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Papers by Dietmar Lehmann

Research paper thumbnail of Phonon-drag images of AlAs quantum wells: the effect of well thickness and effective mass anisotropy

Journal of Physics: Conference Series, 2007

We present a first theoretical study of how phonon drag patterns of AlAs quantum wells change as ... more We present a first theoretical study of how phonon drag patterns of AlAs quantum wells change as function of well thickness and valley occupancy. Our numerical simulations include the phonon focusing, the acoustic anisotropy of the electron-phonon coupling and the conduction-band anisotropy. From such an analysis, in connection with future systematic experimental studies, one can draw information about the effective mass and the electronphonon coupling parameters. A comparison of our numerical results with a first experimental drag image of an AlAs well shows very good agreement. The main features of the experimental image can be explained.

Research paper thumbnail of Rigorous theorems for surface energies of finite and semi-infinite jellia

Research paper thumbnail of Phonon-Drag Effect in 1-Dimensional Electron Gases

Die Kunst of Phonons, 1994

Research paper thumbnail of Phonon Spectroscopy and Low-Dimensional Electron Systems

ABSTRACT The generation and propagation of pulses of nonequilibrium acoustic phonons and their in... more ABSTRACT The generation and propagation of pulses of nonequilibrium acoustic phonons and their interaction with semiconductor nanostructures are investigated. Such studies can give unique information about the properties of low-dimensional electron systems, but in order to interpret the experiments and to understand the underlying physics, a comparison with theoretical models is absolutely necessary. A central point of this work is therefore a universal theoretical approach allowing the simulation and the analysis of phonon spectroscopy measurements on low-dimensional semiconductor structures. The model takes into account the characteristic properties of the considered systems. These properties are the elastic anisotropy of the substrate material leading to focusing effects and highly anisotropic phonon propagation, the anisotropic nature of the different electron-phonon coupling mechanisms, which depend manifestly on phonon wavevector direction and polarization vector, and the sensitivity to the confinement parameters of the low-dimensional electron systems. We show that screening of the electron-phonon interaction can have a much stronger influence on the results of angle-resolved phonon spectroscopy than expected from transport measurements. Since we compare theoretical simulations with real experiments, the geometrical arrangement and the spatial extension of phonon source and detector are also included in the approach enabling a quantitative analysis of the data this way. To illustrate the influence of acoustic anisotropy and carrier confinement on the results of phonon spectroscopy in detail we analyse two different applications. In the first case the low-dimensional electron system acts as the phonon detector and the phonon induced drag current is measured. Our theoretical model enables us to calculate the electric current induced in low-dimensional electron systems by pulses of (ballistic) nonequilibrium phonons. The theoretical drag patterns reproduce the main features of the experimental images very well. The sensitivity of the results to variations of the confining potential of quasi-2D and quasi-1D electrons is demonstrated. This provides the opportunity to use phonon-drag imaging as unique experimental tool for determining the confinement lengths of low-dimensional electron systems. By comparing the experimental and theoretical images it is also possible to estimate the relative strength of the different electron-phonon coupling mechanisms.In the second application the low-dimensional electron system acts as the phonon pulse source and the angle and mode dependence of the acoustic phonon emission by hot 2D electrons is investigated. The results exhibit strong variations in the phonon signal as a function of the detector position and depend markedly on the coupling mechanism, the phonon polarization and the electron confinement width. We demonstrate that the ratio of the strengths of the emitted longitudinal (LA) and transverse (TA) acoustic phonon modes is predicted correctly only by a theoretical model that properly includes the effects of acoustic anisotropy on the electron-phonon matrix elements, the screening, and the form of the confining potential. A simple adoption of widely used theoretical assumptions, like the isotropic approximation for the phonons in the electron-phonon matrix elements or the use of simple variational envelope wavefunctions for the carrier confinement, can corrupt or even falsify theoretical predictions.We explain the `mystery of the missing longitudinal mode' in heat-pulse experiments with hot 2D electrons in GaAs/AlGaAs heterojunctions. We demonstrate that screening prevents a strong peak in the phonon emission of deformation potential coupled LA phonons in a direction nearly normal to the 2D electron system and that deformation potential coupled TA phonons give a significant contribution to the phonon signal in certain emission directions.

