genius PHYSICS Energy Bands. Types of Solids.

Transcription

1 gnus HYSIS Solds and Sm-conductor 1 nrgy ands. In solatd atom th valnc lctrons can xst only n on of th allowd orbtals ach of a sharply dfnd nrgy calld nrgy lvls. ut whn two atoms ar brought narr to ach othr, thr ar altratons n nrgy lvls and thy sprad n th form of bands. nrgy bands ar of followng typs (1 Valnc band Th nrgy band formd by a srs of nrgy lvls contanng valnc lctrons s known as valnc band. At 0 K, th lctrons flls th nrgy lvls n valnc band startng from lowst on. ( Ths band s always fulfll by lctron. ( Ths s th band of maxmum nrgy. ( lctrons ar not capabl of ganng nrgy from xtrnal lctrc fld. (v o flow of currnt du to such lctrons. (v Th hghst nrgy lvl whch can b occupd by an lctron n valnc band at 0 K s calld frm lvl. (2 onducton band Th hghr nrgy lvl band s calld th conducton band. ( It s also calld mpty band of mnmum nrgy. ( Ths band s partally flld by th lctrons. ( In ths band th lctrons can gan nrgy from xtrnal lctrc fld. (v Th lctrons n th conducton band ar calld th fr lctrons. Thy ar abl to mov any whr wthn th volum of th sold. (v urrnt flows du to such lctrons. ( Forbddn nrgy gap ( g nrgy gap btwn conducton band and valnc band ( o fr lctron prsnt n forbddn nrgy gap. ( Wdth of forbddn nrgy gap upon th natur of substanc. g (.. mn ( V.. max ( As tmpratur ncrass (, forbddn nrgy gap dcrass ( vry slghtly... g V.. max. mn. max. mn. Typs of Solds. On th bass of band structur of crystals, solds ar dvdd n thr catgors.

2 gnus HYSIS 2 Solds and Sm-conductor S.o. roprts onductors Insulators Smconductors (1 lctrcal conductvty 10 2 to 10 8 Ʊ/m 10 8 Ʊ/m 10 to 10 0 Ʊ/m (2 Rsstvty 10 2 to m (nglgbl m 10 to m ( and structur V.. g (maxmum V.. g (lss V.. (4 nrgy gap Zro or vry small Vry larg; for damond t s 6 V For g = 0.7 V for S g = 1.1 V ( urrnt carrs Fr lctrons Fr lctrons and hols (6 ondton of V.. and.. at ordnary tmpratur V.. and.. ar compltly flld or.. s som what mpty V.. compltly flld.. compltly unflld V.. somwhat mpty.. somwhat flld (7 Tmpratur co-ffcnt of rsstanc ( (8 ffct of tmpratur on conductvty (9 ffct of tmpratur on rsstanc ostv Zro gatv Dcrass Incrass Incrass Dcrass (11 xampls u, Ag, Au, a, t, Hg tc. Wood, plastc, mca, damond, glass tc., S, Ga, As tc. (12 lctron dnsty /m ~ /m S ~ /m Hols n smconductors At absolut zro tmpratur (0 K conducton band of smconductor s compltly mpty and th smconductor bhavs as an nsulator. Whn tmpratur ncrass th valnc lctrons acqurs thrmal nrgy to jump to th conducton band (Du to th brakng of covalnt bond. If thy jumps to.. thy lavs bhnd th dfcncy of lctrons n th valnc band. Ths dfcncy of lctron s known as hol or cottr. A hol s consdrd as a sat of postv charg, havng magntud of charg qual to that of an lctron. (1 Hols acts as vrtual charg, although thr s no physcal charg on t. (2 ffctv mass of hol s mor than lctron. ( Moblty of hol s lss than lctron. Typs of Smconductors.

