第 29 卷 　第 5 期2008 年 5 月

半 　导 　体 　学 　报J OU RNAL O F S EMICOND U C TO RS

V ol . 29 　N o. 5

May ,2008

3 Project supp orted by t he National Natural Science Foundation of China (No. 60206006) a nd t he National Def ense Pre2Research Foundation of China

(No. 51308040103)

­ Corresp onding aut hor . Email :szluan @mail . xidia n . edu. cn

　Received 16 Nove mber 2007 , revised ma nuscrip t received 10 Dece mber 2007 Ζ 2008 Chinese Instit ute of Elect ronics

An Analytical Model of Drain Current for Ultra2Thin Body and Double2GateSchottky Source/ Drain MOSFETs Accounting for Quantum Effects 3

L ua n Suz he n­ , L iu Hongxia , J ia Re nxu , Cai Naiqiong , Wa ng J in , a nd Kua ng Qia nwei( Key L aboratory f or Wide Ba nd2Gap Semiconduct or Materials a nd Devices of Minist ry of Education , School of Microelect ronics ,

Xidia n University , Xi’an 　710071 , China)

Abstract : A comp act drain cur rent including t he variation of bar rier heights and car rier quantization in ult rat hin2body and

double2gate Schot t ky bar rie r MOSF ETs (U TBD G SB F ETs) is developed. In t his model ,SchrÊdinger’s equation is solved u2sing t he t riangular p otential well app roximation. The car rie r density t hus obtained is included in t he sp ace charge density t o

obtain quant um car rier confinement eff ects in t he modeling of t hin2body devices . Due t o t he quantum eff ects , t he f irst sub2band is higher t han t he conduction band edge , w hich is equivalent t o t he band gap widening. Thus , t he bar rier heights at

t he source and drain increase and t he car rier concent ration decreases as t he drain cur rent decreases . The drawback of t he

existing models ,w hich cannot p resent an accurate p rediction of t he drain current because t hey mainly consider t he eff ects

of Schot t ky bar rie r lowering (SBL ) due t o image f orces ,is eliminated. Our research results suggest t hat f or small nonnega2tive Schot t ky bar rier (SB) heights ,even f or zero bar rier height , t he tunneling cur rent also plays a role in t he t otal on2state

cur rents . Verif ication of t he p resent model was car ried out by t he device numerical simulat or2Silvaco and showed good

agreement .

Key words : Schot t ky bar rie r ; quantum eff ects ; t he eff ective mass ; elect ron density

PACC : 7340Q ; 0365 ; 7110C

CLC number : TN386 　　　Document code : A 　　　Article ID : 025324177 (2008) 0520869206

1 　Introduction

The Sc hot t ky ba r rie r MOS F E T has a si mila r de2vice st ruct ure t o t he conve ntional MOS F E T , but t he

source/ drai n regions a re ma de of silicide or metal

rat he r t ha n heavily dop e d se miconduct or [ 1 ,2 ] . The de2vice of f e rs seve ral p ote ntial a dva ntages ove r a con2ve ntional MOS F E T at na nomete r scale . The ref ore ,

scali ng beyond t he li mit of t he conve ntional MOS F E T

is bei ng exp lore d . B y usi ng metal source/ drai n ,

SB F E Ts w ould esse ntially eli mi nate t he p a rasitic re2sista nce , a nd t hus could delive r more on cur re nt t ha n

t he conve ntional MOS F E Ts [ 3 ,4 ] . As mode rn VLSI de2vices scale dow n , t he gate oxide is get ti ng t hi nne r .

Conseque ntly , t he st rong t ra nsve rse elect ric f ield a nd

deep p ote ntial well nea r t he Si/ SiO 2 inte rf ace lea d t o

t he qua ntiza tion of mobile ca r rie r e ne rgy , i . e . , qua n2t um mec ha nical ef f ects (Q M E’s) .

