Luận án Tính chất điện và quang của tạp chất và exciton trong dây giếng lượng tử

Chuong1 HIED UNG BIEN TRlJONG TREN DAy. . K ? GIENGLVdNG TV. .... MOttrongcacbairoandO'Ilgilmtrongv~t1ybandanvad~cbi~trongcac diu trucbandangiamOtchieula svcom~tcuat~pch~tionboa,noth~ hi~nmOtvaitroqUailtrQngtrongcachetalanhi~tdOth~pciingnhu~o ramOtsvdicchchuy~nm~ trongph6quanghQc.Nhieumcgiadilxem xetcactr~g thaivatinhDangluqnglienketcua~pch~trongQWW [13,15,17,29,62,68,70].LeevaSpector[62]lfuldAtitieDdiltinhDang luqnglienketcuamOt~pch~tlo~hydrogend~ttrentn;tccuamOtday hinhtrlfv6iraGthevoh~. HQdilchUngtoduQ'crangDangluqnglienket cuatr~gthaicabanduQ'ckhuechd~leDsov6itfUanghQ'p2,3chi~ukhi thunhobankinhcuaday.Tronggi6ih~ mOtchieu,Dangluqnglienket tieDdenvoh~. Saildo,Bryant[17]dilhoanthi~nmohinhtinhroanbang vi~cxem:xetdayv6iraGthehihlh~ vau.mth~yketquatuO'Ilgphlmv6i ketquacuaLeevaSpector,nghialav6icacdayr~tmanh,cacdi~nri'ro rangoaibi~uhi~nnhucacdi~nri'r3chi~utrongsl;!tacdOngcuaraGthe. Ciingv6ibairoannay,Osorio,DeganivaHipolito[70]dil thl;!Chi~ncho daychi!nh~tv6i tinhch~tb~tdfu1ghuangcuaraGthehUllh~ cuaday. 14 Tuynhien,v6iraothenaykhongchophepchungtatachbientrongvi~c gilriphuangtrlnhSchrodinger,chinhvlly dod6nenkhigilribIDroannay bangphuangphapbienthien,hams6ngthirkhongchuadt;rngnghi~mcua phuangtrlnhSchrodingerchodi~ntUtrongdAy. TrongnhUngDamgandAyban,me)truemghqpduQ'cmare)ngtrong lanhVlJcnaylasvc6m~tcuatrUemgngoai.DieunayduQ'cxemxetdolIng d\lngcuachungtrongcacd\lfigC\lbandAn,d~tbi~tdome)tvaihi~ntuQ'Iig l~thuemgnhuhi~ulIngHallluQ'IlgtU,dichchuy~nStark,cachi~ulIng phatquangc-ijachung...Svanhhuangcuadi~ntruemgngoaitrencacdi~n tU,~pchcfttrongcacQWW [69,76]clingnhucacQW [4,24,25,46,81] duQ'ctinhroanchoDanglUQ'Ilglienk€t, de)dichchuy~nDanglUQ'Ilgva h~sophanctfc.SukumavaNavanthakrishnan[76]dii tinhroande)dich chuy~nDangluqngvah~sophftncvccuame)tdi~ntUtrongme)tQWW vuongraothevoh~. NarayanivaSukuma[69]diinghiencoobIDroan vOisVc6m~tcua~pchcftlo~ihydrogentrongQWW chi!nh~tvo h~ vOidi~ntrUemghuangthfulgg6cvOitl1;lCQWW.Bangphuangphapbien thien,hQdiiurnthefynangluQ'IlglienketgiamtheoDchthu6'cQWW va svtangcuacuemgde)di~ntrUemg.Ngoaifa,ketquatrong[69]concho thcfyh~sophftnctfctangrheaDchthu6'cQWW. Trongchuangnay,chungtoisesird\lngphuangphapTva-Hartreedo BastardvaMarzin[7]duarad~khacph\lcITang~mame)tsocongtrlnh trU6'cdaydiig~pphlritrongvi~cgilriphuangtrlnhSchrodingerd~xacdinh DanglUQ'Ilglienketcua~pchcftrongcacQWW c6tinhbeftdoi XlIng[70] vOitheraoV (x,y) khongth~tachduQ'c.ChungWi sird\lngphuangphap nayd~nghiencooanhhuangcuadi~ntrUemgtren.cacm6hlnhQWW c6 