PERFORMANCE ANALYSIS OF QUANTUM TRANSPORT PHENOMENON IN FULLY DEPLETED DOUBLE GATE DECA NANOMETER SOI MOSFET

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1 oural of Electro evices, Vol. 6, 0, E ISSN: PERFORMANCE ANAYSIS OF QUANUM RANSPOR PHENOMENON IN FUY EPEE OUBE GAE ECA NANOMEER SOI MOSFE Rajiv Sharma,*, Sujata Padey, Shail Bala ai 3,3 eartmet of Electroics ad Commuicatio Egieerig, Guru Gobid Sigh Idrarastha Uiversity, elhi, Idia. eartmet of Electroics ad Commuicatio Egieerig, Amity Uiversity, Sector-5 Noida, Idia. rsa70@rediffmail.com Received 0--0, olie ABSRAC Effects of carrier eergy uatizatio i semicoductor surface regio o erformace of Fully eleted ouble Gate eca Naometer SOI MOSFE is theoretically cosidered. AAS device simulator is used to aalyze oeratio ad erformace of our device. Simulatio of device is based o drift diffusio trasort model ad eergy balace trasort model. etailed comariso of both trasort models shows accuracy ad efficiecy of eergy balace trasort model to redict electrical characteristics of ultrascaled devices due to icororatio of uatum effects i this model. Simulatio results also show effect of carrier cocetratio o erformace of our device for differet cocetratios. Keywords: rift-iffusio () Model, Eergy Balace (EB) Model, Semicoductor Idustry Associatio (SIA), eca-naometer, Volume Iversio ad AAS Simulator I. INROUCION ouble Gate MOSFEs havig thi Si film bodies will ossibly costitute the mai stream CMOS techology at the ed of SIA roadma. he cotiuous scalig of MOS dimesio reuires the use of ultra thi gate dielectric layer ad high substrate doig cocetratio which leads to high trasverse electric field at oxide-semicoductor iterface. Such a strog field at the iterface gives rise to slittig of coductio bad ito discrete sub-bads ad uatum mechaical effects become sigificat -3. he carrier distributio ad the trasort roerties of the carriers uder the ifluece of uatum mechaical effect are uite differet from the classical case. For examle, i classical case, the motio of the carrier is ot restricted i ay directio but the uatum mechaical effect limits the carrier motio i directio arallel to the oxide-semicoductor iterface oly. he electrical characteristics redicted by the classical model could be very differet from the oe redicted usig a uatum mechaical effect based model. I most uatum simulatio beig develoed today, a recursive techiue is used, either for the wave fuctio 4 or, more freuetly, for the gree s fuctio 5-7. hese aroaches have bee uite successful i describig steady state trasort i a wide variety of -, - or 3- semicoductor structures 8-. Recet studies show that i both uatum ad classical trasort frameworks, scatterig mechaisms have sigificat role o the oeratio ad erformace of ouble Gate Naoscale MOSFEs -4. I this aer, we carry out a simulatio based study o trasort mechaisms of Fully eleted ouble Gate Naoscale SOI MOSFE. he commercially M available AAS 5 device simulator has bee used to obtai simulatio results for our device. he AAS software solves

