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The anisotropic Beer-Lambert law in $β$-Ga$_{2}$O$_{3}$: Spectral and polarization dependent absorption and photoresponsivity
Authors:
Md Mohsinur Rahman Adnan,
Darpan Verma,
Chris Sturm,
Matthias Schubert,
Roberto C. Myers
Abstract:
Due to its low symmetry, $β$-Ga$_{2}$O$_{3}$ exhibits a strongly anisotropic optical response. As a result, the absorption spectra change with the polarization state of the incoming photons. To understand this phenomenon, here we calculate the complete electromagnetic wave equation solutions as a function of linear polarization angle and photon energy for $β$-Ga$_{2}$O$_{3}$ using its previously m…
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Due to its low symmetry, $β$-Ga$_{2}$O$_{3}$ exhibits a strongly anisotropic optical response. As a result, the absorption spectra change with the polarization state of the incoming photons. To understand this phenomenon, here we calculate the complete electromagnetic wave equation solutions as a function of linear polarization angle and photon energy for $β$-Ga$_{2}$O$_{3}$ using its previously measured complex dielectric function tensor. The significant off-diagonal terms in this tensor can result in a non-exponential decay in the photon flux, indicating that the Beer-Lambert law is not generally valid in this anisotropic material. However, for above-band-gap spectral regions which depend on crystallographic orientations (> 5.8 eV (001 plane),>5.2 eV (010 plane)) an effective absorption coefficient well approximates the photon flux decay with depth. On the other hand, near the optical absorption edge (4.9 - 5.8 eV (001 plane),4.65 - 5.2 eV (010 plane)) the photon flux decay exhibits a sum of two exponential decays, such that two effective absorption coefficients are necessary to model the loss behavior versus the absorption depth. This behavior manifests from the presence of dichroism in $β$-Ga$_{2}$O$_{3}$. A single effective absorption coefficient can only be recovered for this energy range by augmenting the isotropic Beer-Lambert law with a critical penetration depth and polarization dependence. Using these results, we calculate the polarization-dependent photoresponsivity spectra for light polarized along different crystallographic directions.
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Submitted 30 January, 2024; v1 submitted 30 May, 2023;
originally announced May 2023.
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Determination of acoustic phonon anharmonicities via second-order Raman scattering in CuI
Authors:
Ron Hildebrandt,
Michael Seifert,
Janine George,
Steffen Blaurock,
Silvana Botti,
Harald Krautscheid,
Marius Grundmann,
Chris Sturm
Abstract:
We demonstrate the determination of anharmonic acoustic phonon properties via second-order Raman scattering exemplarily on copper iodide single crystals. The origin of multi-phonon features from the second-order Raman spectra was assigned by the support of the calculated 2-phonon density of states. In this way, the temperature dependence of acoustic phonons was determined down to 10\,K. To determi…
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We demonstrate the determination of anharmonic acoustic phonon properties via second-order Raman scattering exemplarily on copper iodide single crystals. The origin of multi-phonon features from the second-order Raman spectra was assigned by the support of the calculated 2-phonon density of states. In this way, the temperature dependence of acoustic phonons was determined down to 10\,K. To determine independently the harmonic contributions of respective acoustic phonons, density functional theory (DFT) in quasi-harmonic approximation was used. Finally, the anharmonic contributions were determined. The results are in agreement with earlier publications and extend CuI's determined acoustic phonon properties to lower temperatures with higher accuracy. This approach demonstrates that it is possible to characterize the acoustic anharmonicities via Raman scattering down to zero-temperature renormalization constants of at least 0.1\,cm$^{-1}$.
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Submitted 15 September, 2023; v1 submitted 30 May, 2023;
originally announced May 2023.
