Carrirs Conntration in Smionutors - VI 1 Prof.P. Ravinran, Dpartmnt of Pysis, Cntral Univrsity of Tamil au, Inia ttp://folk.uio.no/ravi/smi01 P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Havy Doping Ligt oping: impurity atoms o not intrat wit a otr impurity lvl Havy oping: prturb t ban strutur of t ost rystal rution of bangap v g r P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Mtal-Insulator Transition Avrag impurity-impurity istan = Bor raius Mott ritrion a 1 B 64 If t numbr of onor is igr tan t Mott s ritrion t smionutor to mtal transition will taks pla. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Smionutor quilibrium Carg arrirs ltrons in onutan n = gf n - prob. ns. of ltrons g nsity of stats of ltrons. f - rmi-dira prob. funtion Hols in valn p = gv1 - f p - prob. ns. of ols gv nsity of stats of ols. f - rmi-dira prob. funtion Smionutors at quilibrium t onntration of arrirs will not ang wit tim. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Smionutor quilibrium umbr of ltrons: n 0 g f n 0 xp C C m * n / umbr of ltrons: p 0 g v 1 f p 0 v xp v v m * p / P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Smionutor quilibrium xampl in t probability tat a stat in t onution ban is oupi an alulat t ltron onntration in silion at T = 00K. Assum rmi nrgy is.5 V blow t onution ban. =.8.10 19 f xp xp0.5 /.059 6.4 105 n 0 xp.81019 6.4 10 5 1.810 15 m ot low probability pr stat but larg numbr of stats implis rasonabl onntration of ltrons. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Smionutor quilibrium T xtrinsi Smionutor xampl Consir op silion at 00K. Assum tat t rmi nry is.5 V blow t onution ban an.87 V abov t valn ban. Calulat t trmal quilibrium onntration of s an ols. =.8.10 19 ;v=1.04.10 19. At trmal quilibrium t gnration an rombination rat will b sam an n t ltron an ol onntration will not ang. n xp.810 xp 0.5 / 0.059 1.8 19 15 0 10 m p xp 1.04 10 xp 0.87 / 0.059.7 v 19 4 0 v 10 m P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Carrir Conntration in -typ Smionutor Consir is t onor Conntration i.., t numbr of onor atoms pr unit volum of t matrial an is t onor nrgy lvl. At vry low tmpraturs all onor lvls ar fill wit ltrons. Wit inras of tmpratur mor an mor onor atoms gt ioniz an t nsity of ltrons in t onution ban inrass. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Dnsity of ltrons in onution ban is givn by n m xp T nsity of Ioniz onors is givn by {1 } xp At vry low tmpraturs, t numbr of ltrons in t onution ban must b qual to t numbr of ioniz onors. m xp xp P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI Taking logaritm an rarranging w gt.,0 log log log log k at m m m At 0k rmi lvl lis xatly at t mil of t Donor lvl an t bottom of t Conution ban
P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI Dnsity of ltrons in t onution ban m m m m m n xp ] [ xp } ] [ log xp{ xp } ] [ log xp{ xp } } log { xp{ xp xp 1 1 1 1 1 1
P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI m n m m n m n xp } xp ] [ { xp 4 1 1 1 Tus w fin tat t nsity of ltrons in t onution ban is proportional to t squar root of t onor onntration at moratly low tmpraturs.
Variation of rmi lvl wit tmpratur n-typ To start wit,wit inras of tmpratur inrass sligtly. As t tmpratur is inras mor an mor onor atoms ar ioniz. urtr inras in tmpratur rsults in gnration of ltron - ol pairs u to braking of ovalnt bons an t matrial tns to bav in intrinsi mannr. T rmi lvl graually movs towars t intrinsi rmi lvl i. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
xtrinsi Matrial W an alulat t bining nrgy by using t Bor mol rsults, onsiring t loosly boun ltron as ranging about t tigtly boun or ltrons in a yrogn-lik orbit. 4 mq K ; n 1, K 4 0 r P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI 14
Conpt of a Donor Aing xtra ltrons P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Bining nrgis of Impurity Hyrogn Lik Impurity Potntial Bining nrgis fftiv mass soul b us to aount t influn of t prioi potntial of rystal. Rlativ iltri onstant of t smionutor soul b us insta of t fr spa prmittivity. : ltrons in onor atoms : Hols in aptor atoms Bining nrgis in Si: 0.0 ~ 0.06 V Bining nrgis in G: ~ 0.01 V P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
xtrinsi Matrial Calulat t approximat onor bining nrgy for Gε r =16, m n* =0.1m 0. Answr: 8 * n m q 0 r 4 1.0 10 0.19.1110 88.85 10 1 1 J 1 16 1.6 10 6.610 0.0064 V P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI 19 4 4 Tus t nrgy to xit t onor ltron from n=1 stat to t fr stat n= is 6mV.