2 umerically the Poisso s euatio. Amog the drift-diffusio () model, eergy balace (EB) model ad hydrodyamic (H) model available i AAS library, device simulatio carried out i this aer is based o drift diffusio () trasort model ad eergy balace (EB) trasort model. Curret desity euatios i drift-diffusio trasort model are obtaied by alyig aroximatio ad simlificatios to Boltzma rasort Euatio. rift-iffusio () trasort model eglects uatizatio of electro eergy. he drift-diffusio model is less accurate for aoscale devices as it does ot accout for olocal trasort effects. Ifluece of olocal trasort effects such as velocity overshoot, diffusio associated with the carrier temerature ad the deedece of imact ioizatio rates o carrier eergy distributios is of rime imortace for correct evaluatio of electrical characteristics of ultra scaled ouble Gate SOI MOSFEs. Alicability of eergy balace trasort model to aoscale devices is essetial because i cotrast to covetioal drift-diffusio trasort model, it accouts for olocal trasort effects. Eergy balace trasort model accouts for olocal trasort effects by icludig additioal euatios for the carrier temerature i the curret desity exressios therefore eergy balace trasort model roves to be more accurate comared to driftdiffusio () model. II. HEOREICA MOE ESCRIPION ue to imortace of uatum mechaical effects i the MOS structure characterizatio, simlified ivestigatio methods ad modelig as well as thorough umerical ivestigatios by self cosistet solutio of Schrödiger ad Poisso s euatios are develoed. Sice the self cosistet solutio of Schrödiger ad Poisso s euatios are very comlex ad exesive, some simlified methods of aalysis 335 are emloyed. Quatum mechaical correctios are usually derived either from the triagular well aroximatio (airy fuctio aroximatio) or the variatioal techiue.he most commoly used method is the triagular well aroximatio based o the assumtio of a liear distributio of otetial i the iversio layer i.e. the costat electric field i the iversio layer. his assumtio allows to decoule Schrödiger ad Poisso s euatio. As a result, the aalytical exressio for the electro eergy states is obtaied E i ij h ( m xj,,3,... ) / 3 3 F ( i s ) 4 / 3 () where Fs deotes the effective electric field i the semicoductor surface regio F s where Q N ( k ) () / del s b s B is the deletio layer charge ( s deotes the surface otetial) ad: Q iv. is the total iversio layer charge desity Q., Nij are sub bad occuatio iv N ij ij factors obtaied from Fermi-irac statistics to be: N 0.5Q iv. ( E) f ( E de (3) ij j ) E I s Q del where f (E) is Fermi occuatio factor ad j (E) is two-dimesioal desity of states of a sub bad. All the more desely saced sub bads lyig high i eergy above the bad edge at the iterface may be aroximated by a cotiuous bad. I case of classical descritio, where the uatizatio of electro eergy is eglected, we use drift diffusio trasort model descritio

3 of the semicoductor regio. he curret desity euatios or charge trasort models are usually obtaied by alyig aroximatios ad simlificatios to the Boltzma rasort Euatio. hese assumtios ca result i a umber of differet trasort models such as the drift-diffusio trasort model, the eergy balace trasort model or the hydrodyamic trasort model. he simlest model of charge trasort that is useful is the drift-diffusio model. Util recetly, the drift-diffusio model was adeuate for early all devices that were techologically feasible. he drift-diffusio aroximatio, however, becomes less accurate for smaller feature sizes. More advaced eergy balace ad hydrodyamic models are therefore becomig oular for simulatig dee submicro devices. AAS sulies both driftdiffusio ad advaced trasort models. II.. rift iffusio rasort Model erivatio based o Boltzma trasort theory has show that the curret desity i the cotiuity euatios may be aroximated by a drift diffusio model 6. I this case, the curret desities are exressed i terms of uasi-fermi levels ad as: (4) (5) where ad are electro ad hole mobility. he uasi-fermi levels are the liked to the carrier cocetratio ad otetial through the two Boltzma aroximatios: ( ) ie ex (6) ( ) ie ex (7) where ie is the effective itrisic cocetratio ad is the lattice temerature. hese two euatios may the be re-writte to defie the uasi-fermi otetials: ie (8) l (9) By substitutig these euatios ito the curret desity exressios, the followig adated curret relatioshis are obtaied ( (l )) (0) ie ( (l )) () ie he fial term accouts for the gradiet i the effective itrisic carrier cocetratio, which takes accout of bad ga arrowig effects. Effective electric fields are ormally defied whereby: E ( l ie) () E ( l ie) (3) which the allows the more covetioal formulatio of drift-diffusio euatios to be writte. his derivatio of the drift-diffusio assumes that the Eistei relatioshi holds. I case of Boltzma statistics this corresods to: E (4) E (5) (6) l ie (7) 336

