A Compact Model for an IC Lateral Diffused MOSFET Using the Lumped-Charge Methodology

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1 A Compac Model for an IC Laeral iffused MOSFET Using he Lumped-Charge Mehodology Y. Subramanian 1*, P.O. Laurizen ** and K.R.Green * * Texas Insrumens, Inc, 8505 Fores Lane, allas, TX 75243, USA, y-subramanian@i.com ** Universiy of Washingon, Seale, WA 98195, USA, plauriz@ee.washingon.edu 1 Auhor was a graduae suden a he Universiy of Washingon during he course of his work. ASTRACT A compac model for an IC Laeral iffused MOSFET is developed using he Lumped-Charge Mehodology[1]. Model euaions and key performance characerisics are documened. They saisfy he reuiremens of Power MOSFET models[2], unlike he compeiive macromodels developed from shor-channel, low-power MOSFET models. Keywords: LMOS Model, Lumped-Charge, Power, MOSFET INTROUCTION An imporan measure of he uiliy of a compac model is is abiliy o accuraely represen exernal device behavior in a simple (compuaionally inexpensive) and physically based manner. This principle was cenral o he developmen of he Lumped-Charge Mehodology (or L-C Mehodology) for compac device modeling in he early 1990s[1]. The L-C Mehodology enables he accurae represenaion of complee exernal device behavior using a se of simple, physically based euaions ha use oal charge corresponding o specific regions of a device as a fundamenal uaniy. A figuraive descripion of he L-C Mehodology is given in Fig. 1. The L-C Mehodology is L-C Model 1.Coninuiy Ens 2.olzmann s Relaions 3.Poisson s En 4.Charge Neuraliy Ens 5.iffusion & rif Ens 6.Time erivaives Time dependen volage or curren (inpu) Calculae Lumped Charge Time dependen curren or volage (oupu) Figure 1: The Lumped-Charge Mehodology This projec was a wo-year effor suppored by he NSF- CAIC Indusry-Universiy Research Consorium. Experimenal daa for model validaion was provided by Texas Insrumens, Inc. generally applicable o compac models of mos semiconducor devices. The euaions and performance of a Lumped-Charge based compac model are here given for an IC Laeral iffused MOSFET (Fig. 2), excluding bipolar parasiics. RAIN N N P N N N-RAIN GATE SOURCE GATE P-OY P-SUSTRATE ipolar Parasiic Figure 2: The IC Laeral iffused MOSFET MOEL EQUATIONS RAIN Since simpliciy is reuired of physically based compac models, heir euaions mus balance circui simulaion reuiremens wih he physics of inernal device operaion. To be physically based, hey mus include all inernal behavior whose exernal I-V manifesaions are imporan in circui design. Conversely, o be simple, hey mus no include inernal device behavior whose exernal I-V manifesaions are unimporan in circui design. In he L-C Mehodology, his balance is easily achieved by minimizing he number of discreized charge packes (or L-C nodes-see Fig. 3) used o represen a device, subjec o he minimum model accuracy desired for circui simulaion. For he L-C LMOS model, C as well as AC simulaions were obained wih sufficien accuracy by using he Lumped- Charge represenaion shown in Fig. 3. In his represenaion, he LMOS srucure is divided ino wo MOS subsrucures-he body subsrucure and he drain subsrucure using a minimum number of nodes (see Fig. 3). Figures 1 and 3 form he basis of euaion formulaion for he L-C LMOS Model. The euaions use a robus se

