Four-quadrant one-transistor-synapse for high-density CNN implementations

1998 Fi h IEEE In e na ional Wo kshop on Cellula Neu al Ne wo ks and hei Applica ions, London, England, 14-17 Ap il 1998 I Fou -Quad an One-T ansis o -Synapse o High-Densi y CNN Implemen a ions R. Dominguez-Cas o, A. Rod iguez-V zquez, S. Espejo, R. Ca mona Ins . de Mic oelec onica de Se illa - Cen o Nac. de Mic oelec onica - C.S.I.C. - Uni e sidad de Se illa, Ed . CICA, C/Ta ia s/n, 41012-Se illa, SPAIN. Phone: +34 5 4239923; FAX: +34 5 4231832; email: [email p o ec ed] ABSTRACT: This pape p esen s a linea ; , ou -quad an s, elec ically-p og ammable, one- ansis o synapse s a egy applicable o he implemen a ion o gene al massi ely-pa allel analog p ocesso s in CMOS echnology. I is specially sui ed o ansla ionally-in a ian p ocessing a ays wi h local connec i i y, and esul s in a signGCan educ ion in a ea occupa ion and powe dissipa ion o he basic p ocessing uni s. This allows highe in eg a ion densi ies and he e o e, pe mi s he in eg a ion o la ge a ays on a single chip. 1. In oduc ion The mos impo an end in he elec onic implemen a ion o CNNs is he maximiza ion o he numbe o elemen a y p o- cessing uni s ha can be placed in a single chip. This mus be combined wi h he achie emen o an accep able accu acy o he sys em pa ame e s. The i s end imposes a s ong commi men in he design o he cell ci cui y: a ea-e iciency. A sec- ond bu also impo an objec i e is powe -economy. Un o una ely, in analog p ocessing ci cui s, a ea and powe consump ion o indi idual de ices a e di ec ly ela ed o accu acy [ 1). The e o e, he selec ion o a ci cui s a egy as simple as possible o he p esc ibed p ocessing unc ion is c ucial. This pape p oposes a one- ansis o , ou -quad an s, elec ically-p og ammable, linea synapse o he implemen a ion o massi ely-pa allel analog-a ay p ocesso s in CMOS echnologies. The p oposal is easily ex ensible o gene al a i icial neu al ne wo ks. 2. Analog-A ay-P ocesso s Elemen a y Uni s Each p ocessing uni (o cell) in a massi ely-pa allel analog-a ay p ocesso can be cha ac e ized by an in e connec ion pa em and by an speci ic p ocessing unc ion. These cha ac e is ics a e o en conside ed in a ian om cell o cell, esul ing in an addi ional simpli ica ion o he elec onic implemen a ion. This p ope y, commonly e e ed o as spa ial in a iance o uni o mi y, will be assumed wi hou loss o gene ali y. A common cha ac e is ic o massi ely-pa allel analog p ocessing algo i hms is he local compu a ion (wi hin each cell c) o a weigh ed agg ega ion o con ibu ions om he cells in i s neighbo hood, N yc = 1 Aixi (1) i=l The agg ega ed signal yc is hen used as inpu o a p ocessing-block which ealizes some speci ic unc ion, and gene a es an ou pu xc ep esen a i e o he cell s a e. In um, his ou pu cons i u es he (unscaled) con ibu ion o he cell o i s neigh- bo s. This gene al cell a chi ec u e is illus a ed in Figu e 1. The ou pu xi o each neighbo is weigh ed by a coe icien A;, which is independen o he pa icula ecep o cell c unde he assumed spa ial uni o mi y. Excep o speci ic pu pose sys- ems i is gene ally equi ed ha he scaling coe icien s (o weigh s) Ai be elec ically p og ammable, o e sa ili y easons. -.