Optimum design of power MOSFET's - IEEE Xplore

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IEEETRANSACTIONS ON ELECTRONDEVICES, VOL. ED-31, NO. 1 2 , DECEMBER 1984

Optimum Design of Power MOSFET‘s CHENMING HU, SENIOR MEMBER, IEEE, MIN-HWA CHI,

AND

VIKRAM M. PATEL

Abstract-We present a model for the on-state resistance of power vertical, double-diffused MOS (VDMOS) transistors with emphasis on cell layout optimization and supporting experimental data. Essentially the same minimum Ron can be achieved using any of six different cellularcell geometries including square and hexagonal cells. Specifically, the on-resistances of all cellular designs are essentially identical if they have the Same p-well width and the same ratio of well area to cell area. Cellular designs yield lower on-resistance than linear-cell designs unless the latter, through clever layout perhaps, allows at least 1.6 times smaller well width than the former. Design examples and experimentsillustrate a simple optimization procedure, which starts with choosing the minimump-wellwidth and. depthcompatiblewithproductiontechnology and then finding the optimumspacing between the p-wells.

I. INTRODUCTION

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+-s-a+--s-I OWER MOSFET’s lhave achieved betterperformance in switching speeds, thermal stability, and input impedance than bipolar power transistors. The single ominous weakness is their relatively large on-state resistances [ l ] , [2]. Power MOSFET’s consideredin this paper havc: the self-aligned double-diffused p-well alndn+ source and a lightly doped epilayer as shown in Fig. 1. This structure results in vertical current flow which eliminates the need for drain metalization on n+ the top surface of the chip. The epi-layer supports the applied (b) drain voltage in the off-state. This double-diffusedstructure Fig. 1. (a) The four components of on-resistance are shown for a power has by and large replaced theolder V-groove structure.The VDMOS transistor. (b) Definition of Rj and R@. Current is assumed on-resistance of the two structures have been compared theoto flow in the shaded region. The narrowest part 1s the neck of the retically in earlier works [3]. JFET. The on-resistance consists of several distinguishable components 141 : channel resistance (Rch), accumulation layer resisDifferent power MOSFET manufacturers have adopted diftance (&), JFETor neckresistance (Ri), and epi-resistance ferent cell geometries-stripes, square wells in square cell, and (Repi) as shown in Fig. l(a).In higher breakdown-voltage hexagonal or square wells in hexagonal cell. Althoughthe devices, the epi-layers are thick and lightly doped, resulting in impact of layout design on on-state resistance has been anahigher on-resistances. The most important design trade-off for lyzed before [7] [ l o ] , it is not clear which if any of these power MOSFET’s is thatbetween on-resistance andbreakdown voltage. Theminimizationof on-resistance at a given geometries is superior and how the cell dimensions can be opbreakdown voltage has been studied in the literature in terms timized. The present paper differs from other studies by proof the optimum design of dopant density and thickness of the viding experimental data and design procedure and equations epi-layer [ I ] , [4] and the optimum doping profile in the epi- and by theoretically examining a nearly exhaustive collection layer [SI , [6].Theon-resistance can further be minimized, of cell geometries. The p-well and unit cell geometrj.es togetherwith some as will be shown in this paper, by propercell layout design. parameters used in this paper are shown in Fig. 2. Some clever designs such as serpentine geometries can be approximated as ManuscriptreceivedFebruary 9 , 1984; revised June13,1984.This study is partiallysupported bya grant fromFairchildCameraand linear geometry having someeffectivedimensions. AllresisInstrument Corporation. tances are expressed in ohms for 1 cm2 of active chip area, i.e., C.Hu is with the Department of Electrical Engineering and Compuin units of C2 cm2. Models of on-resistance will be developed. ter Sciences, University of California, Berkeley, CA 94720. M.-H. Chiwaswith theDepartment of ElectricalEngineering and Calculated on-resistance will be compared with experimental Computer Sciences, University of California, Berkeley, CA 94720. He data. Relativemerit of various geometries is then discussed. is now with EXCEL Microelectronics, San Jose, CA. Finally, a general layout design procedure for the minimizaV. M. Pate1 was with Fairchild Camera and Instrument Corporation, Palo Alto, CA 94304. He is now with Avantek, Inc., Santa Clara, CA. tion of on-resistance is proposed and illustrated with examples.

