Analytical description of the injection ratio of self-biased bipolar. transistors under the very high injection conditions of ESD events

Transcription

1 Author mauscript, published i "Solid-State Electroics 5, 5 (007) " Aalytical descriptio of the ijectio ratio of self-biased bipolar trasistors uder the very high ijectio coditios of ES evets A. Gedro *, P. Reaud, M. Bafleur ad N. Nohier Freescale Semicoductor, 34 Av du Gééral Eisehower 303 TOULOUSE Cedex, FRANCE LAAS-CNRS, 7 Av du Coloel Roche 3077 TOULOUSE Cedex 4, FRANCE * Now at Freescale Semicoductor, 00 E. Elliot Rd, TEMPE, AZ 8584, USA hal , versio - May 009 Cotact: philippe.reaud@freescale.com Abstract This paper proposes a -aalytical descriptio of the ijectio ratio of a self-biased bipolar trasistor uder very high curret ijectio coditios. Startig from a expressio of the curret gai based o the stored charge ito the emitter ad base regios, we derive a ew aalytical expressio of the curret ijectio ratio. This aalytical descriptio demostrates the presece of a asymptotic limit for the ijectio ratio at very high curret desities, as the ratio of electro/hole mobilities i the case of a NPN trasistor ad to the ratio of hole/electro saturatio velocities for a PNP. Moreover, for the first time, a base arrowig effect is demostrated ad explaied i the case of a self biased PNP, i cotrast with the base wideig effect (Kirk effect []) reported for lower curret desity. These results are validated by umerical simulatio ad show a good agreemet with experimetal characterizatios of trasistors especially desiged to operate uder extreme coditio such as Electro-Static-ischarge (ES) evets.

2 . Itroductio Protectig high voltage smart power techologies agaist electrostatic discharges (ES) is a great challege [] C. T. Kirk, A theory of trasistor cutoff frequecy (ft) falloff at high curret desities, IRE Tras. o electro devices, pp 64-73, 96. []. Typical protectio structures are based o self-biased NPN bipolar trasistors give their good ES robustess. The mai drawback of the NPN trasistor is its strog sapback behavior [3] [4] [5], that requires stackig several structures to icrease the clampig voltage above the power supply value ad the fulfill the requiremet of latch-up free operatio [6]. To avoid stackig stackig structures, which is detrimetal to both silico area ad o-state hal , versio - May 009 resistace, a solutio cosists i cotrollig this strog sapback effect (mostly desig approach [7]) or usig reduced gai PNP bipolar trasistors that do ot exhibit this effect [8] [9]. I both cases, a deep uderstadig of the ivolved physical mechaisms uder the very high ijectio coditios that occurs durig a ES evet is required to improve the efficiecy of such protectio devices. The aalytical study of the physical mechaisms ivolved i a bipolar trasistor is a topic that has bee extesively studied; with the Boltzma approximatio as a corer stoe of the aalytical explaatio of bipolar effect. However, uder very high ijectio coditio, this approximatio does ot remai valid ad some corrective terms eed to be added. Other derivatios of semicoductor devices fudametal equatios may be better suited to treat the case where the curret desities create a space charge approachig the dopig level of a cosidered regio. Historically, very high ijectio effects were treated for curret desities up to 0 4 A.cm -, because, i most of applicatios, higher curret desities values lead to silico meltig, hece device destructio. However, durig the very short duratio of a ES evet, protectio devices ca briefly sustai curret desities as high as 0 6 A.cm - without destructio. Sice

3 the curret peak lasts oly for a few hudreds of aosecods, the heat geeratio i the protectio device may ot be sufficiet to iduce a meltig of the silico, ad to damage the structure. This paper describes the effect of such level of curret desities ad the impact of the resultig iduced charges o the behavior of a self-biased bipolar trasistor. I a self-biased cofiguratio, base ad emitter are coected or eve the base ca be left floatig. The bias curret is supplied by the avalache curret geerated at the reverse biased base-collector juctio (Figure ). Startig from the same basic equatios the cases of NPN ad PNP will be treated separately. hal , versio - May 009 (a) (b) Figure : Cofiguratio of a self-biased NPN bipolar (a) ad its equivalet circuit (b).. Theoretical cosideratio for the determiatio of curret gai at very high curret desities For the sake of simplicity, ad i the aim of developig aalytical models, we choose here to firstly cosider a oe-dimesioal model of a NPN trasistor i ope-base cofiguratio. This latter choice is motivated by the fact that a approach does ot allow a realistic base biasig. We also cosider costat dopig levels ad abrupt juctios. The recombiatios 3

4 will be eglected sice, i most of the advaced techologies (i particular, CMOS ad smart power techologies), the emitter ad base widths are much smaller tha the diffusio legths of their respective miority carriers. Fially, we will cosider isothermal coditios, that meas we will ot take ito accout the self-heatig of ES protectios. The implicatios of these simplifyig hypothesis will be discussed at the ed of this paper, where we will qualitatively study their effects o the results accuracy. The umerical applicatios will be based o physical parameters values at 300K. I particular for the electros ad holes mobilities, respectively ad p, ad saturatio velocities, respectively v sat, ad v sat,p, we will use the values: hal , versio - May 009 v v pb sat, sat, p cm. s cm. s cm. s 6. V cm. s Previous studies established that the curret gai β of a bipolar trasistor decreases for high curret desities i the followig way [0] [] [] : β C B β 0 C H. V () Where C ad E are respectively the collector ad base curret desities, β 0 is the well kow maximal curret gai expressed as: β ib N EWE 0 ie pe N BW () B Where i is the itrisic carrier desity, ad p the miority carrier diffusio legths, N the dopig cocetratio, W E ad W B the emitter ad base widths, respectively. Idexes E ad B 4