15 ca:-utrUchinhhQckhacMali, Cl;!th~la dayluqngtUbem~tvadayluqng tUchi!nh~traothehUllh::m, 1.1 PhuongphapT1!a-Hartree Xua:-tphattitphuangtrlnhSchrodingerchodaygiengluqngtUvmthegiam OO6tV(x, y) : { n? [ 82 82 ] }- 2m~'8x2+ 8y2 +V(x,y) w(x,y) = EW(X,y). (1.1) ChungtahIll yrang,mQtcachhinhthucphuangtrlnh(1.1)coth~xem 001.1'phuangtrlnhmo18.2 di~ntUtU'angtacthongquathev (x,y) thay chotheCoulomb,vataclingbietrangcacnghi~mcoth~tachcuaphuang trioonaycod::mgW(x,y) =a(x)x(y) duQ'cxayd1fI1gtitnghi~mcuacac phuangtrlnhRartree: { fi2 82 }- 2m*8x2+ J V(x,Y)X2(y)dy a(x) =Exa(x), (1,2) { fi2 82 - 2m'8y2+ f V(x,y)a?(x)dX}X(y) =€yX(Y), (1.3) vmtririeng E= Ex+Ey- J V(x,y)a2(x)x2(y)dxdy. (1.4) 56h::mgcu6iclingtrongphuangtrlnh(1.4)duQ'cduavaod~tranhvi~c t1nh2 IAntUO'rlgtacV(x, y). 16 Trongtruemghqptakh6ngth~conghi~mchinhxaccuacacphuang trlnhHartreetren,taphaisird1]ngphuangphapbi~nthienvakhidochUng tacvcti~uhoaDanglUQ'IlgloanphfuEchukh6ngphaiDanghtQ'Ilgm~t h~tExva Ey. IT6c luQ'IlgTt;ra-Hartreeco th~so sanhvrocacti~pc~ khacnhuphep chi~uphuo'Ilgtrlnh(1.1)trenm~tt~pco sacuachuy~nd~ngtheohu6ng y [6]madu,cgQiIa nghi~mchinhxac : '" . \II(x,y) = L D:n(x)Xn(Y),n (1.5) adfiy,Xn(Y) Ia cacnghi~mcuaphuangtrlnhSchrodingerm~tchieunao do.TrongthlJcti~n,VItaphaidltt6ngtrongphuangmnh(1.5)Denphuang phapnayd~thi~uquakhith~tuangmc2chi~uV (x,y) coth~tachthanh 2 s6h~g U(y) + W(x, y),vaith~giamnh6tW(x, y) nh6hannhieuso vai U(y). Khi do,cachamXn(Y)thichhqpdu,cchQnnhula cacham riengcuaphuangtrlnhchuy~nd~ngm~tchieuvai th~nangU(y). Trong truemghqpdO'Ilgiannhat,khi chidungm~ts6h~g trongphuO'Ilgtrinh (1.5)nghiala w(x,y) = D:l(X)Xl(Y)tmtasethudu,ch~phuangtrlnh: { fi2 82 - 2m' ax2+f W(x,Y)X~(y)dY}0:1(X) =£,0:1(x), (1.6) { fi2 82 }- 2m*8y2+U(y) Xl(Y) =EyXl(Y), (1.7) E=Ex +Ey . (1.8) 17 Tathayrangphuongtrlnh(1.6)tuongtvvmphuongtrlnh(1.2)vmW(x,y) thaychoV(x, y) vaXl(y) thaychoX(y).Tuynhien,trongg~ dUngnay kh6ngcosVphanhoicuanghi~mal (x) trenphuongtrlnh(1,7).Noi each khac,t~pcuahamthirtrongtruemghgpnayh~ ch€ bong~ dungTva- Hartree.Dehow thi~nvand~naytaphailaynhi~uboncaes6h~gtrong phuongtrlnh(1,5). ? 1.2 Anh hulmgcuadi~ntruOngleu caemucDangIUQ'llg trongday luQ'Ilgtit bem~t... Vm phuongphapTva-Hartree,BastardvaMarzin[7]dii tfnhduQ'Ccac mucnangluQ'Ilgcuadi~ntirtrongd~yluQ'Ilgtirb~m~t.Trongdo~ nay, chungt6idiisirdl;lngphuongphapnaydetfnh:inhhuemgcuadi~ntruemg ngoailencacmucnangluQ'Ilgcuadi~ntirtrongd~yluQ'Ilgtirb~m~tvatlr dochungWixacdinhh~s6ph~cvccuadi~ntir. Lx VI +,1V VI VI +,1V ! L, VI Hlnh1.1:TIetdi~nngangcuam'itdaygiengluqngtUb~m~t 18 X6t dayh!Q'Ilgti:rb~m~t(hlnh1.1[7])d~trongmQtdi~ntnrangngoai