Phonon Deformation Potentials Research Articles

Enhancement of electron–phonon coupling due to increased magnetism and applied hydrostatic pressure in FeSe

Inspired by the parabolic trend of the superconducting transition temperature (Tc ) of bulk FeSe under hydrostatic pressure, we investigated the effect of magnetism and hydrostatic pressure on the electron–phonon coupling (EPC) in FeSe using density-functional perturbation theory. We found that both magnetism and hydrostatic pressure enhanced EPC. The enhancement of the EPC is mainly attributed to phonon softening and deformation potential induced by magnetism, rather than Fermi surface nesting. Furthermore, we investigated the effect of spin fluctuations on superconductivity by applying the random phase approximation method. A possible application of our results to the phase diagram of FeSe under hydrostatic pressure was discussed, and we demonstrated that when EPC and spin fluctuations are both considered, a parabolic superconducting Tc may be obtained, providing a plausible explanation for the phase of FeSe under hydrostatic pressure.

Spatially resolved Raman piezospectroscopy for nondestructive evaluation of residual stress in β-Ga2O3 films

In this paper, the piezospectroscopic effect for β-Ga2O3, i.e. the spectral band shift in response to strain/stress, has been calibrated by the indentation method using spatially resolved Raman spectroscopy for quantitative stress evaluation of Ga2O3 devices, taking advantage of the crack-tip tensile stress field and the spatial probe deconvolution. A series of Vickers indentation prints were introduced on (010) and () Ga2O3 single crystals, and the relationships between observed band shifts and residual stresses were clarified to determine the phonon deformation potentials of the Raman bands. Accordingly, a quantitative analysis of the residual stress field in a Ga2O3 thin film grown on (0001) sapphire by plasma-assisted pulsed laser deposition, which revealed the presence of a gradient of incompletely released stress in the depth direction of the film, is shown as an example.

Raman strain–shift measurements and prediction from first-principles in highly strained silicon

This work presents how first-principles simulations validated through experimental measurements lead to a new accurate prediction of the expected Raman shift as a function of strain in silicon (Si). Structural relaxation of a strained primitive cell is first performed to tackle the relative displacement of the Si atoms for each strain level. Density functional perturbation theory is then used to compute the energy of the optical phonon modes in highly strained Si and retrieve the strain–shift trend. The simulations are validated by experimental characterization, using scanning electron microscopy (SEM) coupled with backscattering Raman spectroscopy, of silicon microbeams fabricated using a top-down approach. The beams are strained up to 2% thanks to the internal tensile stress of silicon nitride (Si3N4) actuators, allowing a validation of the perturbation theory in high-strain conditions. The results are compared with the phonon deformation potentials theory, and the uncertainty caused by the various parameters found in the literature is discussed. The simulated strain–shift coefficients of $$-175.77\,{\text {cm}}^{-1}$$ (resp. $$-400.85\,{\text {cm}}^{-1}$$ ) and the experimental one of $$-160.99\,{\text {cm}}^{-1}$$ (resp. $$-414.97\,{\text {cm}}^{-1}$$ ) are found for the longitudinal optical LO (resp. transverse optical TO $$_{1}$$ ) mode, showing good agreement.

Determination of the acoustic phonon deformation potentials in diamond

The interaction between acoustic phonons and electrons in diamond has been investigated by comparing state-of-the-art time-of-flight drift velocity measurements with Monte Carlo simulations. We use a multivariable anisotropic description of acoustic deformation potential scattering. The phonon-electron interaction is the limiting factor for the carrier mobility in ultrapure single crystal diamond. Hence, having a correct description is necessary for both device simulations and for predicting the maximum device performance. The experiments were performed at low temperature and using ultrapure diamond to minimize the influence of other scattering sources. The electronic valley polarization in diamond at low temperatures enables determination of both uniaxial and dilatation deformation potentials in the same experiment. The uniaxial and dilatation deformation potentials are found to be $18.5\ifmmode\pm\else\textpm\fi{}0.2$ and $\ensuremath{-}5.7\ifmmode\pm\else\textpm\fi{}0.3$ eV, respectively.