5 idicate whether the emitter or the base is cosidered. H is the critical curret desity that ca be expressed [] with the base parameters oly: H q B (3) W B N Where q is the electro charge. The previous aalytical expressios are oly valid uder the assumptio of a high trasistor gai. That is to say the emitter ijectio curret e- should be much greater tha the base ijectio curret h. However, the curret gai drastically decreases with the icrease i The itegral boudaries are set by the emitter cotact ad the trasitio from the base quasihal , versio - May 009 curret desity ad the previous assumptio is o more fulfilled. This is why, we propose to re-derive the basic aalytical expressios by takig ito accout both emitter ad base ijectio currets. This way, we should be able to describe the mechaisms ivolved i bipolar trasistors at very low curret gai values, as it is experimetally ecoutered durig ES evets. 3. O the Ijectio ratio e- / h Startig from the formalism ad expressios set by. P. Bailbé [3] it seems appropriate to treat the problem i terms of the total stored charges withi the emitter ad base. The charges are provided both by the extrisic dopig ad by the curret flow. This formalism leads to the followig expressio of the ijectio ratio: γ h BC E BC E p p i i dx dx E peie B ib SB pbib SB ib SE peie SE EiE (4) 5

6 eutral zoe to the base-collector space charge regio. Hece, takig ito accout all differet cotributios, E is the total ioized dopig charge i the emitter, B the total ioized dopig charge i the base, SB the total charge iduced by the electro curret withi the base, SE the total charge iduced by the hole curret withi the emitter. The very geeral expressio (4) is valid for ay curret value. I particular, its validity domai is ot limited by ay curret depedet assumptio, such as the Boltzma approximatio, for istace. We remid that it is importat to differetiate the values of both diffusio coefficiets ad itrisic carrier desities depedig o whether the emitter or base is cosidered, as these two hal , versio - May 009 parameters are greatly depedat o the dopig cocetratio. 4. Evolutio of the ijectio ratio uder very high ijectio a. Prelimiary cosideratios Uder very high ijectio, the charge B is egligible i compariso with the charge SB. Thus the term depedig o B ca be systematically suppressed, ad expressio (4) becomes: γ E peie SB ib SB pbib SE EiE SE peie (5) Noe of the other terms ca be eglected without ay careful evaluatio. First of all, for low ijectio ratio values, electro ad hole currets are i the same rage. Hece SB ad SE are also i the same rage, uless the differece betwee W B ad W E favors the charge storage ito either the emitter or the base. Besides, they should ot be eglected i frot of E, to 6

7 preserve the expressio validity eve at very high curret. b. Geeric trasit time expressios Let us ow express the differet types of charges as a fuctio of the stadard trasistor parameters. The determiatio of the charges resultig from the ioized impurities withi the emitter is trivial: qn W (6) E E E The charges iduced by the curret ito the base ad the emitter are: hal , versio - May 009 τ (7) SB B τ (8) SE E h Where τ B ad τ E are the trasit times, respectively of the holes withi the base ad of the electros withi the emitter. There is ot geeral expressio of the trasit times that ca be aalytically derived, i fuctio of the trasistor parameters. However, we ca use approximated expressios uder some particular operatig coditios []: For low ijectio coditio: τ B W B (9) For high ijectio coditio: τ B W B (0) 4 Equivalet expressios ca be derived for the trasit time of the electros withi the emitter, τ E. Expressio (0) for the high ijectio is oly valid uder the high gai assumptio, which is 7

8 ot the case durig a ES evet. Thus, we eed to derive a specific expressio for the trasit times that applies i our particular case. c. Hole trasit time ito the base Uder very high ijectio coditios, the drift curret ito the base is o more egligible compared to the diffusio curret. To take ito accout both the diffusio ad drift currets, a method cosists i defiig a effective diffusio coefficiet,eff [0]. Whe the low gai assumptio is fulfilled, diffusio ad drift currets become equal, ad the resultig effective diffusio coefficiet is the two times the carrier diffusio coefficiet (,eff ); as hal , versio - May 009 exemplified i expressios (9) ad (0). Usig the same methodology as developed i [0], let us recalculate the expressio of this effective diffusio coefficiet without eglectig the base ijectio curret h. Startig from the cotiuity equatios: d e q E () dx dp h q p pb E pb () dx Where ad p are the electro ad hole cocetratios, d dx ad dp dx their respective gradiets, E is the electric field withi the base quasi-eutral zoe. For high ijectio, the base eutrality implies p, thus () ad () ca be combied as: h q pb d dx (3) 8

9 Usig the defiitio of the ijectio ratio (γ h ), a expressio of e- proportioal to the electro gradiet ca be obtaied: q γ pb d dx (4) This expressio allows defiig the effective diffusio coefficiet: hal , versio - May 009, effectif γ Compared to the previous effective diffusio coefficiet (equals to ), this ew expressio evideces a further icrease by a factor of pb (5). This aticipates that drift curret pb γ becomes the domiat coductio type with respect to diffusio curret. Usig (7), the electro trasit time withi the base becomes: τ B W pbγ 4 B (6) Ad the base curret iduced charge: SB W pbγ 4 B (7) 9

