Ảnh hưởng của phonon giam cầm lên một số hiệu ứng cao tần trong bán dẫn thấp chiều

I HC QUC GIA H NI TRNG I HC KHOA HC T NHIấN - Lấ THI HNG NH HNG CA PHONON GIAM CM LấN MT S HIU NG CAO TN TRONG BN DN THP CHIU LUN N TIN S VT Lí H Ni - 2013 I HC QUC GIA H NI TRNG I HC KHOA HC T NHIấN - Lấ THI HNG NH HNG CA PHONON GIAM CM LấN MT S HIU NG CAO TN TRONG BN DN THP CHIU Chuyờn ngnh: Vt lý lý thuyt v Vt lý toỏn Mó s: 62.44.01.01 LUN N TIN S VT Lí NGI HNG DN KHOA HC GS.TS Nguyn Quang Bỏu PGS.TS Nguyn V Nhõn H Ni, 2013 H Ni - 20 Lời cam đoan Tôi xin cam đoan công trình nghiên cứu riêng Các kết quả, số liệu, đồ thị nêu luận án trung thực chưa công bố công trình khác Hà Nội, tháng 09 năm 2013 Tác giả luận án Lờ Thỏi Hng Lời cảm ơn Tôi xin bày tỏ lòng biết ơn sâu sắc đến GS.TS Nguyễn Quang Báu v PGS.TS Nguyn V Nhõn, hai người thầy hết lòng tận tụy giúp đỡ, hướng dn trình học tập, nghiên cứu hoàn thành luận án Tôi xin chân thành cảm ơn giúp đỡ, hướng dẫn tận tình cỏc Thy cụ b mụn Vt lý lý thuyt Thầy cụ Khoa Vật lý, Trường Đại học Khoa học Tự nhiên-i hc Quc gia H Ni Tôi xin gửi lời cảm ơn đến BGH Trường Đại học Khoa học Tự nhiên-i hc Quc gia H Ni, Phòng Sau Đại học BCN Khoa Vật Lý tạo điều kiện cho hoàn thành luận án Tôi xin gửi lời cảm ơn đến Quỹ phát triển khoa học công nghệ Quốc gia ( ti 103.01-2011.18), ti QG.T.12.01 tài trợ cho việc tham d hi tho, công bố công trình khoa học Tụi xin gi li cm n ti Trng i hc Giỏo dc ni tụi cụng tỏc ó to iu kin cho tụi quỏ trỡnh hc v hon thnh lun ỏn Xin chân thành cảm ơn đến tất người thân, bạn bè đồng nghiệp giúp đỡ, động viên suốt trình nghiên cứu Từ đáy lòng xin gửi lời tri ân sâu sc đến tất người Hà Nội, tháng 09 năm 2013 Tác giả luận án Lờ Thỏi Hng MC LC Danh mc hỡnh v M u Chng Tng quan v s giam cm in t, giam cm phonon bỏn dn thp chiu v phng phỏp phng trỡnh ng lng t 1.1 S giam cm in t v giam cm phonon bỏn dn thp chiu 1.1.1 S giam cm in t v giam cm phonon bỏn dn hai chiu 1.1.2 S giam cm in t v giam cm phonon bỏn dn mt chiu 19 1.2 23 Phng trỡnh ng lng t cho in t lý thuyt hp th phi tuyn súng in t mnh bỏn dn 1.2.1 Hp th súng in t bỏn dn 23 1.2.2 Phng trỡnh ng lng t cho in t v h s hp th phi tuyn súng 26 in t mnh bỏn dn 1.3 Phng trỡnh ng lng t cho phonon lý thuyt tng tỏc tham 29 s v bin i tham s bỏn dn 1.3.1 Cng hng tham s v bin i tham s bỏn dn 29 1.3.2 Phng trỡnh ng lng t cho phonon v biờn trng ngng, h s 30 bin i tham s bỏn dn Chng Lý thuyt hp th phi tuyn súng in t mnh bỏn thp 35 chiu di nh hng ca phonon giam cm 2.1 nh hng ca phonon giam cm lờn s hp th phi tuyn súng in t 36 mnh siờu mng pha 2.2 nh hng ca phonon giam cm lờn s hp th phi tuyn súng in t mnh siờu mng hp phn 52 2.3 nh hng ca phonon giam cm lờn s hp th phi tuyn súng in t 64 mnh h lng t 2.4 Kt lun chng Chng Lý thuyt cng hng tham s v bin i tham s gia phonon 76 78 õm v phonon quang bỏn dn thp chiu di nh hng ca phonon giam cm 3.1 nh hng ca phonon giam cm lờn cng hng tham s v bin i tham 78 s gia phonon õm v phonon quang siờu mng pha 3.2 nh hng ca phonon giam cm lờn cng hng tham s v bin i tham 89 s gia phonon õm v phonon quang dõy lng t hỡnh tr h th Parabol 3.3 Kt lun chng 99 Kt lun 101 Danh mc cỏc cụng trỡnh khoa hc ca tỏc gi liờn quan n lun ỏn 103 Ti liu tham kho 104 Ph lc 116 DANH MC HèNH V Hỡnh 1.1 Mụ hỡnh cu trỳc ca bỏn dn thp chiu 3D, 2D, 1D v 0D Hỡnh 1.2 Gin minh ho sp xp cỏc lp v vựng nng lng khụng gian 12 thc ca hai kiu siờu mng hp phn (a, b) v siờu mng pha bỏn dn loi III-V (c) Hỡnh 1.3 Tng tỏc gia vt cht v súng in t 24 Hỡnh 2.1 Kho sỏt theo Eo v T (phonon giam cm, hp th gn ngng) 48 Hỡnh 2.2 Kho sỏt theo Eo v T (phonon khụng giam cm, hp th gn 48 ngng) Hỡnh 2.3 Kho