Analysis of alo Implante MOSFETs olin McAnrew an Patrick G Drennan Freescale Semiconuctor, Tempe, AZ, olinmcanrew@freescalecom ABSTAT MOSFETs with heavily ope reions at one or both ens of the channel exhibit qualitative ifferences in electrical behavior compare to evices with laterally uniform channel opin These ifferences inclue a istinct peakiness in the transconuctance near threshol, asymmetries in capacitances, an a surprisin ecrease in the statistical variation of the peak ain factor as channel lenth ecreases istorically, accurate moelin of such evices is best one with sectional MOSFET moels ere we present an analytic moel of the behavior of the current an transconuctance of a (unilaterally or bilaterally halo implante MOSFET an show that it preicts the ecrease in variation of ain factor with channel lenth Keywors: MOSFET moelin; SPIE moelin; statistical moelin; halo implant INTODUTION ow voltae MOSFETs historically have uniform lateral opin alo (pocket implants [] were introuce to improve performance an suppress some short-channel effects, an are now stanar Specific heavily ope reions were introuce at the ens of the channel in GMOS technoloies [] to boost performance, an these coul be one selectively at source an/or rain ens, leain to so-calle unilateral an bilateral evices, havin one or both ens ope heavily, respectively These laterally non-uniformly ope evices exhibit qualitatively ifferent behavior compare to laterally uniformly ope evices First, as the ate voltae increases from below to above threshol, the lihtly ope central reion turns on at a lower ate voltae than the more heavily ope en reion(s, an therefore when the en reions start to turn on the channel lenth is effectively the lenth of these heavily ope reion(s As the ate voltae further increases an the level of inversion becomes more uniform in the evice, the channel lenth becomes more the lenth of both the heavily an lihtly ope reions The (D electrical effective channel lenth eff is therefore shorter near threshol than for well above threshol, an this ives a istinct peake m s b behavior near threshol (we assume 0 here A very interestin analysis of halo implante MOSFETs was presente in [3] This work provie a physical threshol voltae moel for bilaterally ope evices, an unequivocally showe that a 3-section MOS moel is neee to capture fine etails of halo implante MOS behavior; merely moelin threshol voltae for a -section moel is insufficient Althouh the peake m behavior is not explicitly note in [3] it is apparent in Fis 0 an in [3] But a moel explainin this behavior an its statistical variation was not provie source s 0 N T ate N Fi MOSFET compose of 3 separately ope reions For a unilaterally ope evice (assumin the heavy opin is on the source sie of the evice, as the evice turns on the rain en inverts before the source en, hence there is a istinct peak in near threshol, an the evice is hihly asymmetric an s, even at 0 Aain, this behavior cannot be capture by a -section MOSFET moel, especially with the emphasis of the past ecae in improvin the symmetry of MOSFET moels For MOSFETs with constant lateral opin, the statistical variation in the peak transconuctance m µ 0oxW chanes with channel lenth; for short evices it is reater than for lon evices ariation in the oxie thickness T ox an the low fiel mobility µ 0 contribute equally to the variations in m for both lon an short evices, but variations in eff affect a short evice more than a lon evice, so the overall variation in m increases as lenth ecreases This behavior is not observe in evices with nonuniform lateral opin In unilateral GMOS evices the measure variation in m is less for short evices than for lon evices We present an analysis that explains this counterintuitive behavior The basic moel unerlyin the analysis is simple, an is not intene to provie a hihly accurate escription of all aspects of evice behavior But it is amenable to analysis that eluciates the unerlyin cause of the unexpecte ecrease in m as channel lenth ecreases Note that DMOS transistors also have laterally nonuniform opin, but this is because their boy reion is forme by out-iffusion an not because of a separate heavy opin reion at the source or rain The analysis here is not irectly applicable to DMOS evices, but oes capture some of the qualitative behavior they exhibit, because a unilaterally ope GMOS evice is qualitatively similar to an DMOS evice NUMEIA BIATEA AO MODE onsier a MOSFET semente into 3 reions, see Fi Ajacent to the source is a reion of lenth an threshol voltae T, in the mile is a reion of lenth an N T rain 594 NSTI-Nanotech 007, wwwnstior, ISBN 4006844 ol 3, 007
