Ind ian JOU rll ,iI or Pu re & Appli ed Phys ics Vo l. 3R. Au gusl 2000. pp. 552-557

Characterization of small geometry LDD MOSFETs with non-pinned flatband voltage

Ekta Kalra, Ani l Kumar. Subhas is Halclar* & R S Gupta

SemiconduclO r Dev ices Research Laboratory

Depart ment or Electron ic Science. Uni vers it y or Del hi South Campus. Benito JU,lrcL M arg. ew Delh i. 10002 1

* Department or Ph ys ics. M otil al Nehru College. Benito Juarez M arg. New Delhi 11 002 1

Recei ved 13 June 2000: accepted 29 Jul y 2000

A se llli -empirica l model to analyze the ~ma ll geometry (short and narrow) erfects in L DD MOSEFTs inco l'pllrat ing the

dependence or Ibthand volt age O il chan llellength and w idth is developed. The ,malysis includes the short channe:. narrow width.

L DD and DIB L elTects. A n expression I'm th reshold vo ltage hased on the efrect ive ch'lrge conta ined in the ch,lIlncl is ohulined

,lIld the I'esults so ohtai ned are ill gOOlI ag l'eement with the ex perimental d,ll,l. I /(noise is also eva luated incorpor,l t ing the vol tage

drop in 1/' reg ion ,md ch;lrge induced due to n,l1 hand vo ll<1ge. which matches well w ith ex perimenta l data.

Introduction Li ght doped drain (LDD) dev ices (Fig. I) have cre­

ated an impact in the fie ld of VLSI des ign ing due to the ir small threshold vo ltage ro il -o il . hi gher breakdown vo lt­age, lower DIBL effec t and hot carrier suppressibilit y. Many models have been deve lopecl for short channe l LDD and FOLD MOS FETs '·-l but no model has been developed to analyze the small geometry effec ts in these' dev ices .

Moreover, the pre requi site of all these models is channe l charge . The charge contained in the channel and at the Si-S i0 2 interface changes drasti ca ll y as dev ice dimensions shrink and thu s an acc urate anal ysi s is Cllt ­c ial for dev ice characteri zati on. An important contribu ­ti on to the channel charge is the charge induced due to the r1 atband vo ltage. All the Illodels deve loped so far considered the f1 atband vo ltage to be pinned at a con­s t ~ t1 1 t va lue ~lIld thi s charge a constant. However, the f1 atband vo ltage actua ll y vari es with dev ice dimensions and channel charge is not co nstant' . As the device length is reduced, the charge induced by the f1 atband vo ltageC> acquires a trapezo idal structure as shown in Fig. 2. The introducti on of 1/ reg ion shifts the non-parall e l sides o f the trapeziulll to the channel interi or7 Scaling the dev ice width -wise cau ses an ex tra charge -t o ell te l' the channel from th e subs trat e due to lateral diffusion of depletion laye r bound ary toward s the fie ld ox ide regionx. The charge induced by the Ibtband vo ltage ca n now be approx imated by a similar trapezium with it s non-paral -

lei sides extending width-wi se. Thus the total charge induced by the flatband vo ltage in the small geo metry LDD dev ice is confined to a strltcture show n in Fig. 3.

Alth ough mini aturi zati on has led to a technologica l revoluti on by increasin g packin g dens ity and operating speed of microelec troni c subsystems, all increase in operating bandwidth and reducti on in suppl y vo ltages has leel to fluctuati ons in output and a dec line in ava il -

Go 1 e

Side wa ll spacer - r.Y77;T;>77-tiT777~T700.

~ Dra in

p- subs trat e

Fig. I - Cross-sec ti oll 01' a L DD (l igh tl y doped draill ) MOSFET

E A D

'" lx do IXd / H

F G 8

1 L-X w (

L Subs! ro I e

Fig. 2 - Change in geometry due to short chanlle l and LOD efrect

KALRA ('/ a/.: SMALL GEOMETRY LDD MOSFETs 553

ab le signal leve l. It is. therefore necessary to study these fluctuations when device dimensions are sca led to sub­micrometer range. The I/(noi se is an important measure of these flu ctuat ions. There are some models on LDD MOSFETs where noise is eva luated')-I I but no anal ys is is done to study the impact of sca lin g the device area on the noise.

In thi s paper, the threshold voltage, drain current , conductances and III noise of sma ll geometry LDD MOSFETs is developed conside ring the contributi on of the charge induced by the flatband voltage. The mod­el led results are compared with the ex perimental data and are found to be in perfect agreement.