Research paper thumbnail of Angular dependence and mode distribution of acoustic phonon emission by hot 2D electrons in GaAs/AlGaAs heterojunctions and quantum wells

We report a detailed theoretical study of the angular dependence and mode distribution of the aco... more We report a detailed theoretical study of the angular dependence and mode distribution of the acoustic phonon emission by hot two-dimensional electron gases in GaAs/AlGaAs heterojunctions and quantum wells and compare the results with some recent heat pulse measurements for carrier temperatures below 50 K. Common to all the experimental results was the strong dependence of the ratio of emitted longitudinal acoustic (LA) phonons to transverse acoustic (TA) phonons from the width of the quantum well and the absence of LA phonons propagating in a direction close to the 2DEG normal for GaAs/AlGaAs heterojunctions. To explain these phenomena and to understand the process of electron–phonon coupling and its dependence on electron confinement we use a model which includes the dynamical screening of the electron–phonon interaction in the 2D electron gas (2DEG), the confinement of the electrons in the direction normal to the 2DEG plane and the strong acoustic anisotropy of the phonon emissio...

Research paper thumbnail of Phonon transport in 6H silicon carbide

Semiconductor Science and Technology, 2002

ABSTRACT We have used the heat pulse technique to study phonon transport in 6H–silicon carbide. W... more ABSTRACT We have used the heat pulse technique to study phonon transport in 6H–silicon carbide. We have directly detected ballistic acoustic phonons which have propagated across the substrate and have observed the arrival of phonons multiply reflected from the surfaces, suggesting high crystal quality. From the heat pulse data, we deduce the velocities of the longitudinal and transverse acoustic modes. We have used phonon imaging techniques to obtain images of the phonon focusing in 6H–silicon carbide and have compared these with the results of theoretical calculations.

Research paper thumbnail of The influence of screening and acoustic anisotropy on the electron–phonon coupling in quantum wires

Physica E: Low-dimensional Systems and Nanostructures, 2000

We have investigated the interaction of nonequilibrium acoustic phonons with quantum wires in sem... more We have investigated the interaction of nonequilibrium acoustic phonons with quantum wires in semiconductor heterostructures. To explain new measurements of the phonoconductivity in short, ballistic GaAs=AlGaAs wires, we studied the change in the conductance caused by a pulsed beam of acoustic phonons. Such angle-and time-resolved studies allow, in connection with the corresponding numerical simulations, more direct information about the electron-phonon coupling and the properties of low-dimensional electron systems than conventional transport measurements. In contrast to earlier theoretical models we considered in detail the in uence of the acoustic anisotropy and screening e ects. Both e ects result in large modiÿcations of the absorption rates both for deformation potential coupling and piezoelectric interaction, particularly in the angular dependence. Our numerical results show not only, in agreement with the experiment, large oscillations in the amplitude of phonoconductivity with shifting the position of Fermi energy relative to the bottom of the subbands, but also dramatic changes in the angular distribution.

Research paper thumbnail of Images of the Response Signal of a 2D Gas of Carriers to a Pulsed Beam of 3D Phonons

Acta Physica Polonica A, 1993

Research paper thumbnail of Magnetic Field Dependence of Phonon-Induced Drag Current of 2D Carriers

Acta Physica Polonica A, 1997

Research paper thumbnail of Phonon-drag studies of (110) AlAs quantum wells

We investigate the possibility of using phonon-drag imaging for the study of 2D electrons in (110... more We investigate the possibility of using phonon-drag imaging for the study of 2D electrons in (110) AlAs quantum wells. Our numerical simulations show that direct information on the strain and quantum confinement dependent valley occupancy of the electrons, on the anisotropic effective mass tensor and on electron-phonon coupling parameters can be obtained.

Research paper thumbnail of Phonon Spectroscopy and Low-Dimensional Electron Systems

The generation and propagation of pulses of nonequilibrium acoustic phonons and their interaction... more The generation and propagation of pulses of nonequilibrium acoustic phonons and their interaction with semiconductor nanostructures are investigated. Such studies can give unique information about the properties of low-dimensional electron systems, but in order to interpret the experiments and to understand the underlying physics, a comparison with theoretical models is absolutely necessary. A central point of this work is therefore a universal theoretical approach allowing the simulation and the analysis of phonon spectroscopy measurements on low-dimensional semiconductor structures. The model takes into account the characteristic properties of the considered systems. These properties are the elastic anisotropy of the substrate material leading to focusing effects and highly anisotropic phonon propagation, the anisotropic nature of the different electron-phonon coupling mechanisms, which depend manifestly on phonon wavevector direction and polarization vector, and the sensitivity t...