Q M E’s have signif ica nt i nf lue nce on MOS F E T

be havior such as t h res hold voltage s hif t [ 5 ] , maxi mum

gate cap acit a nce scali ng , a nd low voltage app lica2t ion [ 6 ] . Theoretical st udies of SB F ETs have f ocused on

assessi ng device op e ration at na nomete r scale , t reati ng

t he t unneli ng t h rough Schot t ky ba r rie rs a nd f it ti ng

t he exp e ri me ntal data [ 7～9 ] . For t hi n body devices ,

qua nt um conf i ne me nt raises t he elect ron e ne rgy levels

i n t he silicon a nd t he ef f ective ba r rie r height . I n t his

p ap e r , t he solution of t he Sc hrÊdinge r equation under

t he t ria ngula r p ote ntial well app roxi mation is coup le d

wit h t he numerical solution of t he Poisson equation .

A n ite ration p rocedure is e mployed t o f i nd t he self2consiste nt results of ca r rie r dist ribution a nd p ote ntial

p rof ile i n t he i nve rsion a nd accumulation laye r i n t he

MOS st ruct ure . A n ef f ective elect ric f ield is def i ne d

by com bi ni ng t he mobile ca r rie r sheet de nsit y a nd de2p letion cha rge s heet de nsit y . The n , a close d f or m of

drai n cur re nt f or U TB D G SB F E T is p rese nted f ully ,

i ncludi ng Q M eff ects . Model ve rif ica tion is ca r ried out

usi ng t he 22di me nsional device si mulat or Silvaco [ 10 ] .

2 　Drain current model ing

2. 1 　Energy band model and quantum charge

The st ruct ure of t he U TB D G SB F E T is dep icte d

i n Fig1 1 . Dete r mi ning t he ca r rie r dist ribution a nd p o2te ntial p rof ile i n t he qua ntized i nve rsion a nd accumu2la tion laye r i n U TB D G SB F E T st ruct ure requi res sol2vi ng coup led Sc hrÊdinge r’s a nd Poisson equations .

半 　导 　体 　学 　报 第 29 卷

Fig. 1 　Illust ration of U TBD G SB F ET wit h silicide/ metal

source and drain

The one2dime nsional (12D ) Poisson equation is give n

as :

d2 <( z)d z2 = -

qεSi

( p - n + Nsub ) (1)

w here <( z) is elect ric p ote ntial ; p a nd n a re hole a nd

elect ron conce nt ration , resp ectively ; a nd Nsub is t he

cha nnel dop i ng conce nt ra tion . I n t he ve rtical di rec2t ion ( t he z2di rection in Fig1 1 ) , t he Sch rÊdi nge r’s

equation was solve d f or each x2p osition i ndep e nde ntly

t o ge ne ra te eige n2e ne rgy of t he it h subba nd a nd jt h

valley E ij a nd t he cor resp onding wave f unction Ψij

-∂ 2

2 m 3zj

×d2Ψij

d z2 - q<( z)Ψij = E ijΨ ij (2)

w here m 3zj is t he eff ective mass along t he z2di rection

of t he jt h valley wit h m 3z1 = 01 916 m0 ( m0 = 91 1 ×

10 - 31 kg) a nd m 3z2 = 01 910 m0 (subsc rip t 1 ref e r ri ng t o

t he unp ri me d valley a nd 2 ref e r ring t o t he p ri med val2ley f or a silicon wit h〈100〉c rystal orie nta tion , ∂ is

t he reduced Pla nc k’s consta nt , a nd m0 t he f ree elec2t ron mass) .

I n ea rlie r w or ks , t he solutions t o e ne rgy levels f or

MOS st ruct ure usi ng p a ra bolic p rof ile a re reasona ble

bot h in t he subt h reshold region a nd i n t he st rong i n2ve rsion region . Howeve r , a n a nalytical solution ca n

not be obtai ne d on t he basis of p a ra bolic p ote ntial .