sỏt theo !! (phonon giam cm, hp th gn ngng) 49 Hỡnh 2.4 Kho sỏt ! theo !! (phonon khụng giam cm, hp th gn ngng) 49 Hỡnh 2.5 Kho sỏt theo Eo, T (phonon giam cm, hp th xa ngng) 49 Hỡnh 2.6 Kho sỏt theo Eo,T (phonon khụng giam cm, hp th xa ngng) 49 Hỡnh 2.7 Kho sỏt theo !! (phonon giam cm, hp th xa ngng) 50 Hỡnh 2.8 Kho sỏt theo !! (khụng giam cm, hp th xa ngng) 50 Hỡnh 2.9 Kho sỏt theo Eo (phonon giam cm, cú t trng) 50 Hỡnh 2.10 S ph thuc ca vo Eo (phonon khụng giam cm, cú t trng) 50 Hỡnh 2.11 Kho sỏt theo !! (phonon giam cm, cú t trng) 51 Hỡnh 2.12 Kho sỏt theo !! (phonon khụng giam cm, cú t trng) 51 Hỡnh 2.13 Kho sỏt theo ! B (phonon giam cm, cú t trng) 52 Hỡnh 2.14 Kho sỏt theo ! B (phonon khụng giam cm, cú t trng) 52 Hỡnh 2.15 Kho sỏt theo Eo v T (phonon giam cm, hp th gn ngng) 59 Hỡnh 2.16 Kho sỏt theo Eo v T (phonon khụng giam, hp th gn 59 ngng) Hỡnh 2.17 Kho sỏt theo !! ( phonon giam cm, hp th gn ngng) 60 Hỡnh 2.18 Kho sỏt theo !! (phonon khụng giam cm, hp th gn 60 ngng) Hỡnh 2.19 Kho sỏt theo Eo v m (phonon giam cm, hp th xa ngng) 60 Hỡnh 2.20 Kho sỏt theo Eo (phonon khụng giam cm, hp th xa ngng) 60 Hỡnh 2.21 Kho sỏt theo !! ( phonon giam cm, hp th xa ngng) 61 Hỡnh 2.22 Kho sỏt theo !! (phonon khụng giam cm, hp th xa 61 ngng) Hỡnh 2.23 Kho sỏt theo dA (phonon giam cm, hp th xa ngng) 61 Hỡnh 2.24 Kho sỏt theo dA (phonon khụng giam cm, hp th xa ngng) 61 Hỡnh 2.25 Kho sỏt theo !! (phonon giam cm, cú t trng) 62 Hỡnh 2.26 Kho sỏt theo !! (phonon khụng giam cm, cú t trng) 62 Hỡnh 2.27 Kho sỏt theo h!B (phonon giam cm, cú t trng) 63 Hỡnh 2.28 Kho sỏt theo h!B (phonon khụng giam cm, cú t trng) 63 Hỡnh 2.29 Kho sỏt theo T v m (phonon giam cm, cú t trng) 63 Hỡnh 2.30 Kho sỏt theo vo T (phonon khụng giam cm, cú t trng) 63 Hỡnh 2.31 Kho sỏt theo Eo v m (phonon giam cm, hp th gn ngng) 71 Hỡnh 2.32 Kho sỏt theo Eo (phonon khụng giam cm, hp th gn ngng) 71 Hỡnh 2.33 Kho sỏt theo T (phonon giam cm hp, th gn ngng) 71 Hỡnh 2.34 Kho sỏt theo T (phonon khụng giam cm, hp th gn ngng) 71 Hỡnh 2.35 Kho sỏt theo !! (phonon giam cm, hp th gn ngng) 72 Hỡnh 2.36 Kho sỏt theo !! (phonon khụng giam cm, hp th gn 72 ngng) Hỡnh 2.37 Kho sỏt theo L v m (phonon giam cm, hp th gn ngng) 72 Hỡnh 2.38 Kho sỏt theo L (phonon khụng giam cm, hp th gn ngng) 72 Hỡnh 2.39 Kho sỏt theo Eo v m (phonon giam cm, hp th xa ngng) 73 Hỡnh 2.40 Kho sỏt theo T v m (phonon giam cm, hp th xa ngng) 73 Hỡnh 2.41 Kho sỏt theo !! (phonon giam cm, hp th xa ngng) 73 Hỡnh 2.42 Kho sỏt theo L v m (phonon giam cm, hp th xa ngng) 73 Hỡnh 2.43 Kho sỏt theo !! (phonon giam cm, cú t trng) 74 Hỡnh 2.44 Kho sỏt theo !! (phonon khụng giam cm, cú t trng 74 Hỡnh 2.45 Kho sỏt theo !! B (phonon giam cm, cú t trng) 75 Hỡnh 2.46 Kho sỏt theo !! B (phonon khụng giam cm, cú t trng) 75 Hỡnh 2.47 Kho sỏt theo L v m (phonon giam cm, cú t trng) 75 Hỡnh 3.1 S ph thuc ca trng ngng vo nhit T 88 r Hỡnh 3.2 S ph thuc ca trng ngng vo vộc t súng q! 88 Hỡnh 3.3 S ph thuc ca h s bin i tham s K1 vo nhit T 89 trng hp khụng tớnh n hiu ng giam cm phonon Hỡnh 3.4 S ph thuc ca h s bin i tham s K1 vo nhit T 89 trng hp tớnh n hiu ng giam cm phonon Hỡnh 3.5 S ph thuc ca trng ngng vo nhit T 97 ! Hỡnh 3.6 S ph thuc ca trng ngng vo vộc t súng q z 97 Hỡnh 3.7 S ph thuc ca h s bin i tham s K1 vo bỏn kớnh R 98 Hỡnh 3.8 S ph thuc ca h s bin i tham s K1 vo nhit T 98 M U t Vic ng dng rng rói cỏc cht bỏn dn in t hc v c bit l s phỏt trin nhanh chúng ca ngnh quang - in t hc t gia nhng nm 60 ó dn n s cn thit hỡnh thnh cỏc phng phỏp to cỏc vt liu bỏn dn mi cú cỏc tớnh cht ỏp ng c nhiu yờu cu khỏc Trong thi gian gn õy, ỏp dng phng phỏp Epitaxy hin i nh