l½ thuyt exciton v  biexciton loi hai trong h»‡ hai ch¥m l°»£ng t»­ v 

VIN HN LM KHOA HC V CNG NGH VIT NAM

VIN VT L

V TH HOA

L THUYT EXCITON V BIEXCITON

LOI HAI TRONG H HAI CHM LNG

T V LP KP GRAPHENE

Chuyn ngnh: Vt l l thuyt v Vt l ton M s chuyn ngnh: 62 44 01 03

TM TT LUN N TIN S VT L

H Ni 2014

Cng trnh c hon thnh ti: Vin Vt l - Vin Hn lm Khoa hc v Cng ngh Vit Nam

NGI HNG DN KHOA HC:

1. GS. TSKH. Nguyn i Vit

2. TS. Ng Vn Thanh

Phn bin 1: GS. TS. Nguyn Ton Thng, Vin Vt l-Vin Hn lm KH&CN Vit Nam

Phn bin 2: GS. TS. Nguyn Quang Bu, i hc Khoa hc T nhin H Ni

Phn bin 3: GS. TS. V Vn Hng, Nh xut bn Gio dc Vit Nam

Lun n s c bo v trc hi ng nh gi lun n cp Vin hp ti: . vo lc gi . ngy .. thng ..... nm.

C th tm hiu lun n ti:

- Th vin Quc gia

- Th vin Vin Vt l

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M U I. L DO CHN TI My tnh in t c th c xem l mt trong nhng pht

minh quan trng nht ca th k 20. Vi s ra i ca thit b ny, con ngi lm vic hiu qu hn, t c nhiu thnh tu khoa hc ng k v lin lc vi nhau mt cch d dng hn. Tuy nhin, my tnh in t cn tn ti nhng hn ch nh tc x l thng tin chm, cho kt qu tnh ton vi sai s ln. c bit i vi cc bi ton chuyn su nh thin vn hc, y hc, sinh hc, ton hc, v.v, my tnh in t khng th gii c hoc nu c phi mt hng trm nm.

Trong bi cnh , my tnh lng t ha hn l mt cuc cch mng bng n trong lnh vc cng ngh thng tin ca th k 21. Mt thit b hon ho khc phc c nhng hn ch nu trn ca my tnh in t v a con ngi n vi mt k nguyn mi v khm ph th gii t nhin.

Hai m hnh my tnh lng t ang thu ht s ch hin nay l my tnh lng t spin v my tnh lng t quang [3, 54, 64, 98, 99, 100, 101]. M hnh my tnh lng t quang s dng 2 exction nm trong 2 chm lng t hay trong cc lp graphene l mt trong nhng m hnh c nhiu ha hn nht. i lng quan trng nht ca m hnh my tnh lng t quang, quyt nh ch v cht lng lm vic ca my l thng s tng tc Frster c trng cho s vng mc lng t gia hai exciton. Trong m hnh ny thc cht l s dng biexciton loi 2 (hay cn gi l biexciton xin). y l mt t hp 4 ht gm hai in t v hai l trng khng nm trong cng khng gian pha, c hnh thnh do qu trnh tng tc gia hai exciton loi 1 (exciton thng) khng c cng khng gian pha, hoc tng tc gia hai exciton loi 2, hoc tng tc gia mt exciton loi 1 v mt exciton loi 2.

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Mt s kt qu nghin cu nghin cu v vi loi exciton loi 2 nh: interface exciton, exciton trong chm lng t bn dn Silic (xin theo khng gian ), exciton trong chm lng t bn dn thng (nhng xin theo khng gian r)... c trnh by trong cc cng trnh [41, 73, 103, 76, 66, 67, 68, 72, 70, 71], nhng hu nh cha c nhiu cc nghin cu v biexciton loi 2 [42, 64].

cng chnh l l do chng ti chn ti nghin cu: L thuyt exciton v biexciton loi hai trong h hai chm

lng t v lp kp graphene II. MC CH CA LUN N

Nghin cu nng lng v mt s thng s vt l khc ca

exciton loi 2 v biexciton loi 2 trong h hai chm lng t v h lp

kp graphene. T , xem xt mt s qu trnh vt l c s tham gia

ca exciton loi 2 v biexciton loi 2, kh nng ng dng cc m hnh

ny trong ch to my tnh lng t quang, linh kin quang - in t

nan v cc thit b da trn cu trc ca graphene.