Spin manipulation and decoherence in a quantum dot mediated by a synthetic spin–orbit coupling of broken T-symmetry

The electrical control of a spin qubit in a quantum dot (QD) relies on spin–orbit coupling (SOC), which could be either intrinsic to the underlying crystal lattice or heterostructure, or extrinsic via, for example, a micro-magnet. In experiments, micromagnets have been used as a synthetic SOC to enable strong coupling of a spin qubit in quantum dots with electric fields. Here we study theoretically the spin relaxation, pure dephasing, spin manipulation, and spin–photon coupling of an electron in a QD due to the synthetic SOC induced spin–orbit mixing. We find qualitative difference in the spin dynamics in the presence of a synthetic SOC compared with the case of the intrinsic SOC. Specifically, spin relaxation due to the synthetic SOC and deformation potential phonon emission (or Johnson noise) shows (or B 0) dependence with the magnetic field, which is in contrast with the (or ) dependence in the case of the intrinsic SOC. Moreover, charge noise induces fast spin dephasing to the first order of the synthetic SOC, which is in sharp contrast with the negligible spin pure dephasing in the case of the intrinsic SOC. These qualitative differences are attributed to the broken time-reversal symmetry (T-symmetry) of the synthetic SOC. An SOC with broken T-symmetry (such as the synthetic SOC from a micro-magnet) eliminates the ‘Van Vleck cancellation’ and causes a finite longitudinal spin–electric coupling that allows the longitudinal coupling between spin and electric field, and in turn allows spin pure dephasing. Finally, through proper choice of magnetic field orientation, the electric-dipole spin resonance via the synthetic SOC can be improved with potential applications in spin-based quantum computing.

Tracing microscopic atomic displacements using polarized Raman spectroscopy: a case study on BaTiO3

Here, we demonstrate the power of polarized Raman spectroscopy (PRS) in tracing microscopic atomic displacements in a single crystalline material. Crystalline materials often show extremely small microscopic atomic displacements as a function of temperature, pressure, electric and magnetic field or across phase transition which can be traced by our defined method using routinely available Raman spectrometers and with the knowledge of Raman tensors and phonon deformation potentials. Importantly, the information is directional and provides a vital information about the root cause of polarization in ferroelectrics, multiferroics. In this article, the method is demonstrated by carrying out the temperature and directional dependent PRS study on BaTiO3 single crystal, where the Ti ion displacement across the various phase transitions is well documented. The value of the ferroelectric polarization and its component along different crystallographic axes as well as their temperature variations calculated from the Ti displacement obtained by our defined method matches well with the reported results obtained from other techniques. This method thus can be applied to obtain quantitative information of atomic displacements in a crystalline solid.

Coherent-interface-induced strain in large lattice-mismatched materials: A new approach for modeling Raman shift.

Strain engineering as one of the most powerful techniques for tuning optical and electronic properties of Ill-nitrides requires reliable methods for strain investigation. In this work, we reveal, that the linear model based on the experimental data limited to within a small range of biaxial strains (< 0.2%), which is widely used for the non-destructive Raman study of strain with nanometer-scale spatial resolution is not valid for the binary wurtzite-structure group-III nitrides GaN and AlN. Importantly, we found that the discrepancy between the experimental values of strain and those calculated via Raman spectroscopy increases as the strain in both GaN and AlN increases. Herein, a new model has been developed to describe the strain-induced Raman frequency shift in GaN and AlN for a wide range of biaxial strains (up to 2.5%). Finally, we proposed a new approach to correlate the Raman frequency shift and strain, which is based on the lattice coherency in the epitaxial layers of superlattice structures and can be used for a wide range of materials.Electronic Supplementary MaterialSupplementary material (Table S1: Values of bulk phonon deformation potentials and elastic constants for GaN and AlN from each reference used in Table 1, Fig. S1: Lattice parameters of SL layers using Eq. (8), and Fig. S2: Raman mapping using Eq. (7)) is available in the online version of this article at 10.1007/s12274-021-3855-4.