2 Model Formulation The combined effect of short channel, LDD and

narrow width result s in the co nfinement of the charge induced by fia tband vo ltage to a structure co nsist ing of fo ur trapezoids enc losing rectangles of different dimen­sions as shown in Fig. ~.

If Q is the charge per unit volume, Nh the substrate dop ing. Xd the height of the trapezoid ABCD, Xdn the height of the rectang le EFG H, then the charge confined in the cuboid, formed by extendi ng EFG H width- wise, is give n by:

... ( I )

where L is the channel lengt h and W is the channe l width The total charge confined to the st ructure formed by

ex tending ABCD width-wise is given as: IV'

I ' J "2 Q N " X" ( L + L - 2 X,, ) d v = Co, VI' Ii , ( L - X" ) X" ()

... (2)

where W' is the average of the two parallel sides of the trapez ium extending width-wise, Xd is the channe l de­pletion depth. Nh is the subst rate dop ing and XIV is the source- drai n depletion wid th .

An expression for X" . whi ch is the slim of the source ~ llld dra in depleti on wid th in LDD MOSFETs7. is given as :

A

, ,

o

Fi g. ~ - Pi ctorial view or the geol11etry lIsed ror calcu lntion

(( 2 W I l~ 1 (( 2 W, l~ 1 X .=r · 1 +--' - I +r" · 1 +--' .. (3)

\I /I r" rl/

where r" is the depth of the 11 region, Wd and W, are drain and source depletion depths respectively, given by"

I

W / = [ 2 E,. N n ( V,,; + VBS + V D S ( (' 1/ ) ) ]C , q N " ( No + N " )

and

I

W" = [ 2 E, N D ( V,, ; + Vas)]2 . q N /, ( NIJ + N" )

where V,,; is the built-in potential of nO-substrate junc­

tion , E, the dielectric permitti vity of bulk semicond uctor, VBS the substrate bias and N n the doping concentration of /I ' region.

The channel depleti on depth Xd is given b/ I

X =(' 2E (2<p,, + VIJS+ Vn S(.-fj l ))2 " .1 q N"

where <Ph is the bulk potential and VDSk fl) is the reduced drain voltage due to LDD given by Eq. ( 10). As the total charge is same for both the geometrica l structures . equat ing the L.H .S of Eqs ( I) and (2) the tlatband voltage is obtained as:

LW V;:II ' = VFII ----­

( L - X". ) Xr/ ... (4 )

The ex pression for threshold voltage of small geome­try LDD MOSFET usin g Eq. (4) is evaluated as:

VT = V 1'1/ ' + <P" + " <P, - VIIS ( K I - K 2 V <p, - VIIS )-

() Vn S{dll - ~ VTI/+ K"V <p, - V/lS ... (5)

where Vrll ' is the effec ti ve fl atba nd vo ltage considering

the small geometry effects, DrBL term () obta ined semi­empiricall / 2 is given by:

() = 16.4 exp(-4.4 Llmeter I(h ... (6)

The factors K I and K2 whi ch represents the short channel and channel impl ant effec t respecti ve ly, are obta ined usi ng lagran gian in te rpolation technique l2

given by: 1 I X ) I' K I = 0.013 (Llmeter)- 10 - 0.227 (Llmerert 10 - +

0.952(Llmeter) 10() - 0.238 ... (7)

Ko = 3.686(Llmeter).\ IO I-l - 2.488 (Llmete r ) ~ 10" O.()346(Llll1eter) 106 + 0.276 ... (8)

. . ( I ) 117 1'1 K . d' . I where KI IS III VO t - W 11 e ~ IS Imenslon css.

554 INDIA N J PURE & APPL PHYS, VOL 38, AUGUST 2000

The dec rease in threshold voltage due to LDD region . . b I , IS g iven y ' t; Vm = :2 ( V"i - tp , ) + I v/) S ( <'/ I I + ( V"i - (P , ) J ( I - l' - UI (" ) . +

= () from Eq. (5) in place of VTO in Eq. ( 12) replacing V D.I hy V DS(eln in Eq.( I I), we obtain the I It noise for small geometry LDD MOSFETs.

4 Drain Current 4

. 7 L slllh - 2 / c' An ex pression for drain current in the linear region is

2 ~ ( Vhj - (P I) 2 + ( V/" - (P , ) I ( V"i - tp ,) + Vo s (,' If) J (e LI/, - I ) obtained by integrating the total charge from source to

. 17 L 4Slllr -? -

_ Ie

... (9)

/1' , be ing the characteri sti c length of the ve locity satu­rated reg ion depending on the permitti vity of Si02 and Si, the depleti on layer thi ckness and the ga te ox ide thickness. VDS(c1f) is the reduced drain vo ltage due to LDD structure and is given by!.' :

v _ V/)s IlS(c lll - ( L )

· 1 +a.~ /1'

... ( 10)

where L". is the length of the 1/ ' region, L the channel length and Vh; the built - in potential of 11 / 17 junction and

a. a filling parameter.