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Anisotropic excitonic photocurrent in $β$-Ga$_{2}$O$_{3}$
Authors:
Darpan Verma,
Md Mohsinur Rahman Adnan,
Sushovan Dhara,
Chris Sturm,
Siddharth Rajan,
Roberto C. Myers
Abstract:
Polarization dependent photocurrent spectra are measured on a (001) $β$-Ga$_{2}$O$_{3}$ Schottky photodetector, where the linear polarization of light is rotated within the ab plane. Three spectral peaks at 4.92 eV, 5.15 eV, and 5.44 eV are observed that vary in intensity with the optical polarization direction. The peak transition energies are consistent with excitons previously reported in $β$-G…
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Polarization dependent photocurrent spectra are measured on a (001) $β$-Ga$_{2}$O$_{3}$ Schottky photodetector, where the linear polarization of light is rotated within the ab plane. Three spectral peaks at 4.92 eV, 5.15 eV, and 5.44 eV are observed that vary in intensity with the optical polarization direction. The peak transition energies are consistent with excitons previously reported in $β$-Ga$_{2}$O$_{3}$ due to interband transitions modified by the valence band p-orbital anisotropy and the electron-hole Coulombic attraction. The measured polarization-dependence of the photocurrent matches our predictions based on electromagnetic simulations of anisotropic absorption using the complex dielectric function tensor extracted from previous ellipsometry studies. These results illustrate the dominance of excitonic absorption and photocurrent in $β$-Ga$_{2}$O$_{3}$ both below and above the band gap, demonstrate a combined theoretical/experimental understanding of anisotropic photocarrier generation, and validate previous atomistic band structure calculations in this low-symmetry ultra-wide band gap semiconductor.
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Submitted 10 March, 2023;
originally announced March 2023.
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Dielectric function of CuBr$_\mathrm{x}$I$_{1-\mathrm{x}}$ alloy thin films
Authors:
Michael Seifert,
Evgeny Krüger,
Michael S. Bar,
Stefan Merker,
Holger von Wenckstern,
Harald Krautscheid,
Marius Grundmann,
Chris Sturm,
Silvana Botti
Abstract:
We study the dielectric function of CuBr$_\mathrm{x}$I$_{1-\mathrm{x}}$ thin film alloys using spectroscopic ellipsometry in the spectral range between 0.7 eV to 6.4 eV, in combination with first-principles calculations based on density functional theory. Through the comparison of theory and experiment, we attribute features in the dielectric function to electronic transitions at specific k-points…
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We study the dielectric function of CuBr$_\mathrm{x}$I$_{1-\mathrm{x}}$ thin film alloys using spectroscopic ellipsometry in the spectral range between 0.7 eV to 6.4 eV, in combination with first-principles calculations based on density functional theory. Through the comparison of theory and experiment, we attribute features in the dielectric function to electronic transitions at specific k-points in the Brillouin zone. The observed bandgap bowing as a function of alloy composition is discussed in terms of different physical and chemical contributions. The band splitting at the top of the valence band due to spin-orbit coupling is found to decrease with increasing Br-concentration, from a value of 660 meV for CuI to 150 meV for CuBr. This result can be understood considering the contribution of copper d-orbitals to the valence band maximum as a function of the alloy composition.
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Submitted 9 September, 2022; v1 submitted 4 July, 2022;
originally announced July 2022.
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Control of Magnetic Order in Spinel ZnFe$_2$O$_4$ Thin Films Through Intrinsic Defect Manipulation
Authors:
Vitaly Zviagin,
Chris Sturm,
Pablo Esquinazi,
Marius Grundmann,
Rüdiger Schmidt-Grund
Abstract:
We present a systematic study of the magnetic properties of semiconducting ZnFe$_2$O$_4$ thin films fabricated by pulsed laser deposition at low and high oxygen partial pressure and annealed in oxygen and argon atmosphere, respectively. The magnetic response is enhanced by annealing the films at 250$^{\circ}$C and diminished at annealing temperatures above 300$^{\circ}$C. The initial increase is a…
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We present a systematic study of the magnetic properties of semiconducting ZnFe$_2$O$_4$ thin films fabricated by pulsed laser deposition at low and high oxygen partial pressure and annealed in oxygen and argon atmosphere, respectively. The magnetic response is enhanced by annealing the films at 250$^{\circ}$C and diminished at annealing temperatures above 300$^{\circ}$C. The initial increase is attributed to the formation of oxygen vacancies after argon treatment, evident by the increase in the low energy absorption at $\sim$ 0.9 eV involving Fe$^{2+}$ cations. The weakened magnetic response is related to a decline in disorder with a cation redistribution toward a normal spinel configuration. The structural renormalization is consistent with the decrease and increase in oscillator strength of respective electronic transitions involving tetrahedrally (at $\sim$ 3.5 eV) and octahedrally (at $\sim$ 5.7 eV) coordinated Fe$^{3+}$ cations.
