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Chng 3: Cc d cu trc

Chng 3: Cc d cu trc

Chng ny cho mt tng quan v tnh cht ca cc d cu trc. l cc bn dn bao gm hn mt loi vt liu. Nhng thay i thnh phn dng iu khin chuyn ng ca cc in t v l trng thng qua k thit vng. Lin kt ca cc vng trong mt lp d chuyn tip m hai vt liu gp nhau l rt quan trng nhng rt kh xc nh thm ch i vi lp chuyn tip c nghin cu tt nht hin nay l Mc d nghin cu ban u tp trung vo cc vt liu c hng s mng gn ging nhau, cc p dng hin nay i hi cc tnh cht ch c th c c bi cc vt liu ghp khng hp cho cc lp bin dng.

Mt lng ln cc linh kin c ch to t cc d cu trc cho c ng dng in t v ng dng quang. Trong chng ny cn cp n php gn ng khi lng hiu dng. l mt s n gin ho chun cho php nghin cu cc in t nh th chng l t do ngoi tr mt khi lng hiu dng thay v s dng cu trc vng phc tp.

Ta b qua bn cht khng trt t ca cc hp kim nh ni gi thit khng c trt t ca cc ion Ga v As cc v tr cation ca mng. V

nguyn tc, khng p dng c nh l Bloch cho cc vt liu nh th do

Chng 3: Cc d cu trc

chng khng c bt bin tnh tin t mng ny sang mng khc. Tuy nhin, c th nghin cu hp kim nh mt tinh th c cc tnh cht c ni suy gia cc tnh cht ca GaAs v AlAs. Cch tip cn ny c gi l php gn ng tinh th o. S sai lch so vi tnh tun hon l tng dn ti nhng nh hng nh s tn x hp kim. l s rt ngn qung ng t do trung bnh ca cc in t v l trng. Nhng nh hng ny thng l nh v c th c nghin cu trong l thuyt nhiu lon theo cng mt cch nh tn x t cc loi tp cht khc.

3.1. Cc tnh cht chung ca cc d cu trc

Ch mt t tnh cht bn dn ca cc vt liu III-V c s dng chung cho cc d cu trc. tng phm vi ca cc tnh cht, ngi ta s dng rng ri cc hp kim trong s cc hp cht khc nhau trong ng ch l hp kim

. N thng c k hiu n gin l AlGaAs. Khng c c n nh l mt cng thc ho hc theo ngha en. 2 tnh cht quan trng ca cc vt liu khc nhau l khe vng cc tiu v hng s mng c v th trn hnh 3.1. Khe vng biu din nh mt bc sng l rt quan trng v


c nhiu p dng ca cc vt liu III V trong quang in t m cn c nhng bc sng ring to ra vic s dng mi trng mt cch tt nht nh cc si quang.

Cc vng tch cc ca cc d cu trc thng thng l ti hoc gn cc giao din. iu ny l ng khng ch i vi cc hp cht III V. Cc in t trong mt tranzito hiu ng trng kim loi xit bn dn (MOSFET) chuyn ng dc theo mt giao din gia Si v . Trong trng hp ny,

Hnh 3.1. S ph thuc ca hng s mng ca cc

bn dn khc nhau vo khe vng cc tiu ca

chng c biu din theo eV v nh mt bc

sng. Cc ng lin nt ch ra khe vng trc tip

v cc ng t nt ch ra khe vng gin tip.

Si l tinh th v l v nh hnh. C

th lin kt 2 vt liu theo cch khng c

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ng khu rp v cc in t b tn x bi cc bt hon chnh sinh ra khi chng i dc theo giao din. S tn x b mt th ny cng nh s tn x t cc khuch tt tch in trong xit gi cho linh ng ca cc in t trong mt MOSFET nhit thp di khong Cc d cu trc III V cn phi c cc giao din gn hon chnh nu chng c to thnh tt hn. iu ny a ra nhng i hi nghim ngt cho vic nui. Nhng i hi ch c tha mn bi nhng qu trnh nui tt nhng tn km nh pitaxi chm phn t (MBE) v kt ta hi ha hc hu c - kim loi (MOCVD).

V nguyn tc, cn phi lin kt 2 vt liu mt cch hon ho trong mt d cu trc l tng. iu ny trc ht i hi rng chng c cng cu trc tinh th (hoc t nht l s i xng) v iu ny c tha mn i vi cc hp cht III V thng thng. Mt i hi th hai nu khng c bin dng trong cu trc cui l 2 hng s mng cn phi gn bng nhau.

Hng s mng ca mt hp kim thng cho bi s ni suy tuyn tnh gia cc thnh phn ca n. N l nh lut Vegard. Chng hn nh nh lut ny d on rng hng s mng ca c cho bi

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Hnh 3.1 gii thch s ph bin ca cc hp kim ny trong hng s mng thay i t hn 0,15% nh mt hm ca x. Nh vy, c th nui cc lp GaAs v AlAs hoc bt k hp kim trung gian no trn nh ca nhau m khng c ng sut quan trng no.

C mt t vt liu khc c th c nui trn cht nn GaAs m khng c bin dng. Mt la chn khc l cht nn InP. 2 hp kim v

c cng hng s mng ging nh InP vi cc khe trc tip v by cc ht ti hiu qu hn. Cc vt liu ny do c s dng cho cc linh kin in t tc cao. C th c s la chn rng hn nhiu nu i hi s tng hp mng b ni lng.

3.2. S nui d cu trc

Cc d cu trc cn phi c cc giao din vi cht lng rt cao nu chng c to thnh tt, ngha l cc cu trc nguyn t ca 2 vt liu cn phi tng hp vi nhau v giao din cn phi khng b nhim bi cc tp cht hoc khng c cc khuch tt khc.Hn na, cc lp c th mng v do ta

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3.2. S nui d cu trc

cn phi thay i thnh phn ca cc lp k tip rt nhanh tt hn l t lp n ny ti lp n khc. Cc phng php nui bn dn trc y nh pitaxi pha lng p ng cc tiu chun v c s dng i vi cc cu trc th hn nh cc laze d cu trc kp nhng ni chung cn phi c nhng qu trnh chuyn su hn. Cc phng php ph bin nht l MBE v MOCVD.

3.2.1. pitaxi chm phn t (MBE)

MBE v nguyn tc l mt k thut kh n gin. Thit b c phc ha trn hnh 3.2. Cht nn nui d cu trc trn trn mt nung nng trong mt b lm bay hi c rt kh n chn khng siu cao (UHV) thng thng mbar hoc tt hn (p sut kh quyn vo khong 1000 mbar). Cc nguyn t cu

Hnh 3.2. Gin n gin ho ca mt

my MBE trong c 3 ng Knudsen,

cht nn trn nung nng quay ca n

v mn hnh quan st RHEED phn

tch b mt.

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3.2. S nui d cu trc

thnh d cu trc m y l Ga, As v Al c bay hi trong cc l nung vi cc l hng v pha cht nn nhng hi b chn li khng n c cht nn bi cc tm chn. Ti p sut thp ny, qung ng t do trung bnh ca cc phn t gia cc va chm l ln hn nhiu so vi b rng bung. l ch Knudsen hay ch dng phn t ca mt cht kh v cc l nung c gi l cc ng Knudsen hay cc ng K. Cc phn t i ra khi cc ng K khng khuch tn nh trong mt cht kh p sut cao m to thnh mt chm phn t i then nhng ng thng m khng xy ra va chm cho n khi chng i ti cht nn hoc mt ch khc. S nui bt u khi cc tm chn c m ra v dng ca mi mt nguyn t c th c iu khin qua nhit ca mi mt l nung.

Cc cht pha tp c thm vo bng cch dng cc ng ph. Cht cho thng thng l Si. N trong nhm IV ca bng tun hon v do khng r n s tc dng nh mt cht cho hay nh mt cht nhn trong hp cht nhm III V. Trong thc t, n thng tc dng nh mt cht cho nhng iu ny c th thay i bng cch nui trn mt b mt khc so vi b mt thng thng l (100). N cng c xu hng tr nn lng tnh v cho c cc cht cho v

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3.2. S nui d cu trc

cht nhn ti nhng nng rt cao (khong Cht nhn thng thng l Be.

Mc d n gin v nguyn l, MBE khng n gin trong thc t. Nhng ming rt mng cn phi c nui vi tinh khit cc k cao cc tnh cht ca chng khng b nh hng bi s nhim. iu ny li i hi cc vt liu ban u tinh khit khng b nhim bi cc ng K. p sut nn trong b lm bay hi cn phi gi p sut thp lm gim s nhim cng nh bo m duy tr ch Knudsen. Dng t cc ng K cn phi ng u qua cht nn hoc c nhng thay i thnh phn qua ming rt mng (gim ti mc cc tiu bng cch quay gi mu trong khi nui). Cc nhit ca cc l nung cng cn phi c iu khin gi cho dng khng i. Nhit ca cht nn l quan trng v cc khuyt tt s khng c thi gian thot ra bng s ti cc nhit thp trong khi s khuch tn khng mong mun s xy ra v lm nhe cc giao din nu nhit qu cao. Hnh thi hc ca b mt ph thuc phc tp vo nhit v AlGaAs v GaAs nui tt hn trong cc iu kin khc nhau.

MBE l mt qu trnh chm v vic nui vt liu vi tc khong mt lp

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3.2. S nui d cu trc

n/ s hay 1m/ h. Cc u im ca MBE bao gm cc chuyn tip t ngt gia cc vt liu khc nhau, iu khin tt qua b dy ca cc lp v s mc li hp l. Cc nhc im r rt ca MBE l gi thnh v thc t l qu trnh MBE khng ph hp cho sn xut cng nghip.

Mt c tnh quan trng ca MBE l n xy ra trong UHV, ngha l c th s dng nhiu k thut chn on theo di s nui. im chung nht ca cc k thut ny l nhiu x in t nng lng cao phn x (RHEED) nh ch ra trn hnh 3.2. Mt chm in t c hng gn nh st qua b mt mu v nh nhiu x thu c quan st thy trn mt mn hnh hunh quang. B mt thay i theo mt cch tun hon khi nui c mt lp n v iu ny c th quan st thy trong cng v hnh nh ca tn hiu RHEED. Nh vy, vic nui c th m c theo cc lp n. Hn na, nh nhiu x bc l cu trc b mt.