d~usongsongvOih1;1ey gommQtgiengluQ'Ilgti:r[0,Ly].Theohu6ngtieD euagienglUQ'Ilgti:r(hu6ngy) tabien d~g dlnhraobangeachkhAeben ngoaivling [-Lx/2, Lx/2] 2 v~ehtheVI + ~V [40]. VOieautnienay,raotheV(x,y)cod~g: V(x,y) =ViB[y(y- Ly)]+~VB(y- Ly)B(x2- L;/4) , (1.9) b dayB(x) If hamHeaviside,Vi la theraoeuagiengluQ'Ilgti:rva~V la thengoaigauvaoraothegiuagiengluQ'Ilgtirvan~n. HamiltonianeuamQtdi~ntirtrongdayduOimedQngeuadi~ntnrang ngoaisongsongvOih1;1ey cod~g : li2V2 H = - - +V(x,y)+eF(y- Yo),2m* (1.10) v6i m* la khoiluQ'Ilghi~udvngeuadi~ntirvaF la euangdQeuadi~n truang.Yo . F=Olagiat:ritrungblnheuay trongtr~gthaikh6ng codi~ntruang.Luu yrang,Yo --+Ly/2 khi Lx --+00. Khi co m~teua di~ntruangngoai,caetr~gthaidi~nti:rsonglaucothetont~neueuang dQdi~ntnrangF kh6ngqua16'11.Taco thecocaetr~gthaigialienket neudi~ukien Ii2ql eFq;1« 2m*' (1.11) duQ'ethoa,b doqi I (i = 1,2)laehi~udaid~etrungeuadQgiamtheo 19 exponentialtronghu6'ngy cuahamsongdi~ntlrkhikh6ngcodi~ntTUang [4]. Chungt6ichQnd~g sauchohamsongcuatr~gthaicobanvatr~g thaikichthichdatiti~n: Wn(X,y) = NnWno(x,y)<Pn(x,y) ,n = 1,2 (1.12) Nn 1ahangso chufuJ.hoa. HamWnO(x,y) la nghi~mcuaphuongtrlnh Schrodingerkh~ngcodi~ntTUangngoai: ... { n? [ 82 82 ] }- 2m* 8x2+ 8y2 +V(x,y) Wno(x,y) =EnoWno(x,y). (1.13) '¥nOduQ'c!trynhutfchcacnghi~mcuacacphuongtrlnhTva-Hartree: { 1i2 82 } --~ +~VPl,yB(x2- L;/4) !n(x)=77n,x!n(x),2m*8x (1.14) { 1i2 82 . }. - 2m*8y2+V1B[y(y- Ly)]+~VPn,xB(y- Ly) gl(y) =El,ygl(y), (1.15) bday Pn,x = fB(x2- L;/4)!(x) dx, Pl,y = f B(y- Ly)gi(y)dy, (1.16) Eno = 77n,x+El,y - 6.VPn,xPl,y, . . 20 D~g tuemgminhcua fn (x) vagl(y) duQ'chonhusau: { sin (n'Tr - k2 h )ekl,neX+~) x <- L. /22 . ,n 2 , - x fn(x) = s~n(k2,nX+n;) f...' -Lx/2 <x <Lx/2 s2n(n1l"+ k2 h )e-kl,neX- 2 ) X >L /22 ,n 2 , - x (1.17) { sina:eqlY , y <0 gl(Y) = s~n(k1Y+0:) , 0 <Y <Ly s2n(k1Ly+0:)e-q2ey-Ly), x >Ly (1.18) ... Ciday k1,n,k2,n,k1, q1va q2duQ'cxac d~ bangvi~cgiai lien tieph~ phuongtrlnhkin : 2 2 2m* k1,n+ k2,n = 7..6. V P1,y, 1r Lx k1,n = k2,nCOtg(n2+ k2,n2) , 2 2 2m* k1+ ql = 7 Vi , 222m * q1+q2 = 7(Vl + ..6.VPn,x), k1 k1 k1Ly = 1r- arctg( -) - arctg( -) , q2 q1 (1.19) Svkha~bi~tgiuanghi~mTva-Hartreevanghi~mchinhxacnhohon 1meV chotr?llgthaicabankhikh6ngcodi~ntIUemgngoai[7].cac s6 li~uthvcnghi~mnh~ duQ'cbCiiGn~us[40]sov6iketquatfnhtoantlr phuongphapTva-Hartreecoth~xemnhudQphAntantrongvi~cdocac duli~uthvcnghi~m[7]. D~nghiencooaM huangcuadi~ntIUemgtencacmucnangluqngcua 21 dAyhrQ'Ilgtirb~m~t,chungWidasird\lngthemm~tphuemgphapquen thu~ckhac,v6ihIDbi€n thienlien ti€p