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Submitted 30 September, 2019;
originally announced September 2019.
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Raman tensor elements of $β\text{-Ga}_2\text{O}_3$
Authors:
Christian Kranert,
Chris Sturm,
Rüdiger Schmidt-Grund,
Marius Grundmann
Abstract:
The Raman spectrum and particularly the Raman scattering intensities of monoclinic $β\text{-Ga}_2\text{O}_3$ are investigated by experiment and theory. The low symmetry of $β\text{-Ga}_2\text{O}_3$ results in a complex dependence of the Raman intensity for the individual phonon modes on the scattering geometry which is additionally affected by birefringence. We measured the Raman spectra in depend…
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The Raman spectrum and particularly the Raman scattering intensities of monoclinic $β\text{-Ga}_2\text{O}_3$ are investigated by experiment and theory. The low symmetry of $β\text{-Ga}_2\text{O}_3$ results in a complex dependence of the Raman intensity for the individual phonon modes on the scattering geometry which is additionally affected by birefringence. We measured the Raman spectra in dependence on the polarization direction for backscattering on three crystallographic planes of $β\text{-Ga}_2\text{O}_3$ and modeled these dependencies using a modified Raman tensor formalism which takes birefringence into account. The spectral position of all 15 Raman-active phonon modes and the Raman tensor elements of 13 modes were determined and are compared to results from ab-initio calculations.
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Submitted 23 June, 2016;
originally announced June 2016.
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Dipole Analysis of the Dielectric Function of Colour Dispersive Materials: Application to Monoclinic Ga$_2$O$_3$
Authors:
Chris Sturm,
Rüdiger Schmidt-Grund,
Christian Kranert,
Jürgen Furthmüller,
Friedhelm Bechstedt,
Marius Grundmann
Abstract:
We apply a generalized model for the determination and analysis of the dielectric function of optically anisotropic materials with colour dispersion to phonon modes and show that it can also be generalized to excitonic polarizabilities and electronic band-band transitions. We take into account that the tensor components of the dielectric function within the cartesian coordinate system are not inde…
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We apply a generalized model for the determination and analysis of the dielectric function of optically anisotropic materials with colour dispersion to phonon modes and show that it can also be generalized to excitonic polarizabilities and electronic band-band transitions. We take into account that the tensor components of the dielectric function within the cartesian coordinate system are not independent from each other but are rather projections of the polarization of dipoles oscillating along directions defined by the, non-cartesian, crystal symmetry and polarizability. The dielectric function is then composed of a series of oscillators pointing in different directions. The application of this model is exemplarily demonstrated for monoclinic ($β$-phase) Ga$_2$O$_3$ bulk single crystals. Using this model, we are able to relate electronic transitions observed in the dielectric function to atomic bond directions and orbitals in the real space crystal structure. For thin films revealing rotational domains we show that the optical biaxiality is reduced to uniaxial optical response.
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Submitted 28 January, 2016;
originally announced January 2016.