Epitaxy chựm phn t MBE (Molecular Beam Epitaxy) [23-25, 42, 48, 49], Epitaxy t cỏc hp cht kim loi hu c MOVPE (Metalorganic Chemical Vapor Deposition) [71], cỏc lp ca hai hay nhiu cht bỏn dn cú cựng cu trỳc cú th ln lt c to ra, tc l thc hin nhiu ln d tip xỳc dng n tinh th Trong cu trỳc trờn, ngoi trng in th tun hon ca cỏc nguyờn t, mng tinh th cũn tn ti mt trng in th ph Trng in th ph ny cng tun hon khụng gian mng nhng vi chu kỡ ln hn rt nhiu so vi chu kỡ thay i th nng ca trng cỏc nguyờn t mng Tựy thuc vo dy ca cỏc lp, chu kỡ ca trng in th ph ln hn t hng chc n hng nghỡn ln so vi chu kỡ ca trng in th tun hon ca cỏc nguyờn t mng vt liu Tu theo trng in th ph m cỏc bỏn dn ny thuc v bỏn dn cu trỳc hai chiu (h lng t, siờu mng hp phn, siờu mng pha tp, mng mng, ), hoc vt liu cú cu trỳc chiu (dõy lng t: hỡnh tr, hỡnh ch nht, ), hoc vt liu cú cu trỳc khụng chiu (chm lng t) Trong cỏc vt liu cú cu trỳc thp chiu, chuyn ng ca cỏc ht ti (in t, l trng, ) b gii hn mnh Ht ti ch cú th chuyn ng t theo hai chiu (h hai chiu, 2D) hoc mt chiu (h mt chiu, 1D), hoc b gii hn theo c chiu (h khụng chiu, 0D) Trong vt liu cú cu trỳc hai chiu thỡ mng tinh th cú th coi nh hai chiu, cỏc ht ti ch cú th chuyn ng t mt phng ca vt liu v b hn ch theo chiu cũn li Chớnh s hn ch v chuyn ng ca in t theo chiu b gii hn, dn n mt trng thỏi ca in t b giỏn on, ph nng lng ca in t khụng liờn tc m cú dng bc thang Trong thc t, ngi ta chia vt liu cú cu trỳc h hai chiu thnh hai loi chớnh, ú l h lng t v siờu mng bỏn GaAs/Ga1-xAlxAs Superlattices, Superlattices & Microstructures 12, pp.463467 [79] Lionel Friedman (1995), Electron-phonon scattering in superlattices, Phys Rev B 32, pp.955961 [80] V L Malevich and I A Utkin (2000) Nonlinear Optical Absorption in a Heavily Doped Degenerate n-GaAs, Semiconductors 34 (8), pp 962-964 [81] Tsuchiya T and Ando T (1993), Electron-phonon interaction in GaAs/AlAs superlattices, Phys Rev B 47 (12), pp 7240-7252 [82] Nguyen Van Thuan, Do Manh Hung, Nguyen Quang Bau (2008), Influence of Magnetic Field on the Nonlinear Absorption coefficient of a Strong electromagnetic Wave by Confined Electrons in Doping Superlattices VNU Journal of Science, Mathematics-Physics 24 (1S), pp 232-235 [83] Yusuf Yakar, Bekir ầakr, Ayhan ệzmen (2010), Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential, Opt Commun 283, pp.1795-1800 [84] L Wendler, R Haupt (1987), Electron-Phonon interaction in Semiconductor Superlattices, Physica status solidi B 143 (2), pp 487510 [85] De Paula, Ana M (1995), Carrier capture processes in semiconductor superlattices due to emission of confined phonons, Journal of Applied Physics 77 (12), pp 6306-6312 [86] Tran, C A (1993), Effect of strain on confined optic phonons of highly strained InAs/InP superlattices, Journal of Applied Physics, Volume: 74 , Issue: , pp 4983 4989 [87] Hess, K (1997), Impurity and phonon scattering in layered structures, Applied Physics Letters 35(7), pp.484 486 [88] Ullrich, B (1989), Quantumconfined subband transitions of a GaAs sawtooth doping superlattice, Applied Physics Letters 54 (12), pp.1133 1135 113 [89] T Dumelow and D R Tilley (1993), Optical properties of semiconductor superlattices in the far infrared, JOSA A 10 (4), pp 633-645 [90] C Colvard, T A Gant, and M V Klein (1985), Folded acoustic and quantized optic phonons in (GaAl)As superlattices, Phys Rev B 31, pp 20802091 [91] Takuma Tsuchiya and Tsuneya Ando (1993), Electron-phonon interaction in GaAs/AlAs superlattices, Phys Rev B 47, pp 72407252 [92] J.