구속 포텐셜에서 반도체 물질(Ge)의 자기장 의존성

This paper proposes an application of artificial neural networks for analyzing electricity market that has insufficient information for calculating equilibrium. Neural networks are constructed and trained on two representative cases in the electricity market. One is for calculating equilibrium price in perfect competition market and the other is for determining whether the transmission congestion occurs. The neural network uses a multilayer structure and learns with backpropagation algorithms for training. The neural networks trained in the case studies calculate the market price with a high probability and also determines an occurrence of the transmission congestion accurately. We study optical quantum transition line shapes (QTLS) showing the absorption power and quantum transition line widths (QTLW) of an electron deformation potential phonon interaction system. In order to analyze quantum transfer, the QTLW and QTLS with the magnetic field dependence was compared in two transfer processes, I.e., intra-Land level transfer process. In order to apply quantum transport theory (QTR) to a system that confines electrons by a square well confining potential, the Liouville equation projected with the Equilibrium Average Projection Scheme (EAPS) was used.

Raman scattering study of GeSn under 〈1 0 0〉 and 〈1 1 0〉 uniaxial stress

The application of strain into GeSn alloys can effectively modulate the band structures, thus creating novel electronic and photonic devices. Raman spectroscopy is a powerful tool for characterizing strain; however, the lack of Raman coefficient makes it difficult for accurate determination of strain in GeSn alloys. Here, we have investigated the Raman-strain function of Ge1−x Sn x along 〈1 0 0〉 and 〈1 1 0〉 directions. GeSn nanomembranes (NMs) with different Sn compositions are transfer-printed on polyethylene terephthalate substrates. External strain is introduced by bending fixtures with different radii, leading to uniaxial tensile strain up to 0.44%. Strain analysis of flexible GeSn NMs bent along 〈1 0 0〉 and 〈1 1 0〉 directions are performed by Raman spectroscopy. The linear coefficients of Raman-strain for Ge0.96Sn0.04 are measured to be −1.81 and −2.60 cm−1, while those of Ge0.94Sn0.06 are decreased to be −2.69 and −3.82 cm−1 along 〈1 0 0〉 and 〈1 1 0〉 directions, respectively. As a result, the experimental ratio of linear coefficient (ROLC) of Ge, Ge0.96Sn0.04 and Ge0.94Sn0.06 are 1.34, 1.44 and 1.42, which agree well with theoretical ROLC values calculated by elastic compliances and phonon deformation potentials (PDPs). In addition, the compositional dependence of PDPs is analyzed qualitatively. These fundamental parameters are important in designing high performance strained GeSn electronic and photonic devices.

The impurity size-effect and phonon deformation potentials in wurtzite GaN

Doping induced changes in lattice parameters are investigated experimentally for the shallow donors silicon and germanium in thin-film wurtzite a-plane GaN. Silicon doping results in a lattice contraction while germanium doping results in a small but measurable lattice expansion. By high-resolution x-ray diffraction, we are able to determine the isotropically averaged size-effect with high accuracy. The analysis procedure yields en passant results for the phonon deformation potentials and .

Theoretical Study of Electron Transport Properties in GaN-Based HEMTs Using a Deterministic Multi-Subband Boltzmann Transport Equation Solver

A high-electron mobility transistor (HEMT) with a GaN channel is simulated using a deterministic multi-subband Boltzmann transport equation solver. A structure that includes an InGaN back barrier is considered. The electron mobility is calculated for the 1-D heterostructure to identify the contribution of each scattering mechanism to the electron mobility. For GaN-based HEMTs, electron transport in a non-equilibrium state is determined by solving the multi-subband Boltzmann equation expanded with Fourier harmonics. The polar optical phonon and the deformation potential phonon are considered to explain the scattering of the device while considering the Pauli principle. The results of a simulation conducted to assess the mobility and ${I}$ – ${V}$ characteristics are compared with experimental results from the AlInN/AlN/GaN/InGaN HEMT structure. The cutoff frequency of the HEMT is also estimated under the quasi-static approximation.

Determination of phonon deformation potentials and strain-shift coefficients in Ge-rich Si1−xGex using bulk Ge-rich Si1−xGex crystals and oil-immersion Raman spectroscopy

The strain-free Raman shift of the Ge–Ge mode, , of Ge-rich Si1−xGex (x: Ge fraction) was determined accurately from the bulk Ge-rich Si1−xGex samples fabricated by the Czochralski (Cz) method. Using the obtained , the phonon deformation potentials (PDPs), p and q, and the strain-shift coefficient bLO of isotropic biaxial strained Ge-rich Si1−xGex thin films were extracted by oil-immersion Raman spectroscopy using Raman peak shifts of longitudinal and transverse optical (LO and TO) phonon modes. As a result, it was confirmed that these parameters are almost constant with small variations and that the strain-shift coefficient bLO is in good agreement with ab initio calculations. The parameters determined in this work are essential to realize accurate strain measurements using Raman spectroscopy for Ge-rich Si1−xGex devices.

