1. Thermal Motion of electrons and holes

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1. Thral Motion of ltrons and hols Eltrons and hols ov at th thral vloity but not in a sil straight lin fashion. Zig zag otion is du to ollisions or sattring with irftions in th rystal.

Thral vloitis of ltrons and hols in silion at roo tratur 3 1 Avrag ltron or hol kinti nrgy kt v th For ltrons ( n = 0.3 0 ) v th 3kT ff 3 3 1.38 10 JK 0.6 9.1 10 1 31 300 kg K 5 7.310 /s.

1 1. Thral Motion of ltrons and hols Eltrons and hols ov at th thral vloity but not in a sil straight lin fashion. Zig zag otion is du to ollisions or sattring with irftions in th rystal. Nt thral vloity is zro. Man ti btwn ollisions is ~ 0.1 s in th rystal, and th distan btwn ollisions is a fw tns of nanotrs or a fw hundrd angstros. Thral vloitis of ltrons and hols in silion at roo tratur 3 1 Avrag ltron or hol kinti nrgy kt v th For ltrons ( n = ) v th 3kT ff JK kg K /s.310 /s Using = , th hol thral vloity is /s. Th tyial thral vloity of ltrons and hols is /s, whih is about 1000 tis slowr than th sd of light. Slid -1 Hot oint Prob an distinguishs N and P ty siondutors. Throltri Gnrator (fro hat to ltriity ) and Coolr (fro ltriity to rfrigration) Not only voltag but also signifiant ltri owr an b ratd with a tratur diffrn aross P and N ty siondutor lnts Th ltrons(hols) around th hot rob hav highr thral vloity and thrfor on avrag ov toward th old sid at a highr rat than th ltrons(hols) on th old sid ov to th hot sid. Th ibalan auss th ltrons(hols) to auulat on th old sid and build u a ngativ(or ositiv) voltag. On th othr hand, if urrnt is fd into it, on st of th juntions bo oolr than th othr. Slid -

. Eltron and Hol Mobilitis Th avrag vloity of th arrirs is no longr zro whn an ltri fild is alid to th siondutor. This nonzro vloity is alld th drift vloity.

2 . Eltron and Hol Mobilitis Th avrag vloity of th arrirs is no longr zro whn an ltri fild is alid to th siondutor. This nonzro vloity is alld th drift vloity. An ltri fild rats a drift vloity that is suriosd on th thral vloity A fastr arrir vloity (drift vloity) is dsirabl, for it allows a siondutor dvi or iruit to orat at a highr sd. Assu that th an fr ti btwn ollisions is τ and that th hol arrir loss its ntir drift ontu, v, aftr ah ollision. An avrag hang in th drift ontu during τ is du to th ltri for, qe. Thn, w an find th stady stat drift vloity, v. Slid -3 Th drift vloity is roortional to E. Th roortionality onstant is th hol obility. Siilarly, ltron drift vloity and ltron obility n ar is th hol obility and n is th ltron obility v = E ; has th dinsions of v/e /s V/. V s Q.) Whih siondutor and whih arrirs (ltrons or hols) ar attrativ for aliations in high sd dvis? Slid -4

3 EX.) Givn = 470 /V s, what is th hol drift vloity at E = 10 3 V/? What is and what is th distan travld btwn ollisions (alld th an fr ath)? drift vloity = E = 470 /V s 10 3 V/ = /s = /q =470 /V s kg/ C = /V s.10 1 kg/c = s = 0.1 s an fr ath () = v th ~ s.10 7 /s =.10 6 = 0 Å = n This is sallr than th tyial dinsions of dvis, but gtting los. Intrinsi obility v in siondutors E qe j nv v E v v E and h v h E h n Slid -5 Two Mhaniss of Carrir Sattring Phonon sattring ; obility drass whn tratur riss Phonons ar th artil rrsntation of th vibration of th atos in th rystalth sa sort of vibration that arris sound. q honon honon honon dnsity arrir thral T v th T 1/ Iurity (Doant) Ion Sattring or Coulobi Sattring 1 1 3/ T 1/ vloity T T Th rulsiv oulobi for btwn th ltron and th ngativ ion and attrativ oulobi for with th ositiv ion an indu th sa fft on th ltron trajtory Th obility du to iurity sattring is thrfor invrsly roortional to th su of th donor and ator ion onntrations. It is also roortional to T 3/. μ v ros stion iurity dnsity T / T N N T / N N At a highr tratur, th ltron has a highr thral vloity and flis by th ion in a shortr ti, and its dirtion of otion is thus lss afftd by th ion. Slid -6