MBE c th to ra vt liu tt nht cho cc ng dng in t. Mt php o n l linh ng cc i ca cc in t trong GaAs tinh khit trn danh ngha m n ch ra nng tp cht ion ho tng cng l

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3.2. S nui d cu trc

Mt php kim tra khc l linh ng ca cc in t trong kh in t 2 chiu m n vt qu tng ng vi qung ng t do trung bnh gn 0,1 nm. Tuy nhin, cn gii quyt mt s vn quan trng chng hn nh tng i d nui mt giao din tt ca AlGaAs trn nh ca GaAs nhng giao din o ngc ca GaAs trn AlGaAs li kh thc hin. Cc vt liu khc thm ch nh s dng rng ri c iu khin km hn nhiu.

3.2.2. S kt ta hi ho hc hu c kim loi (MOCVD)

MOCVD cn gi l pitaxi pha hi hu c kim loi (MOVPE) l mt phng php khc c kh nng ch to cc d cu trc vi cht lng cao. Hnh 3.3 ch ra gin n gin ho ca mt thit b thng hot ng gn p sut kh quyn. Cht nn trn mt khi nung nng trong mt bung m cc kh khc nhau chuyn qua n trong ht ti hir. Thnh phn ca cc kh c th thay i nhanh chng iu khin thnh phn ca vt liu nui. Phn ng c bn l phn ng gia mt alkyl kim loi v mt hirua ca kim loi nhm V nh

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3.2. S nui d cu trc

Hnh 3.3. Gin n gin ha ca mt

l phn ng MOCVD.

Cc cht cho nh Si, S hoc Se c

th c thm vo ging nh cc hirua v imetyl Zn hoc Cd tc dng ging nh cht nhn. Nhiu ha cht khc c s dng nht l trnh cc hirua nhm V c hi.

Thit b cho MOCVD n gin hn nhiu so vi thit b cho MBE mc d vn thc t ch yu l iu khin cc kh rt c (n tng gi thnh chung ti mt mc tng t). Cc kh khn ny sinh t kh ng lc hc bn trong l phn ng m mt lp bin t hm c xu hng to thnh trn cht nn. S nui ph thuc vo nhit c th b gii hn bi tc m ti cc cht phn ng khuch tn qua lp bin ny hoc bi tc phn ng trn b mt mu. Th tch ca h gia s trn ca cc kh v cht nn cn phi lm cc tiu thay i thnh phn kh v bn dn thu c mt cch nhanh

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3.2. S nui d cu trc

chng v cho nhng giao din sc nt. Hn na, hn hp ca cc kh cn phi thay i m khng lm nh hng n dng chy qua bung phn ng.

MOCVD ni ting v n cho php ch to cc linh kin quang in t tt hn so vi cc linh kin c ch to t MBE. N cng nhanh hn v c kh nng sn xut cng nghip do c th nui trn mt lng ln cc ming rt mng mt cch ng thi. Vic nui li m mt cht nn c khun theo mt cch no v sau tr li nui tip c bit c hiu qu i vi MOCVD. Cng c th nui c cc cu trc p bng cch dng cc cht nn vi cc mt l ra trn nhng mt phng khc nhau m c th tm c s ph thuc ca tc nui vo s nh hng cng nh nhit ch to cc linh kin t t chc. Cc kh khn gn vi MOCVD bao gm s nhim bi cacbon v vn an ton thc t nghim ngt.

Mt khong rng ca cc phng php c pht trin mnh t MBE v MOCVD. Mt v d l phng php pitaxi chm ho hc (CBE) hay pitaxi chm phn t hu c kim loi (MOMBE) trong cc ngun rn ca MBE qui c c thay bng cc tin thn tng t vi cc ngun rn dng trong MOCVD. Mt ng dng khc l phng php pitaxi lp nguyn t (ALE)

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3.2. S nui d cu trc

trong cc cht phn ng c cung cp mt cch tch ri nhm nui ht lp ny n lp khc. Tt c nhm tng cng iu khin b dy v thnh phn ca cc lp ci thin hiu sut ca cc linh kin thu c. Cng cc phng php ni trn cng c s dng to ra cc d cu trc Si Ge.

3.3. K thut xy dng vng

Nui d cu trc l mt qu trnh phc tp. Vic nghin cu dng iu ca cc in t v l trng thng qua k thut xy dng vng. Hnh 3.1 chng t rng cc vt liu khc nhau c nhng khe vng khc nhau. By gi ta cn xem xt chi tit hn cc CB v VB v Xt mt lp d chuyn tip gia 2 vt liu A v B vi

L thuyt n gin nht l qui tc Anderson. N da trn i lc in t ca cc vt liu. l nng lng i hi a mt in t t y vng dn

ln mc chn khng m n c th thot ra khi tinh th. i lc in t gn nh c lp vi v tr ca mc Fermi. iu ny khc vi hm cng m n c o t mc Fermi v do ph thuc mnh vo s pha tp. Qui tc Anderson pht biu rng cc mc chn khng ca 2 vt liu ca mt lp d

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Hnh 3.4. Qui tc Anderson i vi nh hng song song

ca cc vng ti mt lp d chuyn tip gia 2 vt liu A

v B da trn nh hng song song ca cc mc chn

khng.

chuyn tip s c sp xp nh trn hnh 3.4.

iu ny chng t

V d GaAs c eV v

c eV v do , eV. Khe vng thay i mt lng

= 0,37 eV v do , eV. Phn khe vng i vo vng dn l Q =

theo m hnh ny.

Mc d d dng o c s khc nhau ca khe vng, iu kh hn nhiu l phn gii s gin on trong cc vng ring. Gi tr Q = 0,85 c s dng t lu cho nhng gi tr nh hn l Q = 0,62 hin nay c

thit lp chc chn i vi x < 0,45 m tn ti khe trc tip. Nhiu th

nghim nh s hp th quang trong cc h lng t hnh ch nht th hin

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ch nhy yu i vi Q. Nhng hnh dng khc ca cc h lng t v d nh cc th parabol cho s phn gii tt hn.

Trong trng hp ca GaAs- AlGaAs, khe vng hp hn c bao bc bn trong khe vng rng hn nh ch ra trn hnh 3.4. Nh vy, mt h nhiu lp vi GaAs ging nh s lm y gia 2 lp AlGaAs by c in t v l trng. N c gi l s nh hng song song loi I hoc s nh hng song song gi ln nhau. C 2 kh nng khc c minh ha trn hnh 3.5 i vi 2 h ca 3 vt liu lp kht mng vi nhau trong ch ra cc khe vng v s gin on. S gin on l dng nu n c du mong mun i vi mt giao din loi I. InP v ch ra s nh hng song song loi II hoc s nh hng song song lch nhau m cc vng a thch cc in t trong InP nhng cc l trng trong Nh vy, mt h nhiu lp sinh ra mt h th i vi loai ny nhng mt ro th i vi loi khc.

Kh nng th ba l 2 khe vng khng xen ph cht no ln nhau v n cho s nh hng song song loi III hoc s nh hng song song ph v khe. V d kinh in l InAs GaSb nh ch ra trn hnh 3.5(b). Trong trng hp

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Hnh 3.5. S nh hng song song ca

cc CB v VB trong 2 h lp kht mng

ca cc bn dn

c s

dng rng ri i vi cc linh kin in

t tc cao v InAs GaSb AlSb m

n ch ra cc loi I, II v III ca s lm

khp. Qui c i

vi loi I.

ny, CB ca vt liu ny ph ln

VB ca vt liu khc 0,15 eV i

vi v d ny. Do , cc in t

v l trng chuyn t pht cho n

khi chng b bin dng li bi trng in t sinh ra ging nh trong vng

ngho ca mt it p n.

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Cp vt liu InAs-GaSb c c tnh th v khc v giao din gia InAs v GaSb c th l mt lp n ca GaAs hoc InSb ph thuc vo trt t nui chnh xc. iu ny c th nh hng n s nh hng song song ca cc vng v c xut l s ph ln nhau ca CB v VB l 0,125 eV i vi giao din GaAs v 0,16 eV i vi giao din InSb. S nui iu khin km hn dn ti mt gi tr trung bnh ca chng.

Cc thnh phn ca mt lp d chuyn tip c th c nhng cc tiu trong cc vng ti nhng im khc nhau trong min Brillouin. V d CB ca GaAs c cc tiu ti trong khi cc cc tiu thp nht trong AlAs gn X. Do , c im ca cc tiu thp nht thay i khi phn x ca Al trong hp kim tng ln. Hnh 3.6 ch ra cc cc tr nh mt hm ca x. Cc tiu thp nht trong CB thay i t (khe trc tip) ti X (khe gin tip) ti trong ly gi tr cc i ca n l 0,35 eV. Khi lng hiu dng v suy bin thung lng thay i t ngt ti ch giao nhau ny v s thay i t khe trc tip n khe gin tip cho s thay i rt ln trong tnh cht quang. Lu rng cc cc tiu L nm khng xa trn cc cc tiu khc gn ch giao nhau. Thng thng c nui vi

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Hnh 3.6. Cc nng lng ca cc y

ca 3 CB thp nht v nh ca VB

trong nh mt hm

ca thnh phn x.

x < 0,4 bo m rng CB

thp nht gi ti Dng iu

i vi x > 0,45 t c thit

lp hn.

3.4. Cu trc xp thnh tng lp: H lng t v hng ro

By gi ta thy cch cc CB v VB c th c xy dng trong qu trnh nui c th thay i theo 1 chiu. Cc cu trc xp lp ny l cc khi xy dng ca

cc linh kin phc tp hn. Xt mt s bin dng (profin) trong mi lin quan vi

cc in t trong CB. Cc l trng trong VB c xem xt mt cch tng t. Thm

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ch CB c nhng s phc tp khi bn cht ca n thay i trong

vi x > 0,45.

3.4.1. Hng ro xuyn hm

Mt v d n gin ca mt hng ro xuyn hm c cung cp bi mt lp AlGaAs c bao quanh bi GaAs (hnh 3.7(a)). Hng ro hnh ch nht l mt trong cc v d c bn c s dng trong c hc lng t. V phng din c in, mt in t s khng th chuyn qua mt hng ro tr khi n c ng nng vt qua nh nhng trong c hc lng t, n c kh nng

Hnh 3.7. Bin dng ca CB

i vi cc cu trc xp lp khc nhau.

