## Tesi etd-05022013-091603 |

Thesis type

Tesi di laurea magistrale

Author

RIDOLFI, EMILIA

URN

etd-05022013-091603

Title

Proprieta spin dipendenti in eterostrutture a semiconduttore

Struttura

FISICA

Corso di studi

FISICA

Supervisors

**relatore**La Rocca, Giuseppe

Parole chiave

- IV-VI semiconductors
- effective g factor
- spin splitting
- band structures
- Spintronics

Data inizio appello

17/05/2013;

Consultabilità

Parziale

Data di rilascio

17/05/2053

Riassunto analitico

There is a growing interest in fundamental physical phenomena related to spin-dependent effects in condensed matter. This has led to the new field of spintronics: instead of using the charge of the electron, one might use another of its intrinsic properties, namely the spin. Fundamental studies of spintronics are: generation of spin polarization, spin relaxation, spin detection. The goal of spintronics is to understand the interaction between the particle spin and its solid-state environment and hopefully to realize useful devices on this basis. It is in this framework that can be useful to understand spin-orbit coupling in solids. In particular, here we focus on spin-orbit coupling effects on the important “effective g factor” parameter determining the spin-splitting due to an external magnetic field.

The Landé g-factor is a fundamental physical quantity which determines the spin splitting of the electronic states in response to an external magnetic field, known as Zeeman effect. For electrons (or holes) in semiconductors the g-factor is renormalized from the bare value 2 by band structure effects, and is referred to as the effective g-factor (g* ). In semiconductor nanostructure g* is further renormalized by the confining mesoscopic potential and can therefore be tuned. The relativistic effects of the spin-orbit interaction are usually small in the electronic structure of solids, but in their presence the spin-degeneracy of Bloch states having a given wavevector is generally lifted in all systems that lack space inversion symmetry, as asymmetric quantum well heterostructure (Rashba effect). In the presence of a magnetic field, the spin degeneracy is always lifted as determined by g* which, however, should consistently include the effects of spin-orbit coupling and possibly of quantum confinement.

Effects of spin-orbit coupling have been extensively studied in III-V semiconductors (such as GaAs), having a direct energy gap at k=0 (the Gamma point), and a spherical surface of constant energy for electrons. We focus here on IV-VI semiconductors, such as PbTe or PbSe, the spintronic properties of which are nearly unexplored. They are characterized by a smaller direct band gap that enhances spin-orbit coupling effects. The gap is at the border of the Brilluoin zone, at the L point; and results in a multi-valley system with ellipsoidal shape of the constant energy surfaces. We study specifically the modifications of the electron g-factor due to the confining potential in multivalley IV-VI semiconductor quantum wells (QWs).

The first part of the thesis is dedicated to the background notions: characteristics of the semiconductors considered; the physical phenomena involved, the kp analysis method and the envelope function approach. The next part covers in detail what has been recently done in III-V materials: the renormalization of the electron g factor by the confining potential in semiconductor nanostructures described by the Kane model of III-V materials Ref([Mesoscopin-spin-orbit-effect]). The band structure of III-V materials around the gap, is described using the kp perturbative theory around the Gamma point, limited to the four bands of interest. Further projecting the other bands on the conduction band, an effective hamiltonian for an electron including all relevant band structure effects is obtained. This effective hamiltonian is studied for bulk semiconductors in the presence of an external magnetic field, focusing on the Zeeman effect. It is solved analytically for the isotropic effective g factor. Then the same kind of effective hamiltonian is introduced taking into account the confining QW potential and the presence of an external magnetic field. The mesoscopic spin-orbit (Rashba type) and Zeeman interactions are taken into account on an equal footing. It is then solved analytically for the electron effective g factor in symmetric QWs. Thus, the anisotropy of the effective g factor is obtained due to the difference between the in plane and perpendicular configurations given by a mesoscopic spin orbit effect having the same origin as the Rashba one. The comparison with available experimental results for quantum wells of varying thickness demonstrates the accuracy of the theory.

The following part focuses on IV-VI heterostructures. Differently from the III-V case, the band structure of IV-VI materials around the gap is described by the Dimmock model, using the kp perturbative theory around the L point and limiting it to the two bands of interest. With a suitable projection, the effective hamiltonian describing the ellipsoidal shape of the multiple electron pockets at the <111> Brillouin zone boundary is obtained. First, the bulk case is analysed giving the anisotropy of the effective g factor due to the bulk ellipsoidal shape of the electron mass tensor. Finally, quantum confinement and magnetic field effects are considered within this model, which is the original part of the present work. In particular, a new effective Hamiltonian for the QW electron states in the presence of an external magnetic field is derived. The mesoscopic spin-orbit (Rashba type) and Zeeman interactions are taken into account on an equal footing. The lifting of the valley degeneracy is considered according to the confinement potential direction. Some cases of interest are studied in detail as PbTe QWs grown along <111>, <110> and <001> crystallographic directions. For QW grown along the <111> crystallographic direction, both longitudinal and oblique valleys are studied; for QW grown along <110>, the perpendicular valleys and for QW grown along <001>, the oblique valleys. The anisotropic electron effective g-factors in IV-VI symmetric QWs is calculated. It is shown to be highly anisotropic and affected (in different ways depending on the various orientations) by both the bulk anisotropy and the quantum confinement contribution akin to the Rashba spin-orbit coupling. The present theoretical results, obtained for QWs of varying thickness, could be compared with experimental data, once these will be available for IV-VI QWs, as recently done for the case of III-V heterostructures.