3 gnus HYSIS Solds and Sm-conductor (1 Intrnsc smconductor A pur smconductor s calld ntrnsc smconductor. It has thrmally gnratd currnt carrrs ( Thy hav four lctrons n th outrmost orbt of atom and atoms ar hld togthr by covalnt bond ( Fr lctrons and hols both ar charg carrrs and n (n.. ( Th drft vlocty of lctrons ( v s gratr than that of hols ( v h (v For thm frm nrgy lvl ls at th cntr of th.. and V.. nh (n V.. (v In pur smconductor, mpurty must b lss than 1 n 8 10 parts of smconductor. (v In ntrnsc smconductor (o h n ( o ( o / 2 g / 2KT nh n AT (o ; whr n lctron dnsty n conducton band, n Hol dnsty n V.., n Dnsty of ntrnsc carrrs. (v caus of lss numbr of charg carrrs at room tmpratur, ntrnsc smconductors hav low conductvty so thy hav no practcal us. t currnt and conductvty Whn som potntal dffrnc s appld across a pc of ntrnsc smconductor currnt flows n t du to both lctron and hols.. = h n Av A n v n v ] Hnc conductvty of smconductor n n ] [ h h whr v = drft vlocty of lctron, v h = drft vlocty of hols, [ h h hol lctrc fld v = Appld lctrc fld moblty of and n moblty of hols v h V ot : ( ~ / m n At room tmpratur h and ( ~ / m S n S onductvty of smconductor ncrass wth tmpratur bcaus numbr dnsty of charg carrrs ncrass. In a dopd smconductor, th numbr dnsty of lctrons and hols s not qual. ut t 2 can b stablshd that n n h n ; whr n, n h ar th numbr dnsty of lctrons and hols rspctvly and n s th numbr dnsty of ntrnsc currs (.. lctrons or hols n a pur smconductor. Ths product s ndpndnt of donor and accptor mpurty dopng. (2 xtrnsc smconductor ( It s also calld mpur smconductor. ( Th procss of addng mpurty s calld Dopng. ( Impurts ar of two typs : Intrnsc smconductor Impurty xtrnsc smconductor ntavalnt mpurty Th lmnts whos atom has fv valanc mpurts.g. As,, Sb tc. Ths ar also calld donor mpurts. Ths mpurts ar also calld donor mpurts bcaus thy donats xtra fr lctron. Trvalnt mpurty Th lmnts whos ach atom has thr valanc lctrons ar calld trvalnt mpurts.g. In, Ga, Al,, tc. Ths mpurts ar also calld accptor mpurts as thy accpt lctron. 8 (v Th numbr of atoms of mpurty lmnt s about 1 n 10 atoms of th smconductor. (v n n h

4 gnus HYSIS 4 Solds and Sm-conductor (v In ths frm lvl shfts towards valnc or conducton nrgy bands. (v Thr conductvty s hgh and thy ar practcally usd. ( Typs of xtrnsc smconductor ( Intrnsc S.. -typ smconductor Fr lctron ntavaln t mpurty Intrnsc S.. -typ smconductor Vacancy Trvalnt mpurty -typs S.. -typs S.. ( Majorty charg carrrs lctrons Mnorty charg carrrs hols Majorty charg carrrs hols Mnorty charg carrrs lctrons ( n >> n h; >> h (v onductvty n (v -typ smconductor s lctrcally nutral (not ngatvly chargd (v Impurty s calld Donar mpurty bcaus on mpurty atom gnrat on. (v Donor nrgy lvl ls just blow th conducton band... V.. Donor nrgy lvl n h >> n ; h >> onductvty n h h -typ smconductor s also lctrcally nutral (not postvly chargd Impurty s calld Accptor mpurty. Accptor nrgy lvl ls just abov th valnc band... V.. Accptor nrgy lvl - Juncton Dod. Whn a -typ smconductor s sutably jond to an -typ smconductor, thn rsultng arrangmnt s calld - juncton or - juncton dod - Juncton Anod athod (1 Dplton rgon On account of dffrnc n concntraton of charg carrr n th two sctons of - juncton, th lctrons from -rgon dffus through th juncton nto -rgon and th hol from rgon dffus nto -rgon.

5 gnus HYSIS Solds and Sm-conductor Du to dffuson, nutralty of both and -typ smconductor s dsturbd, a layr of ngatv chargd ons appar nar th juncton n th -crystal and a layr of postv ons appars nar th juncton n -crystal. Ths layr s calld dplton layr ( Th thcknss of dplton layr s 1 mcron = 10 6 m. ( Wdth of dplton layr 1 Doppng ( Dplton s drctly proportonal to tmpratur. (v Th - juncton dod s quvalnt to capactor n whch th dplton layr acts as a dlctrc. (2 otntal barrr Th potntal dffrnc cratd across th - juncton du to th dffuson of lctron and hols s calld potntal barrr. For V 0. V and for slcon V 0. 7V V Dplton layr 6. On th avrag th potntal barrr n - juncton s ~ 0. V and th wdth of dplton rgon ~ 10 So th barrr lctrc fld Som mportant graphs V V / m 6 d 10 otntal harg dnsty lctrc fld v Dstanc v dstanc Dstanc ( Dffuson and drft currnt caus of concntraton dffrnc hols/lctron try to dffus from thr sd to othr sd. Only ths hols/lctrons crosss th juncton, havng hgh kntc nrgy. Ths dffuson rsults s an lctrc currnt from th -sd to th -sd known as dffuson currnt ( df As lctron hol par (bcaus of thrmal collsons ar contnuously cratd n th dplton rgon. Ths s a rgular flow of lctrons towards th -sd and of hols towards th -sd. Ths maks a currnt from th -sd to th -sd. Ths currnt s calld th drft currnt ( dr. ot : In stady stat df dr so 0 Whn no xtrnal sourc s connctd, dod s calld unbasd. nt

