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17.04.2012 seminar trions_kochereshko

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17.04.2012 seminar trions_kochereshko

1. 1. ВСЕ О ТРИОНАХ Trions at low electron density limit• 1. Charged exciton-electron complexes (trions)• 2. Singlet and triplet trion states• 3. Modulation doped QWs• 4. Trions in optical spectra• 5. Action of magnetic fields on the trions Trions at high electron density limit• 6. Combined exciton cyclotron resonance• 7. Combined trion cyclotron resonance• 8. Combined exciton electron processes in PL spectra• 9. Trion Zeeman splitting
2. 2. LOW 2DEG DENSITYTwo electrons+one hole states •Trions at weak magnetic fields •Trions at high magnetic fields •Excited states of trion
3. 3. Charged exciton – electron complex (trion) Negatively charged Trion X- Positively charged Trion X+ similar to ion H- Similar to ionized molecule H+ − − X + + + - − Xelectrons holes electron hole
4. 4. Singlet and Triplet trion statesWavefunction for two electrons in the trion Sz = +1 ϕ (1,2) = U (1,2) χ (1,2) Sz = 0 triplet Sz = -1 Spatial part of the wavefunction U nlm = 0 1 2 [ ( ) ( ) ( ) ( )] u1 r1 unlm r2 ± u1 r2 unlm r1 Sz = 0 singlet   −α ( r1 + r2 ) Singlet state + Sz = 0 ∝eTriplet state - Sz = ±1,0Unlm ≠ 0 , if l ≠ 0 one electron is in 1S and the second is in 2P state – dark tripletOr if n ≠ 1 one electron is in 1S, and the second is in а 2S state bright triplet
5. 5. Experimental studies of trions
6. 6. Modulation doped structures 100Å 100Å QW 2DEG I e1 1.8eV 3.0eV 1.6eV 2.8eV hh1 lh1 CdMgTe CdTe CdMgTe ZnMgSSe ZnSe ZnMgSSe2DEG density varied from ne=5*109 см-2 to 9*1011 см-2
7. 7. Optical processes with the trion participation B=0, T=1.6K Trion formation time in undoped doped, ne=5 10 cm 10 -2 ZnSe structures is of the 4.8 meV order of 2 –4 psec Signal intensity (a. u.) Ref. Ref. Excited by UV-lines ε electron trion − Pexc=60 mW X − X Xphoton exciton X PL PL 0 0 2,81 2,82 2,81 2,82 Energy (eV) Energy (eV)
8. 8. Изменение концентрации при подсветке
9. 9. Зависимость энергии связи триона от ширины ямы ZnSe-based QWs 10 PL ZnSe/ZnBeMgSe Refl. ZnSe/ZnBeMgSe ZnSe/ZnMgSSe X binding energy (meV) 8 ZnSe/ZnMgSSe 6 4 - + 2 X 0 0 50 100 150 200 QW width (Å)
10. 10. Сила осциллятора экситонаприходящаяся на элементарнуюячейку равна силе осцилляторатриона на один электрон, такжеКак для связанных экситонов Γ T = Cne 0 Γ 0 X
11. 11. Singlet and TripletTrion states in magnetic fields
12. 12. Singlet trion in magnetic fields + σ 0 1 2 3 4 5 6 7 − B=7.5T, T=1.6K σ 1.0 ZnSe 10 -2 ne=6x10 cm ge=+1.15 0.5 ν=1 Degree of polarization 0.0 − X lh Reflectivity (a. u.) 1.0 10 -2 ne=9x10 cm 0.5 ν=1 Xlh 0.0 4.4 meV 1.0 n =1.5x1011 cm-2 − e X hh 0.5 ν=1 ν=2 Xhh ν=3 0.0 5.5 meV 10 -2 0 1 2 3 4 5 6 7 doped, ne=5 10 cm Magnetic field (T) 0 2,81 2,82 2,83 2,84 Energy (eV)The circular polarization of the trion − −absorption (reflectivity line ) in magnetic fields X hh and X lh resonances appearcan be used to determine electron in opposite circular polarizationsconcentration by pure optical method
13. 13. Triplet trion in high magnetic fields 30T Tt d X-1 σ- Tt d X TsPhotoluminescence 45T d 29.5T Tt X-1 Ts d Tt X-1 25T Ts Ts 0T 1610 1620 1630 1640 1600 1620 1640 Energy energy, meV
14. 14. Singlet and Triplet in high fields 1635 T=1.6K 10 -2 ne=3*10 cm Ts + σ- 1630 σ+ Etripbind = 3 meVEnergy, meV 1625 d- TT X+1 X-1 b- TT 1620 - Ts 1615 1610 0 10 20 30 40 Magnetic field, Т
15. 15. EXCITON-ELECTRON SCATTERING(excited states of a trion in magnetic fields)
16. 16. Exciton – electron scattering Exciton – electron scattering - T=1.6K ε electron detected at σ ExCR1 X (1s,hh) Lg I ExCR2 0Tphoton exciton PL intensity 5T B=5T 1,64 1,66 ExCR1 X (1s,lh) In magnetic fields in QWs the exciton electron scattering leads ExCR2 to the electron transitions PLE between Landau levels - ExCR ne=8x10 cm 10 -2 1,63 1,64 1,65 1,66 1,67 Energy (eV) The scattering leads to high energy tail of the exciton absorption line. In magnetic fields it splits into separate lines because the electron spectrum becomes discrete = excited states of trions in magnetic fields.