2 of six parameers direcly obainable from process informaion, six physically significan parameers ha reuire opimizaion for exracion, and four fiing parameers. These parameers are summarized in Table 1. W Lumped ody Inv. Chg, Lumped ody ep/acc. i Charge, ad Lumped rain Inv. Chg, Lumped rain ep/acc i Charge, ad L, L T OX N,N P P-ody ody Subsrucure Figure 3: L-C Represenaion of he IC LMOSFET Process ependen Parameers Widh ody, rain Lenghs Oxide Thickness ody, rain oping Concenraions Parameers wih Physical Significance Reuiring Opimizaion µo Room Temperaure Mobiliy TEMPEXP Coeff for Mobiliy-Temperaure reln. VF ody Flaband Volage LAMA Channel Lengh Modulaion Param. THETA Mobiliy Reducion Facor VM AX Velociy Sauraion Volage Fiing Parameers p1 eermines horizonal posiion of verical axis (line A-see Fig. 3) where Poisson s En is solved for each VS,VGS (see es (2) and (3)). p2, p3, p4 Togeher deermine he influence of rain Resisance on C performance Table 1: Parameers of he L-C LMOS Model A N N N-rain P-Subsrae rain Subsrucure The ody Subsrucure In he body subsrucure, he lumped body inversion charge, i (see Fig. 3) is assumed o represen he average conducance of he channel (for C behavior) as well as oal inversion charge in he body (for capaciive behavior). The oal depleion/accumulaion charge in he body is represened by ad.. i is calculaed by assuming ha i can be represened consisen wih he above definiion by direcly relaing i o oal channel conducance per uni channel lengh (or, euivalenly, oal one-dimensional inversion charge per uni channel lengh) along a verical line A (Fig. 3). The horizonal posiion of A is represened elecrically by assuming ha i bears a fixed relaionship wih erminal volage. For he purpose of obaining close fis beween model characerisics and device daa, flexibiliy is inroduced ino his relaionship hrough he use of fiing parameer p1 (see Table 1). ad is calculaed by assuming ha i can be represened by he oal one-dimensional depleion/accumulaion charge per uni channel lengh along A (Fig. 3). The mahemaical euaions o calculae i and ad are derived from he soluion of Poisson s Euaion along line A (assuming he boundary condiion ha oal gae-bulk volage drop along A is he insananeous gae-source volage, VGS). More informaion on his derivaion is available in [3]. Es (1)-(5) mus be solved ieraively o calculae i and ad. ad where: = 2 N WL exp( 1 ε (1) = inerface-o-bulk poenial along A F = body fermi poenial ; = hermal volage; = elecronic charge; ε= permiiviy of silicon; Le vc = volage drop across he channel. Then, i where = 2 εn WL A (2) A = exp( 2 = exp( F ) 1 ad p1 vc p1 vc (exp( exp( ) (2a) (2b)

3 vc, he volage drop across he channel is calculaed from erminal volage by using he following empirical expression: p4 vc = VS 1 p3 p2 ln(1 exp( VGS VT )) 1 p3 p3 (3) where VT, he nominal hreshold volage is calculaed as: 4εN ATox VT = 2 F (4) ox An empirical approach was chosen because any approach based on firs principles would be oo complicaed o derive and evaluae for a diffused body. ( ) T i ad ox = VGS VF (5) ox where: ε ox = permiiviy of oxide The rain Subsrucure The drain subsrucure is modeled in a similar manner as he body subsrucure, bu because significan C conducion hrough his subsrucure occurs only when i is in accumulaion or depleion, sufficien overall accuracy is obained by de-linking lumped drain charge (for AC behavior) and drain resisance (for C behavior). rain C behavior is accouned for by he fiing parameers used in es. (1)-(3). This assumpion simplifies he drain euaions, wihou losing accuracy. Es (6)-(8) are solved ieraively o calculae i and ad. ad s = 2 N exp( s WL 1 ε (6) where: s = inerface-o-drain poenial; F = drain fermi poenial ; i where = 2 εn WL C (7) C = exp( 1 ad 2 F s s = exp( ) (exp( 1 (7a) (7b) as: ( ) T i ad ox s = VG VF (8) ox where : VG= Gae-rain Volage; VF = rain Flaband Volage and is calculaed VF = VF (8a) where is he approximae body-drain buil-in poenial calculaed using he nominal body and drain doping concenraions, N and N. Curren Calculaion The conducion and displacemen componens of currens corresponding o he wo subsrucures are calculaed and allocaed o he erminals of he composie LMOSFET in he manner shown in Fig. 4. This esablishes he connecion beween he body and drain subsrucures. Noe ha he drain inversion charge is supplied hrough he source-body erminal, and no he drain erminal. d i /dd ad /d d i /dd ad /d I I -d i /d -d ad -d i /d Figure 4: Terminal Allocaion of Conducion and isplacemen Currens. In Fig 4: vc L = P P-ody i µ 2 o N N N-rain P-Subsrae TEMPEXP T 1 T o 1 LAMA VS 1 THETA VGS ( VT) PERFORMANCE I d ad /d Figures 5-10 show he key performance characerisics of he LMOS model versus device daa (provided by Texas Insrumens, Inc.). These figures show ha LMOS C as well as non-c behavior can be represened wih reasonable accuracy using an euaion se (es (1)-(9)) ha (9)