(a) ro xuyn hm; (b) siu mng ch ra

cu trc vng mini; (c) h lng t ch

ra mt trng thi lin kt; (d) ro kp

trong c trng thi cng hng; (e) h

s truyn qua nh mt hm ca nng

lng i vi s xuyn hm qua ro kp trong c mt nh nhn ti nng lng ca mt trng

thi cng hng.

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xuyn hm qua ro. Thm ch mt ro n gin nh ro hnh ch nht c nhng ng dng thc t chng hn ging nh mt van tit lu iu khin bm in t trong mt s tranzito in t nng. H s truyn qua tng nhanh theo nng lng trong ch xuyn hm v do , ro la chn cc in t c nng lng cao.

3.4.2. H lng t

Ngc li vi ro l h lng t v d nh mt lp mng GaAs gia 2 lp dy ca AlGaAs (hnh 3.7(c)). C th tnh c cc nng lng ca cc trng thi lin kt trong h lng t nh mt hm ca su h. Thng s dng vic tnh th i vi mt h su v hn nh phn 1.3.

C mt h trong c CB v VB nu lp d chuyn tip thuc loi I m n bao hm trng hp ca GaAs c bao quanh bi AlGaAs. Trong trng hp ny, h by c din t v l trng v cc mc nng lng c th o c bng cc th nghim quang nh trong phn 1.3.1. Qu trnh ny to thnh c s cho hu ht cc linh kin quang in t.

Thc t l vt liu c 3 chiu v hnh 3.7(c) ch ra s thay i dc theo hng nui c qui c l hng z. Cc in t v l trng gi chuyn

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ng t do trong mt phng vung gc vi hng nui nhng by gi chng ch c 2 chiu t do khc vi 3. S hp th quang b chi phi bi mt trng thi m n many hn gn y vng trong trng hp 2 chiu v gip cho vic cung cp cc linh kin quang in t hiu qu hn.

3.4.3. Ro kp: Xuyn hm cng hng

Mt h lng t c cc ro v cng dy bn ny hoc bn kia. Xut hin hin tng vt l mi khi cc ro l mng nh trn hnh 3.7(d). By gi mt in t trng thi c th lt ra ngoi v n cho mt trng thi gi lin kt hay trng thi cng hng m n khc vi mt trng thi lin kt thc s. Cu trc ro kp cung cp vng hot ng ca mt it tunnen cng hng v n tng t vi mu Fabry-Prot quang.

Xt cc in t i ti ro t bn tri ti nng lng E. Xc sut chuyn qua ro ca chng l h s truyn qua T. Trong a s trng hp, n gn bng tch ca cc h s truyn qua ca 2 ro ring, ngha l C v

l nh i vi cc ro thng thng. c tnh khc bit ca s xuyn hm cng hng l ch T tng ti gi tr cao hn nhiu so vi i vi cc

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nng lng gn cng hng nh trn hnh 3.7(c) theo cng mt cch l s phn x nhiu ln dn ti cc nh nhn trong s truyn qua mt mu Fabry-Prot. Trong mt cu trc vi cc ro ging nhau, c s truyn qua l tng trung tm ca s cng hng. Tuy nhin, cc gi tr ring ca v l nh. B rng ca nh ny t l nghch vi Do , theo mt ngha no th c s truyn qua t hn qua cc ro dy c hn. Ngi ta pht trin cc it tunnen cng hng s dng nhng tn s cc cao.

3.4.4. Siu mng

Ta tng s ro cho s xen k ca cc h v ro nh ch ra trn hnh 3.7(b). By gi, mt in t c th xuyn hm t mt h ti cc ln cn ca n. iu ny khc vi in t i t mt h ra ngoi nh trong ro kp. N ph hng mc lin kt r nt gn vi h v trong trng hp ny, kt qu l mt vng mini. Siu mng cho mt th tun hon v do , c th p dng l thuyt chung i vi cc tinh th 1 chiu phn 2.1. Nh vy, chuyn ng dc theo hng nui b chi phi bi nh l Bloch v cu trc vng.

Cu trc c gi l mt siu mng v n p t mc tun hon th hai ln

22


mc tun hon th nht m n l bn cht tinh th ca cc bn dn. Mt s khc bit ch yu l ch n nh hng n chuyn ng ch theo mt hng. Chu k d nhin l di hn chu k tinh th v th tun hon l yu hn vi kt qu l cc vng v khe xut hin trn mt thang nng lng nh hn nhiu. T xut hin tn vng mini. Cc siu mng c s dng lc nng lng ca cc in t v n ch cho php cc in t bn trong cc vng mini i qua hoc phn x cc in t trong cc khe mini v s hp th gia cc vng mini c th c s dng ghi bc x hng ngoi.

Cc vng tr nn hp hn khi cc ro gia cc h tr nn dy hn v s xuyn hm gia cc h c nh hng t hn n cc tnh cht chung. Gii hn m cc h thc t b c lp c gi l h lng t a lp (MQW). Cc cu trc nh th c s dng rng ri trong cc ng dng quang lm tng th tch hot ng ca linh kin.

Thc t l cc siu mng c s dng rng ri trong mt ng dng m khng phi lm g vi cc tnh cht in t ca chng. N lm tng tnh sch ca vt liu trong khi nui. Trong thc t, thng nui mt siu mng trn nh ca cht nn gc, sau l mt cht m bng GaAs v cui cng l

23


cu trc mong mun. Nhiu giao din by nhiu khuyt tt v tp cht m chng di tr theo cch khc vi s nui v gy ra nhim linh kin.

3.4.5. Bn cht ca vng dn

Hnh 3.6 ch ra cc nng lng ca 3 cc tiu thp nht trong vng dn ca

nh mt hm ca x. Cc tiu thp nht l i vi x < 0,45

Hnh 3.8. Cc ro v h trong

GaAs - v n ch

ra 3 CB thp nht. (a) Ro ca

trong l

cc tiu thp nht khp ni; (b)

Ro ca AlAs trong X l cc

tiu thp nht trong ro; (c) H

ca GaAs c bao quanh bi AlAs.

nhng nm ti X i vi x ln hn. Cc bin dng ca 3 cc tiu c ch ra trn hnh 3.8 i vi mt ro ca v mt ro ca AlAs. C 2 ro c bao quanh bi GaAs. iu ny minh ha vn ny sinh khi 2 vng c

24


cc cc tiu khc nhau trong CB.

Cc tiu l thp nht trong ton b cu trc vi ro ca v iu hp l l c th b qua cc vng cao hn vi iu kin l nng lng ca in t ti di nh ro. l mt vn i vi ro AlAs. Lp xen gia xut hin nh mt ro nu ta xt (cc tiu thp nht bn ngoi) nhng n l mt h t im quan st ca nm thp nht bn trong ro. N cng l mt ro nu ta n gin xt cc tiu thp nht trong CB nhng ta s ly ci g lm cao ca n? N l mt vn khng n gin tr li v i hi cc tnh ton cu trc vng. Mc d ro l thp hn nu mt in t ti chuyn t n X khi n va chm ro, khi lng hiu dng l cao hn ti X v do , hm sng c th phn r nhanh hn. Nh vy, h s truyn qua c th b chi phi bi mc d n khng phi l vng thp nht. S chuyn t ti X cng chu cc gii hn trong khng gian Cc vn ny thng c th trnh c bng cch gi x < 0,4 mc d cc ro ca AlAs c th c s dng trnh s tn x hp kim c bit l trong s xuyn hm cng hng.

Cc vn tng t tc ng xu n cc h v d nh cc h ca GaAs gia

cc ro AlAs c ch ra trn hnh 3.8(c). Cc tiu thp nht trong h l

25


nhng bt k s trn no vo trong thung lng X ti giao din s cho php cc trng thi thot ra ngoi nu v ro cc tiu ny do thit lp gii hn ln cc trng thi lin kt thc trong h.

3.5. Cc d cu trc pha tp

Cc linh kin nh it tunnen cng hng da vo cc in t hoc l trng dn v cc ht ti ny c a vo qua s pha tp. Cng ging nh th i vi quang in t hc trong mt h lng t c th c nhng vo trong mt lp chuyn tip p n to thnh mt laze h lng t. Do , ta s xt nh hng ca s pha tp ln cc gin vng m chng tun theo cc nguyn l chung i vi cc cu trc vng ng nht. Cc d cu trc cho s kim sot xa hn i vi v tr ca cc tp cht v ht ti thot ra.

Cc cu trc kho st l cc cu trc thng ng theo ngha l dng chy dc theo hng nui hoc vung gc vi cc giao din. Trng hp ngc li l cc cu trc nm ngang. trong dng chy song song vi mt giao din. N tng t vi MOSFET v mt ng dng ch yu l cho cc tranzito hiu ng trng d cu trc. Chng s dng kh in t 2 chiu m n l nn tng i vi nhiu cu trc in t.

26


3.5.1. S pha tp bin iu

Mt cch a vo cc ht ti dng trong cc linh kin c in l pha tp cc vng m ta mong mun c cc in t hoc l trng. Cc cht cho hoc cht nhn tch in c li khi cc in t hoc l trng thot ra v tn x cc ht ti qua tng tc Coulomb ca chng (tn x tp cht ion ho). N lm h hi s lan truyn trong cu trc c nui cn thn, lm nho cc mc nng lng v lm t s giao thoa gia cc sng in t cn quan st cc hiu ng nh s xuyn hm cng hng.

Gii php l pha tp t xa hay pha tp bin iu trong s pha tp c nui trong mt vng nhng cc ht ti sau di chuyn ti ch khc. N c minh ho i vi mt lp d chuyn tip gia n-AlGaAs v GaAs khng pha tp trn hnh 3.9. Vt liu l trung ho khp ni v cc vng l

Hnh 3.9. CB quanh mt lp d

chuyn tip gia n-AlGaAs v GaAs

khng pha tp. N ch ra cc in t

c tch nh th no ra khi cc

cht cho ca chng to thnh kh in t 2 chiu.

27


phng nu cc in t trn cc cht cho ca chng trong n-AlGaAs (hnh 3.9(a)). Cc in t i xung quanh sau khi thot ra v mt s in t i vo GaAs. , chng mt nng lng v b by do chng khng th leo ln ro c cho bi Chuyn ng ny tch cc in t tch in m ra khi cc cht cho tch in dng m n thit lp mt th tnh in c xu hng iu khin cc in t quay tr li AlGaAs.