- W! WN Analog weigh -con ml bus Figu e 1. Gene al a chi ec u e o an analog-p ocessing-a ay elemen a y p ocessing uni (cell). A a sys em le el, he equi ed numbe o signal-scaling ci cui -blocks (o synapses) can be compu ed as N imes he num- be o cells. The associa ed a ea and powe consump ion, as well as he ob ious e ec s o he synapse accu acy on he o e all pe o mance o he sys em, ende s he selec ion o he synapse ci cui y a c ucial issue in he design o in eg a ed analog a ay p ocesso s. 3. Elec ically-P og ammable Synapses Elec ically p og ammable synapses mus be d i en by he inpu signal xi, and by a weigh signal w; used o p og am he scaling coe icien Ai. Unde he assumed spa ial uni o mi y, only N di e en weigh alues will coexis h oughou he a ay. The e o e, a educed numbe (N) o global nodes (common o all cells in he ne wo k) sa is y he p og amming- ela ed ou ing equi emen s o he a ay, i he p og amming signals wi a e codi ied as ol ages. Since e e y cell ou pu xc is ansmi ed o N synapses loca ed wi hin i s N neighbo ing cells, i is also app op ia e ha synapse inpu signals x; be codi ied as ol ages. Finally, because scaled signals mus be added a he inpu o each cell’s p ocessing block, i is con enien ha synapse ou pu 0-7803-4867-2/98/$10.0001998 IEEE 243 signals A+; be gi en in cu en o m, elimina ing he need o a dedica ed summing ci cui . Al hough he equi ed unc ionali y o a p og ammable analog synapse may sugges he use o linea analog mul iplie s, he e a e some speci ic ci cums ances common o almos e e y analog-a ay p ocessing algo i hm which expand he se o selec able ci cui blocks. Fi s no e ha while he synapses ou pu cu en is expec ed o be linea wi h he inpu signal xi, i is no equi ed o be lin- ea wi h he weigh signal wi, whose unc ion is simply o allow weigh a ia ions in some p esc ibed ange. The e o e, unc- ion A,(w,) may be nonlinea in gene al. Second, in almos e e y analog-a ay p ocessing algo i hm, he weigh alues a e in a ian du ing p ocessing. The e o e, he dynamic esponse wi h espec o he weigh signal is o li le conce n and, mo e impo an , a e se ing he weigh alues, any e o o de ia ion om he ideal beha io independen o he inpu signal xi (bu in gene al dependen on wi) may be can- celled using au oze oing, be o e pe o ming he p ocessing unc ion. This is a good p ac ice in gene al because he o se o he agg ega ed signal is gi en by he addi ion o he ou pu -cu en o se o he N synapses d i ing each cell. Indeed, his is o en he dominan e o sou ce o his class o sys ems. In he las yea s, synapse ci cui s based on MOS ansis o s ope a ing in hei ohmic egion ha e been employed by se e al au ho s [2], [3]. The choice is based on a combined es ima ion o se e al pe o mance igu es (including a ea occupa ion, accu acy, linea i y, p og amming weigh ange, signal- ange, and powe e iciency) which p edic s impo an ad an ages as compa ed o o he classes o synapse ci cui s based on he quad a ic law o MOS ansis o s in sa u a ion, o he exponen ial law o bipola ansis o s and MOS ansis o s in weak in e sion. Rega dless he amily, p ac ically all synapse ci cui s employ di e en ial o ully di e en ial a chi ec u es o achie e ou - quad an s beha io and also o linea i y easons. Typical examples include hose synapses based on di e en ial pai s, like he Gilbe mul iplie [4], and also he synapses employed in [2] and [3]. In addi ion o he la ge complexi y o he synapse, his usually o ces he use o di e en ial o ully di e en ial a chi ec u es in he p ocessing block as well, hus esul ing in a sub- s an ial inc ease in a ea occupa ion. In he ollowing sec ion we p opose a one- ansis o , ou -quad an s, elec ically-p og ammable synapse ci cui wi h sin- gle-ended a chi ec u e. 4. A One-T ansis o