Research paper thumbnail of How to make best computational use of rigorous theorems connecting total energy and electrostatic potentials at surfaces of small metal particles

Solid State Communications, 1987

ABSTRACT

Research paper thumbnail of Generalisation of the viril theorem and related theorems for jellia with arbitrary background densities and application to special geometries and profiles. II. Application to spherical shell, plane slab and void; work function

Journal of Physics C: Solid State Physics, 1983

ABSTRACT

Research paper thumbnail of Generalisation of the virial theorem and related theorems for jellia with arbitrary background densities and application to special geometriees and profiles. I. General theory and application to the jellium sphere and the semi-infinite electron gas

Journal of Physics C: Solid State Physics, 1982

Research paper thumbnail of Effects of acoustic anisotropy and screening on the energy relaxation of hot electrons. in heterojunctions and quantum wells

Research paper thumbnail of Terahertz phonon optics in GaAs/AlAs superlattice structures

Research paper thumbnail of Phonon-drag thermopower in anisotropic AlAs quantum wells

Research paper thumbnail of Theorems connecting surface energies and electrostatic potentials of finite and semi-infinite jellia and cavities

Solid State Communications, 1985

A Pauli-Hellmann-Feynman theorem for finite neutral jellia derived in an earlier paper by the aut... more A Pauli-Hellmann-Feynman theorem for finite neutral jellia derived in an earlier paper by the authors and connecting energy and electrostatic potential with each other is generalized to the case of non-neutral systems and is shown to split into two theorems. For an arbitrary cavity in an otherwise homogeneous jellium a general theorem is derived. Theorems for cavities with special symmetry (void, tube, slit) are compared with each other and with theorems for corresponding jellia (sphere, wire, slab).

Research paper thumbnail of The phonon-induced drag of charge carriers in heterostructures in weak magnetic fields

Semiconductor Science and Technology, 1996

ABSTRACT

Research paper thumbnail of The Bloch - Grüneisen regime in a one-dimensional electron gas

Semiconductor Science and Technology, 1997

ABSTRACT The momentum relaxation of one-dimensional electrons scattered by acoustic phonons has b... more ABSTRACT The momentum relaxation of one-dimensional electrons scattered by acoustic phonons has been investigated in the Bloch - Grüneisen temperature range. The temperature dependence of mobility follows the same, (for deformation acoustic interaction) and (for piezoelectric interaction), power laws as known for two-dimensional and three-dimensional Fermi gases. The calculations performed estimate to be at and at low electron concentrations. The specific feature of a one-dimensional gas is an intermediate temperature region, where an exponential temperature dependence of mobility is traced.

Research paper thumbnail of Phonon-drag images of AlAs quantum wells: the effect of well thickness and effective mass anisotropy

Journal of Physics: Conference Series, 2007

We present a first theoretical study of how phonon drag patterns of AlAs quantum wells change as ... more We present a first theoretical study of how phonon drag patterns of AlAs quantum wells change as function of well thickness and valley occupancy. Our numerical simulations include the phonon focusing, the acoustic anisotropy of the electron-phonon coupling and the conduction-band anisotropy. From such an analysis, in connection with future systematic experimental studies, one can draw information about the effective mass and the electronphonon coupling parameters. A comparison of our numerical results with a first experimental drag image of an AlAs well shows very good agreement. The main features of the experimental image can be explained.

Research paper thumbnail of Rigorous theorems for surface energies of finite and semi-infinite jellia

Research paper thumbnail of Phonon-Drag Effect in 1-Dimensional Electron Gases

Die Kunst of Phonons, 1994

Research paper thumbnail of Phonon Spectroscopy and Low-Dimensional Electron Systems

