Development of a Method for Determining the Dependence of the Electron Mobility on the Longitudinal-Electric Field in MOSFETs

VLSI DESIGN 1998, Vol. 8, Nos. (1-4), pp. 261-264 Rep in s a ailable di ec ly om he publishe Pho ocopying pe mi ed by license only (C) 1998 OPA (O e seas Publishe s Associa ion) N.V. Published by license unde he Go don and B each Science Publishe s imp in . P in ed in India. De elopmen o a Me hod o De e mining he Dependence o he Elec on Mobili y on he Longi udinal-Elec ic Field in MOSFETs J. B. ROLDAN *, F. GAMIZ and J. A. LOPEZ-VILLANUEVA Depa amen o de Elec 6nica y Tecnologia de Compu ado es, Uni e sidad de G anada, Facul ad de Ciencias, A d., Fuen enue a s/n, 18071 G anada Spain A new expe imen al me hod o de e mining he dependence o he elec on mobili y on he longi udinal-elec ic ield has been de eloped. The de elopmen , alida ion and explana ion o his new me hod has been ca e ully ca ied ou . We ha e applied his p ocedu e o s anda d submic on MOSFETs and a e ha ing ob ained he mobili y dependence on bo h he ans e se- and longi udinal-elec ic ields we ep oduced he expe imen al ou pu cu es. The sa u a ion eloci y has also been calcula ed using he mobili y cu es ob ained by his new me hod. Keywo ds." Elec on mobili y, longi udinal-elec ic ield, sa u a ion eloci y, ou pu cu es, d i - di usion simula ion 1. INTRODUCTION The elec on-mobili y dependence on he longi- udinal-elec ic ield, o ien ed along he channel, has been s udied expe imen ally. A "closed-loop" in es iga ion has been pe o med on he alidi y and accu acy o a new me hod o de e mining he educ ion o he channel mobili y connec ed o he inc ease o he longi udinal ield. This me hod is applicable o s anda d ansis o s. An es ima ion o he sa u a ion elec on eloci y in he channel has been accomplished compa ing a widely used ex- p ession [1]. The da a ob ained wi h his p ocedu e can be used o de elop local models o accoun o he mobili y dependence on he longi udinal-elec ic ield in d i -di usion simula o s. 2. DESCRIPTION OF THE METHOD The basic concep o idea o his me hod is he compa ison o expe imen al d ain cu en e sus d ain ol age cu es Iz-Vos, measu ed in sho - channel ansis o s o he esul s p oduced by a wo-dimensional simula o [2, 3] in which an * Co esponding au ho . 261 262 J.B. ROLD/N e al. accu a e low- ield mobili y is used and he mobili y educ ion caused by he longi udinal-elec ic ield is included. The o al channel leng h L is di ided in N subchannels wi h leng hs Li, 1, 2,..., N, espec i ely. Ins ead o ixing he Li alues, he channel po en ial alues a he ends o he i- h subchannel, Vi-1 and Vi, a e de ined as he sepa a ion be ween he quasi e mi le els a hese poin s, V0 Vs and VN Vz being he po en ials a he o al channel ends. The e o e, he sepa a ion in o subchannels is ob ained by di iding Vz-Vs in o e y small in e als and ixing he channel po en ial a he ends o each subchannel. The numbe o subchannels is high enough and he di e ence Vi-Vi_ in each subchannel is low enough ha he longi udinal-elec ic ield in each subchannel can be conside ed o be uni o m. The applica ion o he me hod is as ollows: 1) S a ing om a e y small VDs, o which one subchannel is enough, he ga e- o-sou ce ol- age is a ied and he low- ield mobili y as well as i s dependence on he ans e se-elec ic ield is ob ained. 