-P Cheng (1993), Resonant electronoptical-phonon interactions for impurities in GaAs and GaAs/AlxGa1-xAs quantum wells and superlattices, Phys Rev B 48, pp.1724317254 [93] Dai-Sik Kim, Abdellatif Bouchalkha, J M Jacob, J F Zhou, and J J Song (1992), Confined-to-propagating transition of LO phonons in GaAs/AlxGa1xAs superlattices observed by picosecond Raman scattering, Phys Rev Lett 68, pp.10021005 [94] Akhilesh K Arora, M Rajalakshmi, T R Ravindran, V Sivasubramanian (2007), Raman spectroscopy of optical phonon confinement in nanostructured materials, Journal of Raman Spectroscopy 38 (6), pp.604617 [95] G Armelles, M Recio, A Ruiz, F Briones (1989), Confined optical phonons in GaAs/GaP strained layer superlattices, Solid State Communications 71 (6), pp.431434 [96] N Bannov, V Mitin, M Stroscio (1994), Confined acoustic phonons in a free-standing quantum well and their interaction with electrons, physica status solidi B 183 (1), pp.131142 [97] J Gong, x X Liang, and s L Ban (2006), Confined Lo-phonon assisted tunneling in a parabolic quantum well with double barriers, Journal of applied physics 100 (2), pp 23707- 23713 [98] H Leon, F Comas (1990), Confined-LO-Phonon-Limited Mobility in a Semiconductor Quantum Well, Physica status solidi B , 160 (1), pp.105115 114 [99] J S Bhat, B G Mulimani, S S Kubakaddi (1994), Free Carrier Absorption in Quantum Well Structures Due to Confined and Interface Optical Phonons, Physica status solidi B 182 (1), pp.119131 [100] X Gao, D Botez, and I Knezevic (2008), Phonon confinement and electron transport in GaAs-based quantum cascade structures, Journal of applied physics 103, pp 73101 - 73110 [101] Balandin, Alexander (1998), Effect of phonon confinement on the thermoelectric figure of merit of quantum wells, Journal of Applied Physics 84 (11), pp.6149-6153 [102] P Kinsler, R W Kelsall, and P Harrison (1999), Interface and confined phonons in stepped quantum wells, Physica B 263, pp.507-509 [103] J Poela, k Poela, and v Jucien (2007), Electron scattering by interface polar optical phonons in double barrier heterostructures, Lithuanian journal of physics 47 (1), pp 41-49 [104] H Rỹcker, M Mora-Ramos, F Comas (1990), Magnetopolaron in a Quantum Well LO-Phonon Confinement Effects, Physica status solidi B 160 (1), pp 117-125 [105] Martin Mosko and Karol Kalna (1999), Carrier capture into a GaAs quantum well with a separate confinement region: comment on quantum and classical aspects, Semicond Sci Technol 14 , pp.790796 [106] J Pozela, A Namajunas, K Pozela, V Juciene (1999), Electrons and phonons in quantum wells, Semicond Sci Technol 33 , pp.956-960 [107] J P Suny, H B Tengy, G I Haddady and M A Stroscioz (1998), Electroninterface phonon interaction in multiple quantum well structures, Semicond Sci Technol 13, pp.147151 [108] Augusto M Alcalde and Gerald Weber (1996), Nonparabolicity Effects on Transition Rates Due to Confined Phonons in Quantum Wells, Solid State Communications 96 (10), pp.63-766 115 [109] Bau, N.Q & Trien, H.D (2011), The Nonlinear Absorption of a Strong Electromagnetic Wave in Low-dimensional Systems, Wave Propagation, Intech, pp 461-482 [110] W S Li, Shi-Wei Gu, T C Au-Yeung, Y Y Yeung (1992), Effects of the parabolic potential and confined phonons on the polaron in a quantum wire, Phys Rev B 46, pp 4630-4637 [111] X F Wang, X L Lei (1994), Polar-optic phonons and high-field electron transport in cylindrical GaAs/AlAs quantum wires, Phys Rev B 49, pp 47804789 116 PH LC Phn kho sỏt s P1 Kho sỏt h s hp th phi tuyn h lng t Chng trỡnh tớnh s ca h s hp th theo cng Eo ca súng in t trng hp hp th xa ngng clc;clear all;close all; T=300;E0=linspace(1e17,4e17, 1000); wq=8e16;Xinf=10.9;X0=12.9;n0=1e20;L=100*1e-10; e0=1.6e-19;e=2.07*e0;m0=9.1e-31;m1=0.067*m0;m2=0.15*m0; h1=1.05459e-34;c=3e8;hnu=36.25e-3*1.6e-19;wq0=hnu/h1; k0=1/(pi*36)*1e-9;kB=1.38e-23;nm=2;n1m=2;mm=1;b=1./(kB*T); nn=(e*pi*h1./(m0*kB*T)).