Determination of Phonon Deformation Potentials in Carbon-doped Silicon

Background and purpose Carbon-doped silicon (Si:C) is used as a stressor to the channel of n-type MOSFET [1]. However, there are few report directly evaluated the strain states of Si:C. The strain-Raman coefficient that relate Raman shift to in-plane strain has not been derived yet. In this study, we determined the strain-Raman coefficient for Si:C using water-immersion Raman spectroscopy in conjunction with X-ray diffraction (XRD) measurement. Experimental method Si:C films were grown on (001) Si substrate by molecular beam epitaxy. The film thickness were 43, 50 and 37 nm, with C concentration of 0.600%, 0.826% and 1.14% respectively. The film thickness and the C concentration were confirmed by cross section TEM and SIMS measurement, respectively. Raman peak shift was measured by water immersion Raman spectroscopy. For the Raman evaluation, the numerical aperture of the water immersion lens and the refractive index of the medium were 1.2 and 1.3, respectively. The wavelength of the excitation light source and the focal length of the spectrometer were 355 nm and 2000 mm. Here, the penetration depth is approximately 5 nm. All the Raman spectroscopy were performed under the LO-active conditions. The in-plane and out-of-plane strain were measured by XRD. Part of the XRD measurement was performed at SPring-8 using synchrotron radiation as X-ray source. Results and Discussion Figure 1 shows the Raman peak shift obtained from Si:C with various C concentration. The spectra were calibrated with the strain-free single crystalline-Si (c-Si) at 520 cm-1. From Fig. 1, the Raman shift is decreased as the C concentration increases. This reflect the tensile strain is applied to Si:C. Table 1 shows the results of the XRD, and the in-plane and out-of-plane strain in Si:C. Here, ε || and ε ⊥ are the in-plane and out-of-plane strain, respectively. The in-plane and out-of-plane lattice spacing of c-Si is 1.357525 Å. From Table 1, it is clear that the tensile strain is applied to Si:C. This is consistent with the Raman spectroscopy result. There should be a relationship such as the following equation between Raman shift and in-plane strain. ω Si:C = ω Si + ax + bε || (1) Here, ω Si:C and ω Si are the Raman shift of Si:C and Si, x is C concentration, and a and b are the alloy-disorder coefficient and strain-shift coefficient, respectively. In this study, we used the value of a coefficient to be 210 cm-1 to determine b coefficient [2]. From Eq. (1), the in-plane strain ε || can be obtained by the following equation using LO phonon Raman wavenumber shift from the strain-free Raman shift ω 0 Δω LO = ω Si:C – ω 0 = bε ||, (2) ω 0 = ω Si + ax = 520 + 210x. (3) Figure 3 shows Raman wavenumber shift Δω LO as a function of the in-plane strain ε || obtained from the XRD. The dotted line is the linear fit to the experimental data. As shown in Fig. 3, although the C concentration x range is very narrow, we confirmed that the Δω LO shows a linear dependence on the in-plane strain ε ||. Finally, we have succeeded to determine the value of strain-Raman (b) coefficient: b = -539.5 cm-1. Acknowledgements The XRD measurement of 0.600 and 1.06% Si:C was performed at SPring-8 (JASRI) with proposal number of 2015A1971, 2015B1925.

(Invited) Strain and Electromechanical Coupling at the Nanoscale in Atomically Thin Transition Metal Dichalcogenides