4 If Fermi irac statistics are assumed for electros, Euatio (3) becomes ( ) F/ F C (8) F / F C where F is the Fermi-irac itegral of the order ad is give by F. A aalogous exressio for holes with Fermi- irac statistics will be ( ) F/ F v. (9) F / F v eergy flux desities are the exressed: (0) () k S K () k S K (3) where ad reresets the electro hole carrier temerature ad S ad S are the flux of eergy from the carrier to the lattice. III. EVICE SRUCURE SIMUAE he structure of the Fully eleted ouble Gate SOI MOSFE used i this aer is schematically reseted i fig.. II.. Eergy Balace rasort Model he covetioal drift-diffusio model of charge trasort model eglects o-local trasort effects such as velocity overshoot, diffusio associated with the carrier temerature ad the deedece of imact ioizatio rates o carrier eergy distributios. hese heomeos ca have a sigificat effect o the termial roerties of aoscale devices. he eergy balace trasort model follows the derivatio by Stratto 3-4 which is derived startig from the Boltzma rasort Euatio. he eergy balace model adds cotiuity euatios for the carrier temeratures ad treats mobility ad imact ioizatio coefficiets as fuctios of the carrier temeratures rather tha fuctios of local electric field. he eergy balace trasort model itroduces two ew ideedet variables ad, the carrier temerature for electros ad holes. A higher order solutio to the geeral Boltzma rasort Euatio cosists of a additioal coulig of the curret desity to the carrier temerature, or eergy. he curret desity exressios from the drift-diffusio model are modified to iclude this additioal hysical relatioshi. he electro curret desity ad 337 Fig. : Schematic diagram of a Fully eleted ouble Gate Naoscale SOI MOSFE. We cosider N chael devices. his symmetric structure is characterized by two idetical Alumium metal gates coected together. he thickess of -tye doed silico ( t si ) is 6m, chael legth () for device is 0m, doig level of -tye silico chael i.e. N b = x0 7 m -3, to/bottom gate oxide thickess i.e. t =.5m. he source/drai regios are uiformly doed at a

5 level of x0 0 m -3. he same gate voltage V is alied to both gates. ow field mobility ( o ) is 750cm / Vs ad all simulatios have bee doe at room temerature i.e. at =300 K. ue to extremely short chael of the modeled device, the carrier behavior withi the chael is exected to be uasi-ballistic, thus allowig a strog velocity overshoot to be reached. As exected, the eergy balace trasort model gives higher currets comared with the driftdiffusio trasort model, due to the electro velocity overshoot with i the chael. Fig. : Structure created o deckbuild of AAS device simulator for rift-iffusio rasort Model ad Eergy Balace rasort Model with chael legth m, =0m, source/drai (+) doig Alumium gates with work fuctio 4.0 electro Volt, to/bottom gate oxide thickess i.e. t =.5m, doig level of -tye silico chael N b = x0 7 m -3 ad thickess of silico chael t si = 6m. Figure shows the structure created o deckbuild of AAS device simulator for driftdiffusio trasort model ad eergy balace trasort model resectively. Figure 3 shows comariso of drai curret ( I d ) versus gate to source voltage ( V ) characteristic for our device emloyed with drift-diffusio trasort model ad eergy balace trasort model. Here, electrical characteristics I d ( V, V ds ) for a double gate fully deleted aoscale SOI MOSFE are ivestigated. he drai curret as a fuctio of gate voltage is lotted i figure 3. he results obtaied from eergy balace trasort model are comared to the driftdiffusio trasort model aroach. Electrical characteristics as redicted by covetioal drift-diffusio trasort model vary from the oe obtaied by uatum effect based model i.e. eergy balace trasort model i our case. 338 Fig. 3: he simulated outut characteristics showig comariso of I ds versus V for rift-iffusio rasort Model ad Eergy Balace rasort Model. Figure 4 shows structure created o deckbuild of AAS showig mobility of simulated device with chael doig N b = x0 7 m -3. Simulated outut characteristic created o deckbuild of AAS showig mobility of simulated device with chael doig N b = x0 7 m -3 is show i figure 5. Figures 6 ad 7 show structure ad simulated outut characteristic resectively created o deckbuild of AAS showig mobility of simulated device with chael doig N b = 5x0 8 m -3. Recet studies o sub 00m bulk MOSFEs have made it clearer that a higher imurity cocetratio ( N 5x0 8 m -3.) i the chael b is idisesable i suressig short chael effects. his uts a strog limitatio o device scalig. he advatage of Fully eleted SOI MOSFEs, esecially a double gate structure is that it ca rovide high short chael effect