^(3/2);% nn=1; C=1.136e10;%hang so tuong tac tinh duoc bang Matlab G0=(4*pi.^2*e^4*n0.*nn.*C./(wq.^3.*c*h1.^2.*b.*m1.*L.*(Xinf)^(1/2))).*(1/X inf-1/X0);mm1=1;BB=0; for m=1:mm1 for n=1:nm for n1=1:n1m lamda0=(2*m1./h1.^2).*((n1.^2-n.^2).*((pi.*h1./L).^2)./(2.*m1)+h1.*(wq+wq0)); B1=(1+((3*e.^2.*E0.^2)./(32.*m1.^2.*wq.^4)).*lamda0).*(lamda0.*sqrt(lamda 0)).*((lamda0+(m.*pi/L).^2).^-1).*(1-exp(h1.*b.*(-wq+wq0))).*exp(b.*n.^2.*((pi.*h1/L).^2)./(2.*m1)); BB=B1.*Imnn(m,n,n1).*Imnn(m,n,n1).*(n~=n1)+BB; end end; end; HS1=G0.*BB; figure(1); plot(E0./1e2,abs(HS1),'b','linewidth',1.5);grid on;hold on; xlabel('Amplitude of EMW (V/cm)');ylabel('Absorption coefficient (1/m)'); title ('In case of confined phonons and far away from its threshold') 117 mm=2;B=0; for m=1:mm for n=1:nm for n1=1:n1m lamda0=(2*m1./h1.^2).*((n1.^2-n.^2).*((pi.*h1./L).^2)./(2.*m1)+h1.*(wq+wq0)); B1=(1+((3*e.^2.*E0.^2)./(32.*m1.^2.*wq.^4)).*lamda0).*(lamda0.*sqrt(lamda 0)).*((lamda0+(m.*pi/L).^2).^-1).*(1-exp(h1.*b.*(-wq+wq0))).*exp(b.*n.^2.*((pi.*h1/L).^2)./(2.*m1)); B=B1.*Imnn(m,n,n1).*Imnn(m,n,n1).*(n~=n1)+B; end end; end; HS=G0.*B; plot(E0,abs(HS),'r','linewidth',1.5); grid on;hold on; gtext('m=1'); gtext('m=2'); Chng trỡnh tớnh s ca h s hp th theo nng lng !! ca súng in t trng hp hp th gn ngng clc;clear all;close all; T=350; E0=3.5e6; wq=linspace(54e12,60e13,1000);Xinf=10.9; X0=12.9;n0=1e20; L=100*1e-10;e0=1.6e-19;e=2.07*e0; m0=9.1e-31;m1=0.067*m0;m2=0.15*m0; h1=1.05459e-34;c=3e8; hnu=36.25e-3*1.6e-19;wq0=hnu/h1; k0=1/(pi*36)*1e-9;kB=1.38e-23; b=1./(kB*T);nn=(e*pi*h1./(m0*kB*T))^(3/2); C=1.136e10;%hang so tuong tac tinh duoc bang Matlab 118 G0=(e^4*n0.*nn.*C./(wq.^3.*c.*L.*h1.^4.*b.^2.*(Xinf)^(1/2))).*(1/Xinf1/X0); B=0; mm=1;nm=10;n1m=10; for m=1:mm for n=1:nm for n1=1:n1m lamda0=(2*m1./h1.^2).*((n1.^2-n.^2).*((pi.*h1./L).^2)./(2.*m1)+h1.*(wq+wq0)); B1=(1+((3*e.^2.*E0.^2)./(8.*m1.*b.*h1.^2.*wq.^4)).*(1+abs(lamda0).*b.*h1.^ 2./(4.*m1))).* exp(-b.*n.^2.*((pi.*h1/L).^2)./(2.*m1)).*exp(b.*h1.^2.*(lamda0+abs(lamda0))./(4.*m1)).*(1-exp(h1.*b.*(-wq+wq0))); B=B1.*Imnn(m,n,n1).*Imnn(m,n,n1).*(n~=n1)+B; end end; end; HS=G0.*B; figure(1); plot(wq.*h1.*1e3./e0,abs(HS),'black','linewidth',1.5); grid on;hold on; xlabel('Energy of EMW h\Omega (meV)');ylabel('Absorption coefficient(1/m)'); title ('In case of confined phonons and close to threshold ') BB=0; mm1=3;nm=10;n1m=10; for m=1:mm1 for n=1:nm for n1=1:n1m lamda0=(2*m1./h1.^2).*((n1.^2-n.^2).*((pi.*h1./L).^2)./(2.*m1)+h1.*(wq+wq0)); 119 B2=(1+((3*e.^2.*E0.^2)./(8.*m1.*b.*h1.^2.*wq.^4)).*(1+abs(lamda0).*b.*h1.^ 2./(4.*m1))).* exp(-b.*n.^2.*((pi.*h1/L).^2)./(2.*m1)).*exp(b.*h1.^2.*(lamda0+abs(lamda0))./(4.*m1)).*(1-exp(h1.*b.*(-wq+wq0))); BB=B2.*Imnn(m,n,n1).*Imnn(m,n,n1).*(n~=n1)+BB; end end; end; HS1=G0.*BB; plot(wq.*h1/e0,abs(HS1),'b','linewidth',1.5); grid on;hold on;gtext('m=1');gtext('m=2'); 2.Chng trỡnh tớnh s s ph thuc ca h s hp th vo nng lng súng in t !! (trng hp cú t trng) clear all;clc;close all E0=5e6;T=300;B=3e9; mm=2;nm=2;n1m=2;Nm=1;N1m=1;Xinf=10.9;X0=12.9; e0=1.60219e-19;m0=9.109389e-31;h1=1.05459e-34; m1=.067*m0;e=2.07*e0;n0=1e23; omega=linspace(3.5e13,1.5e14,300);wq=omega;b=1./(1.3807e-23.*T);c=3e8; hnu=3.625e-4*1.60219e-19;wq0=hnu/h1;k0=(1/36/pi)*1e-9; wqh=e.*B./(c*m1);ac=sqrt(c*h1./(e.*B));N0=1./(b.*hnu);z=wq*h1/e0; L=90e-10; G0=wqh.^2*e^4*n0./(k0*4*pi*wq.^3*L*c*h1*ac.^2*(Xinf)^(1/2).*b)*(1/Xinf1/X0); S1=3*e^2*E0.^2./(16*ac.^2*m1^2*wq.