SIMULATIONS WITH UNIFIED MOSFET MODEL FOR DISTORTIONS ANALYSIS

Transcription

1 SMULATONS WTH UNFED MOSFET MODEL FOR DSTORTONS ANALYSS F. Babarada (a), A. Rusu (a), T. Nculu (a), C. Ravaru (a), D. zreanu (a), C. Moldovan (b), E. Manea (b), C. Dunare (c), M. Mlak (d) (a) Unversty Poltehnca of Bucharest, Electroncs Telecommuncatons and nformaton Technology, DCAE, ERG, (b) Natonal nsttute for Research and Development n Mcrotechnologes, Bucharest, Romana, (c) Department of Electroncs and Electrcal Engneerng, Unversty of Ednburgh, UK, (d) Bucharest Unversty of Economcs, Romana. (a) babflorn@yahoo.com, (b) carmen.moldovan@mt.ro, (c) camela.dunare@ee.ed.ac.uk, (d) mlak.madalna@vrglo.t ABSTRACT The challenges of the ntegrated crcuts and nanotechnology need very accurate models for actve devces. From ths pont of vew the desgn of lnear analog crcuts lacks models for state-of-the-art MOS transstors to accurately descrbe dstorton effects. Ths s produced by the naccurate modellng of the second order effects nduced by hgh vertcal gate feld such as moblty degradaton and short channel seres resstance and second order effects nduced by parallel dran feld lke velocty saturaton n the ohmc regon, channel length modulaton n the saturaton regon, statc feedback and weak avalanche. After a rgorous descrpton of transstor transconductance and channel conductance n ohmc and saturaton regon we ncluded these effects n the MOS transstor model, usng a compact expresson of dran current for computaton reasons. The smulatons usng the new dran current expresson were n good agreement wth expermental data, proves scalablty and large voltage range functonalty. Keywords: Modellng, Smulaton, Desgn, Quantum mechancal effects. 1. NTRODUCTON The advancement of knowledge n the electronc desgn s strongly nfluenced by Technology Computer Aded Desgn TCAD. Here s an nterestng postve feedback, because the computng power helps the desgners to perform modellng, smulaton, optmzaton and desgn of the new devces wth mproved performance whch have the capablty to ncrease the computng power. The today ntegrated crcuts arse the MOSFET lke the most representatve devce. The contnuum scalng, accordng wth Moore s low, requres the permanent updatng of the transstor physcs (Magnus and Schoenmaker 00) and for crcuts models (Arora 199), lke the studes of current trough thn oxdes and the modellng of nsulated structures from substrate, named Slcon on nsulator-so. The devces models, used n crcuts smulaton programs, use frequently quasemprcal methods for optmsaton precson/computng tme report. Obvously these methods trend to be closely to the physcal models (Fu and Wllander 1999). So same parameters result drectly from the physcal structure or devce technology lke Ferm level, flat band voltage, moblty, length/wdth channel report, and so on. The smulaton crcut programs push the physcal models to the unfed models, whch can descrbe by one analytcal expresson the transstor functon n any regme (Lou, Conde and Sanchez 1998). The contnuous transton from weak nverson to strong nverson s realzed by an approprate nterpolaton functon. The today MOS structures has the channel length n the submcron regon but all the models begn wth the long channel study and then make correctons about the channel length. That approach corresponds to the MOSFET scalng from the electrcal behavour pont of vew. The statc characterstcs wll be mantaned wth the dmensons shrnkng, but must be mproved the dynamcal characterstcs. Other characterstc of MOSFET s the two dmensons functonalty because the command by the gate s made transversal on the channel drecton. n ths case precse modellng can be made only wth numercal methods but the numercal solutons can t be used for crcuts analyse (Lundstrom 1990; Rusu 001). The gradual approxmaton can descrbe separately the physcal phenomena on both drectons. Ths approxmaton descrbes wth enough precson only the quaslnear regme of transstor, charactersed by the contnuty of the channel from the source to dran. n order to reduce the nose effects n analog and rado frequency ntegrated crcuts the sgnal ampltude must be ncreased. The large ampltude wll cause hgh dstorton effects due to the nherent nonlnearty of the actve devces used to mplement the crcut functons (Ytterdal, Cheng, Fjeldly 00; Babarada, Profrescu, Rusu and Dunare 004). MOS transstors are the most adequate and effectve devces

