An Analytical Model of Drain Current for Ultra2Thin Body and ...To perf orm the model’s...
Transcript of An Analytical Model of Drain Current for Ultra2Thin Body and ...To perf orm the model’s...
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
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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
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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
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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 .
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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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