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Carrier density driven lasing dynamics in ZnO nanowires
Authors:
Marcel Wille,
Chris Sturm,
Tom Michalsky,
Robert Röder,
Carsten Ronning,
Rüdiger Schmidt-Grund,
Marius Grundmann
Abstract:
We report on the temporal lasing dynamics of high quality ZnO nanowires using time-resolved micro-photoluminescence technique. The temperature dependence of the lasing characteristics and of the corresponding decay constants demonstrate the formation of an electron-hole plasma to be the underlying gain mechanism in the considered temperature range from 10 K to 300 K. We found that the temperature…
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We report on the temporal lasing dynamics of high quality ZnO nanowires using time-resolved micro-photoluminescence technique. The temperature dependence of the lasing characteristics and of the corresponding decay constants demonstrate the formation of an electron-hole plasma to be the underlying gain mechanism in the considered temperature range from 10 K to 300 K. We found that the temperature dependent emission onset-time ($t_{\text{on}}$) strongly depends on the excitation power and becomes smallest in the lasing regime, with values below 5 ps. Furthermore, the observed red shift of the dominating lasing modes in time is qualitatively discussed in terms of the carrier density induced change of the refractive index dispersion after the excitation laser pulse. This theory is supported by extending an existing model for the calculation of the carrier density dependent complex refractive index for different temperatures. This model coincides with the experimental observations and reliably describes the evolution of the refractive index after the excitation laser pulse.
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Submitted 15 January, 2016;
originally announced January 2016.
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The Singular Optical Axes in Biaxial Crystals and Analysis of Their Spectral Dispersion Effects in $β$-Ga$_2$O$_3$
Authors:
Marius Grundmann,
Chris Sturm
Abstract:
We classify and distinguish optically biaxial materials, which can have triclinic, monoclinic or orthorhombic crystal symmetry, by the degeneracy of the indices of refraction of their four singular optical axes (Windungsachsen) in the absorption regime. We provide explicit analytical solutions for angular orientations of the singular optical axes in monoclinic crystals and orthorhombic crystals. A…
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We classify and distinguish optically biaxial materials, which can have triclinic, monoclinic or orthorhombic crystal symmetry, by the degeneracy of the indices of refraction of their four singular optical axes (Windungsachsen) in the absorption regime. We provide explicit analytical solutions for angular orientations of the singular optical axes in monoclinic crystals and orthorhombic crystals. As a model material we analyze monoclinic gallia ($β$-Ga$_2$O$_3$) and discuss in detail the dispersion (i.e. the spectral variation of the angular position) of its singular optical axes. For a certain energy range ($E \approx 7.23$-$7.33$ eV) we find quasi-uniaxial symmetry. At two energies ($E \approx 8.14$ eV and $E \approx 8.37$ eV) we find triaxial spectral points for which one regular optical axis and two singular optical axes exist. Concurrently a Stokes analysis of the spectral dependence of the electrical field eigenvectors is made and discussed for various crystal orientations. For a singular optical axis $|S_3|=1$; for the two degenerate singular axes at the triaxial point the Stokes vector is undefined. For a certain energy ($E=6.59$ eV), the $\langle 010 \rangle$-orientation is close to a singular optical axis, $|S_3|=0.977$. The analysis provided here is prototypical for the treatment of the optical properties of optically biaxial functional materials in the absorption and gain regimes.
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Submitted 14 January, 2016;
originally announced January 2016.
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Dielectric tensor of monoclinic Ga$_2$O$_3$ single crystals in the spectral range $0.5 - 8.5\,$eV
Authors:
Chris Sturm,
Jürgen Furthmüller,
Friedhelm Bechstedt,
Rüdiger Schmidt-Grund,
Marius Grundmann
Abstract:
The dielectric tensor of $β$-Ga$_2$O$_3$ was determined by generalized spectroscopic ellipsometry in a wide spectral range from $0.5\,\mathrm{eV}$ to $8.5\,\mathrm{eV}$ as well as by calculation including quasiparticle bands and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are a…
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The dielectric tensor of $β$-Ga$_2$O$_3$ was determined by generalized spectroscopic ellipsometry in a wide spectral range from $0.5\,\mathrm{eV}$ to $8.5\,\mathrm{eV}$ as well as by calculation including quasiparticle bands and excitonic effects. The dielectric tensors obtained by both methods are in excellent agreement with each other and the observed transitions in the dielectric function are assigned to the corresponding valence bands. It is shown that the off-diagonal element of the dielectric tensor reaches values up to $|\varepsilon_{xz} | \approx 0.30 $ and cannot be neglected. Even in the transparent spectral range where it is quite small ($|\varepsilon_{xz} | < 0.02 $) it causes a rotation of the dielectric axes around the symmetry axis of up to $20^\circ$.