2) Vzs is inc eased in e y small s eps and he expe imen al esul is compa ed o he simu- la ed esul calcula ed by using he low- ield mobili y ob ained in poin (1). New subchan- nels a e in oduced i necessa y. When he expe imen al and compu ed cu en s de ia e mo e han a p e ixed (also e y small) limi , 6L a mobili y educ ion is appa en a he sub- channel placed a he d ain end o he channel. Then, he mobili y in his subchannel is mul i- plied by a ac o o < in o de o ep oduce he expe imen al cu en again. The alues o he ans e se- and longi udinal-elec ic ields in his subchannel a e in oduced in an a ay: E ans (1) and Elong (1), espec i ely. 3) Vzs is inc eased again. In all he subchannels o which he longi udinal-elec ic ield is g ea e han Elong (1), he low- ield mobili y is mul iplied by A and he cu en hus ob ained is compa ed o he expe imen al one. When he de ia ion be ween he compu ed and expe i- men al cu en s is again g ea e han 61, a u he educ ion is assumed in he d ain end o he channel and he mobili y is once mo e mul iplied by A, hus ob aining a alue equal o he low-mobili y mul iplied by A2. The ans- e se- and longi udinal-elec ic ields in his subchannel a e in oduced as a new elemen o he a ay: E ans (2) and Elong (2), espec i ely. A he end o his p ocess, he mobili y alues o a se o pai s ( ans, long ) is ob ained. This is schema ized wi h he e ical solid line plo ed in Figu e 1. 3. VALIDATION PROCEDURE Once we de eloped he algo i hm o ob ain he dependence o he mobili y on he longi udinal- elec ic ield we p oceeded o alida e i . To do so, we simula ed se e al ou pu cu es, using ou d i -di usion simula o o a MOSFET and a supposed mobili y dependence, a e applying ou me hod we we e able o ep oduce his depen- dence, con i ming he co ec ness o he p ocedu e. (Fig. 2). 2 E ,,, )2.5 E ec S e Field (xlO V/cm FIGURE Tables (E ans(/) Elong(/)) used o accoun o he mobili y educ ion as he longi udinal ield ises. They co espond o ou di e en ou pu cu es. The solid line ep esen s a common chosen e ec i e ield o all he ables. This alue will be employed o ob ain he mobili y e sus longi udinal ield cu es. 3979, 1998, 1-4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1155/1998/52301 by Uni e sidad De G anada, Wiley Online Lib a y on [12/12/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License A METHOD FOR MOBILITY DEPENDENCES DETERMINATION 263 400 200 0 o 5 1o Longi udinel Field (x104 V/cm) FIGURE 3 Expe imen al elec on mobili y as a unc ion o he e ec i e- and longi udinal-elec ic ields a oom empe a u e. FIGURE 2 Mobili y cu es e sus longi udinal-elec ic ield ob ained wi h Equa ion o simula e ou pu cu es and alida e his me hod. The VSAT chosen was VSaT 1.1X 10 cm/s, /3 (solid line), /3 1.5 (long dashed line), /3 2 (sho dashed line). The esul s o ou me hod a e plo ed in squa es o /3 1, iangles o /3 1.5 and s a s o l 2. 4. EXPERIMENTAL RESULTS AND DISCUSSION A e ha ing alida ed he accu acy o ou me hod, we applied i o Si MOSFETs ab ica ed by Lucen Technologies wi h LEFF 0.6 gm, WEFF 201am, Tox 157 , NA 1.2 x 10 l cm -3 and RSD 130 . We ha e applied ou echnique o a se o measu ed ou pu cu es wi h 5I 10 -3 mA and A 0.96. The esul s ob ained can be obse ed in Figu e 3, whe e he mobili y e sus e ec i e and longi udinal ield su ace is shown. Exp ession was used o ob ain he/3 pa ame e and he sa u a ion eloci y VSAT. V(Ell, E+/-) /0 (E.l.) Ell +/- ( (#o(E+/-) x E]l) l) lsa The alues ha ga e a be e i we e/3 and VSA T 1.1 x 107 cm/s. These alues we e indepen- den o he e ec i e ield, con i ming he esul by Modelli and Manzini [4]. Using Tho nbe ’s exp ession wi h hese pa ame e s we ha e ied o ep oduce he expe imen al ou pu cha ac e is ics. The esul is shown in Figu e 4. The da a p o ided by his new p ocedu e a e e y use ul in o de o ob ain local mobili y models o d i -di usion simula o s, whe e he dependence o he longi udinal-elec ic ield is included. The in luence o he se ies esis ance and i s bias dependence can be aken in o accoun easily. I is also possible o assess he in luence o elec on eloci y o e shoo e ec s in e y sho channel MOSFETs by using a augmen ed mobili y model [5]. 