KIV = K j + K .. ~ (P , - VIi.I · KIV is ca lled the effecti ve nar­

row gate body factor and expresses the comhined effec t of gate width shrinking and channe l implant effect. The express ions for K, and K4 are given in Refs 8 and IS, K, is in (vo lt )"2 while K .. is dimensionless . .

31lj' Noise The I/jd rain voltage noise power spectrum for short

channel LDD MOSFET in linear reg ion is given by'!· II :

where q is the e lec tron charge, T the temperature, Cnx

the gate ox ide ca pacitance per unit area,fthe frequency, I/m the surface e lec tron co ncentrati on at the source, 11 , the intrinsic carri er density. N; the interface trap concen­trat ion at midgap, VTO the thres hold vo ltage at zero drai n

bias and k the boltzman constant. y is a dimensi onl ess p,II 'Cl llleter ( - .0]26), S (= lOX Clll-

I), V(;/ is the intrin sic

ga te vo lt age given by:

Ve/ = Ves - VTO ... ( 12) Substituting the va lue of VT' the threshold vo ltage

eva luated for small geo metry LDD MOSFET at VDS(d ll

drain:

\I ",eI

/", = - ~l ~ f Q 11/ d VII/ VII/ S

... ( 13)

where the chan nel charge density Q", is g iven by:

Qf1I = Cox (Vf1I~ - V",) + Qc ... ( 14) V",( = V + <P/i) is the e lectrostatic potential of the

channel with respect to the neutral substrate. V is the channel voltage at any point between source and drain

and <P/j - <P rn + <PI'" is the fJ-f1 junction barrie r height. V takes the va lues Vl. ' V~ and V 0 ' whil e V", takes the values Vm~'

Vms and V,,,,I at the gate , source and drain terminal s, respec ti ve ly. Qc is the ex tra charge due to short geo metry effect.. DTBL effect and LDD region and is given by:

Q" = COI l ~ (P .1 - VIIS ( K I- K2 ~ <p .1 - II/I S ) -

as:

o IIn s(<'I/l -t1 VTII+K ... ~ <p,- Vus 1 ... ( 1) )

The final ex press ion for drain curren t is now obtained

/ = _ W (Cox ( V 2 _ V 2 ) _ C V (V - V )) d\ ~l L 2 11/ d fI/ ., fiX ill !.,: II/ t! III S

W - ilL Q,, ( 11 ",,,- V ", , ) .. . ( 16)

Here V the (Tate vo lta(re become~' 111;; ' b b .

and

~, is the effective mobility is given as:

~() Il = ----------~----------

I + e ( V~ - liT ) + e c ( VI)\' ( f'/ f) )

with

" e c = ( L Ee r l and E c = ~ P,

",,,, is the saturati on ve loc ity and p , is the surface Illohil­ity given by:

KALRA ef (II.: SMALL GEOMETRY LDD MOSFETs 555

8 is mobility degradation factor whose va lue lies be­

tween n.()3V- 1 and n.1 V- I and !-I ll is the low fi e ld mobility.

Us i ng Eq. ( 16), the ex pressions for trans-conductance and drain conductance are obta ined as:

and

with

() I _e-Llfl"

B I = - ( L,,_ I - ( L,,_) . , L -I + aT ) 4 -I + a k sll1h-2 I ('

av B~ Ri +~ - a v ()s

... ( 18)

W ( Vns ( elf) 'k B2 =-C", VOS ( "111 T - tp n + 2 - V II/g J6

WQ (,( !-I ] B ~ =--L- L + B" Vns « ' f/l

1+ a-I"-c

I

( ( VIii - <P \ )2 + ( Vf" _ (P , ) ( V", _ (P \ + V,)) ( (' II) ) ( (/ .1/ r _ I )) 2

. , L 4 , 11111 --

2/,.

B) =( (pI, _ I ) (V", - <p , )

( L" ) -I +a-' Ic

, ~lll I L,,_ + ex I

('

B( =_~l2 ( A( -8BI ]

Drain current in the saturation reg ion of small geome­try LDD MOSFETs is given as:

... ( 19)

where ,\'" is the saturation velocity_

Substituting VJlld ( = VDskm + <Pn) by Vd,,,l(dl) + <Pn in Eq_ ( 16) and equating it to Eq . ( 19) one can get:

1 Vl II I r 1/ 2 () /) 1 V "xlI/- D2 1I" ,'"I- D." V " .'"I+ D~ V" ,'"I- /) ) \ ,/ ., ,, ,+ /)(,=

where

II ' ( ( V . - m . ) ( eLiI

I" _ I )) -D - I" T .'