Ridolfi Emilia

1)Mesoscopin spin-orbit effect in the semiconductor nanostructure electron g factor, M.A Toloza Sandoval, A. Ferreira de Silva, E. A. De Andrada e Silva and G. C. La Rocca, Physical Review B 86,195302(2012)

The Landé g-factor is a fundamental physical quantity which determines the spin splitting of the electronic states in response to an external magnetic field, known as Zeeman effect. For electrons (or holes) in semiconductors the g-factor is renormalized from the bare value 2 by band structure effects, and is referred to as the effective g-factor (g* ). In semiconductor nanostructure g* is further renormalized by the confining mesoscopic potential and can therefore be tuned. The relativistic effects of the spin-orbit interaction are usually small in the electronic structure of solids, but in their presence the spin-degeneracy of Bloch states having a given wavevector is generally lifted in all systems that lack space inversion symmetry, as asymmetric quantum well heterostructure (Rashba effect). In the presence of a magnetic field, the spin degeneracy is always lifted as determined by g* which, however, should consistently include the effects of spin-orbit coupling and possibly of quantum confinement.

Effects of spin-orbit coupling have been extensively studied in III-V semiconductors (such as GaAs), having a direct energy gap at k=0 (the Gamma point), and a spherical surface of constant energy for electrons. We focus here on IV-VI semiconductors, such as PbTe or PbSe, the spintronic properties of which are nearly unexplored. They are characterized by a smaller direct band gap that enhances spin-orbit coupling effects. The gap is at the border of the Brilluoin zone, at the L point; and results in a multi-valley system with ellipsoidal shape of the constant energy surfaces. We study specifically the modifications of the electron g-factor due to the confining potential in multivalley IV-VI semiconductor quantum wells (QWs).

The first part of the thesis is dedicated to the background notions: characteristics of the semiconductors considered; the physical phenomena involved, the kp analysis method and the envelope function approach. The next part covers in detail what has been recently done in III-V materials: the renormalization of the electron g factor by the confining potential in semiconductor nanostructures described by the Kane model of III-V materials Ref([Mesoscopin-spin-orbit-effect]). The band structure of III-V materials around the gap, is described using the kp perturbative theory around the Gamma point, limited to the four bands of interest. Further projecting the other bands on the conduction band, an effective hamiltonian for an electron including all relevant band structure effects is obtained. This effective hamiltonian is studied for bulk semiconductors in the presence of an external magnetic field, focusing on the Zeeman effect. It is solved analytically for the isotropic effective g factor. Then the same kind of effective hamiltonian is introduced taking into account the confining QW potential and the presence of an external magnetic field. The mesoscopic spin-orbit (Rashba type) and Zeeman interactions are taken into account on an equal footing. It is then solved analytically for the electron effective g factor in symmetric QWs. Thus, the anisotropy of the effective g factor is obtained due to the difference between the in plane and perpendicular configurations given by a mesoscopic spin orbit effect having the same origin as the Rashba one. The comparison with available experimental results for quantum wells of varying thickness demonstrates the accuracy of the theory.

The following part focuses on IV-VI heterostructures. Differently from the III-V case, the band structure of IV-VI materials around the gap is described by the Dimmock model, using the kp perturbative theory around the L point and limiting it to the two bands of interest. With a suitable projection, the effective hamiltonian describing the ellipsoidal shape of the multiple electron pockets at the <111> Brillouin zone boundary is obtained. First, the bulk case is analysed giving the anisotropy of the effective g factor due to the bulk ellipsoidal shape of the electron mass tensor. Finally, quantum confinement and magnetic field effects are considered within this model, which is the original part of the present work. In particular, a new effective Hamiltonian for the QW electron states in the presence of an external magnetic field is derived. The mesoscopic spin-orbit (Rashba type) and Zeeman interactions are taken into account on an equal footing. The lifting of the valley degeneracy is considered according to the confinement potential direction. Some cases of interest are studied in detail as PbTe QWs grown along <111>, <110> and <001> crystallographic directions. For QW grown along the <111> crystallographic direction, both longitudinal and oblique valleys are studied; for QW grown along <110>, the perpendicular valleys and for QW grown along <001>, the oblique valleys. The anisotropic electron effective g-factors in IV-VI symmetric QWs is calculated. It is shown to be highly anisotropic and affected (in different ways depending on the various orientations) by both the bulk anisotropy and the quantum confinement contribution akin to the Rashba spin-orbit coupling. The present theoretical results, obtained for QWs of varying thickness, could be compared with experimental data, once these will be available for IV-VI QWs, as recently done for the case of III-V heterostructures.

Ridolfi Emilia

1)Mesoscopin spin-orbit effect in the semiconductor nanostructure electron g factor, M.A Toloza Sandoval, A. Ferreira de Silva, E. A. De Andrada e Silva and G. C. La Rocca, Physical Review B 86,195302(2012)

File

Nome file | Dimensione |
---|---|

1 file non consultabili su richiesta dell'autore. |