2 for mplementng analog functons. Wth the contnuous downscalng of feature szes the transstor characterstcs are much affected by the second order effects such as moblty degradaton and short cannel seres resstance due to hgh vertcal feld, velocty saturaton, channel length modulaton, statc feedback and weak avalanche due to the parallel electrc feld. All these effects wll ntroduce addtonal nonlnearty n transstor characterstcs and wll fnally produce output sgnal dstorton. n the analog crcut desgn the MOS transstor can be drven as well by the dran termnal. By example a dran voltage drven MOSFET operatng n the ohmc regon lke a gate voltage controlled resstor wth the resstor lnearty lmted by the transstor dran voltage nduced dstortons. Other example can be the load devce n amplfer crcuts where the dran termnal drves the MOSFET n saturaton. The actual compact MOSFET models fal to predct satsfactorly dran nduced dstorton effects and the conductance g d n the saturaton regon, whch become mportant n amplfer crcuts (Graaff and Klaassen 1990). The DC-bas condtons for whch the thrd-order harmonc becomes zero gve the mnmum dstortons. Contemporary MOS models do not predct these DC-bas condtons and an mproved descrpton of the dran current dependence of dran voltage s necessary. For analog desgn the charactersaton nclude fttng of small-sgnal parameters such transconductance g m and channel conductance g d but ths s not suffcent for proper estmaton of dstorton and ntermodulaton effects because for example the thrd-order harmonc dstorton component depends on the thrd-order dervatve of the devce characterstcs (Babarada, Profrescu, Ravaru, Manea, Dumbrăvescu, Dunare and Uleru 006). n the saturaton regon the gradual channel approxmaton s no longer vald, and as a result two-dmensonal effects, such as channel length modulaton and statc feedback, come nto play. n addton for large values of dran current, heat dsspaton may become sgnfcant and thus selfheatng also has to be taken nto account n the dran current expresson. Furthermore at hgh dran voltage values weak-avalanche effects become apparent and substrate current cannot longer be neglected.. SMOOTHNG FUNCTON Usual s assumed that drft current can be neglected n weak nverson and dffuson current can be neglected n strong nverson. Around threshold voltage s consdered the moderate nverson regon (Tsvds 1987), where both the drft current and dffuson current are mportant. The transton from the ohmc regon to the saturaton regon s contnuous for the dran current. For analog crcut modellng, ths transton should also be contnuous for the hgher-order dervatves of dran current to dran voltage (Babarada, Profrescu, Ravaru, Manea, Dumbrăvescu, Dunare and Uleru 006), or the model should be contnuous. To arse these requres we replace dran-source voltage DS wth an emprcal functon DSsf that changes smoothly from DS n the ohmc regon to DSsat n the saturaton regon. Ths emprcal functon DSsf s usual named smoothng functon. n order to preserve the model symmetry respectvely the dscontnutes of hgher-order dervatves at DS =0, we choose a smoothng functon for whch the dervate reported to DS s equal to unty, at DS =0, (Brews 1978): DSsf DS DSsat = m + m DS DSsat 1 / m (1) where: m s an emprcal parameter, whch can be nteger only; DS s the dran-source voltage and Dssat s the dran-source saturaton voltage. The channel potental