10 d. Electro trasit time ito the emitter The determiatio of the electro trasit time withi the emitter is ot as straightforward. Sice the emitter dopig level ca be rather high, the high ijectio coditio may ot be satisfied over the full duratio of the ES pulse. I particular, the approximatio p caot be applied, i the same way as previously doe for the base. Regardig the emitter, both low ad high ijectio coditios ca be ecoutered durig a ES evet. As previously metioed, a uique trasit time aalytical expressio caot be determied. The, there is o way to have a precise aalytical descriptio of the effects resultig from the curret iduced charge ito the emitter SE. However, most bipolar trasistors used as ES protectios, hal , versio - May 009 exhibit a base that is sigificatly wider tha the emitter, makig possible to eglect SE compared to SB. Usig this ew coditio o the emitter ad base dimesios, a ijectio ratio expressio without the SE terms ca be derived from expressio (5): E SB peie pbib γ (8) SB ib This expressio will be preferetially cosidered i the followig. Besides, we ca take advatage of expressio (5) to give a rough evaluatio of the impact of SE o the ijectio ratio. Two values of SE should be cosidered, oe uder low ijectio ad high gai coditios with trasit time expressio (9): SE W E h pe (9) ad oe uder high ijectio ad low gai coditios with trasit time expressio (0) : 0

11 ' SE SE (0) As the purpose is oly to determie the magitude of the modificatio iduced o the ijectio ratio, it is ot worthwhile to make a more complex computatio uder high ijectio ad low gai coditios. e. Ijectio ratio expressio First, the curret iduced charge ito the emitter SE is ot take ito accout. The computatio is based o expressio (8). By isertig expressios (6) ad (7) of E ad SB, hal , versio - May 009 respectively, we obtai: qn γ This expressio ca be re-writte as: E pe W B W pbγ 4 E ie W pbγ 4 ib B pb ib () γ pb γ pb () Where the parameter, homogeous to a curret desity, is expressed as: q N WE (3) W ib pe ie E B The factorizatio of γ i () leads to the followig secod degree equatio:

12 γ pb γ pb 0 (4) The reduced determiat of the correspodig biomial is: ' Δ pb pb pb > 0 (5) The reduced determiat is positive; equatio (4) has the two mathematical solutios. Oe solutio icreases with the electro curret ad has o physical meaig i our study, thus hal , versio - May 009 oly the decreasig solutio is valid: With: γ r r r pb (6) r (7) Expressio (6) shows that a modificatio of the behavior occurs whe becomes close to the mobility ratio r. The, ca be cosidered as a critical curret desity to which e- has to be compared to characterize the ijectio ratio variatios. To evaluate, expressio (3) ca be re-writte as: γ 0 H (8) Where H is the critical curret desity describig the begiig of the gai fall, give by (3),

13 ad γ 0 the same expressio as the maximum ijectio ratio at low ijectio: N W γ ib E E 0 (9) peie N BWB The tred of the ijectio ratio versus the ormalized electro curret ( e- / ) is plotted i Figure. At 300K, r, the ratio of the electros mobility o the holes oe, is equal to 3.0. hal , versio - May 009 Mobilities Ratio Figure : Ijectio ratio versus ormalized electro curret draw from (6). f. Asymptotic behavior at extreme high ijectio For e- >>, the ijectio ratio expressio (6) has a asymptotic miimum limit equal to the mobility ratio: γ l r (30) A simple maipulatio of expressio (5), i which SE is eglected, allows aalyzig the physical mechaisms associated with this asymptotic behavior: 3

14 γ E peie SB ib SB pbib E peie SB ib r (3) With this expressio, it is obvious that the ijectio ratio reaches its asymptotic limit whe the curret iduced charge withi the base becomes greater tha the dopig charge withi the emitter ( SB >> E ). Cosiderig () ad () cotiuity equatios whe p, a ijectio ratio limit equal to the mobility ratio could oly be reached if, for both electro ad hole currets withi the base, the drift curret due to the electric field becomes domiat compared hal , versio - May 009 to the diffusio curret. This result has a importat implicatio sice, util today, it has bee cosidered that uder high ijectio coditios, the drift curret reaches oly the value of the diffusio curret. To our kowledge, it has ever bee ever reported that for extreme high ijectio coditios, the drift curret could be the mai compoet of a bipolar trasistor curret. We should outlie that we do ot kow at the preset stage of the study if this limit ca be achieved. As depeds o the curret desity, via the modificatio of the iteral base width W E uder high ijectio, we are ot sure that the coditio e- >> ca be fulfilled. Further ivestigatios o that aspect will be performed i the followig of the paper. g. Evaluatio of SE cotributio The purpose is to determie the corrective terms i the ijectio ratio expressio (6), whe SE is take ito accout. As stated before, there is o aalytical expressio of SE valid over the full duratio of the ES stress ad we will oly make a rough evaluatio of its cotributio. At first, the low ijectio withi the emitter is cosidered. By isertig expressios (6), (7) 4

15 ad (9) ito the ijectio ratio expressio (5), we obtai: γ W B qn EW pbγ 4 pe E ie W pbγ 4 ib B pb ib WE E W h pe E h peie ie (3) As previously doe whe SE was eglected, similar mathematical maipulatios lead to a ew expressio of the ijectio ratio: hal , versio - May 009 γ ( r re) ( r re) r re Where r E ad r E are two parameters without dimesios give by: W (33) ib E r E (34) E peiewb W ib E r E (35) peiewb This expressio of the ijectio ratio still exhibits a asymptotic limit whe e- >> : γ l ( r re) ( r re) r re (36) To evaluate the effect of SE, we should compare r E to r ad r E to r. This effect ca be eglected if: 5