Two Mhaniss of Carrir Sattring Whn thr is or than on sattring hanis, th total sattring rat 1 1 1 honon 1 1 honon iurity 1 iurity Th silion hol obility is about on third of th ltron obility This

Whn th arrir onntration is larg, th arrirs an distribut thslvs to artially srn out th oulobi fild of th doant ions. Slid -7 A shati lot of th tratur dndn of obility n.

4 Two Mhaniss of Carrir Sattring Whn thr is or than on sattring hanis, th total sattring rat honon 1 1 honon iurity 1 iurity Th silion hol obility is about on third of th ltron obility This diffrn in obility an b artly xlaind by th diffrn in th fftiv ass. Th invrs roortionality to doant dnsity is not followd at th liit of vry larg N a or N d. Th rason is fr arrir srning. Whn th arrir onntration is larg, th arrirs an distribut thslvs to artially srn out th oulobi fild of th doant ions. Slid -7 A shati lot of th tratur dndn of obility n. At sall doant onntrations, μ drass with inrasing T, indiativ of th doinan of honon sattring. At vry high doant onntration and low tratur, whr iurity sattring is xtd to doinat, μ indd inrass with inrasing T Q) What N d will ak d n /dt = 0 at RT? Saturation vloity Whn th kinti nrgy of a arrir xds th otial honon nrgy, E ot, it gnrats an otial honon and loss th kinti nrgy. Thrfor, th vloity dos not ris abov saturation vloity, v sat of ~10 7 /s Ballisti transort Mobility and vn vloity saturation ar onts that dsrib th arrir otion avragd ovr any sattring vnts. Ths onts bo fuzzy whn w dal with dvis whos sizs ar sallr than th an fr ath. Th otion of arrirs in a narly sattring fr nvironnt is alld ballisti transort.

6 A/ Th total drift urrnt dnsity is th su of th ltron and th hol oonnts: J drift = J,drift + J n,drift = qv - nqv n = (q +nq n )E J drift = E ondutivity (1/oh-) of a siondutor is n : ltron arrir

5 3. Drift Currnt and Condutivity Th drift urrnt dnsity, J, is th harg r sond rossing a unit ara lan noral to th dirtion of urrnt flow. In th P ty siondutor bar of unit ara, th hol urrnt dnsity is Hol urrnt dnsity J = qv A/ or C/ s : Hol arrir dnsity Ex.) If = and v = 10 4 /s, thn J = C /s 1.6 C/s 1.6 A/ Th total drift urrnt dnsity is th su of th ltron and th hol oonnts: J drift = J,drift + J n,drift = qv - nqv n = (q +nq n )E J drift = E ondutivity (1/oh-) of a siondutor is n : ltron arrir dnsity = q + nq n 1/ = rsistivity (oh-) Slid -9 Rlationshi btwn Rsistivity and Doant Dnsity : = 1/ (a) What is th rsistivity () of silion dod with of arsni (As)? Sin As is grou V, w find that = fro N-ty urv. (b) What is th rsistan (R) of a i of this silion atrial 1 long and 0.1 in ross stional ara? R = L/A = / 0.1 = / = Slid -10

6 4. Diffusion Currnt Partils diffus fro a highr onntration loation to a lowr onntration loation. Diffusion urrnt is gnrally not an iortant onsidration in tals baus of thir high ondutivitis. Th low ondutivity and th nonunifor arrir dnsitis ak diffusion an iortant ross in siondutors. If th ltron onntration is not unifor, thr will b an ltron diffusion urrnt, whih is roortional to th gradint of th ltron onntration. dn d J n diffusion qd J, n, diffusion qd Whr, D is th diffusion onstant. In gnral, both drift and diffusion ay ontribut to th urrnt. Thrfor, J TOTAL =J n +J dn J n = J n,drift + J n,diffusion = -qn n E - qd n (+) (+) d J = J,drift + J,diffusion = q E qd (+) ( ) Slid Rlation Btwn th Enrgy Diagra and V, E Whn a voltag is alid aross a i of siondutor, it altrs th band diagra. A ositiv voltag raiss th otntial nrgy of a ositiv harg and lowrs th nrgy of a ngativ harg. It thrfor lowrs th nrgy diagras sin th nrgy diagra lots th nrgy of an ltron. E and E v vary in th oosit dirtion fro th voltag baus thy hav ngativ ltrons. That is, E and E v ar highr whr th voltag is lowr. Th slo of E and Ev indiats th ltri fild. E dv 1 de q dev q 1 Th ltrons roll downhill lik stons in th nrgy band diagra and th hols float u lik bubbls. Slid -1