The t heory of qua nt um mecha nics shows t ha t t he low2e r e ne rgy levels rest on t he p ote ntial dist ribution at

t he bot t om of t he p ote ntial well . Thus , we assume a

t ria ngula r well i n t he cha nnel a nd i nf i nitely high p o2te ntial ba r rie rs at t he silicon/ oxide i nte rf aces along

t he z2di rection . The n , t he solution of SchrÊdi nge r’s

equation i n t ria ngula r p ote ntial well is ,

E ij =∂ 2

2 m 3zj

1/ 3

× 32πqFs i +

34

2/ 3

(3)

To def ine Fs i n Eq. (3) , a n ef f ective elect ric f ield i n

i nve rsion laye r is a dop ted :

Fs = q (ηNe + N d ) /εSi (4)

w here Ne a nd N d a re inve rsion ca r rie r de nsit y a nd de2p letion cha rge de nsity , resp ectively ; a nd η is a f it p a2ra mete r . I n t he accumula tion laye r , N d is ze ro a nd Ne

is t he accumula tion ca r rie r de nsity . I n Refs . [ 11 ,12 ] ,ηis t a ke n as 01 5 . Alt hough t he value of 01 5 is of te n

used i n t he modeli ng of t he unive rsalit y of t he mobili2t y of i nve rsion laye r ca r rie rs (f or elect rons only) , it is

not reasona ble t ha t t he value s hould re mai n un2cha nged w he n app lied i n t he calculation of ca r rie r

de nsit y. I n t his work , it is t a ke n as a n a djusta ble p a2ra mete r .

D ue t o t he conf i ne me nt of elect ron motion nor2mal t o t he i nte rf ace , t he conduction ba nd wit hi n t he

t ra nsist or cha nnel is sp lit i nt o seve ral subba nds , eac h

of w hich is associa ted wit h t he cor resp ondi ng eige n2e ne rgy. He nce , t he elect ron de nsit y i n t he cha nnel

may be exp ressed as

Ne = ∑i∑

j

N ij = ∑i∑

j

D j kB Tl n 1 + expEFn - E ij

kB T

(5)

w here D j = ( g j m 3d j kB T/π∂ 2 ) is t he de nsit y of sta tes

i n t he jt h valley a nd m 3d j is t he de nsit y of sta tes of ef2

f ective mass p e r valley ( m 3d1 = 01 190 m0 , m 3

d2 =

01 417 m0 ) . g1 = 2 , g2 = 4 a re t he dege ne racy of t he

valleys of t he set . EFn is t he quasi2Fe rmi level . The de2vice cur re nt f lows only along t he cha nnel so t ha t t he

quasi2Fer mi level is consta nt across t he silicon2f ilm di2rection ( z2di rection ) . kB is t he B oltzma nn consta nt

a nd T is t he a bsolute te mp e ra t ure . The exp ression of

Ye ( t he ave rage dista nce of all elect rons f rom t he sur2f ace ) f or mulate d assumi ng t he t ria ngula r p ote ntial

well ( TPW) app roxi mation is

Ye =∑

j∑

i

N ij Yij

Ne=∑

j∑

i

N ij Yij

∑j∑

i

N ij

(6)

w here Yij = 2 E ij / 3 Fs is t he ave rage sep a ration of ca r2rie rs i n t he it h subba nd a nd jt h valley.

2. 2 　Drain current model ing

For calculati ng t he drain cur re nt i n a U TB D G

device wit h metal S/ D , two major t ra nsp ort mec ha2nis ms t h rough t he Sc hot t ky contacts a re conside red :

t he r mionic e mission a nd ba r rie r t unneli ng. At a give n

bias , t he net cur re nt de nsit y f lowi ng t h rough a metal2se miconduct or contact is [ 4 ]

J = J t herm + J tun (7)

J t herm = ∑i∑

j

A 3 TkB ∫

∞

q ( <b0 -Δ<b - Va)

[ f s ( E ij ) - f m ( E ij ) ]d E ij

(8)

J tun = ∑i∑

j

A 3 TkB ∫

q ( <b0 -Δ<b - Va)

0Tt ( E ij ) [ f s ( E ij ) -

f m ( E ij ) ] d E ij (9)

f s ( E ij ) =1

1 + expE ij - Efs

kB T

(10)

f m ( E ij ) =1

1 + expE ij - ( Efs - qVa )

kB T

(11)

　　Assume t he conduction ba nd edge i nside t he sili2con as t he ref e re nce p oi nt . f s ( E) a nd f m ( E) a re t he