16 r r E E << r << r (37) Besides, the coefficiets r E ad r E are proportioal to W E W B, which cofirms that SE is egligible for a base sigificatly wider tha the emitter. Regardig the case of high ijectio with low gai, the study shows that the terms r E ad r E should be divided by two. The ijectio ratio is the give by: hal , versio - May 009 γ re r re r r re This reductio of the corrective terms is due to the decrease of the trasit time at high ijectio, which leads to lower charge SE. I this case, the asymptotic limit for e- >> is give by: γ re re re r r r (38) (39) 5. Applicatio to a self-biased bipolar trasistor durig a ES stress. a. O-state resistace (R ON ) of a ES protectio The o-state resistace, R ON, is oe of the most critical parameters of a ES protectio; as it must be sufficietly low to prevet over voltage reachig oxide breakdow. For a protectio based o a self-biased bipolar trasistor, the R ON results maily from high curret effects at the base-collector juctio [8]. The charge iduced by the curret adds up to the base dopig, 6

17 which is virtually higher, ad subtracts to the collector dopig, which becomes virtually lower []. This modulatio of the space charge regio (SCR) leads to a field modificatio resultig i a equivalet resistace. urig a ES stress, the curret iduced charge i the SCR could reach 0 8 cm -3. I smart power techologies, the dopig levels ecoutered are lower or i the rage of this value, meaig that these high ijectio effects have a sigificat impact. Calculatio of the curret iduced charge i the SCR idirectly leads to a estimate of the SCR width variatio ad of the voltage drop i this regio, if we cosider: - The maximum value of the electric field at the base-collector juctio approximately hal , versio - May 009 costat with curret. - A abrupt collector-base juctio with a collector dopig level much higher tha the base oe to approximate a static juctio positio. - The curret iduced charge withi the base is much higher tha the dopig charge. These coditios are ot too restrictive, i particular for high voltage ES protectio. By this way, we ca determie a first approximatio of the R ON variatios without developig a aalytical expressio for the SCR width. b. Curret iduced charge i the base-collector SCR Withi the SCR, the carriers reach their saturatio velocity. Thus, the electros ad holes p cocetratios i the regio ca be expressed as: (40) qv sat, 7

18 p h (4) qv sat, p The resultig total charge withi the SCR becomes: h ρ csr (4) vsat, p vsat, Usig e- h, equatio (4) ca be expressed as a fuctio of the total curret : hal , versio - May 009 ρ scr v sat, p vsat, vsat, p A aalytical expressio of as a fuctio of ca be extracted by usig e- h ad γ h : (43) γ (44) By combiig it with the expressio (6) of the ijectio ratio, we obtai a secod order equatio i e- : r ( ) ( )( r ) 0 (45) whose solutio is: r ( r ) _ ( r ) ( r ) (46) Isertig expressio (46) ito (43), we obtai a aalytical expressio of the SCR charge versus the total curret desity : 8

19 ρ scr v v v r ( r ) _ ( r ) ( r ) sat, p sat, sat, p (47) c. Variatios of the curret iduced charge i the base-collector SCR To plot the evolutio of ρ SCR, it is coveiet to cosider a value ormalized o a critical charge ρ defied as: ρ (48) vsat, vsat, p hal , versio - May 009 From (47), it is straightforward to obtai the expressio of this ormalized value of ρ SCR : With ρ ρ scr r r ( r ) ( r ) r v ( r ) (49) sat, (50) vsat, vsat, p The tred of the ρ SCR ormalized o ρ versus the curret desity ormalized o is plotted i Figure 3, both for a NPN ad a PNP. 9

20 hal , versio - May 009 Figure 3: Normalized charge (ρ SCR /ρ ) versus ormalized curret desity (/ ), plotted for (49). The SCR charge i a NPN ad a PNP is equivalet as far as the curret desity is smaller tha the critical curret. For higher values, the charge i a NPN mootoously icreases, whereas the charge i a PNP decreases whe a threshold curret desity I is exceeded. For the NPN trasistor, the charge variatio results i a cotiuous SCR arrowig, whe the curret icreases. This SCR arrowig teds to reduce the R ON, which is beeficial for the performace of ES protectios. Cocerig the ijectio ratio, the related iteral base wideig leads to a decrease of with curret. If is lower or similar to the curret desity durig a ES stress, the coditio e- >> is fulfilled ad the value of the ijectio ratio teds to the mobility ratio. I the case of a PNP, the charge decrease results i a SCR wideig, which has a detrimetal impact o the R ON. Besides, the ormalized curret desity value keeps lower 0

21 tha sevetee (Figure 3), so that the coditio e- >> may ot be satisfied. This meas the ijectio ratio value here, may ot ted to the mobilities ratio. For further ivestigatios, umerical applicatios are ow udertake., both for NPN ad PNP trasistors. NPN For the umerical applicatio, the parameters r ad r are calculated for the values of mobilities ad the saturatio velocities at 300K defied i the sectio : hal , versio - May 009 r pb 3.0 r v sat, v sat, v sat, p 0.56 The variatios of ρ SCR ca be estimated through the derivative of expressio (47): dρ scr d v sat, p r v sat, v sat, p r ( r ) To evaluate the evolutio with the curret desity, the limits of expressio (5) are calculated for << ad >> : (5) dρ d << l, vsat, (5) dρ d >> r ( ) r v Sat, v Sat, p l ; (53) The ratio of these two limits is:

22 l, l, ( ) r v Sat, p r v Sat, p 0.44 (54) The slope of the charge icrease is approximately reduced by two whe the curret desity icreases. However, this should ot result i a strog degradatio of the ES protectio robustess. PNP Aalytic developmets for the PNP are equivalet to those of the NPN by ivertig the hal , versio - May 009 idexes of holes (p) ad electros (). I the case of a PNP trasistor, the parameters r ad r are give by : r r v pb v sat, p 0.33 sat, p v sat, 0.44 To characterize the PNP behavior, the most importat parameter is the curret desity at which the charge begis to decrease. This optimum is reached for dρ scr d 0. Give expressio (5), the solutio of this equatio should verify: ( r ) [( r ) r r ] (55) Equatio (55) has oly a solutio if: ( r ) r r 0 (56) Usig the chose parameters for the umerical applicatio, it results that this coditio is

23 fulfilled: ( r ) r r ad the solutio of equatio (55) is give by: (( ) r r ) ( ) ( r ) r r r I r [ ] 5.40 (57) To characterize the PNP behavior, it is also importat to determie the ijectio ratio at extremely high curret. As we have to cosider that the total charge preset i the SCR hal , versio - May 009 remais positive: h ρ csr > 0 (58) v v sat, p sat, a ew coditio o the ijectio ratio ca be defied: h sat, p γ (59) v v sat, For a PNP, the ratio of the saturatio velocities ( 0.8) is greater tha the ratio of mobilities ( 0.33), ad hece is the limit of the ijectio ratio. This physical behavior results from the effect of the base arrowig that iduces a icrease of the carrier gradiet ito the base. As a cosequece, the diffusio curret remais sigificat compared to the drift curret. Therefore, the curret iduced charge withi the base SB ever becomes domiat compared to the dopig charge withi the emitter E. The maximum ratio of the drift curret to the diffusio curret ca be determied from the followig geeric expressio: 3

24 rift pe iffusio V T dp dx (60) Where V T is the thermodyamic potetial. From the cotiuity equatios () ad () where, uder high ijectio coditios p, we obtai: h (pe V T pb dp dx ) (6) dp (pe V T dx ) hal , versio - May 009 Give this ijectio ratio expressio, the coditio (59) becomes: rift iffusio v sat,p v sat, pb v sat,p v sat, pb.4 (6) This coditio meas that, i a PNP bipolar trasistor, the drift curret caot exceed 70 % of the total curret. By cotrast, i a NPN oe, the drift curret ca become egligible uder very high ijectio. 6. Compariso with umerical simulatio To validate the proposed aalytical descriptio, we have compared it to fiite elemets simulatio results obtaied with ISE simulatio tool. The simulated devices are a NPN ad a PNP with the same dimesios ad dopig types simply iverted to switch from NPN to PNP. As for the aalytical approach, the dopig levels are costat ad the juctios abrupt. Besides, carriers recombiatio is eglected. The dimesios ad dopig level are chose i the same rage as the oes used for a high voltage ES protectio i smart power techology. 4

25 A emitter width of 0.5m, a base width of 3m ad a collector width of m are chose. The emitter, base ad collector dopig levels are 0 8 cm -3, 0 6 cm -3 ad 0 0 cm -3, respectively. With these parameters, the maximum gai will be high, resultig i importat dyamic fluctuatios. To avoid ay iterferece of very high ijectio effects with thermal effects, the simulatios are carried out uder isothermal coditios that properly reflect the thermal coditios uder very fast ES pulses. a. NPN The simulatios are performed for curret desities from 0 4 A.cm -, at which the high hal , versio - May 009 ijectio assumptio is valid, up to 0 6 A.cm -, which is the maximum reached i a ES protectio. The effective base widths W B are extracted ad the critical curret desities (3) are calculated, for several curret desities (Figure 4). As expected, they icrease mootoously. Sice the order of magitude of the critical curret desity is 0 4 A.cm -, the asymptotic behavior should be reached before the ed of the simulatio at 0 6 A.cm -. Figure 4: Effective base width (W B ) ad critical curret desity ( ) versus the total curret desity, for a NPN. 5 The electro ad hole curret desities withi the base are extracted to determie the ijectio ratio (Figure 5). At high curret desities, its value teds to the mobility ratio, as

26 predicted by (30). The, the ijectio ratio is calculated with the expressios (6), i which SE is eglected, ad (38), i which SE is take ito accout cosiderig high ijectio i the emitter (Figure 5). The agreemet with the simulatio is acceptable, i particular at high curret desities where the assumptios made are completely fulfilled. Besides, the effect of SE results i a slight variatio that ca be eglected. hal , versio - May 009 Mobilities Ratio Figure 5: Ijectio ratio versus curret desity, obtaied from simulatio ad aalytical expressios (6) ad (38). For the proposed aalytical descriptio, the mobilities are cosidered costat i the quasieutral base regio, eve if they rapidly decrease i a very arrow regio closed to the basecollector SCR. This approximatio may explai the differece betwee the simulated ad calculated ijectio ratios. b. PNP The aalytical expressios obtaied for the NPN will be used as referece, keepig i mid that electro ad hole idexes have to be iverted to obtai the expressio for the PNP. The simulatios are performed from 0 3 A.cm -, from which the high ijectio assumptios become valid, ad up to 0 5 A.cm -, above which the approximatio o the electric field gradiet does ot remai valid. As for the NPN, the effective base widths W B ad the critical 6