Nng lng ton phn i vi cc in t l tng ca 2 s hng. S hng th nht l ng nng ca chng c cho bi cu trc vng. N khng thay i theo v tr bn trong tng vt liu nhng thay i ti lp d chuyn tip. nh hng chnh l s gin on S hng th hai l th nng do th tnh in i vi cc in t. N cng vi ng nng cho nng lng ton phn ti y CB nh trn hnh 3.9(b). L l a ra y cng ging nh l l i vi gin vng ca lp chuyn tip p n thng thng ngoi tr thnh phn b sung quan trng S gin on ny c mt nh hng quan trng v n chng li in trng t s tr li ca cc in t ti cc cht cho ca chng. Trng ch c th p st cc in t vo giao din m chng b by trong h th gn ng hnh ch nht. H ny

28


thng thng rng khong 10 nm ti nng lng ca cc in t v cc mc nng lng i vi chuyn ng dc theo z b lng t ho theo cch tng t vi cc mc nng lng trong mt h vung. Thng ch mc thp nht b chim gi. Tt c cc in t khi chim cng trng thi i vi chuyn ng theo z nhng duy tr t do theo 2 hng khc l x v y. l kh in t 2 chiu (2DEG). N l c s i vi a s cc linh kin in t trong cc d cu trc chim cng v tr nh h lng t i vi cc linh kin quang.

S pha tp bin iu t c 2 li ch l n tch cc in t ra khi cc cht cho ca chng lm gim s tn x bi cc tp ion ho v by cc in t ti 2 chiu. S tinh ch to ra bng cch loi b mt lp m ca AlGaAs khng pha tp gia n-AlGaAs v GaAs lm tng s tch ra gia cc in t v cc cht cho. N lm gim tip s tn x nhng phi tr bng gi ct b mt in t trong 2DEG. Mt linh ng cao l ht sc quan trng trong nhiu th nghim vt l trong khi mt in t li khng quan trng. Do , mt m dy thng c s dng nhng cc i hi trong k thut thng l ngc li.

3.5.2. Xy dng cc gin vng

29


Ta s xem xt vic xy dng gin vng trn hnh 3.9 v xem n c th c tng qut ho nh th no cho cc h khc. Xt mt lp d chuyn tip pha tp gia n-AlGaAs (vt liu A) v p - GaAs (vt liu B. Hnh 3.10 a ra cc bc xy dng gin vng i vi lp d chuyn tip ny. Phng php xy dng gn vi phng php i vi mt cu trc ng nht pha tp nhng cn tnh n cc gin on v Cc bc xy dng gin vng

bao gm

(i) Bt u vi cc vng phng trong mi mt vt liu, vi cc vng trong s nh hng song song t nhin ca chng (c cho bi qui tc Anderson hoc mt ci g tt hn) v cc mc Fermi c thit lp bi s pha tp ln mi mt pha. N cho v tr ca cc vng lin quan ti mc Fermi xa lp chuyn tip trn mi mt pha. tm thi xo i nh hng ca s gin on, v cc ng trn pha A ti

Lu rng v do , khe vng hiu dng l nh nhau trn c 2 pha.

(ii) nh hng cc mc Fermi theo cng mt phng. S khc nhau ca mc Fermi xa lp chuyn tip c t bi bt k th hiu tc dng no.

30


Gi thit rng c mt th hiu dch dng v tc dng ln pha B sao cho

(iii) Ni vi

vi bi cc ng cong

song song nh th tnh in.

Dng chnh xc ca cc

ng cong ny ni chung

cn tm bng cch tnh s.

i vi mt bc tranh nh

tnh, phc ha mt ng

cong hnh ch S m cong

Hnh 3.10. Cc bc xy dng

gin vng i vi mt lp d

chuyn tip pha tp gia n-AlGaAs

(vt liu A) v p-GaAs (vt liu B)

31


ca n c cho bi du ca mt in tch. Thng n cho mt im un ti lp chuyn tip.

(iv) By gi khi phc ln pha A ging nh mt ng ti v

ti trong bao hm cc gin on trong v ti lp chuyn tip. iu ny hon thnh vic phc ha gin vng.

Cc vng b b cong gn lp d chuyn tip khi chng trong mt it p n nhng cc gin on trong cc vng lm xut hin c tnh mi l cc ht ti c th b by trong mt h th tip theo lp chuyn tip. C mt lp tch tr ca cc in t trn pha loi p trong v d trc v iu khng ging vi lp chuyn tip ng nht p n m c 2 pha u b ngho i.

Tuy nhin, cn a ra nhng i hi cho dng ca th tnh in. V d th l parabol trong mt vng ngho thng thng vi s pha tp khng i nh trong mt it p n gin on. Mt khc, cc d cu trc thng cha mt m khng pha tp trong c th b qua mt in tch. in trng cn phi l khng i v cc vng nghing tuyn tnh ging nh trong mt it p - i n. Mt nghin cu chnh xc i hi mt nghim s t hp ca phng trnh Poisson i vi th tnh in v phng trnh Schrodinger i vi cc

hm sng v mc nng lng, vi phn b Fermi-Dirac tm s chim gi

32


ca cc mc.

3.5.3. Tranzito hiu ng trng pha tp bin iu

Mt ca mt 2DEG c th c iu khin ging nh trong mt MOSFET bng cch to ra mt t in gia 2DEG v mt cng kim loi. Vic thm vo mt ngun v rnh hon chnh mt tranzito hiu ng trng (FET) gi l tranzito hiu ng trng pha tp bin iu (MOSFET). Mt cu trc n gin i vi mt linh kin tc cao c ch ra trn hnh 3.11. in mi gia cng v knh l AlGaAs trong cu trc ny. N a ra mt ro kh thp trong knh GaAs v cc kt hp khc ca cc vt lu. Lp mng ca GaAs trn b mt chng li s xi ho ca AlGaAs bn di. C mt m khng pha tp ca AlGaAs trn knh c gi rt mng tng mt in t. linh ng l mt

xem xt ph. Dng T ca cng

nhm lm gim tr khng ca n

Hnh 3.11. Tit din n gin ho qua

mt MOSFET GaAs-AlGaAs cao tn.

33


trong lc duy tr s tip xc ca n vi knh v cng trong mt hc. Hc lm cho cng gn knh hn.

Cc linh kin thc c nhiu s tinh ch iu khin cc nh hng k sinh v to iu kin d ch to nhng cc yu t c bn ny vn c duy tr. Cc MOSFET c th tm thy trong cc ng dng cao tn v d nh cc b nhn v tinh pht thanh truyn hnh trc tip ch yu l do nhiu thp ca chng. Nhng kh khn ny sinh do ro nh c cho bi trong GaAs-AlGaAs. Mc d trn InP l tt hn, hiu sut c th c ci thin hn na bng cch loi b gii hn ln cc cu trc lm khp mng. Do , ta s kho st cc lp bin dng tch cc phn tip theo.

3.6. Cc lp bin dng

Hu ht cc v d trong gio trnh ny c ly t h vt liu GaAs- AlAs m n c pht trin tt nht v hin nay n chi phi cc th nghim vt l. Tuy nhin, cc tnh cht ca n khng thch hp trong nhiu ng dng thc t. V d nh ro gi cc in t trong GaAs thng ch l 0,25 eV m n l qu nh by cc in t nhanh trong knh ca mt FET ngn. Trong cc ng dng quang, khe vng 1,4 eV tng ng vi bc sng khong 0,9 m trong

34

3.6. Cc lp bin dng

trong vng gn hng ngoi m n khng thch hp cho vic iu khin cc si quang ko di m mong mun c cc bc sng l 1,3 m hoc 1,55 m.

Mt c tnh ca GaAs v AlAs l ch chng c cc hng s mng gn bng nhau. Do , cu trc vi m ca ting vt liu khng b mo dng trong cc d cu trc. C mt t cp vt liu ging nh th v s la chn b hn ch bi cc thnh phn c bit ca cc hp kim nu i hi cc hng s mng phi nh nhau. V d thc t l v c

lm khp vi cht nn l InP. Mt phm vi rng hn nhiu ca cc vt liu c m ra nu hn ch hng s mng bng nhau b ni lng. V d mt s hp dn ca i vi cc h in t l gi tr ln ca v khi lng hiu dng nh i vi cc in t trong

S tng phn x ca In ln trn 0,53 s ci thin hn na c 2 tnh cht trn vi ci gi phi a vo bin dng. Vic iu chnh phn ca In cng cho php khe vng c lm khp vi cc yu cu ca cc si quang. Mt h bin dng hn na c cho bi hp kim Vic bao hm Si

cho mt tim nng thng mi r rng.

35

3.6. Cc lp bin dng

C 3 l do chnh sau y cho vic s dng cc lp bin dng

- Chng m rng phm vi ca cc vt liu sn c iu chnh cc tnh cht quan tm nh nhng dch chuyn vng v khi lng hiu dng.

- Bin dng c cc nh hng mnh ln VB v do cung cp cng c khc cho k thut xy dng vng.

- Chng c th cho php nui cc lp mong mun ln trn cc cht nn thng khng xng i nhng thun tin.

Tt c cc l do trn ng vai tr quan trng trong nhiu linh kin. Mt iu c lin quan khc l s bn vng trong thi gian di ca cc lp bin dng v vic nui ca nhiu vt liu cn gp nhiu tr ngi nhng cc vt liu c s dng rng ri.

3.6.1. Cc khia cnh cu trc ca cc lp bin dng

C th c 2 kt qu nu mt vt liu c nui trn mt vt liu khc vi hng s mng khc v d nh InGaAs trn GaAs. cn bng, InGaAs c hng s mng ln hn (hnh 3.12(a)). Gi thit rng cht nn GaAs dy n mc n c th b mo ng k. Nu InGaAs l mng, n c th bin dng

36

3.6. Cc lp bin dng

ph hp vi GaAs trong mt phng ca lp chuyn tip nh trn hnh 3.12(b). Nh vy, hng s mng ca n trong mt phng b rt ngn ti hng s mng ca GaAs trong lc phn ng n hi thng thng lm cho n ko do dc theo hng nui. InGaAs b mo nng v nng lng n hi tng ln. ng sut l rt ln so vi cc ng sut chu ng c bi cc mu v m (thm ch cc cu trc GaAs- AlAs thng c coi l khp mng cha cc ng sut ln theo cc chun thng thng). ng sut nh th ch c th chu ng c trong mt mng mng v s hi phc xy ra trong mt mng dy. Do , InGaAs tip tc c hng hng s mng t nhin ca n. S lm khp l tng ca cc nguyn t ti lp d chuyn tip mt gi thuyt

H.3.12. S nui ca

trn cht nn GaAs. (a) Cc lp tch

ra cn bng; (b) Lp mng InGaAs

trn GaAs trong mt phng ca lp d

d chuyn tip;(c) Lp dy hn trong

bin dng b ni lng nh vo mt

lch mng khng khp ti d giao din nh ch ra bi mt du sao.