madaduQ'cBrum[16]sird\illg d~nghienCUllarmhuemgcuadi~ntruanglennangluQ'Ilglienk€t exciton trongQW vagAD.dAyleunangluQ'Ilglienk€t donortrongQWWchi!nh~ voh~do Narayani[69].cacnanghrQ'Ilglienk€t excitonvanangluQ'Ilg lienk€t donordadl1Q'cxacdinhbangphuemgphapbi€n thientrongluc codinhcacthamsobi€n thiennh~ duQ'ctru6cd6tlrgAD.dUngbi€nthien khac. Doi v6id~ngcuahamsongbi€n thien1>n(x,y), chungtoichQnham thir: 1>n(X,y) =exp[-~n(Y- Yo)], (1.20) madaduQ'csird\lngchoQW bOinhi~umcgia[4,13,16,24].~nla tham sobi€n thienvaphai006hemqid~duytrlm~thamsonggiamtrongrao th€ [4],di~uki~nnaysuyratlrdi~uki~n(1.11).Vi~ctinhroantr!trung blnhcuaHamiltonianEn la rAtdai,chungWichi duara b dAyk€t qua cuoicling: En(~n) fi2 - 2m*~~+ 'TJn,x+ €l,y - ~V { p J1 +P (h+h) . n,x J 1,y~ - J1(h +13) } - eF d I J 21J d~n[IJ], (1.21) v6i l=h+h+h, (1.22) 22 trongdo l-L:1:/2 2h = -00 !n(X) dx, lL:1:/2 212 = !n(X)dx,-L:1:/2 h OO 2 13 = !n(X)dx, . L:1:/2 h oo 2 .. J1 = gl(y)exp{-2{3(Y-Yo)}dy,Ly J = I-: gi(y)exp{-2{3(y- YO)}dy . (1.23) CluingWi dathl;tehi~npheptfnhbienthiend6iv6i {3ndexaed!nhcae muenang1uqngeuadi~ntir En =En({3n)min, (1.24) vah~s6phfulel;teeuad~~ntirduQ'ed!nhnghlanhusail : e ap = - F {('l11Iyl'l11)Fj60- ('l11Iyl'l11)F=O}. (1.25) Tacothesuyfa tITdinhnghlathunguyeneuah~s6phfulcl;teIa [L3]nhu daduQ'esirdl;lngtrong[76].caetaegillkhae[69]dasirdl;lngthunguyen [Faraday.L2]ehoh~s6phfulel;te. De tlnhtminbangs6,chungt6ixettruanghQ'peuadAy1uqngtirb~ m~tGa(ln)As - GaAs [40]v6icaethams6daduQ'esirdl;lng1a: m*= 0 0.06mo,Ly =50A, ~=0.15eVva~V =0.8eV. 23 CacketquabangsochonangluQIlgcuatrcplgthaicabanvaklchthlch thunhatEl va E2 nhu la hamcuacuemgdQdi~ntruemgduQ'cbieuhi~n a a tronghlnh1.2chohill truemghqpLx =300A vaLx=600A. Vill giatri cuacuemgdQdi~ntnremgchotronghlnh1.2,di~uki~nchoboophUC1l1g trlnh(1.11)duQ'cthoa.Goc tfnhnanglUQIlga dAyduQ'chQn13.nang luQIlgtrcplgthaicabancuaQW c6l~pvabang69.1meV.Theoketqua machungt6ithuduQ'ctmcacmucnangluQIlgcuadi~nti:rgifunkhicuemg dQdi~ntruemgtang.Tronghlnh1.3,chungWived6thih~sophAncvc O:prheaLx. O:ptangnhykhiLx tang.Ngoairadesosanh,chungt6icling ... xemxettruanghqpdi~ntfUemghu6ngtheophuC1l1gcua~c x. Nhuco thethaytru6'c,chungWidathuduQ'cO:ptrongtruemghqpnayphl;!thuQc m~ vaostJthayd6icuaLx. 24 ,-.. ;> ~'-" ~ 20 -.------.-----.-.-.------.-.------- -.15 L 10 5 .".""".. """""" """ .~.. -------------------------- ---- 0 -5 0 50 7525 100 F (kV/cm) filnh 1.2:Haimuenangluqngthtlpnhtltnhuhamcuaeuemgd~di~ntrlremg.F. Nang 0 0 luqngtn;mgthaicoban: duemgli~nehoLx =300A, duemg~ehehoLx =600A. 0 Nangluqngkiehthfehdautien: duemg~eh-ehtlmehoLx =300A, duemgehtlmehoo' Lx = 600A. 25 2.0 80 ... "..".."