7 6. Einstin Rlationshi btwn D and Considr a i of non uniforly dod siondutor. Th siondutor is at quilibriu, and thrfor th Fri lvl E F is onstant. Th lft sid is or havily dod than th right sid, and so E is losr to E F on th lft sid. Baus E is not a onstant, thr is an ltri fild qual to (1/q)dE /, aording to E q. This fild is intrnally ratd. Baus th siondutor is at quilibriu, thr annot b any J n (or J ). dn J qnμ EqD 0 Eltron dnsity in ondution band n N dn N kt ( E E f ( E E f ) / kt ) / kt de n de kt n kt qe Einstin rlationshi J n D qdne 0 qnne qn kt n kt q n D kt q Q) What is th hol diffusion onstant in a i of silion with = 410 V 1 s 1? kt 1 1 D (6 V) 410 V s 11 /s q 7. Eltron-Hol Robination Lt s say th quilibriu arrir onntrations n 0 and 0. Whn light shins on th sal and gnrat ltrons and hols, thn th total ltron and hol onntrations an b diffrnt fro n 0 and 0. Th diffrns ar alld th xss arrir onntrations dnotd by n and. n n 0 n' 0 ' Charg nutrality is satisfid at quilibriu (n = = 0). Whn a non zro n is rsnt, an qual ust b rsnt to aintain harg nutrality, and vi vrsa. n' ' If harg nutrality is not satisfid, th nt harg will attrat or rl th abundant ajority arrirs until nutrality is rstord. Assu light gnrats n and. If th light is suddnly turnd off, n and day with ti until thy bo zro. Th ross of day is alld robination. Th ti onstant of day is th robination ti or arrir lifti,. Slid -14

8 Robination ti Th ross of day is robination, whrby an ltron and a hol robin and annihilat ah othr. Th ti dndnt hang of ltrons (or hol) an b xrssd by dn n d dt dt Th robination rat (s 1 3 ) is roortional to n and n robination rat: is tyially 1 s in Si, and it rangs fro ~1 ns to ~1 s with th dnsity of iuritis suh as Au and Pt, whih for tras in th band ga with svral nrgy lvls d in th band ga. Ths d tras atur ltrons and hols to failitat robination and ar alld robination ntrs. Slid -15 Dirt and Indirt Band Ga Tra Dirt band ga Exal: GaAs Dirt robination is ffiint as k onsrvation is satisfid. Indirt band ga Exal: Si Dirt robination is rar as k onsrvation is not satisfid Slid -16

9 EX.) Photoondutors A bar of Si is dod with boron(b) at It is xosd to light suh that ltron hol airs ar gnratd throughout th volu of th bar at th rat of 10 0 /s 3. Th robination lifti is 10s. What ar (a) 0, (b) n 0, (), (d) n, (), (f) n, and (g) th n rodut? (a) 0 = N a = (b) n 0 = n i / 0 = () In stady-stat, th rat of gnration is qual to th rat of robination /s- 3 = / = 10 0 /s s = (d) n = = () = 0 + = = (f) n = n 0 + n = ~ sin n 0 << n (g) n ~ = >> n i = Th n rodut an b vry diffrnt fro n i. Slid -17

Lecture 16: Bipolar Junction Transistors. Large Signal Models.

Lecture 16: Bipolar Junction Transistors. Large Signal Models. Whits, EE 322 Ltur 16 Pag 1 of 8 Ltur 16: Bipolar Juntion Transistors. Larg Signal Modls. Transistors prform ky funtions in most ltroni iruits. This is rtainly tru in RF iruits, inluding th NorCal 40A.