Al C-V Photoresponse Mg 3. Workfunction in vacuum (ev)

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1 6.3. MOS nlyi ltbn voltge clcultion If there i no chrge preent in the ie or t the ie-emiconuctor interfce, the flt bn voltge imply equl the ifference between the gte metl workfunction, Φ M, n the emiconuctor workfunction, Φ S. Φ Φ (6.3.) M S he workfunction i the voltge require to etrct n electron from the ermi energy to the vcuum level. hi voltge i between three n five olt for mot metl. It houl be note tht the ctul vlue of the workfunction of metl epoite onto ilicon iie i not ectly the me tht of the metl in vcuum. igure 6.3. provie eperimentl vlue for the workfunction of ifferent metl obtine from meurement of MOS cpcitor function of the meure workfunction in vcuum. he me t i lo lite in ble Workfunction on SiO2 (e) 5 Ag Au u 4.5 Ni 4 Al Photorepone Mg Workfunction in vcuum (e) igure Workfunction of Mgneium (Mg), Aluminum (Al), opper (u), Silver (Ag), Nickel (Ni) n ol (Au) obtine from I- n - meurement on MOS tructure function of the workfunction of thoe metl meure in vcuum. Ag Al Au r Mg Ni Φ M (in vcuum) Φ M (on SiO 2 ) (-) ble 6.3. Workfunction of electe metl meure in vcuum n obtine from - meurement on n MOS tructure. he workfunction of emiconuctor, Φ S, require ome more thought ince the ermi energy vrie with the oping type well with the oping concentrtion. hi workfunction equl the um of the electron ffinity in the emiconuctor, χ, the ifference between the conuction bn energy n the intrinic energy ivie by the electronic chrge n the bulk potentil

2 epree by the following eqution: Eg N (6.3.2) Φ M Φ S Φ M χ t ln( ) q n 2 i or MOS tructure with highly ope poly-ilicon gte one mut lo clculte the workfunction of the gte be on the bulk potentil of the poly-ilicon. Φ Φ poly, S poly, S Φ Φ poly poly Φ Φ S S N, t ln( N t ln( N poly n 2 i, poly ) N ) p - type polyilicon gte n - type polyilicon gte (6.3.3) Where N,poly n N,poly re the cceptor n onor enity of the p-type n n-type poly-ilicon gte repectively. or pmos cpcitor, which h n n-type ubtrte with oping enity N, the workfunction ifference equl: E g N (6.3.4) Φ M Φ S Φ M χ t ln( ) q n 2 i he fltbn voltge of rel MOS tructure i further ffecte by the preence of chrge in the ie or t the ie-emiconuctor interfce. he fltbn voltge till correpon to the voltge, which, when pplie to the gte electroe, yiel flt energy bn in the emiconuctor. he chrge in the ie or t the interfce chnge thi fltbn voltge. or chrge, i, locte t the interfce between the ie n the emiconuctor, n chrge enity, ρ, itribute within the ie, the fltbn voltge i given by: Φ MS i t ρ 0 ( ) (6.3.5) where the econ term i the voltge cro the ie ue to the chrge t the ieemiconuctor interfce n the thir term i ue to the chrge enity in the ie. he ctul clcultion of the fltbn voltge i further complicte by the fct tht chrge cn move within the ie. he chrge t the ie-emiconuctor interfce ue to urfce tte lo epen on the poition of the ermi energy. Since ny itionl chrge ffect the fltbn voltge n thereby the threhol voltge, gret cre h to be tken uring fbriction to voi the incorportion of chrge ion well cretion of urfce tte. Emple 6. lculte the fltbn voltge of ilicon nmos cpcitor with b i N 7-3 l i (