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Submitted 20 July, 2015;
originally announced July 2015.
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Discrete relaxation of exciton-polaritons in an inhomogeneous potential
Authors:
T. Michalsky,
H. Franke,
C. Sturm,
M. Grundmann,
R. Schmidt-Grund
Abstract:
We present indications, that the wave function-stiffness condition during energy-relaxation as observed in single-phase state quantum systems manifests also in a single particle ensemble. This is demonstrated for exciton-polaritons in the strong coupling regime in a ZnO-based microcavity at T = 10 K for non-resonant excitation. It is well known that the pump-induced spatially inhomogeneous backgro…
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We present indications, that the wave function-stiffness condition during energy-relaxation as observed in single-phase state quantum systems manifests also in a single particle ensemble. This is demonstrated for exciton-polaritons in the strong coupling regime in a ZnO-based microcavity at T = 10 K for non-resonant excitation. It is well known that the pump-induced spatially inhomogeneous background potential leads to nearly equally spaced energy levels in the k-space distribution for propagating polariton Bose-Einstein condensates. Surprisingly this particular pattern is also observable for uncondensed exciton-polaritons.
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Submitted 12 January, 2015;
originally announced January 2015.
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Cavity Polariton Condensate in a Disordered Environment
Authors:
Martin Thunert,
Alexander Janot,
Helena Franke,
Chris Sturm,
Tom Michalsky,
María Dolores Martín,
Luis Viña,
Bernd Rosenow,
Marius Grundmann,
Rüdiger Schmidt-Grund
Abstract:
We report on the influence of disorder on an exciton-polariton condensate in a ZnO based bulk planar microcavity and compare experimental results with a theoretical model for a non-equilibrium condensate. Experimentally, we detect intensity fluctuations within the far-field emission pattern even at high condensate densities which indicates a significant impact of disorder. We show that these effec…
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We report on the influence of disorder on an exciton-polariton condensate in a ZnO based bulk planar microcavity and compare experimental results with a theoretical model for a non-equilibrium condensate. Experimentally, we detect intensity fluctuations within the far-field emission pattern even at high condensate densities which indicates a significant impact of disorder. We show that these effects rely on the driven dissipative nature of the condensate and argue that they can be accounted for by spatial phase inhomogeneities induced by disorder, which occur even for increasing condensate densities realized in the regime of high excitation power. Thus, non-equilibrium effects strongly suppress the stabilization of the condensate against disorder, contrarily to what is expected for equilibrium condensates in the high density limit. Numerical simulations based on our theoretical model reproduce the experimental data.
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Submitted 16 November, 2015; v1 submitted 30 December, 2014;
originally announced December 2014.
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Driven-dissipative confined polariton condensate under magnetic field
Authors:
C. Sturm,
D. Solnyshkov,
O. Krebs,
A. Lemaître,
I. Sagnes,
E. Galopin,
A. Amo,
G. Malpuech,
J. Bloch
Abstract:
We investigate exciton-polariton condensation under magnetic field in a single high-quality semiconductor micropillar cavity. We observe successive polariton condensation of each spin component for two distinct threshold powers. Pronounced and non-monotonous variations of both the Zeeman splitting and the circular polarization of the emission are measured across these two condensation thresholds.…
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We investigate exciton-polariton condensation under magnetic field in a single high-quality semiconductor micropillar cavity. We observe successive polariton condensation of each spin component for two distinct threshold powers. Pronounced and non-monotonous variations of both the Zeeman splitting and the circular polarization of the emission are measured across these two condensation thresholds. This unexpected behavior deeply deviates from the so-called spin Meissner effect predicted for a fully thermalized system. Our measurements can be understood in a kinetic approach taking into account spin-anisotropic interactions within the entire system: the polariton condensate and the cloud of uncondensed excitons.