Fer mi2Dirac ( F2D) dist ributions at se miconduct or a nd

metal , resp ectively . Tt ( E) is t he t ra nsmission coef f i2

078

第 5 期 L uan Suzhen et al . : 　A n A nalytical Model of D rain Current f or Ult ra2Thin Body and D ouble2Gate Schot t ky ⋯

cie nt . Va is t he f orwa rd bias ac ross t he Schot t ky con2t act . The ef f ective Richa rdson’s coef f icie nt A 3 is

A 3 =4πqk2

B m 3d j

h3 (12)

　　As a f act or af f ecti ng t he elect rical t ra nsp ort ,

Sc hot t ky ba r rie r loweri ng ( SBL ) due t o t he i mage

f orce ef f ect a nd t he i nte rf acial laye r is also conside re d

i n our st udy ,a nd is

Δ<b =qαFsm

4πεSi+γFsm (13)

He re , Fsm is t he maximum late ral f ield a t t he Schot t ky

contact . The f i rst te r m i n Eq. (13) describes t he SBL

due t o t he i mage f orce ; t he second te r m is ge ne rate d

by t he i nte rf acial f il m .α is a f it ting p a ra mete r . Classi2cal t heory sets it t o one [ 13 ] . However ,f it ti ng t his mod2el t o e mp i rical data suggests t ha t t his value va ries a nd

dep e nds on Vds a nd L . The value of γis usually set t o

11 5～3nm a nd is set t o 11 5nm here .

To p erf or m t he model’s cacula tions , rat he r t ha n

p e rf or mi ng a n i ntegral ove r a n e ne rgy ra nge f or Eqs .(8) a nd (9) , a Rie ma nn sum over a f i ne e ne rgy grid(ΔE = 01 001 t o 01 01eV) was use d. Also ,i nstea d of u2si ng ∞ as t he f i nal e ne rgy i n Eq. ( 8) , a f i nite value

betwee n one a nd t h ree ( dep e ndi ng on V ds ) is equally

usef ul , as t he tail of t he F2D dist ribution becomes ve ry

s mall ve ry quickly. Furt he r more , V ds must also be i n2clude d t o account f or t he dif f e re nce i n F2D dist ribu2t ion betwee n t he source a nd drai n at a give n e ne rgy.

A nonlocal t unneli ng model is e mp loye d based on

t he Fer mi2Dirac dist ribution f unction in our model

a nd t he t unneli ng p roba bilit y based on t he W KB ap2p roximation is

Tt ( E ij ) = exp 2∂ q

m 3d jεSi

Ne×

E ij l nEb + Eb - E ij

E ij

- Eb Eb - E ij

(14)

w here Eb = q ( <b0 - Δ<b - Va ) . The eff ective mass i n

t he a bove equation is a nisot rop ic f or elect rons , w hic h

bri ngs a nisot rop y t o t he t un neli ng cur re nt of elec2t rons . Tunneli ng cur re nt is se nsitive t o t he ef f ective

masses in Eq. (14) . A n accurate dete rmi nation of t he

t unneli ng ef f ective masses f rom exp e ri me nts is t hus

i mp orta nt . U nf ort unately , relia ble exp e ri me ntal da ta

of ca r rie r t unneli ng eff ective masses f or na noscale

contacts wit h a wide ra nge of ba r rie r heights a re not

availa ble . The t un neling cur re nt is calculate d based on

t he f ollowi ng assump tions . The t unneli ng cur re nt

t h rough a Sc hot t ky ba r rie r is domi nated by elect rons

wit h light masses because t hei r tunneli ng p roba bilities

a re muc h la rge r , as exp ecte d f rom Eq. (14) .