3 ubtrte oping N 7 cm -3 n n luminum gte (Φ M 4. ). Aume there i no fie chrge in the ie or t the ie-ilicon interfce. Solution he fltbn voltge equl the work function ifference ince there i no chrge in the ie or t the ie-emiconuctor interfce. Eg N Φ MS Φ M χ t ln 2q ni ln 0.93 he fltbn voltge for nmos n pmos cpcitor with n luminum or poly-ilicon gte re lite in the tble below. Aluminum p poly n poly nmos pmos Inverion lyer chrge he bi umption neee for the erivtion of the MOSE moel i tht the inverion lyer chrge i proportionl with the pplie voltge. In ition, the inverion lyer chrge i zero t n below the threhol voltge ecribe by: inv inv 0 ( ) for > (6.3.6) he liner proportionlity cn be epline by the fct tht gte voltge vrition cue chrge vrition in the inverion lyer. he proportionlity contnt between the chrge n the pplie voltge i therefore epecte to be the gte ie cpcitnce. hi umption lo implie tht the inverion lyer chrge i locte ectly t the ie-emiconuctor interfce. Becue of the energy bn gp of the emiconuctor eprting the electron from the hole, the electron cn only eit if the p-type emiconuctor i firt eplete. he voltge t which the electron inverion-lyer form i referre to the threhol voltge. o jutify thi umption we now emine comprion of numeric olution with eqution (6.3.5) hown in igure

4 hrge Denity (/cm 2 ).E-07 0.E00 -.E-07-2.E-07-3.E-07-4.E-07-5.E-07-6.E-07-7.E-07-8.E-07 Bic Aumption te oltge () Ect olution igure hrge enity ue to electron in the inverion lyer of n MOS cpcitor. ompre re the nlytic olution (oli line) n eqution (6.3.6) (otte line) for N 7 cm -3 n t 20 nm. While there i cler ifference between the curve, the ifference i mll. We will therefore ue our bic umption when eriving the ifferent MOSE moel ince it rmticlly implifie the erivtion, be it while loing ome ccurcy ull epletion nlyi We now erive the MOS prmeter t threhol with the i of igure o implify the nlyi we mke the following umption: ) we ume tht we cn ue the full epletion pprimtion n 2) we ume tht the inverion lyer chrge i zero below the threhol voltge. Beyon the threhol voltge we ume tht the inverion lyer chrge chnge linerly with the pplie gte voltge. he erivtion trt by emining the chrge per unit re in the epletion lyer,. A cn be een in igure (), thi chrge i given by: qn (6.3.7) Where i the epletion lyer with n N i the cceptor enity in the ubtrte. Integrtion of the chrge enity then yiel the electric fiel itribution hown in igure (b). he electric fiel in the emiconuctor t the interfce, E, n the fiel in the ie equl, E : qn E n E qn (6.3.8)

5 he electric fiel chnge bruptly t the ie-emiconuctor interfce ue to the ifference in the ielectric contnt. At ilicon/sio 2 interfce the fiel in the ie i bout three time lrger ince the ielectric contnt of the ie ( ) i bout one thir tht of ilicon (.9 0 ). he electric fiel in the emiconuctor chnge linerly ue to the contnt oping enity n i zero t the ege of the epletion region. he potentil hown in igure (c) i obtine by integrting the electric fiel. he potentil t the urfce, φ, equl: φ 2 qn 2 (6.3.9) M O S ρ M O S E E qn M E qn - q N qn -t () (b) E M O S φ OX q E c E E v - φ E,M 0 Metl Semiconuctor Oie (c) () igure Electrottic nlyi of n MOS tructure. Shown re () the chrge enity, (b) the electric fiel, (c) the potentil n () the energy bn igrm for n n-mos tructure bie in epletion. he clculte fiel n potentil i only vli in epletion. In ccumultion, there i no epletion region n the full epletion pprimtion oe not pply. In inverion, there i n itionl chrge in the inverion lyer, inv. hi chrge incree grully the gte voltge i incree. However, thi chrge i only ignificnt once the electron enity t the urfce ecee the hole enity in the ubtrte, N. We therefore efine the threhol voltge the gte voltge for which the electron enity t the urfce equl N. hi correpon to the itution where the totl potentil cro the urfce equl twice the bulk potentil, φ.

6 φ N t ln n i (6.3.) he epletion lyer in epletion i therefore retricte to thi potentil rnge: 2 φ qn, for 0 φ 2φ (6.3.) or urfce potentil lrger thn twice the bulk potentil, the inverion lyer chrge chnge incree eponentilly with the urfce potentil. onequently, n incree gte voltge yiel n incree voltge cro the ie while the urfce potentil remin lmot contnt. We will therefore ume tht the urfce potentil n the epletion lyer with t threhol equl thoe in inverion. he correponing epreion for the epletion lyer chrge t threhol,,, n the epletion lyer with t threhol,,, re:, qn, (6.3.2), 2 (2φ ) qn (6.3.3) Beyon threhol, the totl chrge in the emiconuctor h to blnce the chrge on the gte electroe, M, or: ) (6.3.4) M ( inv where we efine the chrge in the inverion lyer quntity which nee to etermine but houl be conitent with our bic umption. hi le to the following epreion for the gte voltge, : M φ φ inv (6.3.5) In epletion, the inverion lyer chrge i zero o tht the gte voltge become: 2 qn φ φ, for 0 φ 2 φ (6.3.6) while in inverion thi epreion become: 2 φ 4 qn φ inv inv (6.3.7) the thir term in (6.3.7) tte our bic umption, nmely tht ny chnge in gte voltge beyon the threhol require chnge of the inverion lyer chrge. rom the econ equlity in eqution (6.3.7), we then obtin the threhol voltge or:

7 2 φ 4 qn φ (6.3.8) Emple 6.2 Solution lculte the threhol voltge of ilicon nmos cpcitor with ubtrte oping N 7 cm -3, 20 nm thick ie ( ) n n luminum gte (Φ M 4. ). Aume there i no fie chrge in the ie or t the ie-ilicon interfce. he threhol voltge equl: 4 qnφ 2φ / Where the fltbn voltge w lrey clculte in emple 6.. he threhol voltge voltge for nmos n pmos cpcitor with n luminum or poly-ilicon gte re lite in the tble below. Aluminum p poly n poly nmos e 0.98 e -0.4 e pmos e 0.4 e e MOS pcitnce pcitnce voltge meurement of MOS cpcitor provie welth of informtion bout the tructure, which i of irect interet when one evlute n MOS proce. Since the MOS tructure i imple to fbricte, the technique i wiely ue. o unertn cpcitnce-voltge meurement one mut firt be fmilir with the frequency epenence of the meurement. hi frequency epenence occur primrily in inverion ince certin time i neee to generte the minority crrier in the inverion lyer. herml equilibrium i therefore not immeitely obtine. he low frequency or qui-ttic meurement mintin therml equilibrium t ll time. hi cpcitnce i the rtion of the chnge in chrge to the chnge in gte voltge, meure while the cpcitor i in equilibrium. A typicl meurement i performe with n electrometer, which meure the chrge e per unit time one lowly vrie the pplie gte voltge.

8 he high frequency cpcitnce i obtine from mll-ignl cpcitnce meurement t high frequency. he bi voltge on the gte i vrie lowly to obtin the cpcitnce veru voltge. Uner uch conition, one fin tht the chrge in the inverion lyer oe not chnge from the equilibrium vlue correponing to the pplie D voltge. he high frequency cpcitnce therefore reflect only the chrge vrition in the epletion lyer n the (rther mll) movement of the inverion lyer chrge. In thi ection, we firt erive the imple cpcitnce moel, which i be on the full epletion pprimtion n our bic umption. he comprion with the ect low frequency cpcitnce will revel tht the lrget error occur t the fltbn voltge. We therefore erive the ect fltbn cpcitnce uing the linerize Poion' eqution. hen we icu the full ect nlyi followe by icuion of eep epletion well the non-iel effect in MOS cpcitor Simple cpcitnce moel he cpcitnce of n MOS cpcitor i obtine uing the me umption thoe lite in ection he MOS tructure i trete erie connection of two cpcitor: the cpcitnce of the ie n the cpcitnce of the epletion lyer. In ccumultion, there i no epletion lyer. he remining cpcitor i the ie cpcitnce, o tht the cpcitnce equl: L, for (6.3.9) H In epletion, the MOS cpcitnce i obtine from the erie connection of the ie cpcitnce n the cpcitnce of the epletion lyer, or: L H, for (6.3.20) where i the vrible epletion lyer with which i clculte from: 2 φ qn (6.3.2) In orer to fin the cpcitnce correponing to pecific vlue of the gte voltge we lo nee to ue the reltion between the potentil cro the epletion region n the gte voltge, given by: 2 qn φ φ, for 0 φ 2φ (6.3.6) In inverion, the cpcitnce become inepenent of the gte voltge. he low frequency cpcitnce equl the ie cpcitnce ince chrge i e to n remove from the inverion lyer. he high frequency cpcitnce i obtine from the erie connection of the