27 curret desities (3) are calculated for several curret desities (Figure 6). As theoretically predicted, a base arrowig is observed at high curret. The compariso of the electric field profiles before ad after the occurrece of this base arrowig effect (Figure 7) shows a gradiet reductio, hece a reductio of the charge, resultig i a SCR extesio icrease. Usig expressio (57), we predict that this behavior occurs at a curret desity of A.cm -. This is i good agreemet with the simulatio results. To support the optimizatio of PNP-based ES protectio structures, we ca the use this expressio to avoid detrimetal base arrowig effect o the R ON. hal , versio - May 009 I A.cm - Figure 6: Effective base width (W B ) ad critical curret desity ( ) versus the total curret desity, for a PNP. The calculated curret desity I, where the base variatio chages, is poited out. 7

28 Emitter Base Collector hal , versio - May 009 Figure 7: Electric field profiles at curret desities 4 04 A.cm- (maximum iteral base extesio) ad 0 5 A.cm - (sigificat base arrowig). As for the NPN, the ijectio ratio is directly calculated from the electro ad hole curret desities ad theoretical expressios (6) ad (38) (Figure 8). I accordace with (59), its value does ot ted to the mobilities ratio, but to the saturatio velocity ratio. This cofirms the differece betwee the behaviors of NPN ad PNP at extremely high curret desities. Above A.cm -, the accuracy of the aalytical expressio is acceptable compared to the direct calculatio of ratio betwee hole ad electro curret desities. Saturatio Velocities Ratio 8 Figure 8: Ijectio ratio versus curret desity, obtaied directly for the simulatio ad from the aalytical expressios (6) ad (38).

29 7. Hypothesis iscussio This study of the ijectio ratio uder very high ijectio was possible by the virtue of some hypothesis. The most limitig oes are the approach with floatig base ad the isothermal boudaries. For both of them, the discrepacy with the actual behavior of a ES protectio will be qualitatively evaluate. This complemetary study is madatory to determie how accurate are the results of the aalytical derivatio. a. descriptio As a costrait of the descriptio, the base has to be floatig, although it is usually hal , versio - May 009 coected to the emitter i self-biased bipolar trasistors. Nevertheless, at very high curret, this hypothesis is ot restrictive as the curret flowig to the base cotact become egligible compared to the curret flowig through the emitter cotact. More precisely, the ratio of the avalache-geerated carriers collected at the base cotact o those assurig the reverse ijectio at emitter-base juctio teds to zero [4]. I a ES protectio, the oly purpose of the base cotact is to provide a cotrol o the trigger voltage V t [5] ad the stadby leakage curret. The descriptio assumes that the paths followed by the bias curret ad by the emitter ijectio curret are the same. This hypothesis is valid for most of the self-biased ES protectios, i which the bias curret is geerated by the avalache multiplicatio of the carriers ijected by the emitter (this esures the maximum of the impact ioizatio is located alog the ijectio curret path) [6] [7]. I particular, this hypothesis is valid for the widely-used vertical NPN trasistors. I this type of compoet, the emitter, the base ad the collector are respectively formed by a shallow high-doped N diffusio, a P-well ad a N- buried layer (NBL) biased via a deep N-well (Figure 9). If the distace betwee the emitter ad the NBL is shorter tha the distace betwee the emitter ed the deep N (i.e. the vertical 9

30 base is shorter tha the lateral base), the electros ijected by the emitter flow vertically uder the emitter. Besides, the high avalache regio is located at the P-well-NBL juctio so that, the bias curret flow vertically from this juctio to the emitter. Collector Emitter Base N N P NWell PWell NBL Figure 9: oss-sectio of a vertical NPN trasistor. It is importat to otice the hypothesis restricts the study to the case of the self-biased hal , versio - May 009 trasistor. The results caot be exteded to the more geeral case where the bias curret is directly provided at the base cotact. For this latter case, the base cotact is required, ad the bias curret does ot follow the same path as the emitter ijectio curret. The bias curret comes from the base cotact whereas the emitter ijectio curret flows toward the basecollector juctio. b. Isothermal coditio Besides the very high ijectio coditios, oe of the major specificities of a ES protectio is its strog self-heatig. The mai limitatio i the reductio of the protectio s size is the temperature, which could be high eough to lead to a secod breakdow (betwee 700 K ad 50 K depedig o the structure) [8]. This secod breakdow iduces curret filamets where the temperature sharply icreases up to the meltig poit of the silico ad the degradatio of the protectio [4]. The protectio s behavior is iflueced by these temperature variatios through the modificatios of the silico physical parameters. For the ijectio ratio of a self-biased bipolar trasistor, the most importat parameters are the mobility, the saturatio velocity (both ivolved at very high currets), ad the impact 30

31 ioizatio coefficiet (as the bias curret is provided by a avalachig juctio). Mobility ad saturatio velocity Both the mobility ad the saturatio velocity decrease whe the temperature icreases. At 600K, their values are typically equal to: 30 cm.s.v pb 0 cm.s.v v sat, cm.s v sat, p cm.s hal , versio - May 009 3

32 These variatios does ot modify the aalytical expressio of the ijectio ratio limits, (30) for a NPN ad (59) for a PNP, as the ratio of the electros mobility to the holes oe (based o the model proposed by Arora ad al [9]) remais higher tha the ratio of the electros saturatio velocity to the holes oe (based o the model proposed by Caali ad al. [0]) for the validity rage of these models up to 600K (Figure 0). As a result, the physical effects described i this paper remai valid, i particular the base arrowig for a PNP. Oly the values of the ijectio ratio limits are modified. At 600 K, these limits are equal to.6 for a NPN ad.0 for a PNP. These values remai close to those at 300K, correspodig to variatios of respectively 3% ad 5%. hal , versio - May 009 Figure 0: Electros to holes mobilities ad saturatio velocities ratio, ad vice versa. Impact ioizatio coefficiet I a ES protectio, the avalache pheomeo is strogly iflueced by the temperature, as it is located i a regio where both the curret desity ad the electric field are high ad as a result, the heat geeratio is also high. The amout of carriers geerated by avalache depeds o the impact ioizatio coefficiets, which decrease whe the temperature icreases, for both electros ad holes []. To maitai the avalache curret required to 3