ABSTRACT The generation and propagation of pulses of nonequilibrium acoustic phonons and their in... more ABSTRACT The generation and propagation of pulses of nonequilibrium acoustic phonons and their interaction with semiconductor nanostructures are investigated. Such studies can give unique information about the properties of low-dimensional electron systems, but in order to interpret the experiments and to understand the underlying physics, a comparison with theoretical models is absolutely necessary. A central point of this work is therefore a universal theoretical approach allowing the simulation and the analysis of phonon spectroscopy measurements on low-dimensional semiconductor structures. The model takes into account the characteristic properties of the considered systems. These properties are the elastic anisotropy of the substrate material leading to focusing effects and highly anisotropic phonon propagation, the anisotropic nature of the different electron-phonon coupling mechanisms, which depend manifestly on phonon wavevector direction and polarization vector, and the sensitivity to the confinement parameters of the low-dimensional electron systems. We show that screening of the electron-phonon interaction can have a much stronger influence on the results of angle-resolved phonon spectroscopy than expected from transport measurements. Since we compare theoretical simulations with real experiments, the geometrical arrangement and the spatial extension of phonon source and detector are also included in the approach enabling a quantitative analysis of the data this way. To illustrate the influence of acoustic anisotropy and carrier confinement on the results of phonon spectroscopy in detail we analyse two different applications. In the first case the low-dimensional electron system acts as the phonon detector and the phonon induced drag current is measured. Our theoretical model enables us to calculate the electric current induced in low-dimensional electron systems by pulses of (ballistic) nonequilibrium phonons. The theoretical drag patterns reproduce the main features of the experimental images very well. The sensitivity of the results to variations of the confining potential of quasi-2D and quasi-1D electrons is demonstrated. This provides the opportunity to use phonon-drag imaging as unique experimental tool for determining the confinement lengths of low-dimensional electron systems. By comparing the experimental and theoretical images it is also possible to estimate the relative strength of the different electron-phonon coupling mechanisms.In the second application the low-dimensional electron system acts as the phonon pulse source and the angle and mode dependence of the acoustic phonon emission by hot 2D electrons is investigated. The results exhibit strong variations in the phonon signal as a function of the detector position and depend markedly on the coupling mechanism, the phonon polarization and the electron confinement width. We demonstrate that the ratio of the strengths of the emitted longitudinal (LA) and transverse (TA) acoustic phonon modes is predicted correctly only by a theoretical model that properly includes the effects of acoustic anisotropy on the electron-phonon matrix elements, the screening, and the form of the confining potential. A simple adoption of widely used theoretical assumptions, like the isotropic approximation for the phonons in the electron-phonon matrix elements or the use of simple variational envelope wavefunctions for the carrier confinement, can corrupt or even falsify theoretical predictions.We explain the `mystery of the missing longitudinal mode' in heat-pulse experiments with hot 2D electrons in GaAs/AlGaAs heterojunctions. We demonstrate that screening prevents a strong peak in the phonon emission of deformation potential coupled LA phonons in a direction nearly normal to the 2D electron system and that deformation potential coupled TA phonons give a significant contribution to the phonon signal in certain emission directions.

Research paper thumbnail of Angular dependence and mode distribution of acoustic phonon emission by hot 2D electrons in GaAs/AlGaAs heterojunctions and quantum wells

We report a detailed theoretical study of the angular dependence and mode distribution of the aco... more We report a detailed theoretical study of the angular dependence and mode distribution of the acoustic phonon emission by hot two-dimensional electron gases in GaAs/AlGaAs heterojunctions and quantum wells and compare the results with some recent heat pulse measurements for carrier temperatures below 50 K. Common to all the experimental results was the strong dependence of the ratio of emitted longitudinal acoustic (LA) phonons to transverse acoustic (TA) phonons from the width of the quantum well and the absence of LA phonons propagating in a direction close to the 2DEG normal for GaAs/AlGaAs heterojunctions. To explain these phenomena and to understand the process of electron–phonon coupling and its dependence on electron confinement we use a model which includes the dynamical screening of the electron–phonon interaction in the 2D electron gas (2DEG), the confinement of the electrons in the direction normal to the 2DEG plane and the strong acoustic anisotropy of the phonon emissio...

Research paper thumbnail of Phonon transport in 6H silicon carbide

Semiconductor Science and Technology, 2002

ABSTRACT We have used the heat pulse technique to study phonon transport in 6H–silicon carbide. W... more ABSTRACT We have used the heat pulse technique to study phonon transport in 6H–silicon carbide. We have directly detected ballistic acoustic phonons which have propagated across the substrate and have observed the arrival of phonons multiply reflected from the surfaces, suggesting high crystal quality. From the heat pulse data, we deduce the velocities of the longitudinal and transverse acoustic modes. We have used phonon imaging techniques to obtain images of the phonon focusing in 6H–silicon carbide and have compared these with the results of theoretical calculations.

Research paper thumbnail of The influence of screening and acoustic anisotropy on the electron–phonon coupling in quantum wires

Physica E: Low-dimensional Systems and Nanostructures, 2000

We have investigated the interaction of nonequilibrium acoustic phonons with quantum wires in sem... more We have investigated the interaction of nonequilibrium acoustic phonons with quantum wires in semiconductor heterostructures. To explain new measurements of the phonoconductivity in short, ballistic GaAs=AlGaAs wires, we studied the change in the conductance caused by a pulsed beam of acoustic phonons. Such angle-and time-resolved studies allow, in connection with the corresponding numerical simulations, more direct information about the electron-phonon coupling and the properties of low-dimensional electron systems than conventional transport measurements. In contrast to earlier theoretical models we considered in detail the in uence of the acoustic anisotropy and screening e ects. Both e ects result in large modiÿcations of the absorption rates both for deformation potential coupling and piezoelectric interaction, particularly in the angular dependence. Our numerical results show not only, in agreement with the experiment, large oscillations in the amplitude of phonoconductivity with shifting the position of Fermi energy relative to the bottom of the subbands, but also dramatic changes in the angular distribution.