......".."..".. ,/'".. /" ....,,".."..,"..,,"..,".."..."."..,."'",. .".'"."..".,..'" 601.8 ,.--.. ~ '0...... '-" ~ 1.6 40 1.4 20 1.2 0 200 300 400 500 600 LxU) HiOO1.3:H~s6phfulqIc QpOOuhamcuaLx, cuangd~di~ntn!angF =50kV/crn: duangli~nchodi~ntnIangsongsongt:l11cy (thangtrcH)vaduangg~chchodi~ntnIang songsongti-u,cx (thangphai). 26 1.3 T~pchattrongdaygiengluQ1lgtitdumlac dQngcua di~ntruOng Trongdo?llnay,chungt6iclingsirdl;1ngphuongphapTlJa-Hartreedexem xet3.nhuangcuadi~ntrubngngoail~nnanglugngli~nketvah~s6pball clJccua~pchatlo~hydrogentrongQWW chitnh~tvmraothehihlh~';" Chung ta hay xem xet rnQtQWW chu nh~tv6i 1:nfcz, d~ttrongmQt di~ntruemgngoai thAngg6c vm tfl;1cd§.y.T~pchatxem nhu mQtdi~nncb diemd~tmy ytrongQWW.Trongkhu6nkh6cllagandungkh6iluqng ~ . hi~udl;1ng,HamiltoniancuamQtdi~ntitbaaquanh~pchatdugcchonhu sau: h2\72 e2 H =- +V(x,y)+eF(xcosB+ysinB)- - , 1 ' 2m* E r - ro (1.26) G6ccuah~tQadQdugcchQna tfuncuaQWW,r = (x,y,z) varoo= (xo,Yo,0) tuongUngla tQadQcuadi~ntlrva~pchat.Trongphuongtrlnh (1.26),m* la kh6i lugnghi~udl;lngcuadi~ntlr,E13.hangs6di~nm6ifinh cuaQWW va,.]Jla cubngdQdi~ntrubngcohu6'ngt~on~nrilQtg6c()vm trl;lcx cuaQWW.RaotheV(x, y) cod?llgsau: . . . [ a2 a2 b2 ]V(x,y) = Va B(x2- 4) +B(4 - x2)(}(y2- 4) , (1.27) B(x) 13.hamHeaviside,a vab lacackichthu6'cuaQWW. Nghi~mchinhxaccuaphuongtrlnhSchrodingertuongUngvmHamil- tonian(1.26)kh6ngthetlmdugc.Vi v~y,chungt6isirdl;lllgphuongphap 27 bienthiendenh~nghi~mgandungcuabaitmln.Delamhamsongtr~g thaiCCfban,chUngt6ichQnhamd~gdangiansau: w(x,y,z) = Nwo(x,y)<jJ(x,y,z) . (1.28) Hamw0(x,y) langhi~mcuaphuangtrlnhSchrodingerkhikh6ngcodi~n tfUem.gngoaivas6h~g Coulomb: { 11,2 [ 82 82 ] }- 2m*19x2+()y2 +V(x,y) wo(x,y)=Eowo(x,y). (1.29) MQteachhlnhthuc,cothexemphuangtrlnh(1.29)m6tah~2 di~nti:r tuangmeth6ngquatheV(x, y).Vi v~y,wo(x,y) cothelaynhunchcua caenghi~mcuah~phuangtrlnhTga-Hartreesau: { 11,2 82 [ a2 a2 ] }- 2m*8x2+Va B(x2- 4) +B(4 - x2)py !(x) =Ex!(X) , (1.30) { 11,2 82 [ b2 ] }- 2m*8y2+ Va Pl,xB(y2- 4) + P2,x g(y)=Eyg(y), (1.31) v6itri rieng Eo = Ex+Ey- Va[P2,x+Pl,xPy], (1.32) ? d ' Cf 0: 28 b2 Py = !B(y2- 4)g2(y)dy, a2 P1,x = !B(4" - x2)f2(x)dx, a2 P2,x = !B(x2- 4")f2(x) dx. (1.33) H~2 phuongtrlnh(1.30)va (1.31)dientll 2 bai loangi~ngth~mOt chienmade)caDraoth~naylienk~tv6ixacsuat lmh~tronggi~ngth~. conl~i.HamsonggiamOO6tf (x) va9(y) coth~chQnOOusan: ... { cos(k1~)eql(X+~) x <-~2 ' - 2 f(x) = COS(klX) , -~ <x <~ cos(k1~)e-ql(X-I) x >~2 ' - 2 (1.34) 9(y) duqclaytrongd~g tttongt1!v6i f (x), trongdok1duqciliay bOi k2,ql bOiq2vaa bOib. cac thams6k1,k2,ql vaq2duqcxacdinhtU cach~thac(1.30),(1.31),(1.33)vacacdieuki~nbien.N~uchungta~t P1,x= 1vaP2,x= Py - 0,chungtasenh~ duqcnghi~mdiiduqcsir dlfngbOiOsorio[70]OOudiinoia tren.Chungt6ichQnhamthirc/;(x,y,z) chohamsongdumd~g : c/;{x,y,z) = exp[-.