6 Forward currnt n ma gnus HYSIS 6 Solds and Sm-conductor (4 asng Mans th way of connctng mf sourc to - juncton dod Forward basng ( ostv trmnal of th battry s connctd to th -crystal and ngatv trmnal of th battry s connctd to -crystal b Rvrs basng ( ostv trmnal of th battry s connctd to th -crystal and ngatv trmnal of th battry s connctd to -crystal b ( Wdth of dplton layr dcrass ( R Forward 10-2 (v Forward bas opposs th potntal barrr and for V > V a forward currnt s st up across th juncton. (v ut-n (Kn voltag : Th voltag at whch th currnt starts to ncras. For t s 0. V and for S t s 0.7 V. (v df dffuson dr drft Idf ( Wdth of dplton layr ncrass ( R Rvrs 10 (v Rvrs bas supports th potntal barrr and no currnt flows across th juncton du to th dffuson of th majorty carrrs. (A vry small rvrs currnts may xst n th crcut du to th drftng of mnorty carrrs across th juncton (v rak down voltag : Rvrs voltag at whch brak down of smconductor occurs. For t s 2 V and for S t s V. (v rak down voltag Rvrs voltag Rvrs currnt Kn voltag Forward voltag Idr Int Idf Idr Int Rvrs rakdown and Spcal urpos Dods. (1 Znr brakdown Whn rvrs bas s ncrasd th lctrc fld at th juncton also ncrass. At som stag th lctrc fld bcoms so hgh that t braks th covalnt bonds cratng lctron, hol pars. Thus a larg numbr of carrrs ar gnratd. Ths causs a larg currnt to flow. Ths mchansm s known as Znr brakdown. (2 Avalanch brakdown At hgh rvrs voltag, du to hgh lctrc fld, th mnorty charg carrrs, whl crossng th juncton acqurs vry hgh vlocts. Ths by collson braks down th covalnt bonds, gnratng mor carrrs. A chan racton s stablshd, gvng rs to hgh currnt. Ths mchansm s calld avalanch brakdown. ( Spcal purpos dods

7 gnus HYSIS Solds and Sm-conductor 7 Znr dod It s a hghly dopd p-n juncton whch s not damagd by hgh rvrs currnt. Th brakdown voltag s mad vry sharp. In th forward bas, th znr dod acts as ordnary dod. It can b usd as voltag rgulator Lght mttng dod (LD Spcally dsgnd dods, whch gv out lght radatons whn forward bass. LD S ar mad of GaAsp, Gap tc. hoto dod In ths dods lctron and hol pars ar cratd by juncton photolctrc ffct. That s th covalnt bonds ar brokn by th M radatons absorbd by th lctron n th V.. Ths ar usd for dtctng lght sgnals. Solar clls It s basd on th photovoltac ffct. On of th smconductor rgon s mad so thn that th lght ncdnt on t rachs th p-n juncton and gts absorbd. It convrts solar nrgy nto lctrcal nrgy. - Juncton Dod as a Rctfr. Half wav rctfr Full wav rctfr D1 Input ac RL output dc RL O/ (dc D2 Input ac sgnal Input ac sgnal Output dc sgnal Output dc sgnal D1 D2 D1 D2 Durng postv half cycl Dod forward basd Output sgnal obtand Durng ngatv half cycl Dod rvrs basd Output sgnal not obtand Fluctuatng dc Durng postv half cycl Dod : D 1 forward basd D 2 rvrs basd Output sgnal obtand du to D 1 only Durng ngatv half cycl Dod : D 1 rvrs basd D 2 forward basd Output sgnal obtand du to D 2 only ot : Fluctuatng dc Fltr constant dc. Transstor.