37

3.6. Cc lp bin dng

c bn trc y ca chng ta khng th lu hn na. thay th, s khc bit hng s mng c tip tc bi cc lch mng khng khp nh ch ra trn hnh 3.12(c).

Nhiu lin kt b ph v khi to thnh cc lch mng v n i hi mt nng lng t l vi th tch mu. Nng lng n hi ca mt lp bin dng cng gn ng t l vi b dy ca n. Do , tn ti mt b dy ti hn m khi b dy vt qu n th xut hin cc lch mng. S cn bng ny ca cc nng lng gia bin dng v s pht sinh cc lch mng cho mt dng n gin ho ca tiu chun Matthews-Blakeslee i vi s bn vng ca mt lp bin dng.

T hnh 3.12(c) dng nh l cc khuch tt gn vi mt lp ni lng c nh x bn trong mt phng ca giao din.Cc lch mng khng th n gin bt u hoc kt thc bt c ch no v c th quay v pha trn tr thnh cc lch mng ng ren kt thc trn b mt l ra ca mu. Chng cc k c hi nu chuyn qua vng hot ng ca mt linh kin. Hin nay, ngi ta quan tm n vic nui cc lp m ni lng dy sao cho cc cht nn sn c d dng v r ng ch l Si hoc GaAs c th c s dng

38

3.6. Cc lp bin dng

trong cc vt liu c cc hng s mng khc nhau m chng c la chn cho cc tnh cht in t cao cp ca chng. Vic iu khin cc lch mng ng ren v cc khuch tt khc a ra mt thch thc cng ngh ch yu trong cc cu trc bin cht ny.

3.6.2. nh hng ca bin dng ln cu trc vng

nh hng r rng nht ca bin dng l lm di chuyn cc khe vng. N c biu din theo cc th bin dng m ta s s dng chng tnh tn x in t - phonon. i vi cc in t, vic s dng chnh ca bin dng l iu khin gin on m n cn nht by cc ht ti trong mt linh kin thc. N c khai thc trong cc tranzito hiu ng trng gi hnh vi mt knh bin dng v d nh InGaAs trn mt cht nn GaAs. Cc phc tp ny sinh nu c nhiu thung lng trong CB m ta s xem xt sau i vi Si -Ge.

Bin dng c cc nh hng mnh hn ln cc VB suy bin gn v m ra con ng quan trng khc cho k thut xy dng vng. Mt gii thch n gin i vi nh ca cc VB c cho trong phn 2.6.3 trn c s bc tranh ca cc qu o v N c th c m rng bao hm bin dng.i xng lp phng i hi rng cc qu o ny v cc vng thu

c ca chng b suy bin trong cc tinh th khng bin dng. S mo ca

39

3.6. Cc lp bin dng

Hnh 3.13. nh hng ca bin dng

ln cc vng ca mt bndn v n ch

ra s tch ca VB. Khe vng b thu hp

nhiu. Lp hot ng c hng s mng

nh hn trong (a), khng b bin dng

trong (b) ch ra cu trc vng thng

thng v c hng s mng ln hn

trong (c) m n p dng v d cho

InGaAs trn GaAs. Vect sng

trong mt phng vung gc vi hng

nui m n c ly dc theo hng z.

lp bin dng trn hnh 3.12(b) lm gim i xng ca n ti i xng t gic (i xng quay 4 ln i vi trc nui). nh hng in t quan trong nht ca bin dng l lm thay i nng lng ca qu o nh hng dc theo hng nui trong khi nng lng ca cc qu o c gi suy bin.

40

3.6. Cc lp bin dng

nh hng ca s nn mng trong mt phng ca lp chuyn tip c minh ha trn hnh 3.13(c). Nng lng ca gim v do , VB nh tng t v N l nng dc theo nhng c mt thnh phn nh i vi vect sng trong mt phng xy (lu Do , vng l bt ng hng v chuyn ng trong mt phng ca lp chuyn tip b chi phi bi mt khi lng nh. iu lm tng linh ng ca cc l trng. Vng t nm xa hn so vi khe vng. N l nh i vi v nng i vi Bc tranh b phc tp ho bi lin kt spin qu o nhng gii thch ny tnh n cc c tnh chung ca hnh 3.13. Trt t ngc li ca cc vng c quan st thy trn hnh 3.13(a) trong lp hot ng c hng s mng t nhin nh hn. Mt v d l Si trn Si-Ge.

Cc vng trong mt h lng t bin dng b nh hng bi c bin dng v s giam cm. Chng lm gim s i xng theo cch tng t v s giam cm c nh hng ging nh bin dng trn hnh 3.13(c). Hai nh hng c kt hp vi nhau mt cch hp tc trong mt lp bin dng ca InGaAs gia GaAs v y cc VB nh ra xa hn. N m rng phm vi ca m i vi n VB nh l nh trc khi n gp vng khc. N cng c ngha l

41

3.6. Cc lp bin dng

mt mt l trng ln hn c th c cha ring vng nh trc khi khe vng tip theo cng c nh ch. Hiu sut ca cc laze bn dn c ci thin c bn bi vic s dng cc h lng t bin dng v khai thc nhng thay i ny.

Mc d nh hng r rng nht ca bin dng l lm thay i nng lng ca cc vng, n khng phi l nh hng duy nht. Hiu ng p in cng c s dng giam cm cc in t vo cc dy v chm v cung cp cc trng gn lin dc theo trc nui ca cc h lng t.

3.7. Cc d cu trc silic-gecmani

V tr thng mi ni tri ca Si bo m mt v tr quan trng ca Si i vi cc d cu trc. Cc hng s mng ca Si v Ge nhit phng l 0,543 nm v 0,564 nm v ch khc nhau khong 4%. Do , bin dng l khng th trnh c. Cc khe vng l 1,12 eV v 0,66 eV chuyn thnh cc bc sng 1,1 m v 1,9 m. l cc bc sng quan trng cho cc si n mode. Mt lp bin dng ca Si ln Ge c mt khe thm ch nh hn v n m rng hn khong bc sng sn c. Do khe vng l gin tip nn s pht nh sng l khng chc chn nhng c th ghi c v n lm tng tim nng ca cc

42


linh kin quang in t tch hp.

Mt phm vi rng ca cc lp c nghin cu m n ni chung c th c m t theo mt cht nn m n thit lp hng s mng trong mt phng v mt lp hot ng ca Lp hot ng b bin dng tr khi x = y. Khi , c s ko v s nn u c th xy ra.

nh hng ca bin dng ln cu trc vng by gi thm ch phong ph hn. VB b tch ra nh trn hnh 3.13 vi tt c 3 kh nng c th c. C Si v Ge c nhiu thung lng trong CB nhng chng ti cc im khc nhau trong khng gian l X trong Si v L trong Ge. Cc tiu chuyn qua li gia chng ti trong hp kim khng bin dng i xng gim i ca mt lp bin dng ph v suy bin ca 6 thung lng X trong hp kim giu silic. 2 thung lng dc theo hng nui (gi thit hng (100) trn cht nn) to thnh mt cp tch ra khi 4 thung lng khc trong mt phng ca giao din c k hiu l m chng duy tr s suy bin. 4 thung lng L trong cc hp kim giu gecmani vn tng ng.

Hnh 3.14 ch ra cc tnh ton i vi cc dch chuyn trong CB v VB i vi mt lp hot ng ca m n b bin dng ph hp vi mt

43


cht nn ca Cc dch chuyn c xc nh bi

v Do , mt dch chuyn dng ca c xu hng giam cm cc in t trong cht nn trong khi mt dng giam cm cc l trng trong lp hot ng. Bc nhy sinh ra t s thay i bn cht ca cc cc tiu thp nht ca CB trong 2 vt liu. i vi lp hot ng, n l khi x < y v khi x > y ngoi tr khi c x v y gn 1 khi a vo cc cc tiu L. Hai bc nhy c cng du qua gn ht th v n cho s nh hng loi II hay s nh hng lch nhau. Nhng s nh hng ring i vi 2 d cu trc gia Si v c ch ra trn hnh 3.15.

Hnh 3.14. Cc dch chuyn trong (a)

CB v (b) VB gia cht nn

lp hot ng b bin

dng lm khp cht nn. Cc

dch chuyn c xc nh bi

v

44


Hnh 3.15. Cc nh hng vng ti 2 lp

d chuyn tip gia Si v (a)

Cht nn Si vi lp hot ng bin dng

(b) Cht nn

vi lp hot ng bin dng ca Si. Lu

khe vng thu hp ca Si. y mt bc

nhy hoc dng cho s

giam cm trong lp hot ng.

Si l cht nn trn hnh 3.15(a) vi mt lp bin dng ca Phn ln s dch chuyn l trong VB v bn cht loi II l r rng. Hng s mng t nhin ca lp hot ng l ln hn so vi cht nn v do , cc VB b tch ra theo hnh 3.13(c). N cho mt khi lng nh i vi chuyn ng trong mt phng ca giao din. Mt kh l trng 2 chiu (2DHG) c th b by ti lp d chuyn tip ny v linh ng o c l N tip cn gi tr nh tm c i vi cc in t trong mt

MOSFET. l kh nh by cc l trng mt cch c hiu qu

nhng mt lp b che lp c th c bao hm trong mt cu trc

45


MOSFET thng thng lm tng linh ng ca cc l trng.

iu ny rt quan trng trong thc t v cng ngh bn dn xit kim loi b sung (CMOS) s dng cc MOSFET c knh p v knh n. linh ng thp hn ca cc l trng c ngha l cc linh kin knh p qui c cn phi ln hn cc linh kin knh n tng ng cho cng mt dng i qua. Cc lp bin dng b che lp ca hi phc s cn bng gia 2 cc tnh ca tranzito v iu lm tng mt sp xp v c th c tc .

Si to ra lp hot ng trn hnh 3.15(b) b bin dng ph hp vi mt cht nn Thc t l cht nn thc c th l Si vi lp bin cht dy ca hp kim m n hi phc nh trn hnh 3.12(c). Mc d s nh hng song song cn l loi II, bc nhy ln hn by gi l trong CB v cc in t c th b by trong lp hot ng to thnh mt 2DEG. Cc thung lng thp nht trong CB l cp m chng c khi lng dc nng

dc theo hng nui v khi lng ngang nh trong mt phng ca giao din. Nh vy, chuyn ng trong 2DEG b chi phi bi

m n nh hn khi lng trung bnh l 0,33 trong Si khng bin dng.