\If - TOI]exp[-jJ(xcosB+ysinB)], (1.35) nhunhieumcgillkhac[4,16,24]..:\la thams6bi~nthiend~ctrungcho tttonglacCoulomb,jJ la thams6bi~nthiend~ctnmgcholinhhuOngcua di~ntruemg.Khi dotadedangtinhduqcgiatritrungblnhcuanangluqng tttongangvmHamiltonian(1.26)E (jJ, .:\): 29 = Ed Ey+{>.2+jj2 - 2>.jj[COSII~:+ sin II~:]} [ N2 ( N3 ) N2 - N5 ]- Va P2x +PyNI + PIx 1- NI - NI e2N4 . . Ng ---+eF- E N1 NI ' E({3,A) trongd6 NI =100 dx roo-00 . #.LOO /a/2 / 00 N2 = dx -a/2 -00 1 00 /b/2N3 = dx-00 -b/2 - (1.36) dyj2(X)g2(y)e-2(3(XCOS()+YSin())v(x- XO)2+ (y - YO)2 xKI(2AV(X - XO)2+ (y - YOp, . (1.37) dyj2(X)g2(y)e-2(3(XCOS()+YSin())v(x- xoF + (y - YO)2 XKI(2AV(X - XO)2+ (y - YO)2, (1.38) dyj2(X )g2(y) e-2(3(xcos()+ysin())V(x - XO)2+(y- YoP XKI(2AV(X - XO)2+ (y - YO)2, (1.39) N4 =/00 dx/00. -00 -00 /a/2 1b/2Ns = dx-a/2 b/2 dyj2(X )g2(y) e-2(3(xcos()+ysin()) xKo(2AV(X- xO}2+ (y - YOp, (l.40) dyj2(x )g2(y)e-2(3(xcos()+ysin())V(x - xO)2+ (y - YO)2 XKI(2AV(X - XO)2+ (y - YO)2, (1.41) 30 N6 = foo dxf oo -00 -00 dyf2(X)g2(y)(X - xo)e-213(xcosO+ysinO) xKo(2AV(X- XO)2 +(y - YO)2 , (1.42) N7 = I-:dxi: dyf2(X )g2(y) (y - yo)e-213(xcosO+ysinO) xKo(2AJ(X - XO)2+ (y - YO)2, (1.43) fOO ~rooN8 = -00 dx J-oo dyf2(X)g2(y) e-213(xcosO+ysinO)V(x - XO)2+ (y - YO)2 X (X cos B + y sin B) xK1(2AV(X- xO)2 +(y- YO)2, (1.44) K 0(x) va K 1(x) lfu luQ'tla hamBesselbiend~g b~e0 vab~e1. Chungtaphlrithvehi~nphepbienthientheo/3vaAd~xaedinhnang luQ'I1gtr~gthaieabant~peh~tEimp= E(/3,A)min.NangluQ'I1glienket ~peh~tEbduQ'edinhnghlalahi~ugiuanangluQ'I1gtr~gthaieabandi~n tlrEe -. E(/3rA=O)min(thieu~6h~g Coulombtrong(1.26))vanang luQ'I1gtr~gthaieabaneua~peh~tEimp. Eb =Ee - Eimp. (1.45) H~s6phfuleveeuat~pehfitduQ'edinhnghla[76]: e ap=- F {(wlxcosB+ysinBlw)p#o- (wlxcosB+ysinBIW)p=o}. (1.46) 31 D~thuduqccacketquabangso,chungt{)idfisirdl;lngcacthamso sanchoQW\V GaAs : Va=O.4eV,m* =0.067mova€ =12.53. Trongcaehlnh1.4va1.5,nangluqnglienketEb (lllnh1.4)vah~so phanclJCap(hlnh1.5)cuarn()t~pch~trongrn9tQWWvmd()caorao thehfiuh~ dfiduqcvevaso sanhvmcaeketquacuaQWW v{)h~. ChungWi th~yrangraothehiiuh~ dfi lamgiamnangluqnglienket rn9teachdangk~,d~ebi~ta cackfchthuaedAy006(tlEb ~ 5meVa 0 a =50A). Vm vi~ctangkichthuacQWW,h~sophanelJeclingtamg nhudfiduqc<;jladqi.RaothehUllh~ndfikhuechd~ih~sophanclJCcua ~pch~tlenrn()tcachdangk~. Tronghlnh1.6chungWi