1 - ? " 12 L - sIn 1 2 I e

:112 ( V , - m ) ( e LlII" )

D - I" T .'

-., - LlI (' 112 _ , L 4 (e - I ) slIlh -

2 l e 112 LlI 1/ 2

V,,; - <p , ) L E, (e I" - I )

? .' 12 L _sln1 lli

E,L (- I - () -_1_- _e_Ll

_' ' -)

4. , L

sll1h-2 Ie

ii' L Ec ( V,,; - <p ,) - eLll

' D,=--~-~-~----

,) !.II, 1/ 2 . 2 L 4(e - I ) SII1h

2 1e

... (20)

Dr, = L E I" ( - 1I'lIg - ( K I - K2 "j <P, - \IllS ) V tp, - IIlls + Ci <P /I

_ K 2 ( V'I; - tp \ ) + ( V,,; - <p ., ) ( I - e -- II I, L) 11'+ . , L

4 s lllh-2 I e

Solving Eq_ (20) numeri ca ll y (using the Newton­Raphson method) the saturation in trins ic channel vo lt­age Vds", can be obtained.

The extrin sic saturati on vo ltage obtained consideri ng the vo ltage drop in the 11 region is given as:

.. . (2 1 )

556 INDIAN J PURE & APPL PHYS, VOL 31\. AUGUST 2000

Substitutin g thi s va lue of saturati on voltage in Eq.

( 16), the saturation drai n current is evaluated.

5 Results and Discussion Numerical ca lcul ati on of body factors, threshold volt-

age, dra in current, conductances and noi se is carried oul.

The short channel and channel implantati on effects are

incorporated and the ex pressions for K I and K2 are

developed usin g lagrang ian in terpolat ion technique. Fig. 4 depi cts the variati on of threshold voltage with

<r.·- V,,,. al o ll ~ with the exoerimental data . A ~ood

• . 0 (1) L' )·OJ.l m , W,0 7 J.lm

(2) L')·OJ.lm. W, )2 11m

> 3-2 3) L,I '5pm, W' 27J.l m

~ Pres ent model -0-0-0- Expl . 112 J

~

'" 0 2·. 0 >

~ 1·6 0 L ~

~

L >-

0.8

0 0

Vas' 0 V

Vos ,0·) V

tox:. 2B nm

0·5 1·0 1· 5 2·0

J ¢s - VSS ( Vt/

2)

2·5

Fig. 4 - Va ri at ion or thresho ld voltage wi th -V <PS - \111.1' at ( I ) W

=0.7 p ill . L= I pill (2) W= 1.2 pm. L = I p m. CI) W= 2.7 pmL

= I .Spill. liDS = n.1 V. IIlls = nv. Nt, = 1.2 X IOI 6Icm' . I"x = 2X nlll along with the experimelllal resull s

N

'I

".; .... >

'" > Vl

1()12

lCP

lcF"

1015

-16

000 Experime n1a l

*** Mode l

L,0.87 I1m/ VGS' 2 V

f , 1 k H z

~ W ,1 ·5j.1m /"S;;'a l l·6eamel ry LO O

W,S5j.1m Shart- Ch a nne l LOO

10 ~ ___ ___________________________ ~

0·1

Dra in vol t age I V )

Fi g. 5 - Vari ~tlion or noisc with drain vo lt ~ t g(' ror shorl channel LDD and small geometry LDD MOSFETs along with

cxpc rilll e t1t ~ iI resull s ~ II L = O.X7pIllJ= I I kHz. lIos = 5 X J(} I-l/Ill ' . l1 i = 1.45 x I Olh/m·1.i;;= IOIIl/Ill.Ni=X .X X I02.1/nrleV- 1

agreement is observed between the modelled anci ex­perimental data l 2 at different dev ice geometry.

Fig. 5 shows the va riati on of noi se with drain bi as along with the ex perimental results for short channel and small geometry LDD MOSFETs. The perfect agreement between the predicted and experimental results is ob­tai ned. The ox ide interface traps interact wi th the chan­nel through carrier capture and generation, which causes a change in the scattering rate when the traps become occ upied. With the increase in drain voltage, scattering phenomenon in the channel increases th us increas ing the noise . The figure al so shows that noise is hi gher in small geometry LDD MOSFETs than in short channel LDD MOSFETs. This is because, as the dev ice width is decreased, the lateral elect ric fi e ld increases making the scattering more predominant.

