Electrons In Germanium Research Articles

Spin-to-charge conversion for hot photoexcited electrons in germanium

Spin-to-charge conversion for hot photoexcited electrons in germanium

Hot-electron effect in spin relaxation of electrically injected electrons in intrinsic Germanium

The hot-electron effect in the spin relaxation of electrically injected electrons in intrinsic germanium is investigated by the kinetic spin Bloch equations both analytically and numerically. It is shown that in the weak-electric-field regime with E ≲ 0.5 kV cm−1, our calculations have reasonable agreement with the recent transport experiment in the hot-electron spin-injection configuration (2013 Phys. Rev. Lett. 111 257204). We reveal that the spin relaxation is significantly enhanced at low temperature in the presence of weak electric field E ≲ 50 V cm−1, which originates from the obvious center-of-mass drift effect due to the weak electron–phonon interaction, whereas the hot-electron effect is demonstrated to be less important. This can explain the discrepancy between the experimental observation and the previous theoretical calculation (2012 Phys. Rev. B 86 085202), which deviates from the experimental results by about two orders of magnitude at low temperature. It is further shown that in the strong-electric-field regime with 0.5 ≲ E ≲ 2 kV cm−1, the spin relaxation is enhanced due to the hot-electron effect, whereas the drift effect is demonstrated to be marginal. Finally, we find that when 1.4 ≲ E ≲ 2 kV cm−1 which lies in the strong-electric-field regime, a small fraction of electrons (≲5%) can be driven from the L to Γ valley, and the spin relaxation rates are the same for the Γ and L valleys in the intrinsic sample without impurity. With the negligible influence of the spin dynamics in the Γ valley to the whole system, the spin dynamics in the L valley can be measured from the Γ valley by the standard direct optical transition method.

Intervalley Scattering of Hot Electrons in Germanium at Millikelvin Temperatures

A method is presented to determine the field dependence of the intervalley scattering rate for hot electrons in germanium, based on an analysis of electron straggle in a detector crystal fitted with segmented electrodes. Measurements in high-purity and in lightly doped n- and p-type crystals at millikelvin temperatures demonstrate the dominant role of impurity scattering at low field (\(<\sim \)a few V/cm), whereas phonon scattering takes precedence at higher field intensities. An analysis of the experimental data by reference to past investigations of the acoustoelectric effect in germanium strongly suggests that the impurities involved are the dopant species in the neutral state.

Spin-dependent intravalley and intervalley electron-phonon scatterings in germanium

The spin-dependent electron-phonon scattering in the L and Γ valleys of germanium crystals has been investigated theoretically. For this purpose, the 16 × 16 k · p Hamiltonian correctly describing the electron dispersion in the vicinity of the L point of the Brillouin zone in germanium in the lowest conduction bands and the highest valence bands has been constructed. This Hamiltonian facilitates the analysis of the spin-dependent properties of conduction electrons. Then, the electron scatterings by phonons in the L and Γ valleys, i.e., intra-L valley, intra-Γ valley, inter-L-Γ valley, and inter-L-L valley scatterings, have been considered successively. The scattering matrix expanded in powers of the electron wave vectors counted from the centers of the valleys has been constructed using the invariant method for each type of processes. The numerical coefficients in these matrices have been found by the pseudopotential method. The partial contributions of the Elliott and Yafet mechanisms to the spin-dependent electron scattering have been analyzed. The obtained results can be used in studying the optical orientation and relaxation of hot electrons in germanium.

Temperature dependence of spin lifetime of conduction electrons in bulk germanium

Optically generated spin polarized electrons in bulk n-type Ge samples have been detected by using a radio-frequency modulation technique. Using the Hanle effect in an external magnetic field, the spin lifetime was measured as a function of temperature in the range 90 K to 180 K. The lifetime decreases with increasing temperature from ∼5 ns at 100 K to ∼2 ns at 180 K. We show that the temperature dependence is consistent with the Elliott-Yafet spin relaxation mechanism [R. J. Elliot, Phys. Rev. 96, 266 (1954)].

Intrinsic spin lifetime of conduction electrons in germanium

We investigate the intrinsic spin relaxation of conduction electrons in germanium due to electron-phonon scattering. We derive intravalley and intervalley spin-flip matrix elements for a general spin orientation and quantify the resulting anisotropy in spin relaxation. The form of the intravalley spin-flip matrix element is derived from the eigenstates of a compact spin-dependent $\mathbf{k}$$\cdot$$\mathbf{p}$ Hamiltonian in the vicinity of the $L$ point (where thermal electrons are populated in Ge). Spin lifetimes from analytical integrations of the intravalley and intervalley matrix elements show excellent agreement with independent results from elaborate numerical methods.

