NUMERICAL SIMULATION OF NANOSCALE DOUBLE-GATE MOSFETS

Transcription

1 NUMEICAL SIMULAION OF NANOSCALE DOULE-AE MOSFES olad Sezel, Leif Müller, om Herrma, Wilfried Klix Dearme of Elecrical Egieerig Uiversiy of Alied Scieces Dresde Friedrich-Lis-Plaz, D-69 Dresde ermay ASAC he furher imroveme of aoscale elecro devices reuires suor by umerical simulaios wihi he desig rocess. Afer a briefly descriio of our D/D-device simulaor SIMA, he resuls of he simulaio of D-MOSFEs are rereseed. Sarig from a basic srucure wih a gae legh of m, a calibraio of model arameers was doe based o measured values from lieraure. Aferwards a variaio of gae legh, chael hicess ad doig, gae oxide arameers ad source/drai doig was carried ou i coecio wih he umerical calculaio of device characerisics. hereafer a oimizaio of a D-MOSFE wih a gae legh of 5 m was doe. he oimized srucure shows suressed shor chael behavior ad shor swichig imes of abou.5 s. Keywords Device simulaio, semicoducor devices, double-gae MOSFE NOAION, hole ad elecro desiy ϕ elecrosaic oeial, ioized door ad acceor desiy ε s ermiiviy of semicoducor elemeary charge, curre desiies, recombiaio ad geeraio rae, carrier mobiliies, uaum correcio oeials Θ, Θ bad arameers D, D diffusio coefficies, carrier emeraures olzma cosa S, S eergy flux desiies E elecric field sregh L laice emeraure w, w eergy relaxaio imes m, m carrier effecive masses h reduced Placs cosa γ, γ uaum correcio coefficie κ, κ hermal coduciviies INODUCION Double-ae (D) MOSFEs are cosidered o be oe romisig cadidae for aoscale CMOS. he Ieraioal echology oadma for Semicoducors (5 Ediio) redics ried gae leghs u o 5 m for he ex years. For hese gae leghs coveioal MOSFEs are limied due o differe shor chael effecs. O he oher had srucures wih wo gaes ad exremely hi body demosrae a beer corol of he gae regio ad coseuely a suressio of shor chael effecs. Numerical device simulaio is a imora rocedure for he desig ad oimizaio of ovel semicoducor devices. Advaages are he calculaio of he elecrical behavior before he fabricaio rocess, he calculaio ad visualizaio of ier-elecroic values which are o measurable, he diagosis/faul-deecio i he echological rocess ad coseuely he cos efficiecy. SIMULAION MODELS he uaum hydrodyamic (QHD) models, which are based o a uaum fluid dyamic model, offers exadig ossibiliies for he udersadig as well as he desig of uaum sized semicoducor devices. he advaage of his model is is macroscoic characer, which eables o obai descriio wihou owledge of

2 uaum mechaical deails lie iiial wave fucio [], [], []. he classical hydrodyamic (HD) model for he semicoducor device simulaio ca be exeded by exressios i he rasor ad i he eergy balace euaios hey describe a ieral uaum oeial i he rasor euaio as well as a uaum hea flux i he eergy balace euaio. hese addiioal erms i he classical hydrodyamic model allow o describe coiuous elecro ad hole disribuio i a semicoducor device, accumulaios of carriers i oeial wells ad resoa uelig of carriers, resecively. he sadard model for uiversal device simulaios is he drifdiffusio (DD) model, which ca be derived from he above meioed model [4]. asic euaios of he QHD model are he Poisso euaio ( ) ( ) ( ) A D s N N ϕ ε () coiuiy euaios (idex : holes, idex : elecros) () () rasor euaios ( ) ( ) ( ) D Θ ϕ (4) ( ) ( ) ( ) D Θ ϕ (5) eergy balace euaios ( ) ( ) ( ) ( ) ( ) w w L E S (6) ( ) ( ) ( ) ( ) ( ) w w L E S (7) eergy flux desiy euaios ( ) 5 S κ (8) ( ) 5 S κ (9) ad euaios for he uaum correcio oeial 6 m γ h () m 6 γ h () Furher aroaches are ecessary for carrier mobiliies, geeraio ad recombiaio raes, diffusio coefficies ad eergy relaxaio imes, which are almos maerial deedely. Euaios () o () are solved self-cosisely for he variables (ϕ,,,,,, ). If euaios () ad () are egleced, ha meas for,, QHD model ca be reduced o he coveioal hydrodyamic (HD) model. If carrier emeraures are se o laice emeraure ad euaios (6) o (9) are egleced, he uaum drif diffusio (QDD) model ad addiioally for he coveioal drif diffusio (DD) model ca be obaied. Soluio of he euaios are achieved by a successive algorihm (so called ummel algorihm). For he soluio of he arial differeial euaios a box mehod is used. he resulig o-liear euaio sysems are solved by he