III. NHIM V NGHIN CU - i cng v tng quan v cc h thp chiu v cc h c cu

trc nan, exciton v biexciton. - Nghin cu nng lng ca exciton loi 2 v biexciton loi 2. - So snh kt qu nghin cu c vi cc kt qu ca cc tc

gi khc. - Kh nng ng dng ca kt qu nghin cu trong ch to my

tnh lng t quang, linh kin quang - in t nan, cc thit b da trn cu trc ca graphene. IV. PHNG PHP NGHIN CU

- Phng php nghin cu l lun: Tm hiu cc ti liu (sch v tp ch chuyn ngnh) trong v ngoi nc v cc vn c lin

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quan n ti. Trn c s phn tch, khi qut tng hp thnh c s l lun lm cng c nghin cu ti.

- Cc phng php s dng trong vic gii cc bi ton ca lun n l phng php bin thin hng s, phng php nhiu lon, cc phng php khc ca vt l l thuyt hin i, v ng thi vi vic kt hp tnh ton s minh ha trn my tnh s dng phn mm Mathematica. V. B CC CA LUN N

Phn m u chng ti trnh by l do chn ti, mc tiu nghin cu, nhim v nghin cu, cc phng php nghin cu v s dng trong lun n.

Chng 1 trnh by v cu trc h thp chiu v hnh vi ca in t trong h thp chiu, i cng v exciton v biexciton, s hnh thnh exciton v biexciton trong cc h thp chiu, phn loi exciton v biexciton theo khng gian ta v khng gian pha, mt s kt qu nghin cu trn th gii v exciton v biexciton loi 1 trong cc h thp chiu. Trong chng ny, chng ti xut m hnh biexciton trong bn dn khi thng thng vi th tng tc Morse v nghin cu nng lng ca gi ht ny.

Chng 2 trnh by khi nim chm lng t v cu trc vng nng lng ca chm lng t, cc m hnh my tnh lng t ang thu ht s quan tm hin nay, xut m hnh exciton loi 2 (exciton xin) v biexciton loi 2 (biexciton xin) trong hai chm lng t, t nghin cu nng lng ca gi ht ny trong cc m hnh trn.

Chng 3 trnh by khi nim v graphene v cu trc vng nng lng trong graphene, xut m hnh exciton loi 2 trong lp kp graphene v m hnh biexciton loi 2 trn cc lp graphene, nghin cu nng lng ca exciton loi 2 v biexciton loi 2 trong graphene.

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Phn kt lun chng ti trnh by tm lc li nhng kt qu t c v nhng ng gp mi ca lun n, ng thi a ra hng nghin cu tip theo ca lun n.

Chng 1. TNG QUAN V H THP CHIU

1.1. KHI NIM H THP CHIU Cu trc h thp chiu hnh thnh khi ta hn ch khng gian

thnh mt mt phng, mt ng thng hay mt im, tc l hn ch chuyn ng ca cc in t theo t nht l mt hng trong phm vi khong cch c bc sng Debroglie ca n (c nm). 1.2. IN T TRONG H THP CHIU 1.2.1. Ht chuyn ng trong h th vung gc

Hm sng ca ht:

vi n l, (1.2.1)

vi n chn, (1.2.2)

v nng lng ca ht:

, (1.2.3)

vi l s lng t chnh. 1.2.2. in t trong h hai chiu

Hm sng v nng lng ht: (1.2.4)

. (1.2.5)

1.2.3. in t trong h mt chiu Hm sng v nng lng ton phn: (1.2.6)

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(1.2.7)

1.2.4. in t trong h khng chiu Nng lng ca in t l:

(1.2.8)

Hm sng:

(1.2.9)

1.3. I CNG V EXCITON V BIEXCITON 1.3.1. Exciton Exciton loi 1 Exciton loi 2

* Exciton loi 1 (exciton thng, exciton truyn thng): c hnh thnh bi lin kt cp in t v l trng, trong khng gian pha ca in t hon ton trng vi khng gian pha

ca l trng, y l xung lng v to ca in t, l xung lng v to ca l trng [74, 75, 97].

* Exciton loi 2 (exciton xin): gi ht ny c hnh thnh cng t lin kt cp ca in t v l trng. Tuy nhin, khng gian pha ca in t v l trng khng hon ton trng nhau [73, 103, 76, 66, 67, 68, 72, 70, 71]. 1.3.2. Biexciton Biexciton loi 1 Biexciton loi 2

* Biexciton loi 1 (biexciton thng - truyn thng): l loi gi ht c hnh thnh do s lin kt cp gia hai exciton loi 1 (exciton thng) c cng khng gian pha.