33 bias the bipolar trasistor, the electric field maximum should icrease. This effect teds to wide the base-collector SCR, ad hece to reduce the effective base width, whatever the trasistor type, NPN or PNP. The cosequece o the I-V characteristic of the protectio is a R ON degradatio. To couteract this degradatio ad to obtai a low-r ON protectio, it is madatory to optimize the desig of the structure so as to limit or delay the effects leadig to the base arrowig. I the case of a NPN, this optimizatio ca be achieved by strogly decouplig the avalache ijectio from the bipolar curret gai mechaism that will ted to iduce curret filametatio ad local heatig [6]. Such decouplig ca be obtaied by desigig a very hal , versio - May 009 wide base bipolar trasistor. Usig such desig guidelies, it was show that itroducig a deep trech ito the base to wide it, allows meetig a very high robustess (>8kV HBM) together with a very low-r ON (>>Ω) [4]. I the case of a PNP, sice this base arrowig effect is much more detrimetal ad curret gai caot be degraded sice already very low, the efficiet desig approach cosists i tuig the base ad collector dopig profiles so as to ehace the space charge regio arrowig uder very high ijectio. The proposed aalytical model was used to support the desig of high voltage PNP-based ES protectio structures before ruig TCA simulatios. Similarly to NPN-based protectios, these structures exhibited a very high ES robustess (>0kV HBM) ad a greatly improved R ON (4 times) that allowed sigificatly reducig the ES protectio area of high voltage I/Os i a advaced smart power techology [8]. 8. Coclusio A aalytical descriptio of the curret ijectio ratio of a self-biased bipolar for very high curret desities such as ecoutered durig a ES evet have bee successfully derived. It 33

34 demostrates that the decrease of the ijectio ratio uder very high ijectio coditios has a asymptotic limit that is almost idepedet o the trasistor dopig level ad dimesios. It is also show that this limit is equal to the ratio of the mobilities for the case of a NPN trasistor ad to the ratio of the saturatio velocities for the PNP. This asymptotic behavior is reached whe the iduced curret charge withi the base becomes i the rage of the emitter dopig level (for istace a curret desity of 0 5 A.cm - i the quasi-eutral base regio leads to a carrier cocetratio of 0 8 cm -3 ). At such high curret desity levels, the drift curret withi the base becomes greatly sigificat, which is ot the case at stadard low curret levels. Moreover, the expressio of the ijectio ratio allows determiig the curret hal , versio - May 009 iduced charge withi the base-collector charge space regio ad the aticipatig the ifluece of such ijectio levels o the effective SCR ad base widths. By this way, we have demostrated that uder very high ijectio coditios, i cotrast to the NPN trasistor, the PNP trasistor is subjected to a base arrowig effect (iversio of the stadard "base pushout"). This effect is reported for the first time. The results of this aalytical approach were fully validated by a compariso with umerical simulatio. Fially, the discussio of the most restrictive hypothesis, the aalysis ad the isothermal coditios, has show that our coclusios should remai valid for a actual ES protectio. Besides, this aalytical study allows explaiig several specificities i the developmet of ES protectio. espite the fall of the bipolar gai uder high ijectio, the ES desigers do ot optimize their protectios to reduce this effect. Sometimes, they eve use very low gai trasistors. Such approaches are efficiet because ES protectios are maily based o self-biased bipolar trasistors. I this cofiguratio, the limit of the ijectio ratio at high curret allows preservig the bipolar effect. This is a major differece compared to others domais of the electroics, such as applicatios for power maagemet or high frequecy. I these applicatios, the trasistors are biased i a regular cofiguratio (bias curret provided 34

35 through the base cotact), ad the desigers have ofte to work very hard to keep a high gai value uder high ijectio. Aother specificity i the field of ES is the lack of iterest i PNP trasistors. The few publicatios about PNP trasistors usually coclude o poor ES capabilities due to a high R ON or a low robustess [] [3]. These observatios may be i relatio with the modificatio of the base-collector SCR i a PNP, which is detrimetal for the R ON, i particular if it leads to a base arrowig. The low robustess ca be a direct cosequece of a high R ON, as a higher voltage drop across the protectio results i higher eergy dissipatio. To develop PNP-based ES protectio, it is madatory to apply specific desig rules i order to reduce the effects of the high ijectio o the base-collector SCR. hal , versio - May 009 Based o this thorough aalysis of very high ijectio effects, specific ES desig guidelies were withdraw ad successfully applied to the desig of very efficiet ad robust PNP-based ES protectios. Bibliography [] C. T. Kirk, A theory of trasistor cutoff frequecy (ft) falloff at high curret desities, IRE Tras. o electro devices, pp 64-73, 96. [] Markus P.. Merges, Michael T. Mayerhofer, oost A. Willeme, Matthias Stecher, ES Protectio Cosideratios i Advaced High-Voltage Techologies for Automotive, i Proc. EOS/ES Symposium, September 006, pp [3] M. Merges, W. Wilkeig, S. Mettler, H. Wolf, A. Stricker, W. Fichter, Aalysis ad Compact Modelig of Lateral MOS Power evices uder ES Stress Coditios, i Proc. EOS/ES Symposium, September 999, pp-0. [4] V. e Hey, G. Groeseeke, B. Keppes, M. Nataraja, L. Vacaresse, G. Gallopy, esig ad Aalysis of New Protectio Structures for Smart Power Techology with Cotrolled Trigger ad Holdig Voltage, i Proc. IRPS, pp , 00. [5] G. Bertrad, C. elage, M. Bafleur, N. Nolhier,.M. orkel, Nguye, N. Maura,. Trémouilles, P. Perdu, Aalysis ad Compact Modelig of a Vertical Grouded-Base -p- Bipolar Trasistor Used as ES Protectio i a Smart Power Techology, Solid State Circuits, vol. 36, 9, pp , September 00. [6] M-. Ker, K-H. Li, ouble Sapback Characteristics i High-Voltage MOSFETs ad the Impact to O-Chip ES Protectio esig, IEEE Electro evices Letters, vol. 5, 9, September 35

