Single Electron Devices for Logic Applications

Transcription

1 Sinl Elcron Dvics for Loic Applicaions Rza M. Rad UMB Basd on pas of Nanolcronics and Informaion Tchnoloy,, Rainr Wasr

2 Inroducion Scalin down MOSFETs has bn fundamnal in improvin h prformanc of ULSI circuis Scalin of MOSFETs is nrin h dp sub 50 nm rim Quanum mchanical ffcs ar xpcd o b ffciv in hs small srucur dvics

3 Inroducion A nw dvic havin opraion principls ffciv in smallr dimnsions which uilizs quanum-mchanical mchanical ffcs Sinl lcron dvics rain hir scalabiliy vn on an aomic scal Sinl lcron dvics will rduc h powr consumpion bcaus h numbr of lcrons ransfrrd from vola sourc o round is limid

4 Sinl-lcron lcron box A quanum do conncd wih wo lcrods On lcrod conncd o do hrouh a unnlin juncion Th ohr lcrod, a, coupld wih quanum do via insulaor, lcron canno pass hrouh unnlin

5 Sinl-lcron lcron box Elcrons ar injcd/jcd o/from h do hrouh h unnlin juncion (fi 1)

6 Sinl-lcron lcron box Basic opraion of sinl-lcron lcron box: As h siz of quanum do dcrass, charin nry Wc of a sinl xcss char on h do incrass If Wc is sufficinly larr han hrmal nry, no lcron unnls o/from quanum do Elcron numbr in h do aks a fixd valu Th charin ffc which conrols injcion/jcion of a sinl char o/from a quanum do is calld oulomb Blockad ffc

7 Sinl Elcron Dvics ondiion for oulomb blockad: Wc >> k By applyin a posiiv bias o h a lcrod w could arac an lcron o h quanum do Furhr incras of h a vola causs an lcron o nr h do In sinl-lcron lcron box, h lcron numbr of h box is conrolld, on by on, by uilizin h a lcrod B T

8 Sinl-lcron lcron box ondiions for obsrvin sinl-lcron lcron unnlin phnomna Firs: charin nry of a sinl lcron o h do mus b rar han hrmal nry Scond: unnlin rsisanc R of h unnlin juncion mus b larr han rsisanc quanum h/ This is rquird o supprss h quanum flucuaions in lcron numbr, n, of h do

9 Sinl-lcron lcron box This condiion is obaind as follows: Uncrainiy principl: W. > h l W b h charin nry of h quanum do : W / l b h lifimof Thn : R >> ( h / ).R 5.8 kω h charin:r R > h

10 Sinl-lcron lcron box Bias condiions for oulomb Blockad Effcs Th vola ran which kps lcron numbr a n, is xracd by considrin h fr nry of h sysm F( n) Q Q Q + F(n) ) fr nry havin n lcrons in h island Wc(n) ) : harin nry A(n) ) : Work don by h vola sourc conncd o a in ordr o chan h lcron numbr from 0 o n Polarizaion char in capaciors: du o rarranmn of lcrons W Q c ( n) n V A( n) and char on h unnlin Q Q ar h polarizaion juncion and a capaciors

11 Sinl Sinl-lcron box lcron box Bias condiions.. Bias condiions.. c n V n n F n F V V n Q V d V I n A V n Q Q n W ] 1 [ ] 1 [ 1) ( ) ( : To mainain lcron numbr in quanum do ). ( ) (, 1 ) ( + < < ± < Σ Σ Σ Σ Σ

12 Sinl-lcron lcron box Bias condiions.. Fr nry chan in h ransiion of numbr from n o n F( n, n + 1) Whr: Q c F( n [ : + 1) F( n) ] 1 ( Q lcron Q c )

13 Sinl-lcron lcron ransisor Schmaic srucur of a sinl-lcron lcron ransisor (SET) is shown in h fiur (fi 3)

14 Sinl-lcron lcron ransisor Opraion of a sinl-lcron lcron ransisor [ n 1 d Th circui conncd o h unnlin juncion of sourc is shown in h fiur (fi4a) Th condiion for mainainin lcron numbr a n is: 1 ] [ n + d < V V ] < V d + V + < d d 1 d d < [ n + [ n + 1 ] V + ] d

15 s Sinl-lcron lcron ransisor Th circui conncd o h unnlin juncion of drain is ransformd o h circui shown in h fiur (fi 4b) Th condiion o mainain h lcron numbr a n is 1 + [ n + + V ] > V d > s 1 + [ n + V ]

16 Sinl-lcron lcron ransisor Fiur (fi 5a) shows h drain-a vola rlaion Gray aras ar coulomb blockad aras whr lcron numbr in h do is fixd

17 Sinl-lcron lcron ransisor Grn aras ar rions wih wo prfrabl lcron numbrs (on for sourc and on for drain) In ara labld A: Prfrabl lcron numbr for sourc is 1 and for drain is 0 Elcron unnls from sourc o do o mak is lcron numbr 1 Thn i unnls from do o drain o chan h lcron numbr of h do o 0