46


N ng gp vo linh ng tm c i vi cc in t ti lp d chuyn tip ny trn gi tr linh ng trong mt MOSFET m n b gii hn bi cc tnh cht ca giao din

Mt ng dng khc ca cc d cu trc Si- Ge l trong cc tranzito lng cc lp d chuyn tip. Chng s dng mt cc pht vi mt khe vng rng hn so vi cc y tng hiu qu ca cc pht. N cho php cc y c pha tp cao hn, lm gim tr khng v loi b mt trong cc gii hn ln hiu sut cao tn. Nhiu nghin cu hng vo cc siu mng Si-Ge. Mt mc ch ring l nhm thay i cu trc CB a cc tiu ti v cho mt khe trc tip. Mc tiu cn cha c thc hin l s pht sng c hiu qu. l mt h qu dn ti c th a cc vt liu III V ra khi cc hot ng thng mi.

3.8. Cc dy v chm

Cc cu trc trn c xp thnh lp v giam cm cc ht ti trong mt mt phng hoc cung cp mt th 1 chiu m cc ht ti chuyn ng qua n. Bc tip theo trong s phc tp ha l a ra 1 chiu khc sao cho chuyn ng t do l c th c ch dc theo 1 chiu. C 2 cch tip cn. Cch th I l

47

3.8. Cc dy v chm

ngi ta c th nui mt cu trc xp thnh lp v chng tip cu trc ln . Cch th II l to ra mu 2 chiu trong qu trnh nui. Cch u c s dng rng ri hn c bit l i vi cc ng dng in t nhng khng th lm khp cc kch thc nguyn t c xut bi s nui c iu khin.

Cc lp thng c to hnh theo 2 bc. Trong bc I, vng mong mun c vch ng ranh gii trong mt lp bo v bi k thut in lit v hnh ny sau c chuyn ti bn dn bng cch khc axit vt liu hoc kt ta mt lp khc thng l kim loi ln b mt ca n. Mt v d n gin l vic ch to mt cng kim loi bng k thut in lit chm phn t v phng thng ng ln c ch ra trn hnh 3.16. Lp bo v chng n mn l mt lp mng ca polymetylmetacrylat (PMMA, cn c tn l Perspex hoc Plexiglas). Mt chm in t c qut qua cc vng ca lp bo v c

Hnh 3.16. Ch to mt cng kim loi

bng k thut in lit chm in t v

phng thng ln trn. (a) S phi lp

bo v di chm in t; (b) S pht

trin ca lp bo v; (c) S kt ta ca kim loi; (d) S phng thng ln trn li cng kim loi.

48

3.8. Cc dy v chm

loi b trong mt thit b ging nh mt knh hin vi in t qut. Cc u im ca k thut ny bao gm thang o tinh vi ca cc hnh nh c th v c v tnh a nng ca n. Mt nhc im c bn l n l mt qu trnh ni tip nhau v do rt chm. Chm in t ph v cc chui polyme m chng khi c th c ho tan d dng hn trong thuc ra nh v n li cc vng khng b l ra. Mt lp kim loi mng c lng tip trn ton b b mt. Cui cng mu c nhng trong mt dung mi loi b lp bo v cn li, kim loi trn nh ca lp bo v c phng thng ln trn v ch li kim loi kt ta trn b mt bn dn. Cc mp ca lp bo v cn phi thng ng hoc vic tin rnh trong cho s phng thng ln trn cn phi ng tin cy m n thng i hi cc lp bo v 2 lp hoc thm ch 3 lp.

C mt phm vi rt rng ca ca cc qu trnh s dng khc. c bit l lp bo v cn li c th c s dng nh mt mt n chng li s khc axit cho vng bn di. S khc axit c th l m khi s dng cc ho cht trong dung dch hoc kh m c s dng mt plasma. Khc axit m to ra t h hng v nhiu qu trnh la chn c pht trin di chuyn vt liu

49

3.8. Cc dy v chm

tc ph thuc vo thnh phn ca n hoc thm ch s nh hng tinh th ca n. Khc axit kh to ra cc cc cu trc sc nt hn vi cc tng bn thng ng nhng thng vi ci gi h hng vt liu di b mt khc axit.

Hnh 3.17 ch ra 3 cch giam cm cc in t trong mt 2DEG trong mt bng hp to thnh mt dy lng t (quantum wire) m chuyn ng t do ch c th c dc theo chu di. Cc cu trc ny r rng c lin quan n cc ng dn sng in t. C l phng php r rng nht l khc axit vt liu khng mong mun, loi b 2DEG b li mt g hoc ni mt bn hp c cha dy. Mt c tnh ca GaAs l tn ti cc trng thi b mt m chng hp th mt mt ln ca cc in t hoc l trng v pht sinh cc vng ngho di khng cha in t. Nh vy, b rng hot ng ca dy nh hn nhiu so vi b rng ca g trn hnh 3.17(b). Bt k h hng no

Hnh 3.17. Gii hn ca mt 2DEG

cho mt dy bi (a) khc axit su, (b)

khc axit nng v (c) th hiu dch

m trn cng tch.

50

3.8. Cc dy v chm

xy ra trong khi khc axit c gi trnh khi vng hot ng. Phng php th ba nhm lng mt cng tch ra trn b mt. Mt th hiu dch m trn cng ny y cc in t pha trc, li mt knh hp di khe m n to thnh dy. Chiu rng ca dy c th c iu khin qua th hiu dch trn cc cng. l mt u im quan trng i vi cc linh kin th nghim. K thut ny chng t l cc k a nng v c s dng nh ra cc knh phc tp hn nhiu so vi mt dy n gin. Mt v d l s co tht hp dng chng minh dn lng t ho ca mt h 1 chiu.

Mt nhc im chung ca c 3 phng php l ch th ca cc in t c iu khin kh lng lo. Cc chiu ngang nh khe gia cc cng b gii hn bi s x l v thng ln hn 50 nm. Cc in t cng thng di b mt 50 nm hoc hn. Mc d th tnh in mp ca mt cng c th c m hnh ho nh l mt bc sc nt, n m rng khi n i xung ti 2DEG. Vic iu khin dy chnh xc hn c th thu c nu cc ht ti b giam cm theo c 2 chiu bi cc lp d chuyn tip. Do , c nhiu th nghim nui cc dy mt cch trc tip. Phn ln cc phng php i hi rng cht nn c to hnh theo mt cch no trc khi nui v hnh3.18

51

3.8. Cc dy v chm

Hnh 3.18. S nui ca cc dy trn

mt cht nn xa trc. (a) Cht nn

trc khi nui ch ra cc cc nn v

bc trn b mt xa trc; (b) Dng

AlAs p dng (vi chuyn ng ca

cc nguyn t trn b mt) cho cc

bc m chng gn cht vo ; (c)

Vic hon thnh mt na lp n

ca AlAs; (d) Vic nui tip mt na

lp n ca GaAs; (e) Vic nui nhiu

lp ch ra s pht trin ca siu mng.

ch ra mt phng php c hiu qu.

Cht nn c ch to c tch xa mt cht b mt (001) thng c s dng nui. Trn thang nguyn t, b mt ca cht nn xa trc nh vy bao gm cc nn ngn c tch ra bi cc bc. Khi mt dng ca Al v As i vo, cc nguyn t ri xung b mt. Cc iu kin c chn sao cho chng d bin i v c th khuch tn xung quanh b mt. Chng thch gn

52

3.8. Cc dy v chm

cht ti cc bc hn l gia cc nn. Nu c cc cht phn ng cho mt na lp n v b mt ly trng thi c nng lng thp nht, cu trc thu c trn hnh 3.18(c). Vic lp li qu trnh nui mt na lp n ca GaAs lm hi phc cc bc ti cc v tr ban u ca chng trong mt phng nhng mt lp n cao hn. Chui ni tip ca cc mt na lp c lp li v kt qu l tng nh ch ra trn hnh 3.18(e). Vic iu khin nui tinh t l rt quan trng v mt s cu trc ng ch c nui chng hn bi MOCVD.

Nhiu k thut m t mt chng mc no c m rng giam cm cc in t theo c 3 chiu v n to thnh cc chm lng t (quantum dot). iu quan tm l vic nui cc cu trc khng cn n k thut in lit hoc khc axit. Mt lp mng ca InAs trn GaAs c xu hng t nhin t li vo trong cc chm v cc cu trc t t chc ny hin nay ang thu ht s quan tm c bit ca cc nh nghin cu.

3.9. S giam cm quang

trn ta ch xem xt s giam cm ca cc in t v l trng nhng trng quang cng cn phi c giam cm trong mt cu trc quang in t. Bi

53


ton ny l rt tng t v nguyn l mc d bn cht vect ca nh sng lm cho cc tnh ton kh khn hn. S sng v tn s ca cc ht lin h vi nhau bi trong khi i vi cc photon,

y, l hng s in mi phc v l chit sut. Cc h thc gia s sng v tn s i vi cc ht v cc photon l tng t nhng c mt s s khc nhau c bn. S sai khc l m trong mt ro v n cho mt s sng o trong khi n him khi thc i vi Mt

khc, hng s in mi l phc vi mt phn o thng biu din s tn hao. N m t s hp th ca cc photon nhng cc in t cn phi c bo ton v do khng th c mt hng s in mi phc.

nh sng c xu hng lan truyn trong cc min vi mt chit sut cao hn theo cng mt cch nh cc ht c th b by trong cc min c th nng thp hn. iu ny c th xem nh s phn x trong ton phn ca cc tia trong mi trng c chit sut cao hn. Mt khe vng nh hn thng gn vi mt chit sut ln hn v lp kp nh GaAs gia cc lp AlGaAs do c xu hng dn c cc ht v cc sng trong GaAs.L thuyt ca cc ng dn sng

nht l rt tng t vi l thuyt ca mt ht trong mt h th hu hn. Cc

54


thang chiu di l tng i khc nhau do bc sng khong 1m i vi nh sng nhn thy nhng chng 50 nm i vi cc in t. Nh vy, mt cu trc d th kp (DH) nh hnh 3.19(a) dn sng mt cch c hiu qu ch khi n rng n mc s lng t ho ca cc trng thi in t l khng quan trng. Mt h hp vi cc mc nng lng cch nhau rng cho s giam cm rt yu ca mode quang. Mt gii php l giam cm nh sng v cc ht mt cch tch ri vi mt h bn trong hp i vi cc ht v mt vng bn ngoi rng hn i vi nh sng. 2 bin dng chung l d cu trc giam cm tch ri (SCH) vi mt thnh phn to bc v d cu trc giam cm tch ri ch s bc (GRINSCH) nh ch ra trn cc hnh 3.19(a) v (c). Vng bn trong c

Hnh 3.19. Bin dng ca CB v VB

v chit sut qua cc lp thit k

dn nh sng v by cc ht ti: (a)

D cu trc kp (DH); (b) D cu trc

giam cm tch ri (SCH); (c) D cu

trc giam cm tch ri ch s bc

(GRINSCH).