3 I D (A/m) I D (A/m) NEWON-mehod ad corresodig liear euaio sysems by recodiioed gradie mehods. All models are imlemeed full hree-dimesioal i he rogram sysem SIMA [5] [6]. ASIC SUCUE SIMULAIOND VEIFICAION Sarig oi of he simulaios is a basic srucure, rereseed i Figure, as fucioal releva deail of he real device. he differe arameers are assumed as followig: gae legh L m, source/drai leghs L S L D m, gae-o-source ad gae-o-drai disaces L S L D m, silico film hicess Si m, gae oxide hicess ox m, chael doig 6 cm -, source/drai doig cm -. / 5 / 5 /,, / 5, 6 :, ), 6 : 6 5 E / Fig. : asic srucure of he D-MOSFE he simulaed ouu characerisics drai curre I D versus drai-o-source volage are loed i Figure for differe gae-o-source volages V S. Verificaio of he simulaio resuls ad calibraio of he model arameers were doe by comariso wih exerimeal values from [7]. A srucure similar o Figure wih L 45 m, ox.5 m, cm - was simulaed ad comared wih he measured values. he resuls rereseed i Figure show a good agreeme. A furher successful verificaio was doe by resuls from [8]. V S.V V S.V 4 Simulaio [SIMA] Exerime [7] V.5V V S.8V V S.6V - V S.4V Fig. : Ouu characerisics of he basic srucure V S Fig. : rasfer characerisics - Simulaio ad exerime PAAMEE VAIAIOND OPIMIZAION o sudy he ifluece of he srucure arameers o he elecrical device characerisics differe arameers are modified. I Figure 4 ad 5 he ouu ad he rasfer characerisics a differe gae leghs are deiced. A shorer gae leghs a hreshold volage roll off ca be observed as a yical shor chael effec i aricular ich-off behavior disaears for L < m. A he same ime drai sauraio curre icreases srogly.

4 I D (A/m) I D (A/m) I D (A/m) I D (A/m) 4 L m L 5m V S V 5 4 L m L m L 5m L m L 45m L 9m L 45m L 9m -4 V Fig. 4: Ouu characerisics a differe gae leghs V S Fig. 5: rasfer characerisics a differe gae leghs Variaio resuls of he silico film hicess are rereseed i Figure 6. hicer chaels lead o larger drai curres bu also o a dislaceme of he hreshold volage oward smaller values. herefore he film hicess should be o larger ha m. hier gae oxides resul i icreasig drai curres (Figure 7) ad rascoducaces ad i a beer ich-off behavior. Accordig o ha he smalles ossible oxide hicess should be alied. 4 4 V S V Si m V S V Ox m Si 5m Ox.5m Si m Ox m Si 5m Ox.5m Si m Ox m Si 5m Fig. 6: Ouu characerisics a differe chael hicess Fig. 7: Ouu characerisics a differe gae oxide hicess Variaio of he chael doig causes a decrease of he drai curre for doig desiies greaer ha 7 cm - (Figure 8). Furhermore he hreshold volage is srogly iflueced by doig chages. For oimizaio of he srucures, chael doig ca be used o adjus he reuired hreshold volage. he source/drai doig should be high eough o reduce series resisaces whereas he doa diffusio io he chael has o miimize o reve shor chael effecs. I his case raid hermal aealig rocesses are a esseial reuireme. Figure 9 shows he corresodig ouu characerisics.