trlnhbayh~sophanclJcapnhurn()tham 0 0 cuagoc()chotruanghQ'pQWW cokfchthuaca =100A, b =50A, Xo=Yo=0vaF =200kV/em.H~sophanclJcgiamkhitang()bm VI trongtwanghQ'pnayd()giamnhotla 100nh~tdQctheotrl;lcy maa 0 dokfchthuacQWWla 50A va()=900.R6 rangrangd()caoraothe hUllh~ dfikhuechd~slJph1;1thu()ecuah~sophancvcvaohuOOgdi~n truang. caehlnh1.7va1.8trlnhbaynangluqnglienketEbvah~sophan 0 eve.ap theoV!tri t~peh~tYoehoa =b =100A, () =90°,XQ= 0 va F ~ 100kV/cm.O;red~euaduangeongnangluqnglienkettronghlnh 1.7duqedmdikhicorn~teuadi~ntruang.Vm QWW coraothev{)h~, svdmdi euaeved~la it honsovmQWW coraothehUllh~, di~unay coth~hi~uduqenhusan: med()ngcanITasvdi ehuy~neuadi~ntirv~ meptraiQWW coraothehiluh~ kernhO'IlQWWcoraothev{)h~. Sv di ehuy~neuadi~ntirv~phfatraiQWW (nguqe hi~udi~ntruang)cling 32 gi\ynensvtangeuah~s6phi\nevekhi t~peh~tdi ehuy~nv~pillaphai QWW OOUdiiduQ'ebi~uhi~ntronghlnh1.8. Tiepthea,chUngt{)ixemxetanhhuemgeuatieldi~nkh{)ngvu{)ngeho QWW v6i di~nneheuatieldi~nngangkh{)ngd6i. H'mh1.9bi~uhi~n nangluqnglienketEb IDeokiehthuaea euaQWW ehoa X b=canstva Xo=Yo=O.Khi kh{)ngco di~ntruOng,Eb it thayd6i ehocaeQWW co kiehthuaegfubangOOau.Svthayd6iladangk~khikiehthuaeeuam~t e~ la gfu g~pd{)ikiehthuaeeuae~ eonI~i.V6i s1;teom~teuadi~n truOng,nohu.ydi t1nhd6iXUngvaehochungtam~tqUaIlsatdangehu y: trongkhisveoeuakiehthuae ~ IDeohuangdi~ntruOng(~e y) ~oram~thayd6i000trongEbtill svmar~ngkiehthuaeIDeohuangdo l~iHullgiltmOOanhnangluqnglienketocaethayd6inayxltyraladoxu huangei\nbanggiitaeaeb6ehinhvaoEbgi\ybmhi~uUnggiamOO6tva hu6'ngeuadi~ntrUOng.D6iv6ieaeQWW eokichthuaelan,eved~eua nangluqnglienketacaee~ bangOOaubiOOoedi.H~s6phi\nevetrong hlnh1.10chUngtom~tdangdi~utuongtv.Tuynhien,takh{)ngqUaIlsat th~yeved~trongduOngeongh~s6phi\nevengayeltehoQWW eokieh thuae000.Com~tsvtangOOanheuah~s6phi\nevedosvmar~ngkieh thuaeQWW rheahu6'ngdi~ntrUOngvagiltmeh~ dosveokiehthuae QWW IDeohuangnay. Ket lu~n : Trongehuongnay,bangphuongphapTva-Hartree,chUng t{)idii giltiquyetvfu d~eotinhphuongphaplu~ ehovi~egiaiphuong trlnhSchrodingert ongh~QWW co raothebfitd6ixUng,elfth~la hID m{)hlnhQWW b~m~tvaehitOO~t.Chungt{)idiixemxets1;tl nhhuemg euadi~ntrUOngleucaemuenangluqngtrongdi\ygiengh1qngtirb~m~t 33 vaxacdiM h~s6phancl;Tcuadi~nt:irtrongdayluqngt:irb~m~t.D6iv6i cacQWW chitnh~t,chungt6inghiencli'unangluqnglienketvah~s6 phancl;TCcuam(>tt~pcha:ttrongsl;Tcom~tcuadi~ntruang.Chungt6ifun tha:ychungph\!thu(>cm~ VaGthegiamnh6t,vi tricua~pcha:t,hu6ng cuadi~ntruangvatietdi~nkh6ngvu6ng.Chodennaychuacoba:tleY m(>tth6ngbaanaGv~cacs6li~uthl;Tcnghi~mtrongvi~cdoh~s6phan cl;Tcuat~pcha:ttrongQWW.Vi~cdoh~s6phancl;Tcselam(>tcosaxem xetdangdi~ud(>nghQccuacach~tfutrongQWW. .