55


th l mt h lng t a lp khc vi mt lp n

Ngay khi cc in t c th b giam cm nhiu hn trong cc dy, nh sng c th b giam cm theo 2 chiu sng nh cc sng viba trong mt ng dn sng kim loi thng. Nhiu k thut c s dng trong c 3 k thut c ch ra trn hnh 3.20. D cu kp b che lp l phc tp cho vic ch to do mt ni mt bn cn c khc axit gii hn vng hot ng v sau l vic nui li mt vt liu vi chit sut thp hn dn nh sng song song vi cc giao din ban u. u im l c th t c s giam cm mnh. S dn nh sng trn hnh 3.20(b) l d ch to hn nhiu v ch i hi khc axit b mt nhng dn nh sng yu hn. Cui cng hnh 3.20(c) ch ra mt ng dng quang ca mt siu mng. nh sng i dc theo dn nh sng tri qua mt nhiu tun hon do cc nh ngang b khc axit vo trong lp dn

Hnh 3.20. Cc tit din qua 3 v d

dn sng quang giam cm bn: (a) D

cu trc b che lp; (b) Dn sng g;

(c) B phn x Bragg phn b trn

mt dn sng g.

56


sng. Chng gy ra s phn x theo iu kin Bragg v c th c dng to ra mt hc quang trong mt laze. Phng php ging nh s hi phc phn b (DFB) hay mt b phn x Bragg phn b (DBR) ph thuc vo cu hnh. Cc laze nh th c rng vch nh hn so vi cc laze s dng mt hc Fabry-Prot qui c. Cc siu mng cng c th c to ra bng cch nui nh trong phn 3.4.4 v c dng lm cc b phn x Bragg phn b to thnh hc trong cc laze pht x b mt thng ng.

Mt siu mng xp thnh lp sinh ra mt khe vng ch i vi chuyn ng theo mt hng v khng c nh hng song song vi cc lp. Vic to hnh tip cho mt th tun hon 3 chiu nh trong mt tinh th rn c th to ra mt phm vi ca cc tn s hoc khe vng photon m khng c cc mode nh sng no c th lan truyn. Vic iu khin cc linh kin qua cc tnh cht quang c bit l s pht x t pht ca chng c th dn ti cc linh kin quang in t ci tin.

iu ny kt thc tng quan v phm khng l ca cc d cu trc trong ng dng. Trc khi nghin cu cu trc in t chng, ta xem xt php gn ng khi lng hin dng nn tng l thuyt v cc bn dn d th.

57

3.10. Php gn ng khi lng hiu dng

Mt trong nhng s n gin ho c s dng trn y l cn gi thit rng cu trc vng ca cc bn dn tinh th phn ln c th c b qua v ch gi li nng lng v khi lng hiu dng ti im tn cng ca mi mt vng. By gi ta s tm hiu php gn ng khi lng hiu dng, xem xt cc gii hn ca n v lm sng t xem n c th c s dng an ton u.

Gi s ta thm mt nhiu lon nh mt tp cht vo mt tinh th l tng. Tng qut hn, nhiu lon c th l mt h lng t, ro th, siu mng hoc th t mt cng m hnh trong mt 2DEG. Phng trnh Schrodinger c dng

y, l ton t Hamilton i vi tinh th l tng v l ng gp b sung t tp cht. Kh gii phng trnh (3.2) i vi mt tinh th l tng v do phng trnh ny a ra mt thch thc rt ln.

Mt khc, cc gio trnh c bn a ra cc kt qu n gin i vi mt cht cho hoc mt cht nhn trong mt bn dn. Mt cht cho c dng iu nh th n c mt in tch ion dng ph c b tr bi mt in t ph vi cc du o ngc i vi cc cht nhn. Do , tp cht c dng iu ging

58


vi mt nguyn t hir nhng khi lng c nh thang li ti khi lng hiu dng ca cc in t hoc l trng v in tch c che chn bi hng s in mi ca vt ch. C 2 nh hng lm gim nng lng ion ho mt cch pang k t 13,6 eV trong hir xung ch cn 5 meV i vi mt cht cho trong GaAs. Qui trnh n gin ny c chng minh bi l thuyt khi lng hiu dng (hoc hm Hamilton hiu dng). iu hp dn l l thuyt em li mt kt qu d hiu nh th nhng cn phi ch r cc gii hn ca l thuyt ny.

Xt mt h 1 chiu n gin ha k hiu. Gi s ta gii phng trnh Schrodinger i vi tinh th l tng:

Cc nghim ca (3.3) to thnh mt h (phn 1.6). Hm sng ca h vi tp cht do c th c khai trin theo thnh

trong l cc h s khai trin. N c c mt tng theo mi vng n v mt tch phn theo k trong min Brillouin bao hm mi trng thi. C

59


th thay (3.4) vo (3.2) tm D nhin, n cn l mt nghim chnh xc v khng d lm v nguyn l hn so vi vic gii phng trnh ban u mt cch trc tip. Hm sng cn phi c n gin ho to ra s tin trin xa hn. Ta s thc hin mt h ca cc php gn ng mnh t c mt kt qu d hiu v xt xem chng c th c hi phc sau nh th no.

Bc I l gi thit rng cc hm sng ch t mt vng ng mt vai tr quan trng v do c th b i vic ly tng theo n. Khi ly mt cht cho trong GaAs lm v d, ta hi vng cc trng thi c ly phn ln t vng dn y

VB v CB cao hn ch c ng gp nh. Nng lng ca cht cho gn vi mp CB nhng xa cc vng khc. Do , php gn ng c th l tt.

Bc II l gi thit rng cc trng thi ch t mt vng nh ca khng gian k c ng gp quan trng vo tch phn. Trong trng hp ca mt cht cho, ta hi vng rng k nm xung quanh 0 khi y CB By gi, cc hm Bloch c th c vit thnh trong l mt hm tun hon ca x. Gi thit rng phn ln s thay i ca theo k xut pht t sng phng v c th c nghin cu khng ph thuc vo

60


k trong mt vng nh ca khng gian k. Nh vy, ta c

i vi cc gi tr nh ca k.

Vi 2 s n gin ho trn y, hm sng (3.4) ly dng ca mt php bin i Fourier ngc

l kt qu chnh u tin ca l thuyt khi lng hiu dng c minh ha trn hnh 3.21. Hm sng gn ng l tch ca hm Bloch ca cc tr a phng ca cc vng nng lng ca vt ch v hm bao Gi thit

ch cha mt khong nh ca cc s sng , ngha l cn phi l mt hm thay i chm trong khng gian thc. iu ny cn c kim tra

chng hn nh bn knh ca mt cht cho vo khong 10 nm trong GaAs m

n l ln so vi hng s mng l 0,5 nm.

Hnh 3.21. Hm sng xung quanh mt tp v n

ch ra hm bao lm bin iu hm Bloch

cho hm sng y

61


Ta cn mt phng trnh cho hm bao. Thay (3.4) vo (3.2). Bi ton chnh l nh hng ca Nu ta lm php rt gn ti mt vng n gin, ton t ny cho

Ton t tc dng ln x v do ch nh hng n N l mt hm ring ca phng trnh Schrodinger (3.3) i vi tinh th thun tu v do , ton t c th c thay bng tr ring ca n. Cui cng, ta thc hin php gn ng (3.5) i vi cc hm Bloch. Tip theo, khai trin vng nng lng thnh mt chui ly tha ca k: N cho

i vi bin i Fourier ca mt o hm,

62


Nh vy, bin i Fourier ngc ca l v n c th tng qut ho chng t rng bin i ngc ca l

(3.8) tr thnh

Biu thc khng n gin hn so vi mt s vit tt i vi phng trnh bn tri. N c ngha l ngi ta cn ly khai trin n theo mt chui ly tha ca k v thay k bng id/ dx mi mt s hng. Ni chung, c mt s v hn cc s hng v do , l mt biu thc gy kh chu bt k s xut hin r rng ca n.

Nh vy, ta rt gn phng trnh Schrodinger (3.2) ti mt dng n gin ng k do cc s hng cn li v n gin l s nhn vi hm sng. H s chung trit tiu c

Kt qu cui cng l phng trnh Schrodinger i vi ring hm bao trong

63


cha ton t Hamilton hiu dng. Cc hm Bloch b trit tiu ging nh c th tun hon ca vt ch v n to iu kin cho mt ton t ng nng phc tp cha cu trc vng. Trong trng hp 3 chiu, c thay bng S chun ho hm bao l mt bi ton ph do hm sng y l tch ca v

Ton t Hamilton hiu dng cn cc k phc tp nu vn gi cu trc vng y . Tuy nhin, ta cng gi thit rng hm sng c rt ra ch t mt vng nh ca khng gian v ta c th n gin ho thch hp vi iu . V d y CB trong GaAs gn ng bng

v vic thay cho

Khi thay n vo trong phng trnh Schrodinger hiu dng (3.11), ta thu c

l mt phng trnh Schrodinger ging vi phng trnh Schrodinger i

vi cc in t t do ngoi tr khi lng hiu dng vi nng lng o t

y CB.

64


Trong trng hp ca mt cht cho vi th Coulomb ht, phng trnh Schrodinger tr thnh

N ging nh phng trnh Schrodinger i vi mt nguyn t hir ngoi tr khi lng hiu dng s dch chuyn nng lng t CB v hng s in mi ca bn dn (dng nh t nhin n xut hin mc d ta khng chng minh n). Ta c th lng ghp cc hng s vo cc kt qu i vi hir. iu ny chng minh rng nng lng ca trng thi thp nht l trong l nng lng Rydberg. Hm sng tng ng l trong l bn knh Bohr. Nng lng

Rydberg v bn knh Bohr ph thuc vo v trong lc cc gi tr ca

i vi cc in t trong GaAs.