ltron-hol Rombination T quilibrium arrir onntrations ar not wit n0 an p0. T total ltron an ol onntrations an b iffrnt from n0 an p0. T iffrns ar all t xss arrir onntrations n an p. n p n 0 n' p 0 p' P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Carg utrality Carg nutrality is satisfi at quilibrium n = p = 0. Wn a non-zro n is prsnt, an qual p may b assum to b prsnt to maintain arg quality an vi-vrsa. n' If arg nutrality is not satisfi, t nt arg will attrat or rpl t majority arrirs troug t rift urrnt until nutrality is rstor. p' P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Gnration an Rombination lif tim of Cargs In an intrinsi smionutor t numbr of ols is qual to t numbr of fr ltrons. Trmal agitation, owvr, ontinus to gnrat nw ol-ltron pairs pr unit volum pr son, wil otr ol-ltron pairs isappar as a rsult of rombination. On an avrag, a ol an ltron will xist for ζ p ζ n sons bfor rombination. Tis tim is all t man liftim of t ol ltron. Gnration an rombination prosss at to ang t arrir onntrations, an trby inirtly afft urrnt flow P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Rombination Liftim Assum ligt gnrats n an p. If t ligt is sunly turn off, n an p ay wit tim until ty bom zro. T pross of ay is all rombination. T tim onstant of ay is t rombination tim or arrir liftim,. Rombination is natur s way of rstoring quilibrium n = p = 0. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Trmal Gnration is t rombination liftim. n an p ar t xss arrir onntrations. n = n0+ n p = p0+ p Carg nutrality rquirs n = p. rat of rombination = n / = p / If n is ngativ, tr ar fwr ltrons tan t quilibrium valu. As a rsult, tr is a nt rat of trmal gnration at t rat of n /. Morn Smionutor Dvis for Intgrat Ciruits C. Hu P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
Quasi-quilibrium an Quasi-rmi Lvls Wnvr n = p 0, np ni. W woul lik to prsrv an us t simpl rlations: n p v f f v / / But ts quations la to np = ni. T solution to tis problm is to introu two quasi-rmi lvls fn an fp fn / su tat n p v fp v / vn wn ltrons an ols ar not at quilibrium, witin a group t arrirs an b at quilibrium. ltrons ar losly link to otr ltrons but only loosly to ols. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
XAMPL: Quasi-rmi Lvls an Low-Lvl Injtion Consir a Si sampl wit =10 17 m - an n =p =10 15 m -. a in f. n = = 10 17 m - = xp[ f/] f = 0.15 V. f is blow by 0.15 V. ot: n an p ar mu lss tan t majority arrir onntration. Tis onition is all low-lvl injtion. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
XAMPL: Quasi-rmi Lvls an Low-Lvl Injtion ow assum n = p = 10 15 m -. b in fn an fp. n = 1.0110 17 m - = fn / fn = ln/1.0110 17 m - = 6 mv ln.810 19 m - /1.0110 17 m - = 0.15 V fn is narly intial to f baus n n0. P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI
XAMPL: Quasi-rmi Lvls p = 10 15 m - = v fp / fp v = lnv/10 15 m - = 6 mv ln1.0410 19 m - /10 15 m - = 0.4 V v f fn fp v P.Ravinran, PHY0 Smionutor Pysis, 17 January 014 : Carrirs Conntration in Smionutors - VI