^4); A=0; for n=1:2 for m=1:2 for n1=1:2 for N=0:1 for N1=0:1 if (Imnn5(m,n,n1)~=0)&(Imnn5(m,n,n1)~=inf); 120 A1=(e^2*wq0.*N0./(2*pi*L*h1^2)*(1/Xinf1/X0)).*Imnn5(m,n,n1)*(n~=n1) s=(1+S1.*(N+N1+1)).* (exp(-b.*((N+1/2)*h1*wqh+pi^2*h1^2*n^2/(2*m1*L^2)))- exp(-b.*((N1+1/2)*h1*wqh+pi^2*h1^2*n1^2/(2*m1*L^2)))).* sqrt(A1.*abs(N-N1))./(abs(N-N1)* (h1*wq-h1*wq0+(N-N1)*h1*wqh+pi^2*h1^2*(n^2n1^2)/(2*m1*L^2)).^2+A1.*h1^2) A=A+s.*G0*(n~=n1)*Imnn5(m,n,n1)*Imnn5(m,n,n1)*(n~=n1); end; end; end end end end figure(1);%subplot(2,1,1) plot(z*1e3,abs(A),'k','linewidth',1.5);grid on;hold on title('truong hop phi tuyen') ylabel('Nonlinear absorption coefficient');xlabel('(MeV)'); Chng trỡnh tớnh s s ph thuc ca h s hp th ! vo tn s cyclotron (trng hp phi tuyn) clear all;clc;close all E0=4.5e6;T=300;B=linspace(4.5e8,7.5e9,180); mm=2;nm=2;n1m=2;Nm=1;N1m=1;Xinf=10.9;X0=12.9; e0=1.60219e-19;m0=9.109389e-31;h1=1.05459e-34; m1=.067*m0;e=2.07*e0;n0=1e23; omega=5e13;wq=omega;b=1./(1.3807e-23.*T);c=3e8; hnu=3.625e-4*1.60219e-19;wq0=hnu/h1;k0=(1/36/pi)*1e-9; wqh=e.*B./(c*m1);ac=sqrt(c*h1./(e.*B));N0=1./(b.*hnu);Z=wqh*h1/e0; L=80e-10; 121 G0=wqh.^2*e^4*n0./(k0*4*pi*wq.^3*L*c*h1*ac.^2*(Xinf)^(1/2).*b)*(1/Xinf1/X0); S1=3*e^2*E0.^2./(8*ac.^2*m1^2*wq.^4); A=0; for n=1:nm for m=1:mm for n1=1:n1m for N=0:Nm for N1=0:N1m if (Imnn5(m,n,n1)~=0)&(Imnn5(m,n,n1)~=inf); A1=e^2*wq0.*N0./(2*pi*L*h1^2)*(1/Xinf1/X0).*Imnn5(m,n,n1).*(n~=n1) s=(1+S1.*(N+N1+1)).* (exp(-b.*((N+1/2)*h1*wqh+pi^2*h1^2*n^2/(2*m1*L^2)))- exp(-b.*((N1+1/2)*h1*wqh+pi^2*h1^2*n1^2/(2*m1*L^2)))).* sqrt(A1.*abs(N-N1))./(abs(N-N1)* (h1*wq-h1*wq0+(N-N1)*h1*wqh+pi^2*h1^2*(n^2n1^2)/(2*m1*L^2)).^2+A1*h1^2); A=A+G0.*s.*Imnn5(m,n,n1).*Imnn5(m,n,n1).*(n~=n1);; end end end end end end figure(1);% subplot(2,1,1) plot(Z*1e3,abs(A),'k','linewidth',1.5);grid on title('truong hop phi tuyen') ylabel('Nonlinear absorption coefficient');xlabel('(MeV)'); Chng trỡnh tớnh s s ph thuc ca h s hp th vo rụng h lng t(trng hp phi tuyn) clear all;clc;close all 122 E0=6.75e6;T=300;B=3e9; nm=2;n1m=2;mm=2;Nm=1;N1m=1;Xinf=10.9;X0=12.9; e0=1.60219e-19;m0=9.109389e-31;h1=1.05459e-34; m1=.067*m0;e=2.07*e0;n0=1e23; omega=6.75e13;wq=omega;b=1./(1.3807e-23.*T);c=3e8; hnu=3.625e-4*1.60219e-19;wq0=hnu/h1; k0=(1/36/pi)*1e-9; wqh=e.*B./(c*m1);ac=sqrt(c*h1./(e.*B));N0=1./(b.*hnu);Z=wq*h1/e0; L=linspace(55e-10,100e-10,200); G0=wqh.^2*e^4*n0./(k0*4*pi*wq.^3.*L.*c*h1*ac.^2*(Xinf)^(1/2).*b)*(1/Xinf -1/X0); S1=3*e^2*E0^2/(8*ac^2*m1^2*wq^4); A=0; for n=1:nm for m=1:mm for n1=1:n1m for N=0:Nm for N1=0:N1m if (Imnn5(m,n,n1)~=0)&(Imnn5(m,n,n1)~=inf); A1=e^2*wq0.*N0./(2*pi.*L.*h1^2)*(1/Xinf1/X0).*Imnn5(m,n,n1).*(n~=n1) s=(1+S1.*(N+N1+1)).* (exp(-b.*((N+1/2)*h1*wqh+pi^2*h1^2*n^2./(2*m1.*L.^2)))- exp(-b.*((N1+1/2)*h1*wqh+pi^2*h1^2*n1^2./(2*m1.*L.^2)))).* sqrt(A1.*abs(N-N1))./(abs(N-N1)* (h1*wq-h1*wq0+(N-N1)*h1*wqh+pi^2*h1^2*(n^2n1^2)./(2*m1.*L.^2)).^2+A1*h1^2); A=A+G0.*s.*Imnn5(m,n,n1).*Imnn5(m,n,n1).*(n~=n1) end end end end 123 end end figure(1);%subplot(2,1,1) plot(L,abs(A),'k','linewidth',1.5);grid on;hold on title('truong hop phi tuyen') ylabel('Nonlinear absorption coefficient');xlabel('(m)'); PL2 Tớnh s v v th kt qu chng Kho sỏt s ph thuc ca Eth vo vector súng q cu phonon clcclear all; n1=1;n2=0;l1=1;l2=1; R=7*10^-9;L=100*10^-9; w00=0.036250*1.6*10^(-19)/(1.05457*10^(-34));% quang w0=3.01265*10^13;% tan so hieu dung h=1.05457*10^(-34);v=5370; kb=1.38065*10^(-23);e=1.602177*10^(-19); t=72;omega=200*10^(12); m=0.067*9.109389*10^(-31);b=1/(kb*t); %ham w syms q r m1 m2; w=v*sqrt(q^2+(m1*pi/R)^2+(m2*pi/R)^2); %ham A a=h^2*q^2/(2*m)+h*w0*(2*n2+l2+1)-h*w0*(2*n1+l1+1)+h*r; %ham gama