Nhng ci g mt i trong cc php gn ng? Gi tr ca dng n gin nht i vi ton t Hamilton nh ton t Hamilton trong (3.14) b gii hn bi php gn ng parabol cho vng nng lng. Thm ch trong h GaAs-

AlGaAs vi cc dch chuyn nh, ta thng xt cc nng lng

65


t mp ca mt vng. Php gn ng parabol l khng r rng ti mt nng lng ln nh th v cc kt qu tnh s s khng ly mt cch qu nghim ngt.

Hn ch cho mt vng n gin l mt php gn ng nghim ngt m n cn c ni lng trong mt s ng dng trong bao gm

(i) Cc vt liu nh Si c mt s thung lng tng ng trong CB m tt c chng cn phi c gi li i vi cc trng thi in t.

(ii) VB cha cc l trng nng v nh m chng l suy bin ti nh tch ra t vng th ba ch bi s tch spin- qu o yu. Ta cn gi vic ly tng theo tt c cc vng ny trong hm sng.

(iii) Ta cn gi c CB v VB m t cc hiu ng gia cc vng nh s hp th quang trong mt h lng t (h.1.4). N dn ti mt bi ton xa hn. Cc vng xung quanh khe c bn trong mt bn dn c th c m t bng cch dng mu Kane m theo n, cc khi lng hiu dng nh sinh ra t vic trn cc hm sng gia CB v VB khi tng t 0. Php gn ng c to ra trong (3.5) l s thay i phn tun hon ca cc hm Bloch c th c b i v iu ny do cn phi c xem xt k lng.

66


Khi gi li mt s vng, ton t Hamilton hiu dng tr thnh mt ma trn ca cc phng trnh vi phn tc dng ln mt vect cha cc thnh phn ca mt hm sng trong mi mt vng.

Php gn ng khi lng hiu dng l php gn ng mnh v ni chung l c hiu qu mc d cn phi c bit thn trng khi tnh cc phn t ma trn quang.

3.11. L thuyt khi lng hiu dng trong cc d cu trc

Cn thn trng hn mt cht trc khi p dng l thuyt khi lng hiu dng cho cc d cu trc. Cc c tnh quan trng l phn Bloch ca hm sng v phng php lm khp ca cc hm bao.

Hm sng y l tch ca hm bao thay i chm v hm Bloch ca cc tr a phng trong cu trc vng ca vt ch (phng trnh (3.6)). Cc hm Bloch trong 2 vt liu bn ny hay bn kia ca mt lp d chuyn tip cn phi tng t nh nhau bo m gi tr ca php gn ng khi lng hiu dng. Mt iu kin r rng l chng cn phi thuc v cng mt im trong iu ny khng t c i vi CB ti mt lp chuyn tip

67


gia GaAs v AlAs trong cc CB ti v X trong 2 vt liu. Thm ch ni m cc cc tiu l nh nhau ging nh trong GaAs v

c th phng on rng cc hm Bloch cn phi gn ging nhau. iu ny l do ng nng ca chng l ln c 10 eV t hnh 2.16 v do cc khc bit ca cc hm Bloch c th d dng a vo cc sai s nng lng khong 0,1 eV m ta thng gp. Cc tnh ton chi tit xc nhn rng l thuyt khi lng hiu dng c chp nhn mc d c s khc nhau ca cc hm Bloch.

im th hai lin quan n vic lm khp cc hm bao ti giao din. Xt mt lp chuyn tip ti z = 0 gia cc vng trung ho ca cc vt liu A v B (GaAs v vi x < 0,45 lm v d). Phng trnh Schrodinger i vi hm bao trong 2 vng (nu ch xt 1 chiu cho n gin) l

S khc nhau ti cc y ca cc CB c dng iu ging nh mt th bc vi

vt liu B cao hn Nu cc vt liu l nh nhau, n gin

68


ta s lm khp gi tr v o hm ca hm sng ti giao din m chng cho cc iu kin thng thng

trong c ngha l mt ca giao din trong vt liu A,v.v... iu kin n gin ny l khng chnh xc i vi mt lp d chuyn tip trong 2 khi lng hiu dng l khc nhau v (3.18) khng bo ton dng. Mt h chnh xc ca cc iu kin lm khp l

iu kin lm khp o hm by gi bao hm khi lng hiu dng. Do o hm ch yu l ton t xung lng nn (3.19) i hi tc cn phi nh nhau c 2 bn bo ton dng. Hm bao t c nt tht ti mt giao din nu

iu kin lm khp sai s (3.18) ngm gi thit rng phng trnh Schrodinger ly dng

69


N khng phi l dng Hermite (hoc dng Sturm- Liouville) nu thay i v do lm mt nhiu tnh cht quan trng ca cc hm sng. S thay i tm thng b ngoi ca vic vit li (3.20) di dng

lm hi phc bn cht Hermite v c th c bin minh mt cch y hn. C 2 dng thu gn ti phng trnh Schrodinger thng thng i vi mt cu trc ng nht nhng dng th hai bo m rng cc hm sng l trc giao v dng c bo ton v duy tr cc iu kin khc. Bt li l iu kin (3.19) i vi s lm khp.

Nt tht trong hm bao ti mt d giao din gy ra nghi ng v gi tr ca n do cc hm bao thc cn phi trn. Cc tnh ton ch ra rng php gn ng khi lng hiu dng tip tc c gi tr vi iu kin l hm bao thay i chm trn thang bc nguyn t. iu kin ny khng c p dng cho th. Hnh 3.22 ch ra mt v d ca hm sng y (bao hm cc hm Bloch) cho mt h lng t 6 nm. Hm ny l trn nhng hm bao c xy dng th bng cch kt hp cc nh nhn c s thay i t ngt v dc ti d giao din. Nh vy, nt tht trong hm bao sinh ra bi iu kin lm khp (3.19) chnh xc phn nh mt s thay i ca hm sng y trn

70


Hnh 3.22. Hm sng i vi trng thi thp

nht trong mt h lng t 6 nm trong mt

d cu trc trong bao hm cc hm Bloch.

ng cong mnh l mt hm bao gn ng

ni cc nh nhn ca hm sng y .

thang bc nguyn t.

iu ny kt thc nhng s phc

tp c a vo bi cc lp d

chuyn tip. Bc tip theo l s dng ng thi cc kt qu ca 3 chng u xt xem ti sao cc in t c th c dng iu nh th chng b giam cm ch trong 2 chiu hoc t hn.

71

Bi tp chng 3

3.1. Tnh tc nui vi gi thit rng s nui b gii hn bi vic cung cp Ga c p sut trong t bo K vo khong ti C th s dng cc cng thc bit tm thng lng ca cc nguyn t Ga ti ming ca t bo K c din tch Nu cht nn khong cch

t t bo K th thng lng m rng qua mt bn cu c din tch nhng gp i gi tr trung bnh theo hng v pha trc. Tm thi gian nui mt n lp. iu c ch l chuyn thi gian ny thnh thi gian nui mt b dy l 1 m.

3.2. Tnh mc nhim bn trong vt liu nui n gin nh l t s

trong l thi gian nui mt n lp v l thi gian ph mt n lp kh phng ln b mt. Hir khng phi l mt vt liu thc xem nh mt cht bn. Vt liu tt cn phn tp cht ny di v do , gi thit h s dnh ca cc nguyn t ti dnh bm vi b mt c cn tt khng?

3.3. Chng minh rng qung ng t do trung bnh L ln hn nhiu so vi kch thc dng c. Nu cc phn t c ng knh d, chng s va chm vi tt c cc phn t khc trong th tch trong khi i c khong cch x.

72

Bi tp chng 3

V trung bnh, chng va chm vi mt phn t khc khi i c qung ng t do trung bnh v do c tnh L i vi c kh phng v chm phn t khi s dng cc iu kin ni trn.

3.4. S dng s liu trong Ph lc 2 tm cc thnh phn ca v

m chng c th c nui khng cn bin dng trn cht nn InP.

3.5. S dng qui tc Anderson xc nh cc gin on trong CB v VB i vi 2 h lm khp mng GaAs - AlAs v InAs GaSb. Cc khe vng v i lc in t c cho trong Ph lc 2. Cc kt qu thu c ph hp nh th no vi cc gi tr c chp nhn ch ra trn hnh 3.5?

3.6. Hnh 3.15 ch ra s nh hng ca cc vng i vi 2 ghp cp ca Si v

Lp li n i vi Ge v C cc loi nh hng no v xut cc ng dng i vi chng?

3.7. Phc ha gin vng i vi mt d chuyn tip gia p-AlGaAs v n-GaAs. Chng t rng n c th by mt kh l trng 2 chiu ti giao din.

3.8. Cc kt qu l th c th t c i vi lp d chuyn tip loi II (xp

73

Bi tp chng 3

lch nhau) (hnh 3.5). Phc ho cc vng i vi c 2 chuyn tip p n v n p v xc nh xem cc in t hoc l trng c th b by ti giao din hay khng?

3.9. Phc ha gin vng i vi mt it n p chuyn tip ng nht trong GaAs vi gi thit rng c th s dng thng k bn dn c in (phn 1.8.3). Cho bn tri v bn phi. Xc nh v tr mc Fermi trong 2 vt liu v dng n phc ho gin vng cn bng. Ly cc mt d trng thi hiu dng l

Cng xc nh th hiu gn vo trong c nh ngha nh l s khc nhau ca cc mc Fermi gia 2 bn khi cc vng l phng sao cho

3.10. Cc in t b by trong mt h vi khi lng hiu dng rt khc so vi khi lng hiu dng ca cc ro. Ci g xy ra i vi iu kin bin ti d chuyn tip. Xt c v

74

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As

Al

In

x

x

-

1

.

1

2

=

Ln

d

p

.

3

,

0

7

,

0

Ge

Si

.

8

,

0

2

,

0

Ge

Si

24

3

23

10

.

7

,

10

.

7

,

4

=

=

-

V

C

N

m

N

3

21

10

.

2

-

=

m

N

D

.

)

(

)

(

p

F

n

F

bi

E

E

eV

-

=

3

23

10

-

=

m

N

A

.

3

-

m

bi

V

B

W

m

m

p./ppB/ppW/ppm/ppm/pp>

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