Fig. 2 　Inversion layer car rier density ( a ) and accumula2tion layer car rie r density ( b) by analytical solution under

t he t riangular p otential well app roximation (symbols) and

by numerical simulation (line)

3 　Results and discussion

The model was validated by a n exte nsive comp a r2ison wit h a qua nt um numerical si mulation using t he

2D device si mulat or Silvaco. Figures 2 a nd 3 show t he

elect ron de nsit y i n t he inve rsion laye r a nd t he hole

de nsit y i n accumulation laye r , resp ectively. W he n ηis

t a ke n as 01 75 f or t he i nve rsion laye r a nd 01 80 f or t he

accumulation laye r , t he ca r rie r de nsit y coi ncides wit h

t he f ully numerical calculation . The diff e re nce of ηf or elect rons a nd f or holes may lie i n t he dif f e re nt

subba nd st ruct ure of t he tw o ki nds of laye rs . I n t he

Fig. 3 　A nalytical charge densities are depicted against

gate voltage wit h diff e rent tSi

178

半 　导 　体 　学 　报 第 29 卷

Fig. 4 　Imp act of silicon f ilm t hickness on t he drain cur rent f or

U TBD G SB F ET

calculation , t he coef f icie nt in equation (4) is 01 75 f or

t he i nve rsion laye r ( elect ron ) a nd 01 8 f or t he accu2mulation laye r ( hole) .

I n Fig1 3 , t he a nalytical cha rge de nsities a re de2p icted agai nst gate voltage wit h dif f e re nt t hicknesses

of silicon f il ms ( tSi ) , agreei ng wit h t he numerical si m2ula tion results . The f igure shows t ha t t he elect ron

de nsit y i nc reases as tSi scales dow n . The results of our

model agree wit h numerical results a nd t he e r ror be2comes la rge r as tSi decreases betwee n t he results con2side ri ng Q M eff ects or not . Figure 4 s hows f urt he r

calculation of drai n cur re nt wit h a nd wit hout Q M

eff ects f or t he S/ D Schot t ky ba r rie rs ( t he gate w or k

f unction f or t his device was selecte d t o p roduce a n

of f2cur re nt of 1 nA/μm) . The Q M model p e rf ectly re2p roduces tw o esse ntial p he nome na : t he i mp act of

qua nt um eff ects on drai n cur re nt is i nc reasi ngly sig2nif ica nt w he n tSi is scale d dow n ; a nd t he drai n cur re nt

dep e nds on tSi in the subthreshold region , but above the

threshold ,the drain current depends much less on tSi .

The valida tion p rocedure was conti nued by a n i n2dep t h i nvestigation of t he model’s cap a bilit y t o ac2count f or ca r rie r qua ntization eff ects . For t his p ur2p ose , t he i nve rsion cha rge de nsity Ne ( i n bot h t he

classical a nd qua nt um cases) wit h tw o dif f e re nt cha n2

Fig. 5 　Variation of t he inversion charge density Ne in classi2cal and quantum mechanical cases

Fig. 6 　Energy band diagrams of t he 20nm U TBD G SB F ET wit h

Schot t ky bar rie r height zero

nel le ngt hs is comp a red t o numerical results a nd ve ry

good agree me nt is f ound i n Fig. 5 . Figure 6 s hows t he

f i rst subba nd p rof ile of t hese SB F E Ts unde r on2sta te

conditions beyond a ce rtai n gate voltage . Somew hat

surp risingly , a t unneli ng ba r rie r still exists f or <b0 = 0 .

The cur re nt of t he SB F E Ts wit h ze ro eff ective ba r rie r

heights is li mite d by t he t unneli ng ba r rie r a t t he

source rat he r t ha n t he t he r mic ba r rie r i n t he cha nnel .

For t his t hi n body device , qua ntum conf i ne me nt raises

t he elect ron e ne rgy levels i n t he silicon a nd t he ef f ec2t ive ba r rie r height .

Figure 7 shows t he e ne rgy ba nd of SB F ETs i n on

a nd of f sta tes wit h a SB H of <b0 = 01 56eV comp risi ng

Q M eff ects . W he n t he device is in t he of f2state , t he

e ne rgy ba nd rese m bles t ha t of a conve ntional MOS2F E T wit h a la rge e ne rgy ba r rie r betwee n source a nd