sh1=m^(3/2)/(2*sqrt(2*pi*b)*h^2*q); sh2=(1-exp(b*h*r)); thu1=-b*w0*h*(2*n2+l2+1); a2=a*a; thu2=b*m*a2/(2*q^2*h^2); sh3=exp(thu1-thu2); gama=sh1*sh2*sh3; theta=L*m/(2*pi*h^3*b)*(1/a)*sqrt(2*m*pi/b)*(exp(-b*w0*h*(2*n2+l2+1)exp(-b*w0*h*(2*n2+l2+1)-b*w0*h*(2*n1+l1+1)))); 124 %ham Eth Eth1=2*m*omega^2/(e*h*q) Eth2=subs(gama,r,w)*subs(gama,r,w00) Eth3=(subs(theta,r,w)-subs(theta,r,w-omega))^2 Eth4=(subs(gama,r,w)-subs(gama,r,w-omega))^2; Eth=Eth1*sqrt(Eth2/(Eth3+Eth4)); lll=5; ll=0:1:lll; u=logspace(7.5,9.5,200); for i=1:lll+1 g(i)=subs(Eth,m1,1); g(i)=subs(g(i),m2,ll(i)); end for i=1:lll+1 giatri(i,:)=subs(g(i),q,u); end t=u(27:117); x=giatri(5,25:115); figure(1) plot(t,x,'k','linewidth',2.5);legend('Eth(q) giam cam');hold on;title('do thi Eth(q)'); xlabel('q(1/m)');ylabel('Eth(V/m)'); Eth=subs(Eth,m1,0); Eth=subs(Eth,m2,0); u=logspace(7.5,9.5,200); for i=1:200 giatri(i,:)=subs(Eth,q,u); end figure(1) t=u(25:115); x=giatri(5,25:115); plot(t,x,'k');grid on;hold on;axis([5*10^7 45*10^7 3.5*10^8]); 125 legend('Eth(q) phonon giam cam','Eth(q) phonon khong giam cam'); % Chng trỡnh v th K1 vo T function [I1,K1]=hs(j1,j2,T) syms x vs=5370; % van toc song am; e=1.602177e-19; Kb=1.38065e-23;m1=0.067*9.109389e-31; r0=5230;% mat tinh the; h=1.05459*1e-34; q=4.364*1e7;f0=1e23; X1=10.9;X2=12.9; ome0= 1e12;si=13.5*e;w0=5.507e13;beta=1./(Kb*T);k0=9e9; R=5e-8;L=100e-9;V=pi.*L.*R.^2;E0=1e6;om=25e13; lamda=i*e*q*E0/(m1*om); a0=sqrt(h./(m1.*ome0)); LG=[-1 2*x-4 (-3).*x.^2+18.*x-18 4.*x.^3-48.*x.^2+144*x-96;-3.*x.^2+18.*x-18 -6.*x+18 12.*x.^2-96.*x+144; -3.*x.^2+18.*x-18 -6.*x+18 -6 24.*x-96; 4.*x.^348.*x.^2+144*x-96 12.*x.^2-96.*x+144 24.*x-96 24] gama0=0; G=0; for l1=1:4 for n1=1:4 for l2=1:4 for n2=1:4 hsong1=1/sqrt(L)*sqrt(2*factorial(n1)/factorial(n1+abs(l1)))*exp(x^2/(2*a0^2))*(x/a0)^abs(l1)*LG(n1,l1)/a0; hsong2=1/sqrt(L)*sqrt(2*factorial(n2)/factorial(n2+abs(l2)))*exp(x^2/(2*a0^2))*(x/a0)^abs(l2)*LG(n2,l2)/a0; f=hsong1*hsong2*exp(i*q*x); I=2/R*int(f,0,R); I1=double(I); Cq=sqrt(si^2/(2*r0*vs*V)*sqrt(q^2+(j1*pi/R)^2+(j2*pi/R)^2)); Dq=sqrt(w0*e^2/(2*V*k0)*(1/X1-1/X2)*1/(q^2+(j1*pi/R)^2+(j2*pi/R)^2)); H=h*ome0*(2*n1+l1-2*n2-l2)+h^2*q^2/(2*m1)+h*w0; 126 A=1/(h*ome0*(2*n1+l1-2*n2l2)+h^2*q^2/(2*m1)+h*w0)*L*f0/(2*pi)*sqrt(2*m1*pi./(h^2*beta)).*exp(beta*ome0*h*(2*n2+abs(l2)+1)).*(exp(-beta*h*ome0*(2*n1+abs(l1)-2*n2abs(l2)))-1); B=L*m1/(q*h^3)*f0*exp(-beta*m1*H^2/(2*q^2*h^2)beta*h*ome0*(2*n2+l2+1)).*exp(h*beta*w0/2).*sinh(h*beta*w0/2); G=G+(-1)/h*lamda/om*abs(I1)^2*Cq*Dq*A; gama0=gama0-abs(Dq*I1)^2*B; end end end end gama0=gama0/h; K1=abs(G./(2*gama0)); 127 [...]... s gia phonon õm v phonon quang trong siờu mng pha tp [45, 50], trong h lng t [39, 40] cng ó c nghiờn cu bng phng phỏp phng trỡnh ng lng t cho phonon Tuy nhiờn trong cỏc nghiờn cu v hiu ng cao tn trong bỏn dn thp chiu, cỏc tỏc gi cha quan tõm n nh hng ca phonon giam cm (ch xột phonon khi) Trong nhng nghiờn cu lý thuyt v thc nghim gn õy, ó cú rt nhiu cụng b quc t ó ch ra nh hng rừ nột ca phonon giam cm... ca chỳng di chuyn i trong c hai cht liu t di tn 0 n tn s cao nht ca cht liu mm hn trong ngha co dón i vi phonon quang, chỳng to ra cỏc vựng hp vi tõm im gn 280cm-1 trong GaAs v 380cm-1 trong AlAs khong mt tn s tng ng mode quang trong GaAs, khụng tn ti mode truyn trong AlAs Do vy phi xut hin hiu ng lng t húa vi phonon 1.1.1 S giam cm in t v giam cm phonon trong bỏn dn hai chiu Trong h bỏn dn hai chiu,... ca lun ỏn, chỳng tụi tp trung vo nghiờn cu: 5 nh hng ca phonon giam cm lờn s hp th phi tuyn súng in t mnh bi in t giam cm c chỳng tụi nghiờn cu trong siờu mng v h lng t trong c hai trng hp cú mt t trng v vng mt t trng ngoi, vi