computaton for the dran current s very dffcult n moderate nverson and to ensure the contnuty between the weak and strong nverson current and ts dervatves an emprcal approach s used. We used the next emprcal nterpolaton functon: GS T = + GS T m 0 u T ln 1 exp () m 0 u T. UNFED MODEL The physcs of sold begn from the characterzaton of all energy form usng the Hamltonan. After some approxmatons, lke the unelectron assumpton, we arrve at Maxwell s equatons. Dstncton between the drft and the dffuson component of the dran current should be mantaned n all nverson regons, for an accurate descrpton of the moderate nverson regon: = drft df () D + For model symmetry the drft current expresson s gven by usual formula (Babarada, Profrescu, Rusu and Dunare 004), and makng a Taylor expanson around 1/ ( ψ sl ψ s0), lke n (Babarada, Profrescu, Ravaru, Manea, Dumbrăvescu, Dunare and Uleru 006): drft ψsl ψ s0 ψsl+ ψ s0 = β GBeff+ G γ ( ψsl ψ s0) (4) where: β s the gan factor; GBeff = GS + SB - FB, G s determned by transton from dran nduced barrer lowerng-dbl n weak nverson to statc feedback n strong nverson; ψ sl s the surface potental at the dran sde; ψ s0 s the surface potental at the source sde; γ s the body effect coeffcent. The dffuson current s: 4

3 ψ s0 DS ΦF df = β γ ut ψ s0+ ut exp ut ψ s0 ψ sl DS SB ΦF ψ + ψ sl sl ut exp ut (5) and the total dran current expresson, takng nto account: dran saturaton voltage, dran nduced barrer lowerng, moblty degradaton, seres resstance, velocty saturaton, channel length modulaton, statc feedback and weak avalanche, s gven by: D L( + ) drft dft ( )( L ) + ( + ) = µ µ Leff β β 0 R Th / DS DSsf GS ( 1+ G ) av (6) where: L s the channel length; µ o s low feld bulk moblty; µ s carrers moblty (Babarada, Profrescu, Rusu and Dunare 004); L eff s the effectve channel length; L s the channel length modulaton; β R ncludes the seres resstance; β Th ncludes self heatng; G av s the weak avalanche, GS- has the expressons: 1 1 = GS GS 1 GS 1 ε (7) where ε s a smoothng factor and GS-1 has the next expressons: = / / 1 GS FB Φ F γ + (8) DSsf ΦF SB DSsf GS + 4. MEASUREMENT AND RESULTS The hgher-order dervatves have been performed by applyng a snusodal sgnal to the termnal under nvestgaton and by measurng the hgher-order harmoncs n the dran current, lke n the confguraton from fg. 1. The sgnal frequency s a few KHz n order to neglect the nfluence of capactances. n ths stuaton the dstortons can be completely determned by the MOS transstor steady state. The dran current D can be expanded n a Taylor seres: D = d 0 + d1 v + d v + d v +... = d v =0 v s a snusodal sgnal sn( ωt) coeffcents d v (9) = and the 1 D =.! G ( D ) S Do, Go, Bo The dran current expresson can be rewrtten n terms of sn(nωt): Fgure 1: Dstorton Measurement Confguraton The coeffcents a 1, a and a are the sgnal harmoncs ampltudes and were measured wth the spectrum analyser, fg. 1. The coeffcents can be wrtten as: 5 5 a1 = d1 + d + d a = d d 4 d a = d d 5 d (11) For small enough values of the sgnal ampltude, the coeffcents (11) reduce to: 1 a 1 d 1 a d ; ; 1 a d 4 (1) n ths way the hgh order dervatves reported to GS notated g m or reported to DS notated g d can be calculated or extracted from the measured harmoncs. Usng the harmonc ampltude notaton HD the second-order and thrd-order harmonc ampltude are: 1 1 D HD = a d = 4 G( D) S (1) 1 1 D HD = a d = 4 4 G( D) S (14) Fg. -5 show the smulated and measured results for the thrd order dervatves g ( D) ( GS ) m = / and g ( ) d = D /( DS ), for n and p type MOS transstors, at SB =0, for dfferent devce geometres W/L and W=10µm, lke n fg. 6 and detaled n fg. 7. A good ft between modelled and expermental results can be observed. D = ao + a1 sn( ωt) + a cos( ω t) + a sn( ω t) +... (10) 5

