responsible for developing high-speed MOS technologies for communication circuits. He joined the Berkeley faculty in 1984, where he is now professor of the Department of Electrical Engineering and Computer Sciences. He was also the director of the Berkeley Microfabrication Laboratory. His present research interests include high-speed VLSI technologies and devices, device modelling for circuit simulation, CAD tools for IC, and electronic neural networks. He has authored and co- authored over 180 research papers. Dr Ko has served on the programme committee of the International VLSI Technology

Symposium and the International Electron Device Meeting. He was associate editor of IEEE Transactions on Electron Devices from 1988 to 1990.

Philip C.H. Ghan received his B.S. degree in electrical engineering from the University of California at Davis, and M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign in 1978. Dr Chan stayed at Illinois initially as an IBM postdoctoral fellow and later as visiting assistant professor in electrical engineering. He joined Intel Corporation, Santa Clara, California in 1981 as a senior engineer in the Technology Development Com- puter-Aided Design Department. Later he became a principal engineer and senior project manager. Dr Chan had corporate responsibility for circuit simulation tools, VLSI device modelling and process characterization. In 1990, he transferred to the Design Technology Department of Microproducts Group and developed the first functional 486-based multi-chip mod- ule at Intel. From 1991 to the present, he has been with the Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong, as a reader and currently as an associate dean of engineering. His research interests are electronic design automation, VLSI devices, circuits and systems, CAD/CAE/CAM technologies and integrated sensors.

modelling of split-drain magnetic field-effect transistor (magfet)

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