5 I D (A/m) I D (A/m) I D (A/m) I D (A/m) 4 4 V S V V S V x cm - x 6 cm - 5x cm - x 7 cm - x cm - x 8 cm - x cm - 5x 9 cm - 5x 8 cm - x 9 cm Fig. 8: Ouu characerisics a differe chael doig Fig. 9: Ouu characerisics a differe source/drai doig he owledge from differe variaios was used for he desig of a oimized srucure. A miimal echologically racicable gae legh of L 5 m ad a gae oxide hicess of ox.5 m are secified. Furher objecives are hreshold volage of V h. V, large drai sauraio curre ad imroved dyamical behavior. Afer several ieraios he furher arameers are deermied as follows: Si m,.8 9 cm -, 7 cm -. he resulig ouu characerisics are rereseed i Figure. Figure shows he comariso bewee rasfer characerisic of he oimized ad basic srucure. A elarged drai curre as well as a imroved rascoducace ca be observed. 6 4 V S.V V V S.V V S.8V V S.6V asic srucure Oimized srucure V S.4V Fig. : Ouu characerisics of he oimized srucure V S Fig. : rasfer characerisics of he basic ad he oimized srucure For he deermiaio of he dyamical behavior he gae-o-source volage was swiched from V o V o fid he ur-o ime ( ON ) ad from V o V o fid he ur-off ime ( OFF ). Figure shows he ime resose of he drai curre. herefrom he swichig imes resul o ON OFF.5 s. Comared wih he basic srucure he swichig imes are reduced by he facor.6 due o he srucure reducio rimarily.

6 I D (ma/m) V OFF (V S V -> V) - ON (V S V -> V) -... (s) Fig. : Swichig behavior of he oimized srucure CONCLUSION he scalig dow of laar bul MOSFEs accordig he Ieraioal echology oadma for Semicoducors reuires ew srucures such as mulile-gae MOSFEs. Oe of he romisig ossibiliies are double-gae rasisors. he imlemeaio will be challegig wih umerous ew ad difficul issues. I his case umerical device simulaio is esseial. Variaios of differe srucure arameers have bee carried ou o calculae he ifluece o device characerisics. ased o hese resuls a oimized srucure wih a gae legh of 5 m was creaed. he oimized srucure shows suressed shor chael effecs ad swichig imes of abou.5 s. EFEENCES [] arder,c.l.: he uaum hydrodyamic model for semicoducor devices. SIAM. Al. Mah., 54 (), 994, [] Che, Z.: A fiie eleme mehod for he uaum hydrodyamic model for semicoducor devices. Comu. Mah. Al.,, 996, [] Wesei, A. - Sche, A. - Ficher, W.: Quaum device simulaio wih he desiy-gradie model o usrucured grids. IEEE ras. Elecro Devices, 48 (),, [4] Selberherr, S.: Aalysis ad Simulaio of Semicoducor Devices. erli, ermay, Sriger-Verlag 984. [5] Klix, W. - Sezel,.: SIMA-User Maual. h:// [6] Höschel,. - Sezel,. - Klix, W.: Simulaio of uaum rasor i moolihic ICs based o I.5 a.47 As-I.5 Al.48 As Ds ad HEMs wih a uaum hydrodyamic rasor model. IEEE ras. o Elecro Devices, 5 (5), 4, [7] Lee,.H., e al: Suer self-aliged double-ae (SSD) MOSFEs uilizig oxidaio rae differece ad selecive eiaxy. IEDM, ech. Diges, 999, [8] Vie, M., e al: oded laar double-meal-gae NMOS rasisor dow o m. IEEE Elecro Device Leers, 6 (5),. 7-9