drai n , a nd t he cur re nt is li mite d by t he r mic e mission

over t he ba r rie r at t he source . At t he drai n side , t he

Sc hot t ky ba r rie r f or holes is t hi n , w hich allows holes

t o tunnel f rom t he drai n te r mi nal i nt o t he cha nnel

a nd causes ext ra lea kage cur re nt . Thus , t he of f2sta te

cur re nt is comp osed of eit he r t he r mionic or t un neli ng

comp one nts , dep e ndi ng on t he gate work f unction a nd

bias . U nder highe r ga te bias , a conduction ba nd sp i ke

app ea rs at t he source . The SB of elect rons

on t he source side is t hi n , w hic h allows elect rons t o

Fig. 7 　Conduction and valence band f rom source t o drain

f or U TBD G SB F ETs

278

第 5 期 L uan Suzhen et al . : 　A n A nalytical Model of D rain Current f or Ult ra2Thin Body and D ouble2Gate Schot t ky ⋯

Fig. 8 　 I ds2Vgs curves f or U TBD G SB F ETs wit h diff erent

Schot t ky barrier heights f or elect rons

t unnel f rom t he source te r mi nal i nt o t he cha nnel .

Furt he r more , t he ba r rie rs a re t hicke r i n t he ce n2te r of t he cha nnel . The SBL ( not s how n i n Fig1 7) is

also smalle r i n t he ce nte r of t he c ha n nel . Thus , t he f a2vora ble p at h f or t he t unneli ng cur re nt is nea r t he sur2f ace ra t he r t ha n t h rough t he ce nte r of t he cha nnel .

The lowe r t he SB is f or elect rons , t he highe r t he SB is

f or holes . As a result , t he t unneli ng cur re nt of holes

decreases ,w hic h exp lains t he re duced holes f or lower

elect ron SB i n Fig1 8 . The mini mum lea kage cur re nt is

i nse nsitive t o t he SB Hs a nd is t he conseque nce of a

t ra deof f betwee n elect ron a nd hole cur re nt . The mi ni2mum lea kage cur re nts of t he ze ro ba r rie r a nd t he mid

gap SB F E Ts a re si mila r . The reason f or t his is t ha t t he

gate oxide ( t ox = 1nm) i n our model is ve ry t hi n , a nd

t he SB is also ve ry t hi n a nd esse ntially t ra nsp a re nt f or

ca r rie rs . The cur re nt is , t he ref ore , li mited by t he r mic

e mission over a ba r rie r wit h t he height of t he ba r rie r

dete r mi ne d by t he conduction/ vale nce ba nd i n t he i n2te rior of t he c ha n nel . Tunneli ng t h rough t he metal/

se miconduct or ba r rie r va ries wit h t he ba r rie r height

a nd t he bias , w hic h p lays a minor role ( because t he

ba r rie r is so t ra nsp a re nt ) comp a re d t o t he ba r rie r i n

t he silicon body. A bove t he t h res hold , t he sit uation is

dif f e re nt . The t unneli ng resista nce li mits t he on2sta te

Fig. 9 　I ds2Vgs wit h diff erent SB H at source/ drain calculated

by t he QM model and validated

Fig. 10 　Drain cur rent wit h diff e rent channel lengt hs calculat2ed by t he QM model and validated

cur re nt a nd t he ze ro ba r rie r delive rs more on2cur re nt .

Moreove r , as Figure 9 s hows , t he a nalytical solutions

f ully comp risi ng Q M eff ects wit h t he t ria ngula r p o2te ntial well app roxi mation a re i n agree me nt wit h t he

numerical results . The model wit h only SBL overesti2mates t he value of t he drai n cur re nt , as show n i n

Fig1 8 .

The drai n cur re nt wit h dif f e re nt c ha nnel le ngt hs

is show n i n Fig1 10 . D ue t o t he existe nce of a Schot t ky

ba r rie r a t t he source/ drai n , t he ef f ect of drai n bias on

t he c ha n nel is sc ree ned. Thus , t he s hort cha nnel ef f ect(SC E) is eli mi na ted . The model is i n agree me nt wit h

t he nume rical si mula tion .