Magneto-optical analysis of the effectivegtensor and electron spin decoherence in the multivalley conduction band of bulk germanium

We present a comprehensive study of electron spin decoherence in bulk germanium. As a first cornerstone, the effective $g$ tensor of $L$-valley electrons in germanium is deduced from time-domain magneto-optical experiments. The decay of the ensemble spin polarization is then found to be closely related to intervalley scattering. In particular, the angular and temperature dependences of the experiment are well described in a model including Elliott-Yafet-type spin-flip processes as well as dephasing due to scattering between valleys exhibiting different effective $g$ factors.

Measurement of Compton scattering on bound electrons by the coincidence method

A review of results of the new method for measuring the Compton scattering on bound electrons in germanium, introduced by the presented authors, is given. It is based on the application of two detectors that operate in the coincidence mode. One detector is used as the scatterer and the other as the detector of scattered radiation. Two conditions, simultaneity of pulses from the two detectors and constant energy sum, result in very clean spectra in broad energy regions. Normalization of the Compton spectra to the Ge K X-ray escape peaks, which are measured simultaneously with the Compton spectrum, gives reliable double-differential Compton-scattering cross sections on an absolute scale. Several versions of the impulse approximation are compared to the cross sections obtained by the present method for incident photon energies in the range from 60 to 105 keV. The non-relativistic impulse approximation gives the best agreement to the experimental data. We point out the suitability of the new method for an investigation of the incoherent scattering function at small photon momentum transfer.

Anisotropy and non-linearity of absorption of intensive IR light by free electrons in germanium

Anisotropy and non-linearity of absorption of intensive IR light by free electrons in germanium

Hall mobility of electrons in Ge in the vicinity of the L1 ⇄ Δ1 heterovalley transition induced by a high pressure

The data on the Hall mobility of electrons in germanium with a two-charge gold level are presented versus the hydrostatic pressure up to 7 GPa at 295 K. The parameters S = 0.57 ± 0.10 and S′ = 0.29 ± 0.12 characterizing the intensity of electron scattering between the nonequivalent L1 and Δ1 valleys in the vicinity of the heterovalley transition nave been calculated.

Determination of the inelastic mean free path (IMFP) of electrons in germanium and silicon by elastic peak electron spectroscopy (EPES) using an analyser of high resolution

The IMFP of electrons is a fundamental material parameter of surface analysis by AES, XPS, EPES and EELS. In surface analysis calculated IMFP values are used. Their experimental determination is rather difficult. The IMFP of amorphous Ge and polycrystalline Si was determined by comparing the elastic peak intensity ratios with electrolytic Ni reference sample of 1 nm surface roughness, achieved by dedicated Ar + ion bombardment cleaning and examined by STM. Experimental results obtained with a hemispherical analyser type ESA 31 developed by ATOMKI Debrecen have been evaluated by Monte Carlo analysis, based on Jablonski's differential elastic scattering cross sections and elaborated for the HSA analyser angular window. Due to the 5 × 10 −5 energy resolution of the ESA 31 no spectrometer correction was needed. The ratio of the background to the elastic peak was < 1% at 4 keV. The energy range was extended to 5keV using Ashley's IMFP data. Reasonable agreement was found with our previous CMA experimental results in the overlapping energy range and with Ashley. They exhibit systematically higher values by 15–20%. EPES proved to be an efficient tool for IMFP measurements.

Electronic Raman Scattering of Photoexcited Electrons in Germanium

We measured electronic Raman scattering originating from photoexcited L valley electrons in undoped, p-type ( N h =10 17 cm -3 ), and n-type ( N e =10 17 cm -3 ) germanium crystals at lattice temperature from RT to 76 K when stimulated by 1.58-eV laser light. From analysis of the power dependence of Raman intensity in the three samples and comparison of the spectral shape with reported data on heavily doped n-type crystal, the origin of this scattering is ascribed to electrons in the L valley. We analyzed this Raman scattering by using Ipatova's theory, and found that phonon assisted intervalley scattering was dominant in the temperature dependence of the width (FWHM of modified Lorentzian) of the electronic Raman scattering spectra. We also succeeded in reproducing the temperature dependence of scattering intensity taking into account the temperature dependent diffusion constant of electrons.

Energy-resolved electron momentum densities of diamond-structure semiconductors

The linear muffin-tin orbital (LMTO) method has been used to calculate energy and momentum distributions of valence electrons in diamond, silicon, germanium and grey tin along (100), (110) and (111) directions and as the spherical average over the irreducible wedge of the Brillouin zone. These data can be used for interpreting results of (e,2e) experiments on single-crystal, polycrystalline and amorphous targets.