Synapse Ci cui well-known i s -o de app oxima ion The DC cu en o an MOS ansis o ope a ing in i s s ong-in e sion ohmic egion can be desc ibed by he ollowing whe e and e e y symbols has i s well es ablished meaning in MOS li e a u e. Eq. (2) p edic s an inc emen ally linea ela ion be ween and Vcs , and an app oxima ely linea dependence wi h VDS o DS << 2 [ cS - + SB)] . These conside a ions ha e been widely exploi ed o many applica ions, including MOS implemen- a ions o ac i e RC il e s [5], analog mul iplie s o RF communica ion ci cui s [6] and also synapse ci cui s o massi ely- pa allel analog p ocessing sys ems [2], [3] using di e en ial a chi ec u es. The use o a single ansis o o implemen an elec ically p og ammable synapse wi h signals ep esen ed by single-ended ol ages equi es ha one o he di usion e minals be se o a ixed ol age le el. The ga e and he o he di usion e minals can hen be employed as inpu poin s, while he ou pu is ob ained om he cu en lowing ou o he ixed- ol age di usion e minal. This is concep ually illus a ed in Figu e 2a in which a nulla o and a DC ol age sou ce ep esen he ideally null- impedance inpu e minal o he p ocessing block in Figu e 1. Such a i ual- e e ence le el is equi ed because he ou pu impedance o he synapse is low due o i s ope a ion in he ohmic egion. The inpu impedance a he di usion inpu is also low, while ha a he ga e inpu is high. Two al ema i es can hen be conside ed: using he ga e e minal o xi and he di u- sion e minal o wi, o he o he way a ound. This has implica ions on he ou pu -impedance equi emen s o ei he he cell p ocessing-block o he ol age sou ces d i ing he analog-weigh con ol bus, bu he majo decision ac o is ela ed o lin- ea i y. Equa ion (2) is alid only o DS 2 o and he e o e, he use o he no a ion in oduced in Figu e 2a equi es an independen conside a ion o he wo possible cases A 5 L and A s VL . S ill, simple analysis esul s in he ollowing combined exp ession o IN, alid in ei he o he wo cases, wi h No e ha he second summand in (5) is independen o Vc and ha he i s summand is linea wi h G . Since we need a 244 linea beha io wi h espec o one o he inpu s (xi) and we can elimina e any sys ema ic o se in a p e ious s ep, i seems s aigh o wa d ha we can chose xi= G and wi A , as shown in Figu e 2a. -- Figu e 2. a) One ansis o synapse concep , b) Cell ( op) and pe iphe al (bo om) ci cui y o independen - e ms subs ac ion. The e is s ill ano he issue ela ed o he ob en ion o a ou -quad an s beha io . While he wo possibili ies VA 2 VL and A 5 L p o ide double sign capabili y o he weigh , C mus always be posi i e. The e o e we mus selec a su icien ly high e e ence le el on he ga e ol age o ac as he ze o le el o xi. Le us de ine: (7) x- - x + VXO =3 , = x - Vxo =xi and in he same manne , e e ing he weigh ol age o L , his is, selec ing IV0 = L , we ha e w = i + VL * , = w - VL = w; Using his new no a ion, equa ions (5) and (6) can be ew i en espec i ely as: V whe e bo h , and ,~ can be ei he posi i e o nega i e and s ill, he i s summand in (9) is linea wi h V, and he second one is independen o , . We de ine he weigh and he ou pu o se o he synapse, espec i ely, as G(Vw) = PV, (11) ]"(Vu.) = G(V )(V -I' - -2 i x0 T L "1 2 This allows (9) o be w i en in he ollowing o m lN(VW' V$ = G(V,,V, + 10(V,) Le us now assume ha we can elimina e he e m ~~( ,~), Then, we can de ine lN= +/o~ln = IN-I,,-Ai~; and ew i e (1 3) as IJV,<, V,) = G(Vu.)VX (1 5) which is he equa ion o a ou -quad an s, elec ically-p og ammable, linea analog synapse. This elies only on he sepa a ed dependencies shown in (13), and no on he speci ic o ms o G( ,) and I~(V,J, a ac ha will become ele an o he conside a ion o second o de e ec s in a la e sec ion 5. Cell and Con ol Ci cui y In o de o p ese e he high a ea e iciency p o ided by he one- ansis o synapses, he ci cui y employed wi hin each cell o he elimina ion o he N second summands (one pe synapse) should be as simple as possible. This is made easie by he ac ha he cell ci cui y i sel compu es he sum o hese summands, which can he e o e be elimina ed al oge he . Unde he assumed spa ial in a iance o he weigh signals, common o mos analog-a ay p ocessing sys ems, he e m o 245 be elimina ed in each cell is also spa ially in a ian . The e o e, we can ep oduce i s alue in a small ci cui y, sha ed by all he cells in he ne wo k and placed a he pe iphe y o he cell a ay, and subs ac i a he inpu nodes o each cell p ocessing block. This can be achie ed, wi hou addi ional cos in he cell ci cui y, h ough p ope weigh -dependen biasing o he p o- cessing-block inpu s age. As an example, Figu e 2b desc ibes a simple echnique. The op pa o he igu e ep esen s he cell ci cui y (iden ical o Figu e 1 using one- ansis o synapses) which includes a class-A inpu s age as pa o he p ocessing-block inpu ci cui y (bias cu en sou ce is no shown o simplici y). The ci cled ansis o pe o ms he subs ac ion o he N second summands in (13). The lowe pa o he igu e desc ibes he equi ed biasing de ices, placed a he pe iphe y o he cell-a ay and sha ed by he whole ne wo k. This echnique elies on he use o ma ched cu en -con eyo s [4] a he pe iphe al ci cui y and a he inpu node o he cells p ocessing-block. Thei elec onic implemen a ion can be shown o be highly e icien in e ms o a ea and powe con- sump ion [3]. I migh be a gued ha la ge-dis ance misma ch e ec s could esul in cancella ion e o s o he independen e ms. How- e e , as men ioned ea lie , i is gene ally con enien o employ au oze oing echniques. Such au oze oing, which can be easily implemen ed wi h a ea-e icien cu en memo ies [7] in he cases conside ed (cu en -ou pu synapses), would elimina e he cancella ion e o as well. Indeed, he use o au oze oing may ende unnecessa y he p oposed subs ac ion ci cui y, since i could be used o elimina e he comple e sum o independen e ms a he han hei emaining e o . Al hough combining high- signal- anges and high-absolu e-accu acy is o en di icul , he ecen ly p oposed class o S21 cu en memo ies [SI may p o- ide a good solu ion. 6. Ope a ion Limi s and Second O de E ec s MOS ansis o , which can be app oxima ed by One undamen al limi a ion o he ope a ion ange o he p oposed synapse is imposed by he ohmic egion limi s o he 'GS' 'D.7' i SB) (1 6) (17) Subs i u ion o he p e iously employed no a ion in his equa ion yields he ollowing lowe limi o he ga e ol age >{VL+V+VW) ; w' L x- VW'V+VL) ; w' L Excep o his limi , no o he es ic ions exis on he p oposed synapse, on he basis o he i s o de model conside ed. I can be shown ha he e is only one second o de e ec , mobiliy deg ada ion, which ep esen s a ele an de ia ion om he unc ional dependence exp essed in (1 3). O he second o de e ec s a ec only o he p ecise o m o G( ,+,) and I& ,) , some- hing i ele an o ou discussion. Mobili y deg ada ion models p edic a educ ion in he e ec i e ca ie s mobili y (p in equa ion (3)) wi h ans e sal (no - mal o channel su ace) elec ic