ECE65R : Reliability Physics of anoelectonic Devices Lectue : CI Time Exponents Date : Dec. 4, 6 Classnote : Saakshi Gangwal Review : Lutfe A Siddiqui. Review We have spent seveal weeks discussing discussing BTI and TDDB elated eliability issues. ow fo the next thee/fou classes, we will be discussing MOSFET degadation elated to ot Caie Injection (CI. In the last class we saw the basic physics of CI. If we take a MOSFET which is switching, V G is changing while V D is held constant, thee is a cuent flow though the channel. ea the dain junction, a pecipitous voltage dop takes place and electons get acceleated. This takes place in the cone, i.e., towads the dain end. So in the last class we saw a qualitative pictue of the C effect. Boken Bonds Si-O Si- ~V th V D / V D V G. to.5 In this class, we will look at a possible hypothesis fo way the time dependence is t.1 Time Dependence Stess Phase The inteface-tap geneation ate fo CI can be witten similaly to that of BTI as a balance between dissociation and annealing ates of Si- bonds d kf( O - -k ( dt Geneally is small compaed to O and deivative of w..t time is smalle compaed to the fluxes on the ight hand side (see discussion of BTI time-exponents fo details, so that kfo (. k y x Fig.1 a Co-odinate Sytem b -Diffusion pofile in BTI y
Fo BTI, we see that the diffusion was taking place in a ight tiangula pism fashion, while fo CI it is in conical fashion since it takes place only nea the dain-end. y t t Fig. a Co-odinate System b -D Diffusion pofile in CI c -D Diffusion pofile in CI, at t t, diffusion peak also inceases. t 1 In CI, Volume unde the cuve: 1 ( p ( D t (1 Also, k f k O ( ( Fom equation, (1 and (, we can wite: 1 kf O p ( D t k So fo diffusion, t exponent is.5. Remembe that in the case of BTI, we get the exponent as.5 only if diffusing species is positively chaged ( +. When ydogen molecule ( diffusion is assumed, the CI time dependence can be found to be shown as: kf ( 1 p k 6 ( D t O 1 ee the time exponent is 1/. In geneal theefoe, we expect a time-exponent of n1/- 1/ fo CI degadation duing the stess phase. This value of the exponent has been obseved in wide vaiety of expeiments involving MOS tansistos.
. Relaxation Degadation in CI is lage than BTI while the Recovey is smalle. This is due to the fact that in the case of CI, the annealing involving passivating a boken Si- bonds towads a point of boken Si- bonds. ow let us ty to pove it mathematically. Potion eaten away duing ecovey Fig. Figue showing the effective left afte elaxation phase (t Fig 4. Vaiation of with time Log t Log(t In analogy to BTI degadation, the amount of annealing involves the inveted pyamid egion in Fig., so that ( e ( t+ t p D t ( ( e ( t+ t~ p D ( t + t (4 Also Fig. 4 allows us to wite a consevation of total taps at time (t+t equation: ( t+ t + ( t+ t ( t (5 Remaining Annealed Total Taps at the Taps Taps beginning of stess phase
Fom Eq. (-(4, we find ( t+ t e t ( t+ t ( t + t (6 Substituting equation (6 in (5, we get: ( t+ t ( t 1+ ( t+ t ( t+ t e t ( t 1 + ( t + t ( t+ t ( t+ t 1 ( t e t 1 + ( t + t Fo pin-hole diffusion e ~ (1/ to 1/ At tt, ( t 1 4 Fo e 1/, ( 1 t t 5 1 + ( t + t Fo e 1/, ( t 1 6 ( 1 t t 7 1 + ( t + t Remembe that fo BTI, ( t ( t ence we see that the ecovey is slowe in the case of CI (because the has to diffuse towads a point. Ove a peiod of time, the fequency esponse with AC stess is:
. Fequency Dependence Just like BTI, ot caie effect is also fequency independent. A geneal popety is: If, (i At n i.e, has follows a powe law dependence and (ii ( t a ( t i.e, R ar 1, hee a is a constant. then, one can wite the ecusive elation as: R 1 n k 1 ak -,1( ( kt 1 1 ( 1 1 ( ( ( T kt 1 n T kt kt, n ee,,1 (T : geneated fo the total time T with AC fequency f 1, (T : geneated fo the total time T with AC fequency f To sum up: CI is a localized effect with highe diffusion slope but lowe ecovey compaed to BTI. oweve, both BTI and CI is fequency independent. So fa we have talked about the time behavio of ot caie effect. Going ahead, we will now talk about the physics of k f. This will pepae us fo the next lectue which will discuss the voltage dependence of CI degadation duing the stess phase..4 and Physics of K f A good expeiment involving usage of Deuteium instead of ydogen evealed the physics behind k f Fo the expeiment, a Silicon wafe was taken and put in the high vacuum MBE chambe. People wee pedicting vaious popeties of bae suface of Silicon and how it would be econstucted once it is passivated with ydogen. The STM based expeiments was supposed to pobe the dynamics of suface econstuction as is absobed o desobed fom the suface. oweve, when simila expeiment involving Deuteium instead of ydogen was pefomed. It was found that the numbe of hydogen poduced pe injected electon (called yield o Y in Fig. 5a educed significantly when deuteium was used. The eduction was of the ode of 1-1 times. This obsevation fom STM expeiments inspied a goup fom Illinois to popose eplacing by D fo passivation of Si/SiO inteface. Si-D would be moe difficult to beak at a given stess they easoned and it would incease CI lifetime. Indeed, this hypothesis was poven coect with a facto of -4 eduction in tap-geneation ate with Si-D bonds and almost a facto of incease in oveall CI lifetime.
lny D 1 - (t Log D 1-1 ~X-4 t Log(t Fig 5 (a Yield (/D poduced pe injected electon vs. Tip Voltage (b Vaiation of total with time Although the geneal hypothesis was poven coect, one might wonde why Fig. 5(a and 5(b has such significant diffeences in dissociation ates. The likely eason is that CI in MOSFET beaks both Si- and Si-O bonds. The amount of boken Si-O bonds ( can be deduced fom the following agument. The atio of inteface bonds ceated with Si- and Si-D is given by (see Fig. 5b O + 4 D + O D O: umbe of boken Si-O Bonds D: umbe of boken Si-D Bonds : umbe of boken Si- Bonds Fom Fig. 5(a D ~.1, so that 4 O +.4 O + and ~ O. In othe wods, thee-fouth of boken bonds ae Si- and theefoe the dynamics of Si- bond dissociation govens the time-exponent of CI, as discussed in Sec. (.1-.. One could ask the eason why Si-D bonds ae moe difficult to beak compaed to Si- bonds. Initially people thought that since D is heavie, a given foce (CI injection can not displace it fa fom its equilibium location (bonded to Si and theefoe bond dissociation is moe difficult fo D compaed to. Moe pecise calculations late showed that the pope explanation is somewhat moe subtle. It was ealized that since Deuteium has highe mass compaed to ydogen, the vibational specta is fo Si- and Si-D ae somewhat diffeent (see Fig. 6(a. The vibational fequency of Si-D bond happens to be fa close to fequency of the tansvese optical (TO mode of the bulk Si than that of the Si- bond as shown in Fig 6(b. As a esult, the vibational mode of the Si-D is moe stongly coupled to Si(TO than that of the Si- mode and thus the vibational enegy of the Si-D bond can flow/decay into the TO mode of bulk Si at a faste ate than that of Si- bond. So cascading (which eventually leads to bond dissociation in Si- is much easie than that in Si-D since immediate elaxation takes place in the latte due to good coupling.
Si-D Si Si- Si U x Bending Mode Tansvese Optical Bending Mode 45 46 65 1 Stetch Mode h? (cm -1 Fig 6.(a Vaiation of potential with distance (into oxide fo Si-D case (b Fequencies associated with vaious Modes.5 Conclusion Today we saw the tempoal dependence of ot caie effect. Also we noticed the fequency independence as we have peviously seen in BTI. Going ahead we will see the Electic field and Tempeatue dependence in the next two classes.