36 004. [7] K. Reyders, V. e Hey, M. Zubeidat, Electrostatic ischarge Protectio evice, Europea Patet Applicatio EP48554A, ecember 004. [8] A. Gedro, P. Reaud, P. Besse, C. Salamero, M. Bafleur, N. Nolhier, Area-Efficiet Reduced ad No-Sapback PNP-based ES Protectio i Advaced Smart Power Techology, i Proc. EOS/ES Symposium, pp , Sep [9] P. Reaud, A. Gedro, M. Baflaur, N. Nolhier, Efficiet High Voltage No-Sapback ad Low Ro ES Protectio evice for Smart Power Techologies, i Proc. Iteratioal Electrostatic ischarge Workshop, May 007. [0] W.M. Webster, O the Variatio of uctio-trasistor Curret-Amplificatio Factor with Emitter Curret, Proceedigs of the IRE, ue 954, pp [] E.S. Ritter, Extesio of the Theory of the uctio Trasistor, Physical Review, vol. 94, 5, ue 954, pp hal , versio - May 009 [] G. Rey,.P. Bailbé, Some Aspects of Curret Gai Variatios i Bipolar Trasistors, Solid- State Electroics, vol. 7, 974, pp [3].P. Bailbé, Cotributio à l Etude Physique des Trasistors Bipolaires, State octorate Thesis, 744, Paul Sabatier Uiversity, Toulouse (Frace), February 8, 977. [4] K. Esmark, evice Simulatio of ES Protectio Elemets, Series i Microelectroics, vol. 8, ISBN , 00. [5] A. Amerasekera, A. Chatterjee, A Ivestigatio of BiCMOS ES Protectio Circuits Elemets ad Applicatios i Submicro Techologies, i Proc. EOS/ES Symposium, pp , 99. [6]. Tremouilles, G. Bertrad, M. Bafleur, N. Nolhier, L. Lescouzeres, esig Guidelies to Achieve a Very High ES Robustess i Self-Biased NPN, i Proc. EOS/ES Symposium, pp. 8-88, September 00. [7] N. ese, G. Groos, M. eiso, Kuzmik,. Pogay, E. Gorik, M. Stecher, Coupled Bipolar Trasistors as Very Robust ES Protectio evices for Automotive Applicatios, i Proc. EOS/ES Symposium, pp , Sept [8] A. Amerasekera, M-C. Chag, A. Seitchik, A. Chatterjee, K. Mayaram, -H. Cher Self-Heatig Effects i Basic Semicoductor Structures, IEEE trasactios o Electro evices, vol. 40, 0, October 993. [9] N.. Arora,.R. Hauser,.. Roulso, Electro ad Hole Mobilities i Silico as Fuctio of Cocetratio ad Temperature, Solid State Circuit, vol. 36, 9, pp , September 00. [0] C. Caali, G. Maji, R. Mider, G. Ottaviai, Electro ad Hole rift Velocity Measuremet i Silico ad their Empirical Relatio to Electric Field ad Temperature, IEEE Trasactio o Electro evices, vol. 35, 5, pp , 075. [] S. Reggiai, E. Gai, M. Ruda, G. Baccarai, C. Corvasce,. Barlii, M. Ciappa, W. Fichter, M. eiso, N. ese, G. Groos, M. Stecher, Experimetal extractio of the electro impactioizatio coefficiet at large operatig temperatures, i IEM techical digest, pp ,

37 [] M-. Ker, K-H. Li, The Impact of Low-Holdig-Voltage ad the esig of Latch-up Free Power-Rail ES Clamp Circuit for LC rivers Ics, IEEE oural of Solid State Circuit, vol. 40, 8, pp75-59, August 005. [3]. Li, R. Gauthier, K. Chatty,. Kotos, M. Muhammad, M. Woo, C. Putma, C. Russ,. Alvarez,. Scheider, P.T. Ta, PMOSFET-based ES Protectio i 65 m Bulk CMOS Techology for Improved Exteral Latchup Robustess, i Proc. EOS/ES Symposium, pp , September 005. [4] A. Gedro, C. Salamero, N. Nolhier, M. Bafleur, P. Reaud, P. Besse, eep Trech NPN trasistor for Low-RON ES Protectio of High-Voltage I/Os i Advaced Smart Power Techology, Bipolar/BiCMOS Circuits ad Techology Meetig (BCTM'006), Maastritch (Pays-Bas), October 7-0, 006. hal , versio - May