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11. EPITAXIALLAYERRESISTANCE

In this paper, Repi is defined as the resistance between the n' substrate and an imaginary electrode covering the "neck" area oftheJFET.In Fig. l(b), this imaginary or effective e l w trode is represented by the dotted lines and is of widtha' a:ld spacing s'. Twootherquantitiesin Fig. 1(b), a and s, are easier to understand. s is the width of the p-wells and a (for accumulation region) is the distance between the wells. a' a:ld s' are related to a and s by

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Fig. 3. repi calculatedwiththreemethods describedin text (solid curves) as well as the fixed-spreading-angle model (broken curves) for a linear-geometry design with the neck area equal to 50 percent of the total cell area.

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a and s are known or measurable, but A can only be estimated as suggested in (1). A is usually much smaller than s and a ( i n good designs) such that it can be neglected ((1)). On the otfer hand, one may assign A its upper limit, the depletion region , , 0.I 0.2 0.5 I .O 2.0 5.0 IO width, and thus overestimate &pi and Ri. Each designer may w make h s ownestimatefor A. Similarly, each designer mxy make his ownestimateof y , the depth at which the ne:k Fig. 4. repi calculated with 45'-spreading-angle model for linear geometry. The percentage of neck area is a parameter. occurs. We suggest 1 I I I I I

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is low when compared with the exact solution. The trapezoid model with the spreading angle varying as a function of a', s', and W [4] overestimates repi. We also examined a model assuming uniform current distributionwithin a trapezoid(the shaded region in Fig. 1(b)) where A is the total active device (array) area, W is the thick- having a fixed spreading angle, a. The results are also plotted ness of the epi-layer, and p is the resistivity. The epi-resistance in Fig. 3. It was found that if a fixed 45" spreading angle is used, the resultsare within 5 percent of the exact solution. normalized with respect to Rided,i.e., Furthermore, the expression for repi is relatively simple

Repi is always larger than the ideal resistance

Repi

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is called the spreading resistance factor. where W ' (= s'/2 for 45" spreading angle) is the depth below the surface at whichadjacent trapezoids merge together as shown in Fig. l(b). If adjacent trapezoids do not touch each repi has beencalculated for linear (interdigitated)layout using 1) approximateformula [ l ] , 2 ) theassumptiontkat other (i.e., W < s'/2), W' = W. Fig. 4 plots re,i calculated with current spreads out uniformly within a trapezoid with vari:d (3) as well as the exact solutions with the ratio of the neck spreading angle [4] , and 3) exact analysis by conformal msp- area to the total cell area, a'/(s' + a ' ) , as a parameter. The ping, which results in an infinite series in elliptic integrals ['i] , new model, clearly, is accurate over the whole range of a' and [ l l ] . Fig. 3 shows repi calculated bythesemethods versus s'. In addition, the 45" spreading angle model has been shown s ' / W for a' = s'. R e p i calculated with the approximate formula to achieve good agreement with experimental data [ 121 .

A . Repi of Linear Designs

IHU et al.: OPTIMUM DESIGN OF POWER MOSFET'S

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B. Repi of Cellular Designs Almost all commercial power MOSFET's use cellular designs. 'The designs are summarized in Fig. 2 , where various p-well geometries(square,circle, and hexagon) and unit cell geometries(square and hexagon)are included.Theonlyother possible unit cell is a triangular unit cell; it is judged unattractive and hence is excluded. We propose that the epi-resistance of cellular design VDMOSFET be calculated using the 45"-spreading-angle model also as illustrated in Fig. 5 for asquare well inhexagonalunit cell design. This assumption is inspired by the observation that the fixed-spreading-angle model worked well over a wide range of a' and s ' in Fig. 4. Later, limited three-dimensional simulation results also support this proposedmodel. Referring to Figs. 2 and 5 , the epi-resistance of a design having square-wellsinhexagonal unit cells is, as calculated using the 45'-spreading-angle model

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Fig. 6. Solid curves show the calculated repi for both linear and various cellular geometries with a' = s'. The brok'en curve is the repi for all the cellular geometries with a' adjusted for each geometry so that the neck area is 50 percent of cell area.