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Submitted 17 September, 2014;
originally announced September 2014.
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Realization of a double barrier resonant tunneling diode for cavity polaritons
Authors:
Hai Son Nguyen,
Dmitry Vishnevsky,
Chris Sturm,
Dimitrii Tanese,
Dmitry Solnyshkov,
Elisabeth Galopin,
Aristide Lemaître,
Isabelle Sagnes,
Alberto Amo,
Guillaume Malpuech,
Jacqueline Bloch
Abstract:
We report on the realization of a double barrier resonant tunneling diode for cavity polaritons, by lateral patterning of a one-dimensional cavity. Sharp transmission resonances are demonstrated when sending a polariton flow onto the device. We use a non-resonant beam can be used as an optical gate and control the device transmission. Finally we evidence distortion of the transmission profile when…
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We report on the realization of a double barrier resonant tunneling diode for cavity polaritons, by lateral patterning of a one-dimensional cavity. Sharp transmission resonances are demonstrated when sending a polariton flow onto the device. We use a non-resonant beam can be used as an optical gate and control the device transmission. Finally we evidence distortion of the transmission profile when going to the high density regime, signature of polariton-polariton interactions.
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Submitted 22 May, 2013;
originally announced May 2013.
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Giant phase modulation in a Mach-Zehnder exciton-polariton interferometer
Authors:
C. Sturm,
D. Tanese,
H. S. Nguyen,
H. Flayac,
E. Gallopin,
A. Lemaître,
I. Sagnes,
D. Solnyshkov,
A. Amo,
G. Malpuech,
J. Bloch
Abstract:
We report on a new mechanism of giant phase modulation. The phenomenon arises when a dispersed photonic mode (slow light) strongly couples to an excitonic resonance. In such a case, even a small amount of optically injected carriers creates a potential barrier for the propagating exciton-polariton which provokes a considerable phase shift. We evidence this effect by fabricating an exciton-polarito…
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We report on a new mechanism of giant phase modulation. The phenomenon arises when a dispersed photonic mode (slow light) strongly couples to an excitonic resonance. In such a case, even a small amount of optically injected carriers creates a potential barrier for the propagating exciton-polariton which provokes a considerable phase shift. We evidence this effect by fabricating an exciton-polariton Mach-Zehnder interferometer, modulating the output intensity by constructive or destructive interferences controlled by optical pumping of a micrometric size area. The figure of merit for a π phase shift, defined by the control power times length of the modulated region, is found at least one order of magnitude smaller than slow light photonic crystal waveguides.
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Submitted 7 March, 2013;
originally announced March 2013.
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Single charge sensing and transport in double quantum dots fabricated from commercially grown Si/SiGe heterostructures
Authors:
C. Payette,
K. Wang,
P. J. Koppinen,
Y. Dovzhenko,
J. C. Sturm,
J. R. Petta
Abstract:
We perform quantum Hall measurements on three types of commercially available modulation doped Si/SiGe heterostructures to determine their suitability for depletion gate defined quantum dot devices. By adjusting the growth parameters, we are able to achieve electron gases with charge densities 1-3 X 10^{11}/cm^2 and mobilities in excess of 100,000 cm^2/Vs. Double quantum dot devices fabricated on…
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We perform quantum Hall measurements on three types of commercially available modulation doped Si/SiGe heterostructures to determine their suitability for depletion gate defined quantum dot devices. By adjusting the growth parameters, we are able to achieve electron gases with charge densities 1-3 X 10^{11}/cm^2 and mobilities in excess of 100,000 cm^2/Vs. Double quantum dot devices fabricated on these heterostructures show clear evidence of single charge transitions as measured in dc transport and charge sensing and exhibit electron temperatures of 100 mK in the single quantum dot regime.
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Submitted 21 March, 2012; v1 submitted 13 December, 2011;
originally announced December 2011.