6 0 0.0 0.6 1.2 1.8 2,4 D oin Vol cge (V) FIGURE 4 Expe imen al and simula ed ou pu cu es a T 300 K o a LEFF 0.6 gm MOSFET. The simula ed cu es ha e been ob ained by using he mobili y shown in Figu e 3, whose dependency on he longi udinal-elec ic ield was ob ained wi h his new me hod. 3979, 1998, 1-4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1155/1998/52301 by Uni e sidad De G anada, Wiley Online Lib a y on [12/12/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License 264 J.B. ROLD/N e al. 5. CONCLUSIONS Au ho s’ Biog aphies A new expe imen al me hod o de e mining he dependence o he elec on mobili y on he longi- udinal-elec ic ield has been de eloped, alida ed and applied o s anda d submic on MOSFETs. This me hod can be easily implemen ed in a 2D d i -di usion simula o . All he di e en depen- dencies o he elec on mobili y on he longi- udinal-elec ic ield can be aken in o accoun a he same ime by means o his me hod. A sa u a ion- eloci y alue o 1.1xl0Ycm/s was calcula ed by compa ing he mobili y cu es o Tho nbe ’s exp ession. Acknowledgemen s Juan B. Rold in g adua ed wi h a deg ee in physics in 1993, and ecei ed he Ph.D. in 1997 om he Uni e si y o G anada. Since 1993 he has been wo king on he MOS de ice physics including 2D anspo , non-local e ec s and Mon e Ca lo simula ions. Cu en in e es s a e also ela ed o SiGe and SiC de ices. He is a Teaching Assis an a he Uni e si y o G anada. F ancisco G imiz g adua ed wi h a deg ee in physics in 1991, and ecei ed he Ph.D. in 1994 om he Uni e si y o G anada. Since 1991 he has been wo king on he cha ac e iza ion o sca e ing mechanisms and hei in luence on he anspo p ope ies o cha ge ca ie s in semiconduc o he e os uc u es. His cu en esea ch in e es includes he e ec s o many-ca ie s on he We would like o hank Jos6 Ldpez Se ano om elec on mobili y and he in e p e a ion o he Lucen Technologies (Spain) o p o iding he in luence o high longi udinal elec ic ields ha e MOSFETs (0.9 lam echnology) we ha e used in on MOS ansis o s. Cu en in e es a e also ou s udy. This wo k has been ca ied ou ela ed o SiGe and SiC, and SCI de ices, and wi hin he amewo k o esea ch p ojec TIC quan um anspo . He has coau ho ed se e al 95-0511, suppo ed by he Spanish Go e nmen pape s in all hese subjec s. He is an Associa e (CICYT). P o esso a he Uni e si y o G anada. Juan A. Ldpez- illanue a g adua ed in 1984, Ph.D. in 1990 (Uni e si y o G anada) wi h a Re e ences hesis on he deg ada ion o MOS s uc u es by [1] Tho nbe , K. K. (1980). "Rela ion o d i eloci y o low- Fowle -No dheim unneling. Since 1985 he has ield mobili y and high- ield sa u a ion eloci y", J. Appl. been wo king on deep-le el cha ac e iza ion and, Phys., 51, 2127. [2] Rold in, J. B., G imiz, F., L6pez-Villanue a, J. A. and mainly, MOS de ice physics, including Fowle - Ca celle , J. E. (1995). "Mon e Ca lo simula ion o a No dheim and di ec unneling, quan um e ec s, submic on MOSFET including in e sion laye quan iza- 2D anspo , e ec s o nonpa abolici y, sca e ing ion", 4 h IWCE, p. 37. [3] Rold/m, J. B., G/ miz, F., L6pez-Villanue a, J. A. and mechanisms and Mon e Ca lo simula ion o Ca celle , J. Eo (1997). "Dependence o he elec on cha ge anspo . He has coau ho ed se e al mobili y on he longi udinal elec ic ield in MOSFETs", Semieond. Sci. Technol., 12, 321-330. pape s in all hese subjec s. His cu en esea ch [4] Modelli, A. and Manzini, S. (1988). "High- ield d i in e es includes, simula ion and modelling o eloci y o elec ons in silicon in e sion laye s", Solid-S a e Elec on., 31, 99. elec on de ices. His educa ional ac i i ies also [5] Rold/ n, J. B., G imiz, F., L6pez-Villanue a, J. A. and include analog sys ems o elec onic ins umen a- Ca celle , J. E. (1997). "Modeling e ec s o elec on ion and powe elec onics He is an Associa e eloci y o e shoo in a MOSFET", IEEE T ansc. on Elec on De ices, 44, 841-846. P o esso a he Uni e si y o G anada. 3979, 1998, 1-4, Downloaded om h ps://onlinelib a y.wiley.com/doi/10.1155/1998/52301 by Uni e sidad De G anada, Wiley Online Lib a y on [12/12/2024]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License