8.0 Negative Bias Temperature Instability (NBTI)

Transcription

1 EE650R: Reliability Physics f Naelectric Devices Lecture 8: Negative Bias Temerature Istability Date: Se Class Ntes: Vijay Rawat Reviewed by: Saakshi Gagwal 8.0 Negative Bias Temerature Istability (NBTI) It has bee see i e case f tye metal-xide-semicductr field-effect trasistrs (PMOS) at e reshld vltage shifts gradually ver a erid f time. This shift is caused by e stress geerated e gate xide by e gate vltage ad temerature. This effect is kw as Negative bias temerature istability r NBTI. 8.1 Emirical bservatis regardig NBTI: A PMOS-secific Prblem: The rblem f NBTI has always bee assciated wi PMOS. It was first bserved i 1960 s whe e PMOS were dmiat. The reas why it is s cmmly bserved i PMOS ca be uderstd frm figure 1. Gate xide Gate Figure 1: le traig at e /O 2 iterface i a PMOS. Whe a egative vltage is alied t e gate f a PMOS device fr a rlged erid f time, it creates iterface tras. These iterface tras are daglig bds which will be exlaied i e ext secti. The iterface tras, lcated at e iterface betwee ad O 2, tra hles ad hece, lead t shiftig f e reshld vltage. After 1980 s, wi e arrival f NMOS ad buried chael PMOS, is rblem disaeared. This effect is t see i NMOS because e daglig bd csists f a atm wi a extra Gate xide Gate ( + ly) Figure 2: le trasrt i a buried chael PMOS. electr i its uter shell. I case f buried chael PMOS, e hle trasrt is t takig lace

2 clse t e /O 2 iterface as shw i figure 2, hece is effect is t see. wever, wi e advet f dual ly gate ad surface-chael PMOS, NBTI has agai becme a majr issue fr device reliability NBTI ad Pb ceters: P b ceter is a daglig bd at e /O 2 iterface. Due t e usatisfied atm, ese P b ceters are dr-like tras ad ca attract hles. The behavir f e uaired si i e daglig bds i resece f magetic field revealed e aramagetic ature f ese bds hece e abbreviati P. The subscrit b arises frm e fact at iitially ree defects were idetified, called P a, P b, ad P c, resectively. wever, while P b was s crrelated t daglig bd at e /O2 iterface, P a ad P c tured ut t be surius rcess related defect. O Itesity P b O Pb ceter O Magetic Field Figure 3: /O 2 iterface shwig a Pb ceter. Figure 4: ESR measuremet cfirmed e aramagetic ature f daglig bd. Cmaris betwee BTI (bias temerature istability) ad NBTI: BTI is bserved i PMOS wi sdium i imurities. The resece f ese iized imurities leads t shift i PMOS arameters such as I sat ad V. As it ca be see i e figure belw at alicati f sitive r egative bias e imurity i mves i site directi ad as a result e charge distributi wii e xide layer chages. + + Gate Gate xide Na + i + + Figure 5: The chage i directi f Na+ i mti chagig e gate bias.

3 The chage i vltage due t resece f imurities is give by, V G = T x 0 xρ( x) dx Thus, e chage i distributi f imurities leads t shift i C-V lt as shw i figure belw. k ε C V Figure 6: The shift i C-V curves crresdig t e mvemet f Na+ is as a resse t gate bias Temral Degradati: Stress Phase: The reshld vltage fllws a wer law behavir wi time (t). V = At, r l( V ) = l( A) + * l( t) wi ~ Als, it ca be see frm e wer law exressi at,