The introduction of mechanical strain is a well-established technique for engineering electronic and optical properties in a broad range of semiconductor materials. In atomically thin materials such as graphene and mono- or few-layer transition metal dichalcogenides (TMDCs), the deliberate introduction and engineering of strain becomes an even more powerful approach for controlling material properties due to the high levels of elastic strain that can be accommodated and the feasibility of achieving precise, highly inhomogeneous strain distributions at the nanoscale. Full realization of and control over these possibilities will require the ability to characterize and control strain, and accompanying changes in electronic, optical, electromechanical, or other properties, in such materials at the nanoscale. To this end, we have used a variety of proximal probe microscopy and spectroscopy techniques to characterize strain and associated material properties in TMDC materials with nanoscale spatial resolution. We first describe the use of tip-enhanced Raman spectroscopy (TERS) and tip-enhanced photoluminescence (TEPL) to characterize strain and optical properties of atomically thin MoS2 to which local strain has been applied via transfer onto a nanopatterned substrate. In these studies, plasmonic modes at the apex of a metal-coated scanning probe tip are excited by laser illumination at or near the plasmon resonance wavelength, enabling Raman scattering and photoluminescence signals to be detected from nanoscale volumes with precise positional control. In tip-induced resonant Raman spectroscopy of monolayer and bilayer MoS2, we observe large enhancements in Raman signal levels measured for MoS2 associated with excitation of plasmonic gap modes between an Au-coated probe tip and Au substrate surface onto which MoS2 has been transferred. Transitions in exciton photoluminescence intensity between monolayer and bilayer regions of MoS2 are observed and discussed. Significant differences in nanoscale Raman spectra between monolayer and bilayer MoS2 are also observed. The origins of specific resonant Raman peaks, their dependence on MoS2 layer thickness, and spatial resolution associated with the transition in Raman spectra between monolayer and bilayer regions are described. In TERS and TEPL studies of bilayer MoS2 with inhomogeneous strain created by transfer to a nanopatterned Au-coated substrate, we observe clear shifts in Raman peak positions and intensities which we correlate with MoS2 phonon deformation potentials and strain-induced changes in electronic structure and phonon dispersion. We then present an example of previously unobserved physical behavior that can arise in connection with nanoscale variations in strain in atomically thin TMDC materials, specifically in the area of electromechanical coupling – the interplay between strain and dielectric polarization in materials. Piezoelectricity, in which there is a linear relationship between dielectric polarization (or an applied electric field) and strain in materials lacking inversion symmetry, is the most well-known of such phenomena. Flexoelectricity, in which strain gradients induce a dielectric polarization field (or its converse, in which gradients in an applied electric field induce strain), is present in all materials but has been much less thoroughly studied, in large part due to the difficulty of achieving sufficiently large strain gradients in conventional crystalline materials. Atomically thin TMDCs offer unique opportunities to explore these and related phenomena. For example, in-plane piezoelectricity was theoretically predicted and subsequently observed experimentally to occur in monolayer and odd-layer MoS2, arising due to the reduction in crystal symmetry in the atomically thin limit. Here, we discuss piezoresponse force microscopy measurements in which out-of-plane electromechanical response, which we have tentatively attributed to flexoelectricity, is observed in monolayer MoS2 and other TMDCs. The estimated effective flexoelectric coefficients are found to be very consistent with those predicted by a simple physical model, and lead to electromechanical coupling response comparable in size to piezoelectric effects in the same materials.

Determination of Phonon Deformation Potentials in Carbon-Doped Silicon

Carbon-doped silicon (Si:C) is used as a stressor to the channel of n-type metal oxide semiconductor field-effect-transistor (MOSFET). In this study, we determined phonon deformation potentials (p and q) of Si:C to realize evaluation of anisotropic biaxial strain by using water-immersion Raman spectroscopy. Raman peak shift in longitudinal and transverse optical (LO and TO) phonon modes were measured by water-immersion Raman spectroscopy. Furthermore, in-plane and out-of-plane strain were measured by X-ray diffraction (XRD). Based on the Raman shift and the in-plane strain, p and q in each sample were derived. As a result, it took a different value from pure-Si, and the PDPs tended to increase as the C concentration increased.

Optical and structural study of deformation states in the GaN/AlN superlattices

We report on the effect of strain on the optical and structural properties of 5-, 10-, and 20-period GaN/AlN superlattices (SLs) deposited by plasma-assisted molecular beam epitaxy. The deformation state in SLs has been studied by high resolution transmission electron microscopy (HRTEM), X-ray diffraction, and micro-Raman, Fourier transform infrared (FTIR), and photoluminescence spectroscopy. HRTEM images showed that the structural quality of the SL layers is significantly improved and the interfaces become very sharp on the atomic level with an increase of the SL periods. A combined analysis through XRD, Raman, and FTIR reflectance spectroscopy found that with increasing number of SL periods, the strain in the GaN quantum wells (QWs) increases and the AlN barrier is relaxed. Based on the dependence of the frequency shift of the E2High and E1TO Raman and IR modes on the deformation in the layers, the values of the biaxial stress coefficients as well as the phonon deformation potentials of these modes in both GaN and AlN were determined. With increasing number of SL periods, the QW emission considerably redshifted in the range lower than the GaN band gap due to the quantum confined Stark effect. The influence of strain obtained by the XRD, Raman, and FTIR spectra on the structural parameters and QW emission of GaN/AlN SLs with different numbers of periods is discussed.