is simple, fully coninuous and subsanially physically based. I(1mA/div) VGS=1V VGS=0V VGS=4.5V VGS=3.0V VGS=-1V VS(2V/div) Figure 5: Oupu C Characerisics a 300K for model(solid) and daa(doed).

4 is simple, fully coninuous and subsanially physically based. I(1mA/div) VGS=1V VGS=0V VGS=4.5V VGS=3.0V VGS=-1V VS(2V/div) Figure 5: Oupu C Characerisics a 300K for model(solid) and daa(doed). Figure 8: CG vs VS for model(solid) & daa(sars) I(A) I(A) (Log) VS=2.5V VS=0.1V VGS=4.5V VGS(V) Figure 6: Subhreshold Characerisics a 300K for model(solid) and daa(doed) I(A) VS(V) Figure 9: Oupu C Characerisics a 423K for model(solid) and daa(doed). VS=5V VS=1V VS=9V VS=13V VS(V) Figure 7: CGS vs VGS for model(solid) & daa(sars) Figure 10: Oupu C Characerisics a 233K for model(solid) and daa(doed).

5 CONCLUSIONS AN FUTURE WORK The L-C Mehodology is able o accuraely represen C as well as non-c behavior in an IC LMOSFET using a single se of simple euaions wih a subsanial physical basis. Since he cenral variable is charge, he L-C LMOS euaions represen composie LMOSFET behavior in a fundamenally sound fashion, and saisfy he reuiremens of power MOSFET modeling[2], unlike radiional subcircui-based approaches involving models of shor-channel, low-power MOSFETs. More informaion on he L-C mehodology, including is applicaion o a verical MOSFET, as well as a comparison of L-C LMOS C performance o he subcircui-based approach is available in [4]. The simpliciy of he L-C approach should ensure is usefulness for compac model developmen, especially when sandard modeling languages (e.g., VHL-AMS and Verilog-AHL) become available. Currenly, he L-C LMOS model is being evaluaed wih help from circui design engineers. A new version of his model has been developed in which he number of fiing parameers is reduced from four o one, bu his new model has no ye been validaed. Parasiic bipolar models have also been developed for his srucure[5]. Fuure work also includes he addiion of self-heaing effecs. REFERENCES [1] Ma, C.L., Laurizen, P.O., Pao-Yi Lin, udihardjo, I., Sigg, J, "A Sysemaic Approach o Modeling of Power Semiconducor evices based on Charge Conrol Principles" PESC 94 Record, vol. 1 pp , [2] udihardjo, I.K., Laurizen, P.O., Manooh, H.A., Performance Reuiremens of Power MOSFET models, in IEEE Trans. Power Elecronics, vol. 10., no. 3, pp , May [3] Tsividis, Yannis, Operaion and Modeling of he MOS Transisor, McGraw Hill, , [4] Y. Subramanian, P.O. Laurizen, K.R. Green, Two Lumped-Charge ased Power MOSFET Models, o be published in Proceedings of he Sixh IEEE Workshop on Compuers in Power Elecronics, Como, Ialy, July [5] i, Yafei, Compac Modeling of Power ipolar Transisor and Parasiic ipolar Transisor, M.S.E.E. Thesis, Universiy of Washingon, Seale, 1998.

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P. Bruschi: Project guidelines PSM Project guidelines. Projec guidelines. 1. Rules for he execuion of he projecs Projecs are opional. Their aim is o improve he sudens knowledge of he basic full-cusom design flow. The final score of he exam is no affeced by