4 Fgure : Modelled (Lnes) and Measured (Symbols) alues of Gate nduced Dstorton g m at Low Dran Bas ( DS =50m) as a Functon of Gate oltage for n- type MOS Transstor. Fgure 5: Modelled (Lnes) and Measured (Symbols) alues of Dran nduced Dstorton g d at GS =-1, as a Functon of Dran oltage for p-type MOS Transstor. Fgure : Modelled (Lnes) and Measured (Symbols) alues of Dran nduced Dstorton g d at GS =1, as a Functon of Dran oltage for n-type MOS Transstor Fgure 6: Dfferent W/L Transstors Array. Fgure 4: Modelled (Lnes) and Measured (Symbols) alues of Gate nduced Dstorton g m at Low Dran Bas ( DS =-50m) as a Functon of Gate oltage for p- type MOS Transstor. Fgure 7: Detal of Dfferent W/L Transstors Array. The transstors array s performed n 0,5µm technology wth transstors n and p enhanced type and 6

5 n + polyslcon gate for transstors type n and p + polyslcon gate for transstors type p. The gate oxde thckness s about 4nm and the maxmum allowed supply voltage DD s,5. The LDD structure s no longer used and descrpton of gate voltage dependent seres resstance become redundant and the model wll be a constant source and dran resstance. 5. CONCLUSONS Precse physcal descrpton of channel surface potental s very mportant for precse modellng of dran current n all nverson regons. The unfed model gves an accurate descrpton of harmonc dstorton n all nverson regons ncludng dran saturaton voltage, dran nduced barrer lowerng, moblty degradaton, seres resstance, velocty saturaton, channel length modulaton, statc feedback and weak avalanche effects. The model has a low number of parameters for both n and p type of transstors. The parameters extracton requres the measured current-voltage characterstcs, whch can be performed wth usual testng tools. The unfed model s well scalable and the dran current and ts hgher order dervatves are precsely descrbed over a large geometres range and termnal appled voltage values. The model can be used for modern CMOS technologes n whch both the n-channel and p-channel transstors are of the enhancement-type and LDDstructures are no used, t was found that an adjusted expresson of hole moblty and a constant seres resstance have to be used. n ths manner the unfed model can be used wth good results even for deep submcron technologes. REFERENCES Arora, N., 199. MOSFET Models for LS Crcut Smulaton, Theory and Practce. Wen:Sprnger- erlag. Babarada, F., Profrescu, M., Rusu, A., Dunare, C., 004. Carrer Moblty and Seres Resstance MOSFET Modellng. BoMEMS and Nanotechnology-SPE, vol , pp , Perth Australa. Babarada, F., Profrescu, M., Ravaru, C., Profrescu, O., Manea, E., Dumbrăvescu, N., Dunare, C., Uleru, D., 006. MOSFET Modellng ncludng Second Order Effects for Dstorton Analyss. Appled Smulaton and Modellng-ASTED, pp , Rhodes Greece. Brews, J., A Charge-Sheet Model of the MOSFET. Sold-State Electron, ol. 1:pp Fu, Y., Wllander, M., Physcal Models of Semconductor Quantum Devces. Kluwer/ Academc Publshers. Graaff, H.C., Klaassen, F.M., Compact Transstor Modellng for Crcut Desgn. Wen:Sprnger-erlag. Lou, J.J., Ortez-Conde, A., Garca-Sanchez, F., Analyss and Desgn of MOSFETs, Modelng Smulaton and Parameter Extracton. Kluwer. Lundstrom, M., Fundamentals of Carrer Transport. Addson-Wesley. Rusu, A., 001. Toward a Demonstraton of the Non- Lnear Electrcal Conducton Law. nternatonal Semconductor Conference, pp , Snaa Romana. Tsvds, Y.P., Operaton and Modelng of the MOS Transstor, New York:McGraw-Hll. Ytterdal, T., Cheng, Y., Fjeldly, T., 00. Devce Modelng for Analog and RF CMOS Crcut Desgn. England:Jhon Wley. Magnus, W., Schoenmaker, W., 00. Quantum Transport n Sub-Mcron Devces. Germany:Sprnger-erlag. AUTHORS BOGRAPHY Florn N. Babarada receved the M.Sc. degree n Electroncs & Telecommuncatons n 198 and the Ph.D. degree wth dssertaton Mcroresonant Sensors n Planar Slcon Technology n 000, both at Unversty Poltehnca from Bucharest, Romana. n 1984 he joned to Technology Department from Mroelectonca S.A. C factory. From 1994 was member of the begnnng team