* Biexciton loi 2 (biexciton xin): Gi ht ny c hnh thnh c th l do qu trnh tng tc gia hai exciton loi 1 (exciton thng) khng c cng khng gian pha, hoc gia hai exciton loi 2, hoc gia mt exciton loi 1 v mt exciton loi 2.

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1.4. EXCITON LOI 1 TRONG CC H THP CHIU 1.4.1. Phng trnh Wannier

. (1.4.1)

Phng trnh (1.4.1) c gi l phng trnh Wannier [37]. 1.4.2. Trng hp h hai chiu v ba chiu

Nng lng lin kt exciton trong h 3D:

vi , (1.4.2)

Nng lng lin kt ca exciton trong h 2D:

vi (1.4.3)

1.4.3. Trng hp h mt chiu Nng lng lin kt ca exciton trong h 1D: , (1.4.4)

i vi cc th giam cm thc nh dy GaAs/GaAlAs, c th bng . 1.4.4. Trng hp h khng chiu

Nng lng ca exciton khi tnh n tng tc gia hai ht [8]:

. (1.4.5)

S hng th hai trong biu thc (1.4.5) chnh l nng lng lin kt ca exciton trong QD GS:

. (1.4.6)

V , do , bn knh chm cng gim th nng lng lin kt cng tng. Nng lng ny ln hn rt nhiu so vi nng lng lin kt ca exciton GS trong h 3D ( ), 2D ( ), v 1D ( ).

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1.5. BIEXCITON LOI 1 TRONG CC H THP CHIU 1.5.1. Biexciton trong ging lng t

. (1.5.1)

Gi tr ca c c trong trng hp 2D ph hp vi gi tr thc nghim [11,29] l khong [89]. 1.5.2. Biexciton trong ng nan

Nng lng lin kt ca biexciton t l nghch theo :

. (1.5.2)

1.5.3. Biexciton trong chm lng t Nng lng lin kt ca biexciton c xc nh:

. (1.5.3)

Khi t s khi lng v t s hng s in mi th nng lng lin kt phn t ln hn nng lng Rydberg

exciton khi. Hiu ng phn cc in mi cng ng vai tr quan trng, n lm cho nng lng lin kt khi (c phn cc) tng hai ln so vi khi (khng phn cc).

Chng 2. EXCITON V BIEXCITON LOI 2 TRONG H HAI CHM LNG T

2.1. MY TNH LNG T Hai loi my tnh lng t c trin vng nht ca cng ngh

nan l my tnh lng t s dng spin v my tnh lng t quang trong h hai exciton lin kt (c entanglement). 2.1.1. M hnh my tnh lng t spin

Mu thit k my tnh lng t spin t cp QD da trn cng ngh Si, Ge v GaAs v ang l nn tng ca cng nghip in t - vin thng hin i [33, 34, 47]. M hnh my tnh lng t ny cho php s dng spin tht ca in t. Do tng tc Coulomb v

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nguyn l loi tr Pauli, trng thi c s c nng lng thp nht ca cp in t lin kt l Singlet c vng vu lng t cao. 2.1.2. M hnh my tnh lng t quang

M hnh my tnh lng t quang s dng 2 exciton nm trong 2 QD hay cc lp graphene l m hnh c nhiu ha hn nht. i lng quan trng nht ca m hnh my tnh lng t quang, quyt nh ch v cht lng lm vic ca my l thng s tng tc Frster c trng cho s vng mc lng t gia hai exciton. 2.1.3. Biexciton trong bn dn khi

* Th Morse i vi phn t exciton (biexciton) , (2.1.1)

y l khong cch trung bnh gia hai exciton, l nng lng phn li, l thng s Morse c dng iu chnh rng ca ging th. t Rydberg exciton v bn knh Bohr ca exciton

l n v i vi chiu di v nng lng, chng ta c th vit (2.1.1) di dng khng th nguyn nh sau:

, (2.1.2) vi , v

. Nng lng ca phn t exciton (biexciton):

. (2.1.3)

* So snh vi thc nghim v cc l thuyt khc

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Hnh 2.1. Th tng tc exciton-exciton. ng khng lin nt v ng

chm ln lt l kt qu ca Heitler v London [40] v Brinkman[15].

Th hiu dng Morse i vi tng tc exciton-exciton trong b