Residual stress measurement in a metal microdevice by micro Raman spectroscopy

Large residual stress induced during the electroforming process cannot be ignored to fabricate reliable metal microdevices. Accurate measurement is the basis for studying the residual stress. Influenced by the topological feature size of micron scale in the metal microdevice, residual stress in it can hardly be measured by common methods. In this manuscript, a methodology is proposed to measure the residual stress in the metal microdevice using micro Raman spectroscopy (MRS). To estimate the residual stress in metal materials, micron sized β-SiC particles were mixed in the electroforming solution for codeposition. First, the calculated expression relating the Raman shifts to the induced biaxial stress for β-SiC was derived based on the theory of phonon deformation potentials and Hooke’s law. Corresponding micro electroforming experiments were performed and the residual stress in Ni–SiC composite layer was both measured by x-ray diffraction (XRD) and MRS methods. Then, the validity of the MRS measurements was verified by comparing with the residual stress measured by XRD method. The reliability of the MRS method was further validated by the statistical student’s t-test. The MRS measurements were found to have no systematic error in comparison with the XRD measurements, which confirm that the residual stresses measured by the MRS method are reliable. Besides that, the MRS method, by which the residual stress in a micro inertial switch was measured, has been confirmed to be a convincing experiment tool for estimating the residual stress in metal microdevice with micron order topological feature size.

Determining the directional strain shift coefficients for tensile Ge: a combined x-ray diffraction and Raman spectroscopy study

In this work the calibration of the directional Raman strain shift coefficient for tensile strained Ge microstructures is reported. The strain shift coefficient is retrieved from micro-Raman spectroscopy measurements in combination with absolute strain measurements from x-ray diffraction using focused synchrotron radiation. The results are used to fit the phonon deformation potentials. A linear dependence of the phonon deformation potentials p and q is revealed. The method can be extended to provide strain calibration of Raman experiments also in other material system.

On the origins of anomalous elastic moduli and failure strains of GaP nanowires

Previous reports suggest that Raman peaks in uniaxially loaded nanowires with diamond cubic and zinc blende crystal structures shift at rates that are significantly different from bulk specimens. We have investigated the first order Raman scattering from individual, free-standing, [111] oriented GaP nanowires ranging from 75 to 180 nm in diameter at uniaxial tensile stresses up to 5 GPa. All of the phonon modes were shifted to frequencies lower than previously reported for bulk GaP, and significant splitting of the degenerate transverse optical mode was observed. A general analysis method using single and double Lorentzian fits of the Raman peaks is presented and used to report more accurate values of the phonon deformation potentials (PDPs) that relate uniaxial strains to Raman peak shifts in GaP. A new set of PDPs determined from the nanowires revealed that the they have elastic moduli and failure strains that are consistent with bulk GaP. The analysis method eliminated the anomalous, inconsistent deformation behavior commonly reported in Raman-based strain measurements of nanowires, and can be extended to other materials systems with degenerate phonons.

Phonon frequencies of a highly strained AlN layer coherently grown on 6H-SiC (0001)

Phonon frequencies of a high-quality AlN layer coherently grown on a 6H-SiC (0001) substrate are investigated by Raman scattering. Owing to the largest strain in our coherent AlN layer among heteroepitaxially grown AlN layers ever reported, phonon frequencies of the E2 (low), E2 (high), and A1 (LO) modes are considerably shifted to 244.5 (−3.3, compared with bulk AlN), 672.1 (+16.3), and 899 (+11)cm−1, respectively. Full widths at half maximum of the phonon modes in the coherent AlN are almost equal to those of high-quality bulk AlN, clearly indicating its high crystalline quality and uniform strain. We discuss accuracy of phonon deformation potentials reported by several other groups thorough comparing our experimental results.