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28 2. Resonant tunneling in all II-VI semiconductor devices a) 0.20 b) E res eV 0.15 0.10 0.05 0.00 6 8 10 12 d qw nm d/nm material doping/cm -3 10+10+30 Al+Ti+Au 30 ZnSe 2·10^19 15 Zn(0.97)Be(0.03)Se 1·10^18 10 ZnSe i 6 Zn(0.8)Be(0.2)Se i d qw Zn(0.92)Mn(0.08)Se i 6 Zn(0.8)Be(0.2)Se i 10 ZnSe i 10 Zn(0.97)Be(0.03)Se 1·10^18 100 ZnSe 2·10^19 300 Zn(0.97)Be(0.03)Se 2·10^19 20 Zn(0.9)Be(0.1)Se i 50 ZnSe i 200 Zn(0.97)Be(0.03)Se 2·10^19 buffer GaAs i substrate GaAs:Si 1.5·10 18 Figure 2.9: a) Comparison of the peak positions (blue dots) determined by a flat band TM model to experimentally observed peak positions (red dots) for DMS RTDs of various quantum well widths. For a description of the error bars, see text. b) layer stack of the DMS RTDs barrier materials [Ohno 90]. Moreover, we did not account for changes to the conduction band offset in the quantum well layer by the incorporation of the magnetic impurities [Dai 94]. Any deviations from the assumed digital iodine doping profile will also result in a bending of the conduction band profile, shifting the quantum well state with respect to the emitter. The error bars for the of the calculated level positions in fig.2.9 (blue dots) are generated by running calculations for worst case combinations of the individual parameter variations. We assume an error of ±40 meV for the barrier height, as well as a variation of the barrier thickness of ±0.5 nm. Both effects the confinement of the state and thus changes its eigenenergy. As is clear from the vertical error bars, errors due to a change in the confinement are most prominent for levels located at the top of the quantum well, where the confinement is already weak. We furthermore assume an uncertainty of ±0.5 nm for the actual width of the quantum well layers used in the measurements, which results in the horizontal error bar of the red dots. There will also be a small variation in the symmetry of the device as well as in the contact resistances. This is all captured within the lever arm of the device. From experience, we assume a variation for the lever arm of ±0.2. The vertical error bars of the red dots are dependent on the energy of the quantum well state, as dE = V Res /l − V Res /(l + dl). Additionally, also the aforementioned shift of 30 meV of the quantum well conduction band could very well also show a weak dependence on the quantum well width, we however assume that this error is smaller than the one stemming from the variation of the quantum well layer thickness.
2.6. Empirical modeling of resonant tunneling conductance 29 2.6 Empirical modeling of resonant tunneling conductance Having established the transmission spectra of a double barrier heterostructure both as a function of the incident electron energy and the applied bias voltage, this section will now discuss if the latter is applicable for the modeling of the I-V characteristics of all II-VI semiconductor RTDs. Assuming that the transmission through the double barrier region of the RTD is described by running a TMM on a self-consistent conduction band profile, the calculated line width for the resonance is very sharp (sub meV). Near the resonance this transmission line shape is described by a Lorentzian [Lury 89] and thus reads T (E e ) = 4T LT R (T L + T R ) 2 γ 2 (E − E e ) 2 + γ 2 (2.13) where γ is the intrinsic width of the resonant state and T L and T R are the transmittances of the left and right barrier, respectively. The transmission spectra is however only a measure for the probability of an electron of energy E e to traverse the underlying potential landscape. It does not yet fully describe the current through the RTD. An intuitive picture for the 3D-2D tunneling current is given by [Lury 85] and is briefly reviewed in the following. Assuming conservation of the lateral momentum, only emitter electrons of a certain k z value are able to tunnel into the quantum well state. The selection of a single k z value is a result of the afore discussed narrow intrinsic width of the resonant transmission through the quantum well state. Which k z values are selected depends on the energetic position of the resonant state with respect to these emitter states. As soon as there is an overlap with occupied states in the emitter, the resonant level in the quantum well, as well as unoccupied states in the collector, the resonant current sets in. This overlap of the density of states in the emitter and the density of states in the quantum well is schematically shown for three bias voltages