17. 17. We can neglect the trion binding energy because Eex >> ωc >> ETr b b e + ph ⇒ Ex + e* 1 3 c ω e + ω = Eexc + ω e c 2 2 The intensity of the ExCR absorption line is comparable with the intensity of the exciton line
18. 18. Combined exciton –cyclotron resonance ExCRThe ExCR line shifts LINEARLY from theexciton resonance to high energies withincrease of magnetic fields me ω ExCR = Nω ec (1 + ) M
19. 19. Combined processes in Dense 2DEGThree electrons+one hole states
20. 20. In the dense 2DEG two-electron processes emerge in the spectra TrCR There are two electrons in the initial state; an incident photon creates an exciton which binds with one of the electrons forming a trion; and the second electron excites on the second Landau level e + e + ph ⇒ Tr + e*1 1 3 ω ec + ω ec + ω = Etr + ω ec2 2 2 1 ω = Etr + ω ec 2
21. 21. Trion Cyclotron Resonance 1,618 10 -2 open symbol - σ − ne=8x10 cm + solid symbol - σ 1,616Line position (eV) 1,614 ExCR2 ExCR1 1.00 meV/T 1,612 X 1,610 TrCR1 0.64 meV/T 1,608 − X 1,606 3 2 1 0 1 2 3 4 5 6 7 8 Magnetic field (T)
22. 22. Line of the TrCR is observable at filling factors > 1.The intensity of the TrCR line is proportional to the second power of the 2DEG density TrCR (a) 11 -2 1×10 cm ExCR Reflectivity 10 -2 8×10 cm Intensity of TrCR-line 10 -2 6×10 cm − + σ X X 0 20 40 60 80 100 120 − T=1.6K 2 20 -4 σ B=2.5T ne (10 cm ) 0 1,605 1,610 Energy (eV) (b) 11 -2 1×10 cm T=1.6K Intensity of TrCR-line 0 10 8×10 cm -2 0 2 4 6 8 10 10 -2 Electron concenctration, ne (10 cm ) 10 6×10 cm -2 ν =1 ν =1 ν =1 0 0 1 2 3 4 5 Magnetic field (T)
23. 23. Surprising Trion stability against free electron screening
24. 24. Экситон исчезает из спектра при относительно малых концентрациях электронов, а трион остается ZnSe/ZnMgSSe 80A CdTe/CdMgTe 80A − 11 -2 ZnSe/ZnMgSSe X 1.2x10 cm − − X X 11 1.2x10 cm -2 X X 8x10 cm 10 -2 − 10 -2 X 6x10 cmReflectivity Reflectivity − 10 -2 X 4x10 cm X 0 X 0 − 10 3x10 cm -2 10 <10 cm -2 X X 0 9 4x10 cm -2 0 0 T=1.6K 0 X B=0T T=1.6K X B=0T 0 1.620 1.625 1.630 0 2.810 2.815 2.820 2.825 Energy (eV) Energy (eV)
25. 25. Сила осциллятора экситона не зависит от плотности 2DEGЗатухание экситонарастет с ростомплотности
26. 26. Спектры поглощения (PLE) как функция концентрации
27. 27. 2.0 Absorption (arbit.un.) 1.5 a 1.0 0.5 0 1605 1610 1615 1620 Energy (meV) 1.5Absorption (arbit.un.) b 1.0 0.5 0 1605 1610 1615 1620 Energy (meV)
28. 28. Trion Zeeman splitting as a function of the electron density
29. 29. The value of the exciton and trion Zeeman splitting? einit + ph → Tr = ( Ex + e fin )Because the initial and the final state of the electron arethe same (the same spin and the same Landau level)we should see only the exciton Zeeman splitting on excitonand on trion line ε electron trion photon exciton
30. 30. Photoluminescence In PL the exciton and trion Zeeman splitting are equal 1,626 1,625 H=0T Energy, eV 10 -2 1,624 ne=4x10 cmPL Intensity, a.u. 1,623 1,622 1,615 1,620 1,625 1,630 Energy, eV 0 1 2 3 4 5 6 7 8 Magnetic Field (T)
31. 31. Exciton and trion Zeeman splitting at high electron concentrations 1,630 1,629 1,628 Exc 1,627 Energy (eV) 1,626 1,625 1,624 1,623 T 1,622 1,621 0 1 2 3 4 5 6 7 8 0,8 0,6 Exc 0,4 Splitting (meV) 0,2 0,0 -0,2 -0,4 -0,6 10 ne=8x10 cm -2 T -0,8 0 1 2 3 4 5 6 7 8 Magnetic field (T)