tng tỏc in t giam cm phonon quang giam cm l ch yu nh hng ca phonon giam cm lờn cng hng v bin i tham s gia phonon õm v phonon quang c chỳng tụi nghiờn cu vi siờu mng pha tp v... lng t khi cha k nh hng ca phonon giam cm thy rừ nh hng ca phonon giam cm Chng 3, Dnh cho vic nghiờn cu nh hng ca phonon giam cm lờn cng hng tham s v bin i tham s gia phonon õm v phonon quang trong bỏn dn thp chiu Chỳng tụi tớnh toỏn thu c biu thc gii tớch ca biờn trng ngng v h s bin i tham s trong siờu mng pha tp v dõy lng t hỡnh tr th Parabol thy rừ nh hng ca phonon giam cm, chỳng tụi ó kho sỏt... bỏo trong tuyn tp hi ngh khoa hc quc t Progress in Electromagnetics Research Symposium v 01 bỏo cỏo hi ngh Vt lý lý thuyt ton quc ln th 37 7 CHNG 1 TNG QUAN V S GIAM CM IN T, GIAM CM PHONON TRONG BN DN THP CHIU V PHNG PHP PHNG TRèNH NG LNG T 1.1 S giam cm in t v giam cm phonon trong bỏn dn thp chiu Trong cỏc h vt liu thp chiu (hỡnh 1.1), ú chuyn ng ca in t trong h b gii hn theo mt s chiu xỏc nh trong. .. trong h thp chiu C th trong siờu mng l cỏc cụng trỡnh [32, 84-95], trong h lng t l [40, 96-108] T nhng phõn tớch trờn, vi mc ớch hon thin nghiờn cu lý thuyt v hiu ng cao tn trong bỏn dn thp chiu, chỳng tụi la chn ti nghiờn cu nh hng ca phonon giam cm lờn mt s hiu ng cao tn trong bỏn dn thp chiu 2 Mc ớch v nhim v nghiờn cu Mc ớch ca lun ỏn l nghiờn cu nh hng ca phonon giam cm lờn hai 4 loi hiu ng cao. .. bi in t trong bỏn dn khi Trong mc 1.3, chỳng tụi trỡnh by v bi toỏn cng hng v bin i tham s gia phonon õm v phonon quang; phng trỡnh ng lng t cho phonon t ú xõy dng phng trỡnh tỏn sc, iu kin cng hng, biu thc trng ngng, h s bin i tham s gia phonon õm v phonon quang trong bỏn dn khi Chng 2, Nghiờn cu nh hng ca phonon giam cm lờn s hp th phi tuyn súng in t mnh bi in t giam cm trong bỏn dn thp chiu Chỳng... c trong quỏ trỡnh nghiờn cu ti nh hng ca phonon giam cm lờn mt s hiu ng cao tn trong bỏn dn thp chiu, c b cc nh sau: ngoi phn m u, kt lun, ti liu tham kho v ph lc Lun ỏn cú 3 chng, 11 mc Trong ú cú 3 hỡnh v, 55 th v 111 ti liu tham kho, tng cng cú 102 trang Chng 1, Gii thiu tng quan v s giam cm ca in t, giam cm phonon trong h bỏn dn thp chiu v Phng phỏp phng trỡnh ng lng t Mc 1.1, trỡnh by v s giam. .. k trờn, chỳng tụi c bit chỳ ý ti nh hng ca phonon giam cm lờn hiu ng cao tn trong cỏc h bỏn dn thp chiu (siờu mng, h lng t, dõy lng t) Hiu ng cao tn ó c nghiờn cu trong bỏn dn khi v c trong mt s loi bỏn dn thp chiu, bng nhiu phng phỏp khỏc nhau C th, bi toỏn hp th phi tuyn súng in t mnh bi in t giam cm trong siờu mng hp phn [28], siờu mng pha tp [60, 82], trong h lng t [61] ó c nghiờn cu bng phng phỏp... hng gia phonon õm v phonon quang trong bỏn dn thp chiu t c mc ớch ú, chỳng tụi thc hin cỏc nhim v sau: Th nht, thit lp biu thc gii tớch cho h s hp th phi tuyn súng in t mnh bi in t giam cm trong bỏn dn thp chiu cho c hai trng hp vng mt v cú mt t trng ngoi, khi xột n nh hng ca phonon giam cm Th hai, thit lp biu thc gii tớch cho biờn trng ngng v h s bin i tham s gia phonon õm v phonon quang trong h ... Chng Tng quan v s giam cm in t, giam cm phonon bỏn dn thp chiu v phng phỏp phng trỡnh ng lng t 1.1 S giam cm in t v giam cm phonon bỏn dn thp chiu 1.1.1 S giam cm in t v giam cm phonon bỏn dn hai... phonon giam cm 3.1 nh hng ca phonon giam cm lờn cng hng tham s v bin i tham 78 s gia phonon õm v phonon quang siờu mng pha 3.2 nh hng ca phonon giam cm lờn cng hng tham s v bin i tham 89 s gia phonon. .. t cha k nh hng ca phonon giam cm thy rừ nh hng ca phonon giam cm Chng 3, Dnh cho vic nghiờn cu nh hng ca phonon giam cm lờn cng hng tham s v bin i tham s gia phonon õm v phonon quang bỏn dn