threshol voltae, an ajacent to the rain is a reion of lenth an threshol voltae T The source an bulk are assume to be at zero olts an voltaes an are applie to the ate an rain For operation in stron inversion non-saturation, at small, the currents (normalize to µ 0 ox W in each of the 3 sections, which must be equal, are approximately T 05 ( i + B 05 ( i T + B 05( (3 i ( where an are the voltaes between the left (source an center sections, an between the center an riht (rain sections, respectively, an B an B are the boy effect factors for the central an riht reion, respectively The terms involvin the last two parameters are require because the effective backate bias for the center an riht sections (takin the source as the reference is not zero an in ( throuh (3 vary with ate bias Iteratively solvin for these, as a function of ate bias an overall ate lenth + +, then computin the current an m (an normalizin with respect to the m at just above threshol, ives the results shown in Fi one to specifically eluciate the effects of the non-uniform lateral opin an to not have them confoune with other physical phenomena As observe in experimental ata, the m exhibits a peake characteristic (aain, this is not from series resistance or vertical fiel mobility eraation, which increase the peakiness, the latter uniformly over lenth an the former more for short than for lon evices; it is purely from the intrinsic nature of the laterally non-uniform opin for a laterally uniformly ope evice m woul be inepenent of bias in Fi Note that the peakiness is non-monotonic in lenth Asymptotically as 0 the evice appears, for N N, to be laterally uniformly ope, an as the relative effect of the en reions becomes vanishinly small, therefore the m m, max curve shoul be flat for both of these cases Fi 3 shows the peakiness (the ratio of the peak m to its value for lare as a function of (reciprocal channel lenth Fi 3 m peakiness vs reciprocal channel lenth Startin from short evices (rihtmost abscissa values in Fi 3, as the channel lenth increases (movin to the left, the peakiness increases, as is observe in practice For very lare lenths the peakiness aain ecreases, as is expecte from the qualitative analysis above Fi Normalize m vs for various lenths For the simulations use to enerate Fi, 008µ m (the simulations here were base on the technoloy of [], which is a 04µm MOS technoloy with a minimum eff of 05µm from the GMOS structure, T T 04 an 0 Note that for the simulations series resistance is inore an mobility reuction ue to both vertical an lateral fiels is not inclue, so surface rouhness scatterin an velocity saturation are inore; this is 3 ANAYTIA BIATEA AO MODE Instea of numerically solvin ( throuh (3, analytically ifferentiatin with respect to, an roppin neliible terms,, an are small, ives (4 (5 + T m, + m, NSTI-Nanotech 007, wwwnstior, ISBN 4006844 ol 3, 007 595
(6 T m, (etaile calculations that keep the omitte terms for now an eliminate them later are extremely teious an lea to the same results iven below Because the current throuh each section must be the same, the chane in each current with must the same, so equatin (4 an (6 ives (7 Equatin (5 an (6 an usin (7 ives (8 T T + T + T T + T T Substitutin (8 into (4 an rearranin, ives (aain normalize to µ 0 ox W (9 T + T( T + ( T( m ( T + T( T + T( Note the inherent symmetry an consistency of (9; settin any of reion lenth to zero (notin that if 0 then 0, if 0 then, an if 0 then reuces the expression to an obviously similar form; as oes settin the parameters of one reion to those of an ajacent reion Assumin a symmetric halo implant, an T T, then for small, equatin ( an (, an notin that at low for a symmetric evice, (0 + T This inicates that moelin the evice as the series connection of separate reion channel resistances, as in [3], is reasonable owever, our explicit solution for the internal noe voltaes verifies this approach alculation of the transconuctance ives ( m + ( + This is simpler than the form (9 yet almost as accurate owever, it is still not intuitive how this varies with eometry an statistical fluctuations Aain for left an riht en reions with the same physical characteristics (lenth, opin, threshol voltae, for a lon evice from (9 m (3 0,, + Because >, this approximation preicts that m increases as increases, which is qualitatively ifferent from the behavior in Fi This is because it oes not take into account the better approximation (0 A tihter upper boun is (4 m + For a short evice (5 m 0 5, 05, + (As 0, because the central reion has a lower opin an hence lower threshol than the en reions, it is turne on more than the ens, an has a lower resistance; thus approaches (which is clearly the expecte result for The current in the transistor is then, normalize to µ 0 ox W, ( I + Fi 4 Normalize m from analytic approximations 596 NSTI-Nanotech 007, wwwnstior, ISBN 4006844 ol 3, 007