18 Sinl-lcron lcron ransisor Fiur (fi 5b) shows h oscillain I ds vrsus V characrisic of h SETs Typical I ds vrsus V ds characrisics ar shown in fiur (fi 5c)

19 Sinl-lcron lcron ransisor Fiur (fi 6) dmonsras a implmnaion of a circular disk quanum do sandwichd bwn sourc and drain and surroundin a

20 Sinl-lcron lcron ransisor Fiur (fi 7) shows Ids-V characrisics of h fabricad SET, ins of h fiur is h lcron addiion nris and par b shows h nry rquird for addin lcrons

21 Sinl-lcron lcron ransisor Advanas and disadvanas of SETs compard o MOSFETs SETs: low powr consumpion Good scalabiliy Opraion of SETs is limid o low mpraurs Hih oupu impdanc (R( mus b much hihr han 5.8 kohms) Sourc-drain vola of h SETs mus b smallr han h a swin vola For room mpraur opraion, do mus b much smallr han 10 nm, fabricaion of a 10 nm srucur is difficul in currn chnoloy

22 Ohr Sinl Elcron Dvics Ohr sinl lcron dvics Sinl lcron urnsil and sinl lcron pump ar dvics ha can conrol imin of sinl lcron unnlin Fabricaion of sinl lcron dvics Sinl lcron dvics hav bn fabricad in a variy of marials such as aluminum, hrosrucurs and silicon Fabricaion on silicon is don by fin- lihoraphy or by rowh of silicon dos by dposiion procss

23 Applicaion of sinl lcron dvics o Inroducion loic circuis Many amps hav bn mad o dvlop loic circuis consisin of sinl lcron dvics Two approachs in loic applicaions: Rprsnin a bi by a sinl lcron and usin sinl lcron dvics o ransfr lcrons on by on Rprsnin a bi by mor han a sinl lcron and usin sinl lcron dvics o swich h currn on/off Formr uss lss powr, lar rsuls in mor opraion sabiliy

24 Applicaion of sinl lcron dvics o loic circuis Analyical modl of SET for circui simulaion Assumpions Sourc and drain of h SETs ar conncd o capaciors much larr han oal capacianc of h SET island or biasd by consan vola sourcs Sourc and drain rsisancs ar assumd o b h sam (Rs( RsRd RdR) A ach ivn a vola, h wo mos probabl numbrs of lcrons in h SET island ar akn ino accoun Tunnlin rsisanc is supposd o b much larr han quanum of rsisanc h/ ~5.8kOhms

25 Applicaion of sinl lcron dvics o Drivaion of h modl loic circuis I-V V characrisics of SET havin n or n+1 lcrons is ivn by I n ~ V ~ V s, n ds whr R Σ Σ V ΣVds, V s, n ~ ~ ~ ~ ( Vs, n Vds )sinh( Vds / T ) ~ ~ ~ ~ sinh( V / T ) V sinh( V s ( + s ~ kbtσ T, R d Σ ). V ds ds R 1 n, + R ds ( R ~ / T ) R s R d )

26 Applicaion of sinl lcron dvics o loic circuis I corrsponds o on priod of oulomb oscillaions Ga vola ivin pak of oulomb oscillaions is: V s + n + ( + s d ). V ds onsidrin h priod of oulomb oscillaions /, a vola ran is obaind as n ( + s d ). Vds ( n + 1) ( + s + < Vs < + d ). V ds

27 Applicaion of sinl lcron dvics o loic circuis Fiur (fi 13) shows coulomb oscillaions ovr a vola ran

28 Applicaion of sinl lcron dvics o loic circuis Fiur (fi 14) shows h Id-Vs characrisics for a SET havin s d 1 af,, 3 af and R 10 MΩ

29 Applicaion of sinl lcron dvics o loic circuis Fiur (fi 15) shows a SET invrr Simulaions ar prformd usin SPIE

30 V V Applicaion of sinl lcron dvics o loic circuis Loic circuis wih sinl-lcron lcron ransisors SETs Bias condiions for SETs (o urn SETs on) Fiur (fi 16) shows a SET circui whr h SET is usd as a pull up dvic ON, up mus b urnd on vn a a sourc - drain vola around zro, hnc : V V ds s s s V V V dd ds V 1 [ + V, + n] a V OUT dd 1 [ V s + V ds + n] V ds ON, up 0 V V OUT ON, up V dd + 1 [ + n]

31 Applicaion of sinl lcron dvics o ondiions o urn SETs off a V s ( Dsin schm 0, loic circuis + V s ds ) is < V rquird o b : ds < ( Fiur (fi 19) is a schmaic of SET loic circuis SET loic r consiss of pull-down SETs only lock Low: prchar priod, load capacior is chard rardlss of inpus of SETs lock Hih: Evaluaion priod, pull-down dvic is urnd on, loic sa of h oupu will b drmind dpndin on h inpus (similar o MOS dynamic loic) + s )

32 Applicaion of sinl lcron dvics o loic circuis

33 Applicaion of sinl lcron dvics o loic circuis Fiur (fi 0) shows a 4-inpu 4 XOR mad wih SETs Fiur (fi 1) shows h simulaion rsuls