6 (SCE) immuity with a low cocetratio chael (lightly doed). Aalyzig the erformace of device o the basis of varyig the doig cocetratio i the chael, it is observed that lower cocetratio (fig. 5) i double gate fully deleted SOI MOSFE results i higher mobility ad therefore better erformace whereas high cocetratio (fig. 7) degrades carrier mobility thereby resultig i oor device erformace. Fig. 6: Structure created o eckbuild of AAS device simulator with doig level of -tye silico chael i.e. N b = 5x0 8 m -3. Chael legth = 0m, source/drai (+) doig of x0 0 m -3, Alumium gates, with work fuctio of 4.0 ev, to/bottom gate oxide thickess i.e. t =.5m, ad thickess of silico chael t si is 6m. Fig. 4: Structure created o deckbuild of AAS device simulator with chael legth =0m, source/ drai (+) doig of x0 0 m -3, Alumium gates, with work fuctio of 4.0 ev, to/bottom gate oxide thickess i.e. t =.5m, doig level of -tye silico chael i.e. N b =x0 7 m -3 ad thickess of silico chael t si = 6m. Fig. 7: he simulated outut characteristics showig variatio of mobility with distace alog the chael for chael doig N b = 5x0 8 m -3. Fig. 5: he simulated outut characteristics showig variatio of mobility with distace alog the chael for chael doig N b = x0 7 m IV. CONCUSION We reset results of Fully eleted ouble Gate SOI eca Naometer MOSFE erformace carried out usig AAS -CA

7 device simulator. Ifluece of o local trasort effects is of rime imortace for correct evaluatio of electrical characteristics of ultrascaled double gate SOI MOSFEs. Covetioal drift-diffusio trasort model is ot efficiet i caturig these o-static effects. Eergy balace trasort model accouts for o local trasort effects by icludig imact ioizatio coefficiet as a fuctio of temerature, therefore eergy balace trasort model roves to be more accurate comared to drift-diffusio model. Further device simulatios were carried out with two differet doig cocetratios i silico chael. As exected, simulatio results cofirm the fact that Fully eleted ouble Gate SOI MOSFEs with low imurity cocetratio rovides better erformace. Refereces. he Iteratioal echology Roadma for Semicoductor, 007. Olie. Available: htt://ublic.itrs.et.. F. Ster, Self-Cosistet results for -tye silico iversio layers, Phys. Rev. B. Codes. Matter, 5, 489 (97) 3.. Ado, A.B. Fowler ad F. Ster, Proerties of -dimesioal electro system, Rev. Mod. Phys., 54, 437 (98) 4. M.. Gilbert, R. Akis, ad. K. Ferry, Efficiet three-dimesioal modelig of fully deleted ballistic silico-o-isulator-metaloxide-semicoductor field-effect trasistor,. Al. Phys., 95, 7954 (004) 5. A. Svizheko, M. P. Aatram,. R. Govida, ad B. Biegel, wo-imesioal uatum mechaical modelig of aotrasistors,. Al. Phys., 9, 343 (00) 6.. Wag, E. Polizzi, ad M. udstrom, A three-dimesioal uatum simulatio of silico aowire trasistor with the effective-mass aroximatio,. Al. Phys., 96, 9 (004) 7. M. Bescod, K. Nehari,.. Autra, N. Cavassilas,. Muteau, ad M. aoo, 3 uatum modelig ad simulatio of multi-gate aowire MOSFEs, Proceedi of IEM ech. ig., Washigto, USA, 67 (004) 8. M. P. Aatram ad. R. Govida, Coductace of carbo aotubes with disorder: A umerical study, Phys. Rev. B., 58, 488 (998) 9. G. Fiori, G. Iaaccoe, M. udstrom, ad G. Klimeck, hree-dimesioal atomistic simulatio of carbo aotubes FEs with realistic geometry, Proceedi of ESSERC, Greoble, Frace 537 (005) 0. R. ake ad S. atta, Noeuilibrium gree sfuctio method alied to double-barrier resoat tuelig diodes, Phys. Rev. B., 45, 6670 (99). R. Veugoal, M. Paulsso, S. Goasgue, S. atta, ad M. S. udstrom, A simle uatum mechaical treatmet of scatterig i aoscale trasistors,. Al. Phys., 93, 563 (003). A. Svizheko ad M. P. Aatram, Role of scatterig i aotrasistors, IEEE ras. Electro evices, 50, 459 (003) 3.. S. Marti, A. Bourel, ad P. ollfus, O the ballistic trasort i aometer-scaled double gate MOSFE, IEEE ras. Electro evices, 5, 48 (004) 4. P. Palestri,. Essei, S. Emiete, C. Fiega, E. Sagiorgi, ad. Selmi, Uderstadig uasi-ballistic trasort i ao-mosfes: Part -Scatterig i the chael ad i the drai, IEEE ras. Electro evices, 5, 77 (005) 5. Silvaco, AAS user s maual, device simulatio software, Silvaco Iteratioal, Sata Clara, CA, USA, (004) 6. S. Selberherr, Aalysis ad Simulatio of Semicoductor evices, Sriger-Verlag, Wei-New York (984),