9 ie cpcitnce n the cpcitnce of the epletion lyer hving it mimum with,,. he cpcitnce re given by: L n H, for, (6.3.22) he cpcitnce of n MOS cpcitor clculte uing the imple moel i hown in igure he otte line repreent the imple moel while the oli line correpon to the low frequency cpcitnce obtine from the ect nlyi. pcitnce () 2.E-07 2.E-07 2.E-07.E-07.E-07.E-07 8.E-08 6.E-08 4.E-08 2.E-08 0.E00 Simple moel Ect olution te oltge () Low frequency cpcitnce High frequency cpcitnce Deep epletion cpcitnce igure Low frequency cpcitnce of n nmos cpcitor. Shown re the ect olution for the low frequency cpcitnce (oli line) n the low n high frequency cpcitnce obtine with the imple moel (otte line). N 7 cm -3 n t 20 nm lcultion of the flt bn cpcitnce he imple moel preict tht the fltbn cpcitnce equl the ie cpcitnce. However, the comprion with the ect olution of the low frequency cpcitnce hown in igure revel tht the error cn be ubtntil. he reon for thi i tht we hve ignore ny chrge vrition in the emiconuctor. We will therefore now erive the ect fltbn cpcitnce. o erive the fltbn cpcitnce incluing the chrge vrition in the emiconuctor, we firt linerize Poion' eqution. Since the potentil cro the emiconuctor t fltbn i zero, we epect the potentil to be mll we vry the gte voltge roun the fltbn voltge. Poion' eqution cn then be implifie to: 2 φ φ q qn qn φ (6.3.23) t ( N p) ( e ) 2 t

10 hrge ue to ionize onor or electron were eliminte, ince neither re preent in p-type emiconuctor roun fltbn. he lineriztion i obtine by replcing the eponentil function by the firt two term of it ylor erie epnion. he olution to thi eqution i: φ φ e D, with L L D t qn (6.3.24) Where φ i the potentil t the urfce of the emiconuctor n L D i clle the Debye length. he olution of the potentil enble the erivtion of the cpcitnce of the emiconuctor uner fltbn conition, or:, φ φ ( ) LD φ L D (6.3.25) he fltbn cpcitnce of the MOS tructure t fltbn i obtine by clculting the erie connection of the ie cpcitnce n the cpcitnce of the emiconuctor, yieling: (6.3.26) LD Emple 6.3 Solution lculte the ie cpcitnce, the fltbn cpcitnce n the high frequency cpcitnce in inverion of ilicon nmos cpcitor with ubtrte oping N 7 cm -3, 20 nm thick ie ( ) n n luminum gte (Φ M 4. ). he ie cpcitnce equl: t n/cm 2 he fltbn cpcitnce equl: L 73 D n/cm 2 where the Debye length i obtine from:

11 LD t qn nm he high frequency cpcitnce in inverion equl: H, inv 73 9, n/cm 2 n the epletion lyer with t threhol equl:, 2 (2φ ) qn nm he bulk potentil, φ, w lrey clculte in emple Deep epletion cpcitnce Deep epletion occur in n MOS cpcitor when meuring the high-frequency cpcitnce while weeping the gte voltge "quickly". uickly men tht the gte voltge mut be chnge ft enough o tht the tructure i not in therml equilibrium. One then oberve tht, when rmping the voltge from fltbn to threhol n beyon, the inverion lyer i not or only prtilly forme. hi occur ince the genertion of minority crrier cn not keep up with the mount neee to form the inverion lyer. he epletion lyer therefore keep increing beyon it mimum therml equilibrium vlue,, reulting in cpcitnce which further ecree with voltge. he time require to rech therml equilibrium cn be etimte by tking the rtio of the totl chrge in the inverion lyer to the therml genertion rte of minority crrier. A complete nlyi houl inclue both the urfce genertion rte well genertion in the epletion lyer n the qui-neutrl region. A goo pprimtion i obtine by coniering only the genertion rte in the epletion region in eep epletion,,. hi yiel the following eqution: time q( inv, L n ) qni ( 2τ ( 2 φ qn, ) µ τ ) n t n (6.3.27) where the genertion in the epletion lyer w ume to be contnt. he rte of chnge