V 1 ,V 2 and V max by the gray discs in fig. 2.10b. We omit the collector states, as for bias voltages much greater than the bandwidth of the emitter, there will always be empty states available in the collector. At V max and k z = 0 the maximum overlap of the density of states is reached and a further increase in bias voltage will produce a sharp cutoff in the I-V characteristic (assuming a sufficiently sharp transmission spectrum). For a specific k z , the area where the density of states in the emitter and the quantum well overlap is given by ∮ ∫ ∞ I ∝ A I (k z ) = [ 0 1 + exp 1 ( 2 k 2 r +kz−k 2 F 2 2m eff k B T )]k r dk r dφ (2.14) Figure 2.10 depicts this finite temperature extension to Luryi’s picture for resonant
Page 1 and 2: A Comprehensive Study of Dilute Mag
Page 3: To My Wife
Page 7 and 8: Publications Parts of this thesis h
Page 9 and 10: Contents Zusammenfassung 1 Summary
Page 11 and 12: Zusammenfassung Diese Doktorarbeit
Page 13 and 14: Zusammenfassung 3 haben. Zunächst
Page 15 and 16: Summary We investigate transport me
Page 17 and 18: Summary 7 self-assembled quantum do
Page 19 and 20: Chapter 1 Introduction The hope for
Page 21 and 22: 1. Introduction 11 resonance at ver
Page 23 and 24: Chapter 2 Resonant tunneling in all
Page 25 and 26: 2.1. The (Zn,Be,Mn,Cd)Se material s
Page 27 and 28: 2.2. The transfer matrix method 17
Page 33 and 34: 2.3. Tilted conduction band profile
Page 35 and 36: 2.4. Implications of contact resist
Page 37: 2.5. Comparison to experiment 27 RT
Page 41 and 42: 2.6. Empirical modeling of resonant
Page 43 and 44: 2.6. Empirical modeling of resonant
Page 45 and 46: 2.7. The non-resonant background cu
Page 47 and 48: 2.8. The DMS RTD as a voltage contr
Page 49 and 50: 2.8. The DMS RTD as a voltage contr
Page 51 and 52: Chapter 3 Zero field spin polarizat
Page 53 and 54: 43 225 1.3K device A 14T 400 1.3K d
Page 55 and 56: 45 200 150 40 mK 1.3 K 15 K I[µA]
Page 57 and 58: 47 40 V app =0.1[V] load line V ↓
Page 59 and 60: 49 in the B=0 T I-V app characteris
Page 61 and 62: 51 B [T] 14 12 10 8 6 4 2 0 0 0.05
Page 63 and 64: Chapter 4 0D interface states in a
Page 65 and 66: 55 two 5.5 nm thick Zn 0.8 Be 0.2 S
Page 67 and 68: In summary, the apparent reduction
Page 69 and 70: Chapter 5 A voltage controlled spin
Page 71 and 72: 5.1. Measurement and single channel
Page 73 and 74: 5.1. Measurement and single channel
Page 75 and 76: 5.2. The two channel model 65 a) b)
Page 77 and 78: 5.2. The two channel model 67 a) sa
Page 79 and 80: 5.2. The two channel model 69 a) B
Page 81 and 82: 5.3. Zero magnetic field operation
Page 83 and 84: 5.3. Zero magnetic field operation
Page 85 and 86: Chapter 6 Fermi-edge singularity in
Page 87 and 88: 6.2. Measurement and analysis 77 ba
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6.2. Measurement and analysis 79 I
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6.2. Measurement and analysis 81 (a
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Chapter 7 Simultaneous strong coupl
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7.2. Quantum dot coupled to both ba
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7.3. A comparison of various magnet
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Chapter 8 Resonant tunneling throug
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97 a) 50 40 T=1.7 K 60 40 T ⩵ 1.7
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99 These changes probably have two
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Chapter 9 Conclusion and outlook In
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103 To enhance these effects we rep
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Appendix A Numerical solution of a
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A.2. Computing the path along a spi
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Appendix B Scientific publishing wi
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111 a) b) c) Figure B.2: a) Exporti
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Bibliography [Aban 04] D. A. Abanin
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BIBLIOGRAPHY 115 [Frey 10] A. Frey,
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BIBLIOGRAPHY 117 [Maha 07] S. Mahap
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BIBLIOGRAPHY 119 [Taru 96] [Tito 02
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Of course, I am very grateful to al
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Ehrenwörtliche Erklärung gemäß
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