4 V V ( t ) 1 ( t ) 2 t = t 1 2 l( V crit ) Thus, e uit f time des t matter. It has bee bserved at l( V ) versus l(t) lt remais liear fr icrease i mre a six rders f magitude f time. l( V ) Recvery: It has bee bserved at e brke bds durig NBTI rcess, recver wi e assage f time ulike er degradati rcesses at saturate after a erid f time. S NBTI is a self-aealig rcess. Arximately half f e iterface tras may recver durig is hase. l(t) Figure 7: Plt shwig wer law behavir f NBTI rcess Frequecy Ideedece: Whe device is stressed at tw differet frequecies, f1 ad f2, e et degradati after a give amut time, T, is frequecy ideedet, i.e. V t Stress Stage Relaxati Stage DV(k1/f1)=DV(k2/f2)=DV(T) ere, k1 ad k2 are umber f erids f stress at e resective frequecies. - bd dissciati - bd recvery Time Figure 8: Plt shwig recvery rcess durig NBTI degradati Temerature Activati The umber f free bds brke due t NBTI degradati is a fucti f temerature ad ca be exressed by a Arrheius relatishi, wi e activati eergy (E a ) f arximately 0.1eV. Ea kt V = A e * t There is sme debate if e temerature deedece shuld be activated r disersive ad what e crresdig meds f rjecti wuld be.

5 8.1.5 Field Deedece: The NBTI rcess is a field deedet ad t a vltage deedet rcess. Fr examle, if i a -MOSFET e gate vltage is chaged, eier icreased r decreased, ad e gate xide ickess is chaged accrdigly, such at e electric field iside e xide layer remais e same, e e degradati due t NBTI rcess will als remai same. Als, if NMOS is biased at accumulati (hles ear e iterface) at e same electric field at at f PMOS, e NBTI degradati is shw t be idetical (due t Flat-bad vltage shift, is meas alyig e vlt higher t NMOS a PMOS). May grus ecasulate e field deedece i exetial vltage deedece, while ers use a wer law, i.e. γ V=Ae e- t r V=AEe- t T EE E/KT a m E/KT a T where γ E is e field accelerati factr ad m is e field accelerati wer-law exet. 8.2 Statistical bservatis (Emirical): NBTI failure amg a large set f trasistrs shws a rmal distributi while i a smaller set f trasistrs it shw iss s distributi. avig discussed e emirical bservati regardig NBTI degradati, we will w csider e hysical mdel at ca iterret e abve metied bservatis csistetly. 8.3 Reacti-Diffusi Mdel fr NBTI degradati (Physical Mdel): Accrdig t is mdel, wi e alicati f a egative bias at a elevated temerature, e - bds reset at /O 2 iterface are brke, leadig t geerati f iterface tras Figure 9: Schematic shwig e - bd dissciati ad recvery rcesses. The rate f geerati f iterface tras is directly rrtial t e umber f - bds left ad e umber f iterface tras clse t e iterface at have recvered. Thus,

6 dn dt = k f ( N N ) k N r N x= 0 here N is e ttal umber f - bds, N is e umber f iterface tras, N is e umber f free hydrge atms, ad k f ad k r are e rate cstats fr e - bd dissciati ad recvery rcesses, resectively. Als, e rate f geerati f iterface tras is deedet e drift ad diffusi f e hydrge secies away frm e iterface. Thus, Near a regi very clse t e iterface, ce ca write e et flux equati. Net flux cmig i is (J 1 ) = dn dt Net flux mvig ut is (J 2 ) = dn D µ EN dx + dn J 1 - J 2 = δ* dt This is very small fr a ifiitesimally small δ regi ear e iterface. ece, e ca write: J 1 J 2 = 0 r dn dt dn = D + µ EN dx here E is e electric field, D ad µ are e diffusivity ad e mbility f e hydrge secies. 8.4 Cclusis: We have discussed e emirical bservatis regardig NBTI degradati ad highlighted its time, temerature, ad field deedece. We have als ted at e statistics f NBTI is give by Nrmal distributi. We have just bega iterretig ese emirical bservati by a mdel called Reacti-Diffusi ery. We will slve is equati i e ext class t see hw e varius features f NBTI cme abut.