Axial-channeling radiation from MeV electrons in various crystal targets

Relativistic electrons and positrons under channeling conditions are steered by crystallographic planes (planar channeling) or axes (axial channeling). Their spontaneous transitions between the energy levels available for them in the transverse potential result in the emission of channeling radiation. The transverse axial potential for axially channeled electrons is obtained in the continuum approximation from a Nielsen-type interatomic potential. We introduce a parameter in the axial potential phenomenologically which is written heuristically to reflect the charge state and thermal vibrations of the target atoms. The channeling radiation energies from axially channeled electrons (of a few MeV energy) in diamond (C), silicon (Si) and germanium (Ge) are calculated. In diamond we show the dependence of radiation energies on axial channeling directions. Their dependence on thermal vibrations of target atoms and energy of the projectiles (electrons) is shown in silicon. The thermal vibrations reduce the channeling radiation energies. In germanium, the calculated radiation energy is compared with previous calculations. The agreement between the measured and our calculated values is quite good. Further calculations for Ni, Mo and W crystals have been performed to show that the assumed form of the parameter B is universal.

Study of the fundamental linewidths of 1S-->nP donor transitions in ultrapure germanium.

The fundamental linewidths of dipole transitions of donor-bound electrons in ultrapure germanium were investigated. The experiments were performed on the stress-insensitive D(H,O) donor complex which is present in concentrations of ${10}^{11}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. Various transitions (n=2,3,4,5,6) were tuned with a variable magnetic field to the frequencies of several far-infrared laser lines and the photothermal response was recorded. The transitions 1S\ensuremath{\rightarrow}2${P}_{\mathrm{\ensuremath{-}}}$ and 1S\ensuremath{\rightarrow}3${P}_{\mathrm{\ensuremath{-}}}$ lead to Lorentzian lines with a full width at half maximum (FWHM) of 8.2\ifmmode\pm\else\textpm\fi{}0.4 \ensuremath{\mu}eV. Higher excited states produce lines with a FWHM of around 6.4 \ensuremath{\mu}eV, the narrowest lines for electronic transition ever recorded. The experiments show that the observed linewidths do not depend on the sample temperature below 9 K, the applied electric field below 1.4 eV ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, or band-edge light. The last process creates free electrons and holes which in turn are captured by ionized donors and acceptors. Stark broadening by random Coulomb fields from ionized impurities is thereby greatly reduced. The experimentally determined linewidths are dominated by the excited-state lifetime which results from the electron--acoustic-phonon interaction. This interaction couples the bound excited state to all the other nearby states. The excited-state lifetimes derived from the linewidths are in agreement with the values predicted by the theory of Barrie and Nishikawa.

Radiation from axially channeled 1-MeV electrons in germanium

Energy spectra of the channeling radiation from 0.8 and 1.0 MeV electrons channeled along the 〈111〉 axis of a germanium crystal were measured using a high voltage electron microscope attached with a gas flow proportional counter. Subtracting the yield of the Ge L X-rays and bremsstrahlung, the contribution of the channeling radiation was obtained. Peak energy of the radiation at 0.8 and 1.0 MeV and the incident angle dependence of the channeling radiation intensity are in good agreement with calculated ones.

Anisotropy of Microwave Complex Conductivity Due to Hot Electrons in n-Type Germanium

Anisotropy of Microwave Complex Conductivity Due to Hot Electrons in n-Type Germanium

The effect of high magnetic fields on the ground state of hydrogen‐like impurities in semiconductors

AbstractA variational calculation has been made of the ground state energy of a semiconductor impurity in the effective mass approximation (EMA), in the presence of high magnetic fields. The field dependence of the computed binding energy and the wave function parameters are presented. The calculation was made for isotropic effective mass as well as for a mass anisotropy corresponding to electrons in germanium. The effect of the many‐valley structure of the conduction band in germanium, and the deviations from the EMA, are discussed.

Carrier-Concentration-Dependent Mobility inn-Type High-Purity Germanium

The Hall mobility of electrons in high-purity germanium was studied over a range from 7 to 200 \ifmmode^\circ\else\textdegree\fi{}K in a series of samples both before and after irradiation with $^{60}\mathrm{Co}$ $\ensuremath{\gamma}$ rays. In several unirradiated samples the mobility was limited mainly by lattice scattering down to 7 \ifmmode^\circ\else\textdegree\fi{}K. The mobility at 35 \ifmmode^\circ\else\textdegree\fi{}K decreased with radiation dose for all samples, but the magnitude of the decrease was greater in samples having lower carrier concentrations ${n}_{e}$. This decrease was well correlated with ${n}_{e}$. Measured mobilities at 35 \ifmmode^\circ\else\textdegree\fi{}K were significantly lower than values calculated from the Brooks-Herring impurity-scattering expression for ${n}_{e}&lt;{10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. At ${n}_{e}={10}^{11}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ the measured mobility was 0.01 times the calculated mobility. No satisfactory explanation has been found.

Determination of Effective Mass and the Pair Production Energy for Electrons in Germanium from Zener Diode Characteristics

Reverse I-V characteristics of germanium p-n junctions with breakdown voltage between 2 and 4 volts have been used to obtain the effective mass of the tunneling electrons and the minimum energy required to produce an electron-hole pair. The obtained value of the threshold energy is in good agreement with Shockley's theory.