32. 32. This is possible only in the case if the initial and final spin state of the electron are not the same – we need spin-flip For spin-flip we need spin-orbital interaction. This can be the triplet-singlet splitting of the trion In the initial state the photon creates virtual state of the triplettrion. Because of very fast spin-flip of one of the electrons in the final state we have the singlet trion (already real). This is the process reversal to the ExCR
33. 33. An incident photon creates a virtual trion in the triplet state. This trionproduces a spin-flip with one of the electrons on the first Landau level.As a result, in the final state, we get a trion in the singlet state plus anelectron on the second Landau level with opposite spin. This reaction looks ↑ ↑ ↑ ↓ e + e + ph → Tr + e → Tr + e 1 2 t 1 s 2
34. 34. Фотолюминесценция трионов
35. 35. Спектры ФЛ в зависимости от концентрации электронов Ebex >>EF Ebtr ~EF
36. 36. In heavily doped QW in zero magnetic fields the PL lineis shifted to the low energies from its position in lowdoped structure. The value of this shift is of the order ofFermi energy 1635 PL 1630 Tt 1625 Tt energy, meV X 1620 Ts 1615 Ts − σ 3.7x1 0 cm 11 -2 + σ 1610 − σ 3x1 0 cm 10 -2 SU σ + 1605 0 10 20 30 40 Magnetic field, T
37. 37. В магнитном поле линии триона и экситона «возрождаются» X Τ 1600 1610 1620 1630 1640 энергия, мэВ
38. 38. Combined processes in PL 1650 1635 T=1,6K 11 ne=3.7x10 cm -2 T=1.6K 11 -2 ne=3.7x10 cm 1630 CCR 2ω c 1640 ω c ССR X 1625 (1/2)ω c Tt FL energy, meVenergy, meV 1630 1620 Ts 1620 Ts 1615 − σ ν =2 σ + 1610 ν =3 1610 SU ν =4 0 10 20 30 40 50 0 10 20 30 40 magnetic field, T Magnetic field, T Comparison of PL and reflectivity PL and SU
39. 39. Shake-upShake up процессы SU 11 ne=2x10 cm -2 1/2hωc T=1.6 K B=7.5T 3/2hωc Tr ⇒ ph + e PL Intensity, arb. u. * 5/2hωc 1 Etr = ω + ( N + )ω ec 2 1 ω = Etr − ( N + )ω ec 2 B=0 EF ETr 1,596 1,598 1,600 1,602 1,604 1,606 1,608 1,610 Energy, eV
40. 40. In Emission the initial state is: trion in a ground or excitedstates; ∗ Τr → ph + ethe final state is: an electron above Fermi levelThe energy of the transition is ω = ETr − E ∗ ≤ ETr − EF
41. 41. Linear shift of the trion line in magnetic fields In the final state after the trion recombination a free electron remains. It can appears in the ν =3 ν =4 unoccupied states above Fermi Fermi energy levelEtr = ω + E F ⇒ ω = Etr − E F ν =1 In magnetic fields the Fermi energy LL2 LL1 decreases as ne=const T=1.6K ν =2 1 T=0 K ω ec 2 Magnetic field
42. 42. Theory ± ω ph = Ω c (n ) − E tr ± ∆( B ) − E F ( B ) + αB + βB 2 + E G Figure gives the energy positions of maxima of emitted bands which are described by equation The shape of the states in presented by 1625 the Gaussian form [ ] [ ] eB /( 4π) 1615 exp − E − ω ± ( n ) / 2Γn ( B )  ± 2 2ρ n (E) =  ph  2 2πΓn ( B )   1605 10 30
43. 43. ConclusionsIn 2D structures containing electron gas thescattering effects are enhanced.In the presence of magnetic fields the electronenergy spectrum becomes discreet and thescattering processes revel as combined exciton-electron processes.In such processes we can see directly only theexciton transition but the state of the additionalelectron, which we can not see, reveals only in thefinal result.
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