12 require to oberve eep epletion i then obtine from: t > qni 2 µ nt τ n (6.3.28) hi eqution preict tht eep epletion i le likely t higher mbient temperture, ince the intrinic crrier enity n i incree eponentilly with temperture. he intrinic enity lo ecree eponentilly with the energy bngp. herefore, MOS tructure me with wie bngp mteril (for intnce 6H-Si for which E g 3 e), hve n etremely pronounce eep epletion effect. In ilicon MOS cpcitor, one fin tht the occurrence of eep epletion cn be linke to the minority crrier lifetime. Structure with long (0. m) lifetime require few econ to rech therml equilibrium which reult in pronounce eep epletion effect t room temperture, tructure with hort ( µ) lifetime o not how thi effect. rrier genertion ue to light will incree the genertion rte beyon the therml genertion rte, which we ume bove n reuce the time neee to rech equilibrium. Deep epletion meurement re therefore one in the rk Eperimentl reult n comprion with theory A n emple, we how below the meure low frequency (qui-ttic) n high frequency cpcitnce-voltge curve of n MOS cpcitor. he cpcitnce w meure in the preence of mbient light well in the rk epline in igure pcitnce (p) te-to-bulk oltge () igure Low frequency (qui-ttic) n high frequency cpcitnce meurement of pmos cpcitor. Shown re, from top to bottom, the low frequency cpcitnce meure in the preence of mbient light (top curve), the low frequency

13 cpcitnce meure in the rk, the high frequency cpcitnce meure in the preence of mbient light n the high frequency cpcitnce meure in the rk (bottom curve). All curve were meure from left to right. he MOS prmeter re N - N 4 5 cm -3 n t 80 nm. he evice re i cm 2 igure illutrte ome of the iue when meuring the cpcitnce of n MOS cpcitnce. irt, one houl meure the evice in the rk. he preence of light cue crrier genertion in the emiconuctor, which ffect the meure cpcitnce. In ition, one mut voi the eep epletion effect uch the initil linerly vrying cpcitnce of the high frequency cpcitnce meure in the rk on the bove figure (bottom curve). he lrger the crrier lifetime, the lower the voltge i to be chnge to voi eep epletion. he low frequency meure i compre to the theoreticl vlue in igure he high frequency cpcitnce meure in the preence of light i lo hown on the figure. he figure illutrte the greement between eperiment n theory. A comprion of the eperimentl low (rther thn high) frequency cpcitnce with theory i omewht eier to crry out. he low frequency cpcitnce i eier to clculte while the meurement ten to be le enitive to eep epletion effect. 5.0E-08 pcitnce (/cm 2 ) 4.0E E E-08.0E E te-to-bulk oltge () igure omprion of the theoreticl low frequency cpcitnce (oli line) n the eperimentl t (open qure) obtine in the rk. itting prmeter re N - N cm -3 n t 80 nm Non-Iel effect in MOS cpcitor Non-iel effect in MOS cpcitor inclue fie chrge, mobile chrge n chrge in urfce tte. All three type of chrge cn be ientifie by performing cpcitnce-voltge meurement. ie chrge in the ie imply hift the meure curve. A poitive fie chrge t the ie-emiconuctor interfce hift the fltbn voltge by n mount, which equl the chrge ivie by the ie cpcitnce. he hift reuce linerly one reuce the poition of the

14 chrge reltive to the gte electroe n become zero if the chrge i locte t the metl-ie interfce. A fie chrge i cue by ion, which re incorporte in the ie uring growth or epoition. he fltbn voltge hift ue to mobile chrge i ecribe by the me eqution tht ue to fie chrge. However, the meure curve iffer ince poitive gte voltge cue ny negtive mobile chrge to move wy from the gte electroe, while negtive voltge ttrct the chrge towr the gte. hi cue the curve to hift towr the pplie voltge. One cn recognize mobile chrge by the hyterei in the high frequency cpcitnce curve when weeping the gte voltge bck n forth. Soium ion incorporte in the ie of ilicon MOS cpcitor re known to yiel mobile chrge. It i becue of the high enitivity of MOS tructure to vriety of impuritie tht the inutry crefully control the purity of the wter n the chemicl ue. hrge ue to electron occupying urfce tte lo yiel hift in fltbn voltge. However the pplie voltge i vrie, the ermi energy t the ie-emiconuctor interfce chnge lo n ffect the occupncy of the urfce tte. he interfce tte cue the trnition in the cpcitnce meurement to be le brupt. he combintion of the low frequency n high frequency cpcitnce llow clculting the urfce tte enity. hi metho provie the urfce tte enity over limite (but highly relevnt) rnge of energie within the bngp. Meurement on n-type n p-type cpcitor t ifferent temperture provie the urfce tte enity throughout the bngp.