of the Mcroelectroncs nsttute-mt and then named Natonal nsttute of Mcrotechnology, where he worked n the feld of Mcroelectroncs C and Mcroelectromechancal Systems-MEMS. From 00 he work at the Unversty Poltehnca of Bucharest, Faculty of Electroncs Telecommuncatons and nformaton Technology, Department of Devces Crcuts and Electroncs Apparatus, where he s nvolve n: Modellng, Smulaton and Electronc Desgn Automaton (EDA) of Mcro/Nanoelectroncs and Bo- Mcro/Nanoelectroncs Processes, Devces, Cs, MEMS and NEMS; Software methodology CAD, TCAD and Computer Graphcs n Electroncs and Boelectroncs Engneerng; Computer aded engneerng educaton e- Learnng and e-tranng. emal: babflorn@yahoo.com Adran RUSU s the head of the Devces Components and Electroncs Apparatus Department from Unversty Poltehnca of Bucharest, Faculty of Electroncs Telecommuncatons and nformaton Technology, B- dul ulu Manu 1-, Sector 6, Bucharest Romana. Hs researchng area concerns new electronc devces, technologes and non-lnear conducton through semconductors. emal: adranr@mcma.pub.ro Tudor NCULU s wth the Poltehnca Unversty of Bucharest, Romana, Faculty of Electroncs Telecommuncatons and nformaton Technology, Mcroelectroncs Department, B-dul ulu Manu 1-, Sector 6, Bucharest. He s Senor EEE Member wth hgh performances n artfcal ntellgence, 7

6 mathematcal algorthms, smulaton. e-mal: Crstan RAARU s wth the Poltehnca Unversty of Bucharest, Romana, Faculty of Electroncs Telecommuncatons and nformaton Technology, Mcroelectroncs Department, B-dul ulu Manu 1-, Sector 6, Bucharest, Postal zp: n the lasts years he studed nano-electronc devces, proposed a Nothng On nsulator confguraton, besdes to Boelectroncs devces, cellular nano-electroncs. emal: cravaru@arh.pub.ro Madalna Mlak graduated the Unversty Poltehnca of Bucharest, Faculty Automatzaton and Computers n 199. She s Assstant to Bucharest Unversty of Economcs, Romana, nformatcs Department. She works n the feld of computer network management of physcs, logcal and nformatonal resources, network securty, nteractve nterfaces, and numercal computng methods. emal: mlak.madalna@vrglo.t Dragos zreanu s wth the Poltehnca Unversty of Bucharest, Romana, Faculty of Electroncs Telecommuncatons and nformaton Technology, Telecommuncatons Department, B-dul ulu Manu 1-, Sector 6, Bucharest. He s Senor EEE Member wth hgh performances n dgtal sgnals processng, mages processng and forms recognton, electrc and electroncs measurements. e-mal: dvzreanu@yahoo.com Carmen Moldovan graduated the Faculty Electroncs and Telecommuncaton n 198 and she owns a PhD n Mcrosensors. She worked to Mcroelectronca SA CMOS ntegrated crcuts factory and now to Natonal R&D nsttute for Mcrotechnology, Bucharest, lke Head of the Mcrotechnology Department. She s a member of: EEE and Scence and Technology Commsson of the Romanan Academy and NEXUSPLUS and BRDGE subcontractor (and also a member of the NEXUSPLUS Steerng Commttee). The scentfc actvty s publshed n more than 55 papers n journals, books and communcatons n Proceedngs. emal: carmen.moldovan@mt.ro Elena Manea graduated the Unversty of Bucharest, Faculty of Physcs. Then she worked to Mcroelectronca, Bucharest, MOS.C. Wafer Fabrcaton Dvson, lke Head of MOS.C. Wafer Fabrcaton Dvson. Now work to Natonal R&D nsttute for Mcrotechnology, Bucharest, Wafer Fabrcaton Laboratory, lke Ph.D, senor scentfc researcher and Head of Wafer Fabrcaton Laboratory. She has over 0 years experence n slcon planar technology ncludng: photolthography, dffuson processes for MOS-C, thn flm deposton e.s.o. emal: elena.manea@mt.ro Camela Dunare graduated the Faculty Electroncs and Telecommuncaton n She worked to Mcroelectronca SA, Natonal R&D nsttute for Mcrotechnology and The Scottsh Mcroelectroncs Centre (SMC), Unversty Ednburg GB. The research feld s slcon processng, MOS and MEMS processes development. emal: camela.dunare@ee.ed.ac.uk 8