The height of t he Schot t ky ba r rie r (SB H) at t he

source p lays a signif ica nt role i n drai n cur re nt , as

Fig. 11 　Outp ut characte ristics of U TBD G SB F ET wit h va2rious bar rie r heights 　(a) At t he source ; (b) At t he drain

378

半 　导 　体 　学 　报 第 29 卷

s how n i n Fig1 11 ( a ) . However , t he SB H at t he drai n

has lit tle i nf lue nce on t he device p e rf or ma nce i n

Fig1 11 ( b ) . The sa turation cur re nt i nc reases as t he

ba r rie r height decreases , w hich i mplies i nc rease d t un2neli ng cur re nt due t o t he low Schot t ky ba r rie r height .

As t he ba r rie r height i nc reases , t he drai n cur re nt rai2ses slowly wit h t he drain voltage because t he highe r

f ield is needed t o t unnel t he highe r a nd t hicke r Sc hot2t ky ba r rie r . Moreove r , Figure 11 s hows t hat t he drai n

cur re nt at low drai n bias deviates f rom li nea rit y. The

exp one ntial be havior of t he I ds2Vds p lot f or t he nMOS

device at low drain bias de monst ra tes t he p rese nce of

t he Schot t ky ba r rie r . The model agrees ve ry well wit h

t he nume rical si mula tion .

4 　Conclusion

A s hort cha nnel qua nt um comp act model f or

drai n cur re nt i n t hi n2body double2gate SB F E Ts has

bee n develop ed. For t hi n body devices , qua nt um con2f i ne me nt raises t he elect ron levels in silicon a nd t he

ef f ective ba r rie r height . Previous wor ks merely i n2clude d t he SBL i n t hei r models , eit he r ignori ng Q M

eff ects or ma king t oo coa rse assump tions of t he qua n2t um p ote ntial well ,w hich ove resti mate d t he drai n cur2re nt . The develop me nt of our model conside ri ng t he

a nalytical solutions t o e ne rgy levels wit h t he t ria ngu2la r p ote ntial well app roxi mation was t he sta rti ng

p oi nt . Accordi ng t o our model , t he cur re nt of t he

SB F E Ts wit h ze ro eff ective ba r rie r heights i nvolves

t he t unneli ng cur re nt due t o qua nt um conf i ne me nt .

Rega rdless of ba r rie r height t he mi ni mum lea kage

cur re nt is si mila r due t o t he t hi n gate oxide . Beyond

t he t h reshold , t he lowe r Schot t ky ba r rie r height deliv2e rs more on2cur re nt . The nume rical results valida te

t he p rop osed model .

References

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考虑量子效应的超薄体双栅肖特基源漏 MOSFET电流解析模型 3

栾苏珍­ 　刘红侠 　贾仁需 　蔡乃琼 　王 　瑾 　匡潜玮

(西安电子科技大学微电子学院 宽禁带半导体材料与器件教育部重点实验室 , 西安　710071)

摘要 : 推导了超薄体双栅肖特基势垒 MOSF ET 器件的漏电流模型 ,模型中考虑了势垒高度变化和载流子束缚效应. 利用三角势垒近似求解薛定谔方程 ,得到的载流子密度和空间电荷密度一起用来得到量子束缚效应. 由于量子束缚效应的存在 ,第一个子带高于导带底 ,这等效于禁带变宽. 因此源漏端的势垒高度提高 ,载流子密度降低 ,漏电流降低. 以前的模型仅考虑由于镜像力导致的肖特基势垒降低 ,因而不能准确表示漏电流 . 包含量子束缚效应的漏电流模型克服了这些缺陷. 结果表明 ,较小的非负肖特基势垒 ,甚至零势垒高度 ,也存在隧穿电流. 二维器件模拟器 Silvaco 得到的结果和模型结果吻合得很好.

关键词 : 肖特基势垒 ; 量子效应 ; 有效质量 ; 电子密度PACC : 7340Q ; 0365 ; 7110C

中图分类号 : TN386 　　　文献标识码 : A 　　　文章编号 : 025324177 (2008) 0520869206

3 国家自然科学基金 (批准号 :60206006) 和国防预研究基金 (批准号 :51308040103) 资助项目

­ 通信作者. Email :szlua n @mail . xidia n. edu. cn

　2007211216 收到 ,2007212210 定稿 Ζ 2008 中国电子学会

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