Dynamics of spin-dependent charge carrier recombination [Elektronische Ressource] / vorgelegt von Christoph Böhme

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• Physik

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• Publié par: philipps-universitat_marburg
• Publié le: 01 janvier 2003
• Nombre de lectures: 17
• Langue: English
• Poids de l'ouvrage: 4 Mo

Extrait

Dynamics of spin–dependent
charge carrier recombination
Dissertation
zur
Erlangung des Doktorgrades
der Naturwissenschaften
(Dr. rer. nat.)
dem
Fachbereich Physik
der Philipps–Universit¨at Marburg
vorgelegt
von
Christoph B¨ohme
aus Oppenau
Marburg/Lahn 2002Vom Fachbereich Physik der Philipps–Universit¨at Marburg als
Dissertation angenommen am: 17.12.2002
Erstgutachter: Prof. Dr. W. Fuhs
Zweitgutachter: Prof. Dr. S. Baranovski
Tag der mundlic¨ hen Prufung:¨ 13.01.2003M.C. Escher’s “Moebius Strip” c Cordon Art B.V. – Baarn – Holland. All rights reserved. [1]
“Never stop questioning.” Albert EinsteinContents
Summary IV
Zusammenfassung V
1 Introduction 1
2 Pictures of spin–dependent recombination 7
2.1 A brief history. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Intermediate pairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Ingredients for a general model . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Theoretical considerations 11
3.1 A quantum ensemble of spin pairs . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.1 Hamiltonian of a spin pair . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Electronic transitions . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.3 Spin relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.4 Influence of polarisation . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 The conceptual idea of the TSR experiment . . . . . . . . . . . . . . . . . 20
3.2.1 Coherence and incoherence . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.2 The different time domains of TSR . . . . . . . . . . . . . . . . . . 22
3.3 Larmor–beat oscillation and Larmor–beat echoes. . . . . . . . . . . . . . . 24
3.3.1 Solution of the Liouville equation . . . . . . . . . . . . . . . . . . . 24
3.3.2 Dephasing and rephasing . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Incoherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 Influence of relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.2 I of recombination and dissociation . . . . . . . . . . . . . . 34
3.4.3 Pulse length dependence of recombination decay . . . . . . . . . . . 35
3.5 Rabi oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.1 Spin–spin interactions . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.2 The line shape of TSR transients . . . . . . . . . . . . . . . . . . . 47
3.5.3 Dephasing of TSR transient . . . . . . . . . . . . . . . . . . . . . . 48
3.6 Rabi echoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4 Experimental foundations 55
4.1 Pulsed EDMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.1.1 Time resolution and current sensitivity . . . . . . . . . . . . . . . . 57
III CONTENTS
4.1.2 Microwave–induced currents . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Sample and contact design . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3 Timing of the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Experimental results for microcrystalline silicon 63
5.1 Properties of the used material . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1.1 Material deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1.2 Material characterisation . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.3 ESR measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.1.4 EDMR measurements . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 Detection of the TSR signal . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2.1 Microwave intensity dependence of the TSR spectrum . . . . . . . . 72
5.3 Photocurrent enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.4 Rabi–beat oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4.1 PLD of photocurrent transient . . . . . . . . . . . . . . . . . . . . . 75
5.4.2 Rapid dephasing Rabi oscillation of db centres . . . . . . . . . . . . 77
5.4.3 Rabi oscillation of CE centres . . . . . . . . . . . . . . . . . . . . . 78
5.4.4 Incoherence during the microwave pulse . . . . . . . . . . . . . . . 80
5.5 The recombination echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.5.1 Dependence on microwave intensity . . . . . . . . . . . . . . . . . . 82
5.5.2 Coherence decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5.3 Echo echoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.5.4 Magnetic field dependence of recombination echo . . . . . . . . . . 86