ield, some hing ha a ec s ou p esen discussion because he ans e sal elec ic ield depends on he ga e ol age and hus, he i s summand will no be linea wi h , . Al hough he widely accep ed simple model o mobili y deg ada ion [9]. p edic s a con inuous educ ion o he e ec i e mobili y s a ing jus abo e Gs = + sB), he ac is ha in mos echnologies, he e is an app eciable (-2.0~) Gs ange abo e + SB) wi hin which mobili y educ ion is negligi- ble. Fu he mo e, some highe le el models accoun ing o mobili y deg ada ion employ a speci ic pa ame e o de ine a ield h eshold below which no mobili y deg ada ion occu s (UCRZT in SPICE le el 2 [IO]). Rega dless he con inuous o h esholded modelling o mobili y deg ada ion, we can always de ine a maximum e ec i e ga e ol age 'GEhl,b.x = ' GS- + SB)l (19) below which any easonable linea i y equi emen s a e sa is ied. The ope a ion o he synapse mus be es ic ed o his ange. Pe o ming he app op ia e subs i u ions in (19) yields he ollowing uppe limi o he ga e ol age, The selec ion o L and X,, mus be made based on he limi s imposed by (17) and (20). In um, his will esul in an uppe limi o he allowed signal anges o , and , . Equa ion (17) can be ew i en as, , + xo , + VL + "+VL) , + Vxo 2 VL + + , + VL) ; , 2 0 ; , 2 0 (21 1 Le us deno e he signal anges o w and V, by IV,$( < VWma and IV,I < V,,,, , espec i ely. In he abo e equa ion, he wo s -case limi o ,,, is gi en by he i s inequali y when V, = ,~~~~ and , = - xwax , which yields, 'xo ' 'L + "+'L) + Vwmax + Vxmax (22) 246 Rega ding L , i s alue mus be su icien ly high o p o ide oom o he minimum V_ alue and also o some possible loss o ol age ange due o he limi ed ou pu swing o he ci cui s gene a ing he analog weigh con ol signals, which we deno e as Wmin. This is, VL 2 'wmax + 'Wmin (23) Because an uppe limi o he ol age anges exis due o mobili y deg ada ion, and also because we a e in e es ed in max- imizing he signal anges and/o allowing a educed powe supply ope a ion, we will selec he minimum allowed alue o L . Subs i u ing L = imax + Wmin in (22) esul s in a minimum alue o X0, Vx0 2 'Wmin + 'hVwmax + 'Wmin) + 2 imax + 'xmax (24) Again, we selec xo as i s minimum allowed alue. The esul ing maximum alue o X is hen gi en by X,, = X0 + ,,,, , his is, V~ mx = 'Wmin + "+'wmax + VWmin) + 'Vwmax + "xmax and he wo s case mobili y deg ada ion limi will be imposed by he i s inequali y in (20), when , is mini- mum, his is, w = L- ,:,,, = Wm n, which yields, Vxmax ' VWmin + V+Vwmin) + GEM^ Using (25) in o (26), yields, (27) 1 1 wmax + xmax' 2 -' GEMa - 3 1 V+Vi max + 'wmin)- VP~min)] Fo mode a e linea i y equi emen s, he igh hand side o he abo e equa ion akes alues in he ange o one ol o yp- ical CMOS echnologies, which o ,,,,, = ,,,, p o ides a peak- o-peak signal ange o abou one ol o bo h Vx and VIb . Figu e 3 illus a es he abo e discussion and shows he ol age dis ibu ion selec ed o a pa icula echnology: a s anda d n-well, 0.8pm CMOS p ocess a ailable h ough EUROPRACTICE. Wi h small changes, hese alues should be alid o mos ypical CMOS echnologies. No e ha he minimum powe supply le el should be a leas sligh ly abo e x,,, = 3.4~ o p e- =3 0 L= IV xo - 7 'GEM~ + V+V~min) - 2.8 Figu e 3. Vol age ange dis ibu ion o synapse ope a ion. en he possible loss o ol age ange due o he limi ed ou pu swing o he p ocessing block. S ill, an op imiza ion o he ou - pu swing o bo h he analog weigh con ol d i e s and he ou pu s age o he p ocessing block should allow