Electrons In Germanium Research Articles

Anisotropic phonon scattering of electrons in germanium and silicon

Anisotropic phonon scattering of electrons in germanium and silicon

Cyclotron resonance of hot electrons in germanium : F.I. Bakun and E.M. Gershenzon (Vol. 6, No. 9, pp. 2847–2849).

Cyclotron resonance of hot electrons in germanium : F.I. Bakun and E.M. Gershenzon (Vol. 6, No. 9, pp. 2847–2849).

Line-Broadening of Cyclotron Resonance due to Lattice and Neutral Impurity Scattering in Silicon and Germanium

The relaxation times for electrons in germanium and silicon were measured from the half-width of the cyclotron resonance line at 6 mm wavelength over the temperature range from 1.6° to 20°K for the specimens of different impurity concentration. Above 3°K the reciprocal relaxation times for electrons in high purity specimens are 1/τ 0 =3.6×10 8 T 3/2 sec -1 for germanium and 1/τ 0 =2.6×10 8 T 3/2 sec -1 for silicon, respecitively. These results show that the acoustical lattice scattering is predominant in this region. For impure specimens, deviation from the T 3/2 -dependence was observed at low temperatures. This deviation is due to neutral impurity scattering. The applicability of Erginsoy's formula for neutral impurity scattering was examined. It was found that the conventional Erginsoy,s formula corrected for chemical shift agrees fairly well with the experimental results.

Conductivity anisotropy of warm and hot electrons in silicon and germanium

Experimental results for the anisotropy angle in n-type silicon are given for medium and high electric fields, i.e. for the warm and hot electron regions. Theoretical expressions for the coefficients β and γ characterizing the quadratic departure from Ohm's law are presented for the case of dominating acoustical scattering.

Hot Electron Hall Mobility of n-type Germanium

The Hall mobility of electrons in n-type germanium at high electric fields is studied, taking into consideration the ellipsoidal many-valley band structure. The distribution function of carriers in a many-valley semiconductor is first obtained assuming acoustic phonon, optical phonon and intervalley scattering. Expressions for Hall mobility are then derived using this distribution function and numerical computations made with the parameter values of n-type germanium. It is found that (i) the Hall mobility is anisotropic, (ii) its value is a maximum when the electric field is applied in the direction, and (iii) its value is a minimum when the electric field is in the direction. It is also found that the anisotropy factor is independent of the value of the electric field for predominant acoustic phonon scattering, but depends on the field for predominant optical and intervalley scattering.

Thermal Conductivity of Solids IV: Resonance Fluorescence Scattering of Phonons by Donor Electrons in Germanium

The scattering of phonons from donor electrons in germanium is computed and applied to the problem of heat conduction below the low-temperature maximum. The effective-mass approximation is used for the electronic wave function. The calculation is analogous to that of the dispersive scattering of light by atoms. Since the ground state is split into a singlet and a triplet with a separation of energy within the thermal phonon distribution, anomalous effects due to resonance scattering occur. Apart from these, our results are similar to previous work by Keyes. Taking into account the boundary and isotopic scattering as well as the electron-phonon interaction, excellent quantitative agreement with thermal conductivity data is obtained, with no adjustable parameters, for Sb and As donors in Ge. Certain discrepancies at higher temperatures can be traced to the inadequacy of the effective-mass approximation. In addition, anomalies in the "phonon drag" thermoelectric power can be understood on the basis of our theory. A by-product of our calculation is the lifetime broadening of the triplet state. The slightly different case of $n$-type Si is worked out while a more qualitative treatment of our resonant scattering mechanism is given for $p$-type semiconductors and samples under uniaxial strain.

Anisotropy of Neutral and Ionized Impurity Scattering of Electrons in Germanium

From measurements of the piezoresistance effect in germanium at 20 °K the momentum relaxation time anisotropy Kτ of electrons has been deduced. The results show a pronounced anisotropy when scattering by ions predominates and the values of Kτ(similar 9) are in good agreement with the theory proposed by Samoilovich et al. in 1962. In addition, the results suggest Kτ > 1 for neutral impurity scattering. This anisotropy is seen to be plausible by reference to the scattering of electrons by free neutral atoms.