8 gnus HYSIS 8 Solds and Sm-conductor A juncton transstor s formd by sandwchng a thn layr of -typ smconductor btwn two - typ smconductors or by sandwchng a thn layr of n-typ smconductor btwn two -typ smconductor. mttr (mts majorty charg carrrs ollcts majorty charg carrrs as (provd propr ntracton btwn and basd. ot : In normal opraton bas-mttr s forward basd and collctor bas juncton s rvrs (1 Workng of Transstor : In both transstor mttr - bas juncton s forward basd and collctor bas juncton s rvrs basd. transstor transstor ma A ma ma A ma V V V V Ic Ic V V V V % mttr lctron combn wth th hols n th bas rgon rsultng n small bas currnt. Rmanng 9% lctrons ntr th collctor rgon. I > I c, and I c = I b I c % mttr hols combn wth th lctrons n th bas rgon rsultng n small bas currnt. Rmanng 9% hols ntr th collctor rgon. I > I c, and I c = I b I c ot : In a transstor crcut th rvrs bas s hgh as compard to th forward bas. So that t may xrt a larg attractv forc on th charg carrrs to ntr th collctor rgon. (2 haractrstcs of transstors : A transstor can b connctd n a crcut n th followng thr dffrnt confguratons. ( ommon bas ( ( ommon mttr ( ( ommon collctor ( ( charactrstcs : Th graphs btwn voltags and currnts whn bas of a transstor s common to nput and output crcuts ar known as charactrstc of a transstor. V = nput RL Ic V = output (ma V = 20 V V = 10 V V (n volt V = 0 Ic (ma V (n volt = 1 ma = 10 ma = ma = 0 ma

9 Output sgnal gnus HYSIS Solds and Sm-conductor 9 ( charactrstcs : Th graphs btwn voltags an d currnts whn mttr of a transstor s common to nput and output crcuts ar known as charactrstcs of a transstor. V = nput Ic RL V = output (A V = 0.1 V V = 0.2 V Ic (ma = 0 ma = 20 ma = 10 ma = 0 ma V (n volt Kn voltag V (n volt ( Transstor as an amplfr : A dvc whch ncrass th ampltud of th nput sgnal s calld amplfr. Amplfr Input sgnal Output amplfd sgnal Th transstor can b usd as an amplfr n th followng thr confguraton ( amplfr ( amplfr ( amplfr Input sgna ~ V Ic V RL V amplfr Input sgna ~ V RL V Ic Output sgnal amplfr (4 aramtrs of / amplfrs Transstor as.. amplfr ( urrnt gan ( Small chang n collctor currnt ( c (a ac ; Small chang n collctor currnt ( V (constant ollctor currnt( c (b dc (or mttr currnt ( valv of dc ls btwn 0.9 to 0.99 ( Voltag gan hang n output voltag( Vo Av hang n nput voltag ( V A v = ac Rsstanc gan hang n output powr( o ( owr gan hang n nput powr( owr gan 2 ac Rsstanc gan c Transstor as.. amplfr ( urrnt gan ( (a c ac V = constant b (b dc c b valv of ac ls btwn 1 and 20 ( Voltag gan Vo Av ac Rsstanc gan V ( owr gan o 2 ac Rsstanc gan

10 gnus HYSIS 10 Solds and Sm-conductor ( Rlaton btwn and : or 1 1 (6 omparson btwn, and amplfr xampl xampl: 2 Soluton : (a xampl: ot : Trans conductanc (gm : Th rato of th chang n collctor currnt to th chang n mttr bas voltag s calld trans c AV conductanc... gm. Also gm ; R L = V R L Load rsstanc S.o. haractrstc Amplfr ( Input rsstanc (R 0 to 200 low 1 to 2 k mdum k hgh ( Output rsstanc (R o 1 2 k hgh 0 k mdum k low ( urrnt gan low hgh hgh (v Voltag gan Mdum Hgh Low (v owr gan Mdum Hgh Low (v has dffrnc Zro 180 o Zro btwn nput and output voltags (v Usd as amplfr for currnt owr Voltag A spcmn s dopd wth Al. Th concntraton of accptor atoms s ~10 21 atoms/m. Gvn that th ntrnsc concntraton of lctron hol pars s ~ / m, th concntraton of lctrons n th spcmn s [AIIMS 2004] (a / m (b 1 10 / m (c 4 10 / m (d 10 2 / m n 2 n h n ( n n 10 / m. 17 A slcon spcmn s mad nto a -typ sm-conductor by dopng, on an avrag, on Indum atom 7 28 pr 10 slcon atoms. If th numbr dnsty of atoms n th slcon spcmn s 10 atoms/m, thn th numbr of accptor atoms n slcon wll b 0 (a atoms/cm 1 (b atoms/cm 1 (c atoms/cm 6 (d atoms/cm Soluton : (c umbr dnsty of atoms n slcon spcmn = atom/m = atom/cm xampl: 4 Soluton : (c Snc on atom of ndum s dopd n 10 7 S atom. So numbr of ndum atoms dopd pr cm - of slcon n 1 10 atom / cm A -typ smconductor has accptor lvls 7 mv abov th valnc band. Th maxmum 4 wavlngth of lght rqurd to crat a hol s (lanck s constant h = J-s (a 7 Å (b 7 10 Å (c Å (d Å hc hc = Å xampl: A potntal barrr of 0.0V xsts across a - juncton. If th dplton rgon s m wd, th ntnsty of th lctrc fld n ths rgon s [USAT 2002] (a V / m (b V / m (c V / m (d V / m 6