he ope a ion o he p oposed synapse wi h powe supply le els in he ange o 3.3 , wi h simila signal swings o V, and w . Figu e 4 p o ides an addi ional insigh in o he selec ion o L and xo alues and he associa ed signal anges. I shows he allowed ope a ion egion, delimi ed by (17) and (20) in he x. w plane, wi hin which a squa ed ange (unde he assump- ion V imax = VXmax ) o signals , and V, , cen e ed a ound ( ~ xo) , mus be de ined. The g aphs co espond o L = I and he speci ic pa ame e s o he echnology being employed. No e ha al hough appa en ly, an app eciable inc ease in signal anges could be ob ained by inc easing he alues o L and x0, his is no ue in gene al because he limi s imposed by (17) and (20) will also shi wi h L . In iew o (27), he inc ease would be small. On he o he hand, i would equi e a la ge powe supply. -0.4~ < V,, S 0.4~ x ly- @ 1.51 Ill F 0 VL "W Figu e 4. Signal anges delimi ed by ohmic egion and mobili y deg ada ion limi s. 247 7. Resul s In his sec ion we will illus a e he beha io o he p oposed synapse in a speci ic n-well, 0.8pm CMOS echnology a ail- able h ough EUROPRACTICE. Figu e 5 con ains HSPICE le el 2 simula ed ans e cha ac e is ics o he p oposed synapse. T ansis o s sizes a e W= 6pm and L = 24pm. These geome ies co espond o easonable sizes in a p ac ical applica ion, in which a low aspec a io se es o he pu poses o ha ing easonable cu en le els h ough he analog weigh -con ol lines, as well as mode a e powe dissipa ion in he chip. La ge channel a eas ( ela i e o echnology esolu ion) a e equi ed o ma ch- ing conside a ions [ 11. S ill, low esolu ion echnologies a e highly con enien o ma ching conside a ions and also because mos o he cell a ea is usually dedica ed o con ac s, ou ing, and ac i e egion sepa a ions. Figu e 5a e lec s he o al ansis o cu en IN e sus he o al ga e ol age Vx, o di e en alues o he weigh signal ol age W . The alue o L is 1.0~. Values o ,, , ela i e o VL, ange om - 0.4~ (lowe ace) o + 0.4~ (uppe ace) in 50m inc emen s. The mobili y deg ada ion e ec s a e clea ly isible a he igh side, while hose ela ed o he pinch-o egion can be obse ed a le side, specially o posi i e alues o ,~ . The egion a ound x0 = 3.0~ e lec s he beha io p e- dic ed by (13). Figu e 5b shows he esul ob ained a e subs ac ing he independen e m ~~( ,), by means o he ci cui y desc ibed in Figu e 2b. Wo -case ( ,, = 0.4~) o al ha monic dis o ion (THD) is below 0.05% a 1Hz and 0.7% a 1MHz. Simila esul s a e ob ained om he p-channel e sion o he ci cui y. Figu e 5. HSPICE le el-2 simula ions o he p oposed synapse: a) Cu en IN in Figu e 2 e sus ga e ol age V, o di e en alues o V,. b) Cu en I,, = IN - I, ob ained using he ci cui y desc ibed in Figu e 2b. 8. Conclusions This pape has p oposed and discussed an elec ically p og ammable, one- ansis o , ou -quad an s linea synapse s a - egy o massi ely-pa allel analog a ay p ocessing sys ems, based on MOS ope a ion in he iode egion. Signal anges o bo h he inpu and he weigh signal a e in he ange o l pp, and o al ha monic dis o ion is below 0.7% a IMHz. Ope a ion om educed powe supplies o abou 3.3~ seems easible. The p oposed synapse ci cui esul s in a subs an ial educ ion in a ea and powe consump ion o he basic cell, as compa ed o adi ionally employed synapses based on di e en ial o ully- di e en ial a chi ec u es. This allows he ealiza ion o a ay p ocesso s wi h a la ge numbe o uni s in he same chip. 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