Research paper thumbnail of Images of the Response Signal of a 2D Gas of Carriers to a Pulsed Beam of 3D Phonons

Acta Physica Polonica A, 1993

Research paper thumbnail of Magnetic Field Dependence of Phonon-Induced Drag Current of 2D Carriers

Acta Physica Polonica A, 1997

Research paper thumbnail of Phonon-drag studies of (110) AlAs quantum wells

We investigate the possibility of using phonon-drag imaging for the study of 2D electrons in (110... more We investigate the possibility of using phonon-drag imaging for the study of 2D electrons in (110) AlAs quantum wells. Our numerical simulations show that direct information on the strain and quantum confinement dependent valley occupancy of the electrons, on the anisotropic effective mass tensor and on electron-phonon coupling parameters can be obtained.

Research paper thumbnail of Phonon Spectroscopy and Low-Dimensional Electron Systems

The generation and propagation of pulses of nonequilibrium acoustic phonons and their interaction... more The generation and propagation of pulses of nonequilibrium acoustic phonons and their interaction with semiconductor nanostructures are investigated. Such studies can give unique information about the properties of low-dimensional electron systems, but in order to interpret the experiments and to understand the underlying physics, a comparison with theoretical models is absolutely necessary. A central point of this work is therefore a universal theoretical approach allowing the simulation and the analysis of phonon spectroscopy measurements on low-dimensional semiconductor structures. The model takes into account the characteristic properties of the considered systems. These properties are the elastic anisotropy of the substrate material leading to focusing effects and highly anisotropic phonon propagation, the anisotropic nature of the different electron-phonon coupling mechanisms, which depend manifestly on phonon wavevector direction and polarization vector, and the sensitivity t...

Research paper thumbnail of How to make best computational use of rigorous theorems connecting total energy and electrostatic potentials at surfaces of small metal particles

Solid State Communications, 1987

ABSTRACT

Research paper thumbnail of Generalisation of the viril theorem and related theorems for jellia with arbitrary background densities and application to special geometries and profiles. II. Application to spherical shell, plane slab and void; work function

Journal of Physics C: Solid State Physics, 1983

ABSTRACT

Research paper thumbnail of Generalisation of the virial theorem and related theorems for jellia with arbitrary background densities and application to special geometriees and profiles. I. General theory and application to the jellium sphere and the semi-infinite electron gas

Journal of Physics C: Solid State Physics, 1982

Research paper thumbnail of Effects of acoustic anisotropy and screening on the energy relaxation of hot electrons. in heterojunctions and quantum wells

Research paper thumbnail of Terahertz phonon optics in GaAs/AlAs superlattice structures

Research paper thumbnail of Phonon-drag thermopower in anisotropic AlAs quantum wells

Research paper thumbnail of Theorems connecting surface energies and electrostatic potentials of finite and semi-infinite jellia and cavities

Solid State Communications, 1985

A Pauli-Hellmann-Feynman theorem for finite neutral jellia derived in an earlier paper by the aut... more A Pauli-Hellmann-Feynman theorem for finite neutral jellia derived in an earlier paper by the authors and connecting energy and electrostatic potential with each other is generalized to the case of non-neutral systems and is shown to split into two theorems. For an arbitrary cavity in an otherwise homogeneous jellium a general theorem is derived. Theorems for cavities with special symmetry (void, tube, slit) are compared with each other and with theorems for corresponding jellia (sphere, wire, slab).

Research paper thumbnail of The phonon-induced drag of charge carriers in heterostructures in weak magnetic fields

Semiconductor Science and Technology, 1996

ABSTRACT

Research paper thumbnail of The Bloch - Grüneisen regime in a one-dimensional electron gas

Semiconductor Science and Technology, 1997

ABSTRACT The momentum relaxation of one-dimensional electrons scattered by acoustic phonons has b... more ABSTRACT The momentum relaxation of one-dimensional electrons scattered by acoustic phonons has been investigated in the Bloch - Grüneisen temperature range. The temperature dependence of mobility follows the same, (for deformation acoustic interaction) and (for piezoelectric interaction), power laws as known for two-dimensional and three-dimensional Fermi gases. The calculations performed estimate to be at and at low electron concentrations. The specific feature of a one-dimensional gas is an intermediate temperature region, where an exponential temperature dependence of mobility is traced.