11 Soluton : (a xampl: 6 Soluton : (a xampl: 7 Soluton : (b gnus HYSIS Solds and Sm-conductor 11 V 0.0 = V/m. d 7 10 A 2V battry s connctd across th ponts A and as shown n th fgur gvn blow. Assumng that th rsstanc of ach dod s zro n forward bas and nfnty n rvrs bas, th currnt suppld by th battry whn ts postv trmnal s connctd to A s 10 (a 0.2 A (b 0.4 A 10 (c Zro (d 0.1 A A Snc dod n uppr branch s forward basd and n lowr branch s rvrsd basd. So currnt V through crcut R r d ; hr r d = dod rsstanc n forward basng = 0 So V A. R 10 urrnt n th crcut wll b (a A (b A 0 0 (c A V (d A 20 Th dod n lowr branch s forward basd and dod n uppr branch s rvrs basd A xampl: 8 Fnd th magntud of currnt n th followng crcut [RMT 2001] (a 0 (b 1 amp (c 0.1 amp (d 0.2 amp 4 1 Soluton : (a Dod s rvrs basd. Thrfor no currnt wll flow through th crcut. xampl: 9 Th dod usd n th crcut shown n th fgur has a constant voltag drop of 0. V at all currnts and a maxmum powr ratng of 100 mllwatts. What should b th valu of th rsstor R, connctd n srs wth th dod for obtanng maxmum currnt R 0. V (a 1. (b (c 6.67 (d V Soluton : (b Th currnt through crcut V A 1 voltag drop across rsstanc = = 1 V R 0.2 xampl: 10 For a transstor amplfr n common mttr confguraton for load mpdanc of 1 k (h f = 0 and h o = 2 th currnt gan s (a.2 (b 1.7 (c 24.8 (d 48.78

12 gnus HYSIS 12 Solds and Sm-conductor Soluton : (d In common mttr confguraton currnt gan h 0 A = f 1 h 6 o R L xampl: 11 In th followng common mttr confguraton an transstor wth currnt gan = 100 s usd. Th output voltag of th amplfr wll b [AIIMS 200] Soluton : (c (a 10 mv (b 0.1 V (c 1.0 V (d 10 V Output voltag Voltag gan V out = V n Voltag gan Input voltag V out = V n urrnt gan Rsstanc gan = V n R L = V. 1 xampl: 12 Whl a collctor to mttr voltag s constant n a transstor, th collctor currnt changs by 8.2 ma whn th mttr currnt changs by 8. ma. Th valu of forward currnt rato h f s (a 82 (b 8 (c 8.2 (d 8. c 8.2 Soluton : (a h f 82 b xampl: 1 Soluton : (d xampl: 14 Soluton : (a V c Th transfr rato of a transstor s 0. Th nput rsstanc of th transstor whn usd n th common-mttr confguraton s 1 K. Th pak valu for an ac nput voltag of 0.01 V pak s (a 100 A (b 0.01 ma (c 0.2 ma (d 00 A V c b A 00 A R 1000 In a common bas amplfr crcut, calculat th chang n bas currnt f that n th mttr currnt s 2 ma and = 0.98 [HU 199] (a 0.04 ma (b 1.96 ma (c 0.98 ma (d 2 ma c ma b c ma. R 1mV 1K 10K Vout