for a = 0, i.e.,

Equation (4) and the meaning (not the numelrical value) of g hold true for all other cellular designs. Coefficient g for other geometries are shown in Fig. 2. The solid curves in Fig. 6 show calculated repifor both linear and various cellular cell-geometries with a' = s'. All cellular geometries result in lower repithan the linear geometry for the same a' and s'. One reason for the differences in repi is that, some geometries leave larger areas forthe"top electrode" (the neck area) than others. When a' is adjusted (according to the formula in Fig. 2 ) for each cellular design so that the ratio of neck area to cell area is 50 percent for all designs, repi of cellular designs becomes essentially independent of the cell PdX geometries as indicated by the broken curve in Fig. 6. Using + (4), it can be shown that the largest difference exists between - (s + a)' - (s' - 2 tan 45')' square-well-in-hexagonal-cell and circular-well-in-square-cell. 2 The latter has lower repiby at most 0.1 percent in the range of where (fi/2)(s + a)z is the area of a hexagonal unit cell. The a' and s ' plotted in Figs. 6 and 7. Fig. 7 shows more curves of ratio of Repi to Rided re,i with the percentageneckareaas a parameter. The only three-dimensional simulation results [ 131 for cellular VDMOSFET's (square-well-in-square-cell) agree well withthecalcuy .= ep' ow lation as shown in Fig. 7. The universal cellular-geometry repi curves are compared fi ( s + a)' with the repi of linear designs in Fig. E;. The linear-geometry 2 curves in Fig. 8 canbe made to coincide with the cellulars+a [ ( s t a ) - g ( s ' - 2W') geometry curves with 3 percent difference at most by shifting the former to the right by a factor of 1.6. In other words, the = [I 1' (s + a) +g(s' - 2 w ' ) percentage of gate-drain overlap is a universal parameter for ( s + a ) +gs' both linear and cellular geometries if s ' is 1.6 smtiller for the ( s + a) - gs' linear geometry. Here are some conclusions from this Repi analysis. 1) A 45"d where g = .\/2/fi = 1.0746 for this cell geometry. Coeffi- spreading-angle model is both simpler and more accurate than cient g has a geometrical meaning: g is the square root of the other analytical models forlinear geometry. 2 ) This model has ratio of the p-well area (square) to the unit cell area (hexagon) been extended to cellular cell geometries and the results agree

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Fig. 7. repi for all cellular geometries with the percentage of neck ,uea as aparameter. Also shown are the only available three-dimensional simulation results for 35- and 50-percent neckarea.

DEVICES, VOL. ED-31, NO. 12, DECEMBER 1984

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s/A Fig. 9. Calculated R j / p Wi versus s/A for linear cellular andgeometries.

linear geometry

For cellular geometries

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As expected, the denominator of (7) or (8) is the ratio of area outside the well to total cell area, as shown in Fig. 2 . Fig. 9 plots R j / p y versus s‘/A calculated from ( 5 ) and (6) for linear and cellular geometries with the percentage of neck well with limited three-dimensional simulations. 3) Forthe area as a parameter. As in the case of Repi, all cellular geomsame well width s and the same percentage of neck area all etries result in the same set of curves with less than 0.1 percent cellular geometry designs yield essentially the same resista.r.ce. difference in values. In other words, for the same s and perIn other words, no one cellular geometry is noticeably bel.ter centage of neckarea Ri is also the same for all the cellular than the others. 4) Cellular geometries can result in lower vepi geometries. Fig. 9 shows that cellular geometries can result in than linear geometryforthe same percentage ofneckarea, lower Ri than linear geometry at the same s f and percentage of unless the linear geometry allows a 1.6 times smaller s, j s . , neck area. The asymptotic values of R i / p y when s‘/A is large tighter design rules. are predicted by (7) and (8).

Fig. 8. repi for linear and cellular geometries. For the same Wand percentage neck area, a linear design needs t o have 1.6 times smal3:r s than a cellulardesign in order toachieve the same Repi.

111. JFET RESISTANCE

IV. ACCUMULATION LAYER RESISTANCE

Contrary to the shape suggested before [4], [ 7 ] , the depleThere is an accumulation layer underneath the gate at the tion region is absent at the surface and becomes thicker below surface of the epi-layers when the device operates in the linear the surface as shown in Fig. 1 (b). Thedepletion regicm is region. Due to the voltage drop along the accumulation layer, largely extended into the n- epi-region because of its lojver the resistance between the end of the channel and the drain doping densitythanthat of the p-well. The“neck” t l u s at the bottom is larger than the sum of Repi and Ri as calcumodels. There is no simple way to formedbetweenadjacentdepletion regionspinches current latedbythetrapezoid flow and increases Ri. The region contributing to Ri starts analyze the impact of the accumulation layer on the on-state from the surface and ends at the level of the neck (a distuce resistance in general short of employing numerical simulation h$ below the surface). This “JFET” region is a matter of clef- [7]. However, when the voltage drop along the accumulation inition and the present definition is adopted for mathemat:cal is much smaller than that across the entire epilayer (Ra