Fi 4 compares the simple approximations (4 an (5 with values calculate from numerical simulations base on iterative solution of ( throuh (3 (results from ( are not inclue; they are almost ientical to those from the numerical simulations; results from (5 are also not inclue for the 0µm lon evice as this approximation is only applicable to short evices The lon channel simple approximation (4 is clearly somewhat inaccurate owever, the areement of the very simple analytic moel (5 with the more etaile numerical moel from the iterative solution of ( throuh (3 is quite reasonable 4 ANAYSIS Because the halo reion is more heavily ope than the center of the channel >, an the ratio of the halo to central reion ate overrives in the enominator of (5 is less than The effect of this ratio on the overall evice transconuctance ecreases as ecreases, hence the smaller the the shorter the effective channel lenth in the enominator of (5, an the hiher the m This is the root cause of the peakiness of the m characteristic, an this simple an intuitive theoretical analysis arees both with the qualitative escription in the Introuction an with experimental observation that m is more peake for short than for lon evices More interestinly, consier what happens when,,, or in (5 vary Increasin any of these parameters woul normally, as a first response, be expecte to lea to a reuction in current, an hence m This is seen to be the case for the parameters,, an, but is unexpectely not true if increases Increasin causes to ecrease (at a fixe ate voltae, which reuces the overall enominator in (5 an therefore increases m An alternative viewpoint is that if increases compare to, the central reion is turne on harer when the halo reions invert, this makes the effective channel lenth appear shorter, an hence enhances m Numerical simulations confirm this counter-intuitive behavior Statistical variations in the ain factors come from statistical variations in T ox an µ 0, which (inorin the uncorrelate, or mismatch, component are the same for short an lon evices, an from statistical variations in,,, an For illustrative an comparison purposes we inore the effect of the variations in T ox an µ 0 an consier only the variations in the lenth an threshol parameters Propaation of variance (Po analysis [4] of (5 therefore ives (6 δm m e + 4 δ + δ + where + e δ δ Applyin this Po analysis to the 5µm an 04µm channel lenth evices, for which Fi 4 shows that the approximation (5 is reasonable, ives the results shown in Fi 5 an Fi 6 The contribution of the variations in each of the parameters, at the - level, is shown in these fiures The counter-intuitive conclusion from this analysis arees with experimental observations: the statistical variation in the peak m for halo evices is reater for loner evices than for shorter evices Fi 5 Statistical variations in m for the 5µm evice Fi 6 Statistical variations in m for the 04µm evice Most strikinly, it is the ecrease of the influence of variation in as lenth ecreases on the ain factor that stans out Analytically, the 4 th term in the riht-han sie of (6 shoul ecrease as ecreases, an this is observe in numerical simulations an ata owever, overall contributions in practice are more ifficult to compartmentalize The empirical conclusion from Fi 5 an Fi 6 is that statistical variations in peak m ecrease as channel lenth ecreases, for lenths in a certain rane This conclusion is supporte by experimental ata, which show that the peak m variation for GMOS type evices ecreases as ecreases NSTI-Nanotech 007, wwwnstior, ISBN 4006844 ol 3, 007 597
5 UNIATEA AO ANAYSIS For a evice with an implant only at the source en of the channel, which in some ways is analoous to an DMOS evice, (7 T + T m ( + T an for lon evices 0 an for short evices, hence (3 an (5 still apply, with substitute for ; qualitatively the behavior is ientical The analyses here have been tarete to bilateral halo implante evices, but the oriinal analysis we evelope was base on unilateral evices, to try to unerstan physically why the observe statistical variation in the peak m was smaller for shorter evices than for moerate lenth evices 6 ONUSIONS We have provie an analysis of the rain current of halo implante MOSFETs, at low s, base on equality of the currents flowin in ifferent reions of the evice This enable expressions for the ain factor m s to be erive The analysis eluciates the reason for the qualitative chane in the shape of m s plots, an also for the observe ecrease in statistical variation as channel lenth ecreases Our analyses support the conclusion of [3], that there are qualitative features of the characteristics of halo implante evices that cannot be moele usin a sinle MOSFET moel; a multi-section moel (two or three sections, epenin on the structure of the evice is neee owever, rather than analyzin a evice from the channel resistance perspective, as note in [3], we foun it avantaeous to consier equality of currents in ifferent reions of the evice This le to the physical unerstanin of why the peak m variation for short evices is unexpectely less than for moerate lenth evices, an what physical parameter variations unerlie this behavior EFEENES [] Y Okumura et al, A Novel Source-to-Drain Nonuniformly Dope hannel (NUD MOSFET for ih urrent Drivability an Threshol oltae ontrollability, IEEE IEDM Tech Di, pp 39-394, Dec 990 [] F K hai et al, A ost-effective 05µm eff BiMOS Technoloy Featurin Grae-hannel MOS (GMOS an a Quasi-Self-Aline (QSA NPN for F Wireless Applications, Proc IEEE BTM, pp 0-3, Sep 000 [3] ios et al, A Three-Transistor Threshol oltae Moel for alo Processes, IEEE IEDM Tech Di, pp 3-6, Dec 00 [4] McAnrew an P G Drennan, Unifie Statistical Moelin for ircuit Simulation, Proc MSM-WM, pp 75-78, 00 598 NSTI-Nanotech 007, wwwnstior, ISBN 4006844 ol 3, 007