Fig. 6 shows the va riati on of noise with gate bias along with the experimental results. The close agree­ment between the modelled and experimental results shows the validity of the mode l for LDD MOSFETs. It is also observed that noi se is more in small geometry LDD MOSFETs than in short channel LDD MOSFETs hecause in small geometry LDD MOSFETs, there is an extra charge, wh ich comes into the channel from the substrate. The presence of thi s ex tra charge lead s to inCl'eased scatteri ng. which further causes mobil it y flu c­tuati ons. An increased channel charge also has a greater probability for gettin g trapped and de- trapped in the oxide leading to flu ctuations in the number of carr iers.

N

I N .....

>

'0

> t.Il

1012 r----------------------------------,

1613

-14 10

-15 10

-16 10

1

000 Ex perimen ta l

*** Mode I

VOS ' 0·) V

,0. 87 j.1m

lox' 2 S nm

f , 1 kHz

W , 1.5j.1m Sm a l l' Geo m etry LDD

~ W, 55 j.1m

Shor t - Chan n el LDD

10

Go t e voltage (V)

rig. (1 - Vari ation or noise wilh gale hias rpr ~horl eh;IIlIIel LDD and s lll ~ ill geoilletry LDD MOSFETs along wilh ex perimcntal

resultsaI.L=O.X7plll'/= I kH z. lI"s=5 x iOI4/ 11l 1.lIi 1.45 x

101 (,/ Ill . i;;= J() III/Ill. Ni = X.X x I (l'/11l 1 eY- I . I,,, = 25 11111

KALRA eI 01.: SMALL GEOMETRY LDD MOSFETs 557

Fig. 7 shows the vari ati on of noise w ith freq uency for short geometry LDD MOSFETs. The observed fre­

quency dependence abides by the fact that ox ide traps have a unifo rm spat ia l distribution near the inte rface.

Fig. 8 shows the variati on of drain current with drain vo ltage for small geometry LDD MOSFETs a long with the experimenta l datal.) w he n both the length and width

are in the sub-mi cromete r range down to 0.45 ~m .

6 Conclusion A comprehensive ana lysis of small geometry LDD

MOSFETs is carri ed out and a s imple semi-empirica l mode l va lid for all gate length and w idth is developed . The effect of vari atio n of rl atband vo ltar:e with dev ice

109 r --- ------------,

'. N

~l:J lCP >

<0

-13 10

L~0. 87}Jm

W ~ 0 · 45 p m

1o x ~ 2 5n m

~ 0.4 V

=0 .3V ~VDS~0.5V

~ 0.2 V

'0.1 V

Id5~---~----.l_::_---...l.---...J 10

1 102 10 J 104

F r equenc y ( H z)

Fi g. 7 - Y ;lriation or noi se w ilh rrequency at dirrerent drain

vo ltages at L = D.S7 pm . W = OA 5 pm. lox = 25 nm. n os = 5 x IOI.)/m'. lIi = I A5 x I()I ('/m'. /;,= IOlo/m. Ni = 8.8 X IOD /m ey- I

1· 83 -0-0-0 Expe r im e nta l

*,**Mod. 1

1 46 L '0.45)lm W , 0.45 pm

... VB S ' a 'J '0

"" 1.10

c

~ 0.73

c

" 0

0 ·37

0·1 0.78 1· 46 2 14 2-87 350 Dra i n vol tog e (V )

Fig. X - Varia tion or drain current with drain voltage at dirferent

gale voltages with W = OA5 p ill. L = 045 pm . VII S = OY. Nh = 1.2

x I On/m ' . lox = 12 nl11 ;lI ong with the ex perimental result s

dimensions, the gate and drain bias has been incorpo­rated for the first time. DIBL effe.ct is suitabl y consid­ered to analyze the short channel be haviour. Evaluati on

of noise for small geometry LDD MOSFETs and its compari son with short channel LDD MOSFETs shows

that noise decreases with increas ing gate vo ltage be­cause a bias across the ox ide causes the carri ers to encounte r more deeper traps , which in turn make the

lower frequency region o f power spectrum more pro­nounced . It is also observed that it decreases with the

decrease in drain bias due to reduced scatte ring. It is

hi gher in the small geometry LDD MOSFET than in the short channel LDD MOS FET due to inc reased carri er mobility and numbe r tluctuations resulting from the increase in the latera l e lectri c fie ld and the number of carri e rs in the channel.

Acknowledgement The authors are thankful to DRDO, Ministry of De­

fence, Government of India for providing the necessary financial ass istance.

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