6 Recombination properties of disordered silicon 89
6.1 Hydrogenated microcrystalline silicon . . . . . . . . . . . . . . . . . . . . . 89
6.1.1 Triplet recombination and spin–spin coupling . . . . . . . . . . . . 90
6.1.2 Temperature and light dependence of time constants . . . . . . . . 94
6.1.3 Trap–dangling bond recombination versus direct capture . . . . . . 99
6.2 Outlook on hydrogenated amorphous silicon . . . . . . . . . . . . . . . . . 101
7 Readout concept for Si–based quantum computers 105
7.1 Kane’s silicon–based quantum computer . . . . . . . . . . . . . . . . . . . 105
7.2 Readout with recombination . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.3 Deep donor candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.4 Challenges for an implementation . . . . . . . . . . . . . . . . . . . . . . . 110
8 Conclusions and Outlook 113
Appendix 116
A Theory 117
A.1 Stochastic Liouville equations . . . . . . . . . . . . . . . . . . . . . . . . . 117
A.2 Spin–dipole interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
A.3 Bloch’s equations and quantum mechanics . . . . . . . . . . . . . . . . . . 119
A.4 Bloch spheres and rotating frames . . . . . . . . . . . . . . . . . . . . . . . 120CONTENTS III
A.5 Redfield’s theory of relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 122
A.6 Analytic solution of an ODE . . . . . . . . . . . . . . . . . . . . . . . . . . 123
B Experiments 125
B.1 Continuous–wave electron spin resonance . . . . . . . . . . . . . . . . . . . 125
B.2 Continuous wave EDMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
B.3 Pulse Spell routines for TSR . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Bibliography 133
List of figures 134
List of constants and variables 137
List of author publications 142
Acknowledgements 144
Biography 145IV CONTENTS
Summary
The study presented deals with the dynamics of spin–dependent charge carrier re-
combination between localised band–gap states in semiconductors. A general model
is presented that takes influences of spin–dipole and spin–exchange interactions be-
tween the recombining charge–carrier spin pairs, spin relaxation and triplet recom-
bination into account. A theoretical investigation based on this model predicts a
variety of transient effects on the recombination rate due to the excitation with
coherent electron spin resonance (ESR). These effects can be observed in the time
domain of photocurrents. Depending on the coupling within the spin pairs, rapidly
dephasing Rabi and Rabi–beat oscillation during the ESR excitation can occur,
which is reflected by the magnitude of photocurrent decay transients. The dephased
spin–pair ensembles can be rephased which causes an echo effect (Recombination
echo). After the excitation, the charge carrier ensemble carries out dephasing Lar-
mor and Larmor–beat oscillation. Also, a slow multiexponential relaxation of the
photocurrent transients due to incoherence is predicted that is determined by the
electronic transition probabilities and spin relaxation. An enhancement of the pho-
tocurrent due to non–negligible triplet recombination is possible.
Anewexperimentwasdesignedandimplementedtechnically,thetime–domainmea-
surement of spin–dependent recombination (TSR), which allowed the experimental
verification of the effects that were predicted and described theoretically. A first
demonstration of TSR was performed on hydrogenated microcrystalline silicon (μc-
Si:H) which led to new insights about charge carrier recombination in this material:
Spin–dependentrecombinationchannelsthroughdanglingbond(db) centresarethe
dominant recombination paths of μc-Si:H. Two spin–dependent db recombination
channels exist in μc-Si:H. A dominant db direct capture (dc) and a less dominant
tunnelling transition of trapped conduction electrons (CE) to db states. Spin pairs
ofthedcchannelarestronglycoupled,theirsinglet-andtriplet–recombinationprob-
abilities could be determined. The applicability of TSR could also be demonstrated
on hydrogenated amorphous silicon. In addition, the ability of TSR to detect the
spin coherence of recombining charge carriers allows the measurement of coherence
times of spin quantum bits in semiconductor based spin–quantum computers.CONTENTS V
Zusammenfassung
Die vorliegende Arbeit behandelt die Dynamik spinabh¨angiger Ladungs–
tr¨agerrekombination zwischen lokalisierten Bandluc¨ kenzust¨anden in Halbleitern.
Ein allgemeines Modell wird vorgestellt, in dem die Spin–Dipol und die Spin–
Austauschwechselwirkungen zwischen den Paaren rekombinierender Ladungstrage&