-I 30 15 " "" "- ....."-'- ..... ..............'- ....... ....... ....... ....... ....... ........ ..... "- "- ........"-" " ..... ........ ........ 25 20;-0. ;> I!) 8'-' .Q ~ 10 5 50 100 150 200 250 300 aU) Hlnh1.4:NangluqnglienketEbnhuhamcuakfchthuaca cuaQWW chitnh~tvm 0 . kfchthuacb=150A, t~pch~tb Xo=Yo=0vacUOngdQdi~ntrUOngF =lOOkV/crn, () =450.DuOngli~nchodo thehiiuh~ Vo=O.4eV, duOng~chchodo thevOh~. 34 ~~£..'" b..... '-" ~ 1.25 A 1.00 0.75 1- 0.50'- 0.25'- ./ ./ ./ ./ ./ ./ ./ /' ./ ./ ./ ./ ./ ./ /' /' /' ./ ./ ./ ..... ..... ......--------- 0 50 150 250 300200100 aCl) Hlnh 1.5:H~86phfulcVcO:pnhuham.cl1aDch thu6'ca, cactham86gi6ngnhuh1nh1.4. 35 0.15 0.03 --....... """'...... ......." ....... """'....... """'....... """........ """"....... - ~12,- ,--.... "8t:.. ~.., b ...... '--" 'd' 0.09 0.06 0 0 2.25. 45 67.5 90 8(degrees) 0 Hinh 1.6:H~s6phfulcl;tcapnhuhamcilag6cegiuadi~ntrUOngvatrI,lcx choa = 100A, 0 b=50A, x.o=Yo=0,vaF =200kV/cm.DuOnglien: raothehiIuh~ (Vo=O.4eV), duOngC;lch: raothev6h~. 36 """" >- CI)s'-'.0 ~ /-- - -........ / ...... / "- / "- / : "-"- "- "- "- "- "- "- "- "- "-"-"- ...... 30 25 15 ° 25 50 20 ,- 10 5 -50 -25 YoU) lfmh1.7:Nangluqn.glienketEbnhuhamcuavi tri ~pchatYo,choXo= 0,a = b= 0 100A, F . 100kV/cmvae=90°.DuOngli~n:raothehiiuh~(Yo=OAeV),duOng g~ch: raothev()h~ 37 ~"\= >:.. ;it; b '-" ~c. 0.22 0.18 50 Hinh 1.8:H~soph:lncl;Ccapnhuhamcua~trftl:lPch~tYo,cacthamsogiongnhutrong hinh1.7. 0.14 0.10 0.06 - - ,.../"./ ./ ../ --./".---..--- ---_..--- 0.02 -50 -25 0 25 YoU) 38 100 200 300 30 15.5 ---------/-- -- 15 ~.5 ---. 14.5 ,......... >- iU 8 '-" p:j' 15 / / i, ~ - - - - - - -:.-:-:-.:::.;-:-:.:-:-:..,.,...,~.~.~ ........... 7.5 0 r 0 100 200 300 400 aU) I-fmh1.9:NangluqnglienketEbnhuhamtheekichthUGCacuaQWWchunh~traathe a hihlh~ Vo- O.4eVchaa x b=canstvaXo=Yo=O.Duemglien: a x b=100A a a a xlOOA vaF =0; duemgg~ch-chaIn: a X b =100A xlOOA. F = 100kV/cmva a a a e = 900;duemg~ch: a x b= 200A x200A vaF = 0;duemgchaIn:a X b= 200A a x200A vaF =100kV/cmvae= 90°.I-fmhbentrang: khuechd~cuaduemg~ch. 39 200 300 400 6.0 0.04 1.5 \ , \ \ , \ \ \ \ \ \ \ \ \ \ \ '\ '\. '\. '\. "'....... '....... """"""' - 0.02 4.sot ~ "8 ~ ;!; b ..... '-'" ~c.. 0 3.0 0 0 100 200 300 400 aU) Hlnh1.10:H~sophaneveCtpnhuhamtheoklehthuaea euaQWWchitnh~tdiothe hituh~ Va=OAeV ehoa x b=canstvaXo=Yo=0,F =100kV/cmvae=90°. 0 0 0 0 DuOnglien: a x b= 100A x100A, duOng~eh: a x b=200A x200A. H'Inhben trong:khueehd~ieuaduOnglien. 40