Effects of Phonon Distributions on Hot Electrons in Semiconductors

At liquid helium temperature, electrons in germanium are easily heated with electric fields and hence excited from donor states in the conduction band. Under the condition of complete ionization of donors, the distribution function for phonons is investigated and the current density is calculated by assuming temperature and constant drift velocity for electrons and phonons, respectively. It is shown that the drift of phonons has no appreciable effect on electric current, but that the phonon temperature determind as a function of field strengths affects considerably the magnitude of the current density. The current density, j , calculated is proportional to F 1/5 where F is the field strength, provided that phonons are in equilibrium with the heat bath. If phonon temperature is increased by electric fields and becomes nearly equal to electron temperature, j is proportional to F 5/11 . Conditions for these cases are discussed.

Cyclotron Resonance of Hot Electrons in n-Type Germanium

The cyclotron resonance of electrons heated by the microwave field in n-type germanium is investigated. The half-width of the resonance line is calculated as the function of microwave power on the basis of the classical model and the concept of the electron temperature. The relation between the number of electrons in a valley and their temperature is discussed.

DRIFT VELOCITY OF HOT ELECTRONS IN n-TYPE GERMANIUM

The drift velocity of electrons in n-type germanium has been measured as a function of applied electric field at lattice temperatures of 77° K and 295° K. Three directions of applied field were used, viz. (100), (110), and (111) crystal directions. The range of field strength was from 500 v/cm to 75 kv/cm. A longitudinal anisotropy was observed at 77° K but not at 295° K. All specimens showed saturation of the drift velocity at high fields. At 77° K, all (100) specimens exhibited a breakdown effect, the cause of which is not known. The results are analyzed on the basis of an extension of Stratton's theory to the case of a many-valley semiconductor.

Inelastic Scattering of Electrons in Germanium

ln doped, compensated samples of germanium at low temperatures, a scattering center analogous to the hydrogen molecule ion may be formed in which an electron (or hole) is shared between two donors (or acceptors). Mobile carriers can lose energy through excitation of this molecule. This mechanism of energy loss is probably important in the explanation of the negative resistance observed in lightly doped, compensated germanium at liquid helium temperatures. A calculation of the average rate of energy loss is reported. (auth)

Noise Temperature of Hot Electrons in Germanium

Noise Temperature of Hot Electrons in Germanium

Cyclotron resonance of hot electrons in pure germanium

The frequency dependent non-ohmic behavior of conduction electrons in the static magnetic field, under the influence of applied microwave field, is investigated. As the electrons become hotter, the electron acoustical-phonon interaction becomes larger and the relaxation time shorter, so that the half-width of the cyclotron resonance line (ωτ) -1 grows up. The result of the calculation shows that the relation (ωτ) -1 ∝( P / m x ) 1/ n holds, where P denotes the microwave power. In the case where practically only spontaneous emission of phonons takes place, n takes the one extreme value 2.5, while it does the other extreme value 4 in the case where both emission and absorption of phonons occur in sufficient magnitudes. Evidently, the average electron energy e e is a function of ω c -ω for a given power. Since the relaxation time depends on e e , it is a function of ω c -ω. Hence the absorption line deviates from the ordinary Lorentzian curve in which the relaxation time is taken constant throughout the rang...

Infrared Absorption in Heavily Dopedn-Type Germanium

Measurements of the infrared absorption spectrum of compensated and uncompensated heavily doped $n$-type germanium at 80, 200, and 295\ifmmode^\circ\else\textdegree\fi{}K are reported. The edge absorption in the doped samples differs strongly from the edge absorption in pure germanium. Both the indirect and the direct energy gap change with doping. The change depends on the total impurity concentration ${N}_{A}+{N}_{D}$ approximately as ${({N}_{A}+{N}_{D})}^{\frac{1}{3}}$. For ${N}_{A}+{N}_{D}=4.7\ifmmode\times\else\texttimes\fi{}{10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ the change of the indirect gap is about 0.07 ev, the change of the direct gap about 0.06 ev. The absorption due to indirect transitions rises more rapidly with the photon energy in $n$-type germanium than in pure germanium. This extra absorption is proportional to the free electron concentration and must be due to virtual electron-electron scattering between the $〈000〉$ and $〈111〉$ valleys.It is shown that the effective electron density in heavily doped $n$-type germanium is larger than in most metals. The properties of the conduction electrons in germanium with $ng{10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ correspond to the properties of a dense electron gas (${r}_{s}l1$).

The Infra-red Faraday Effect in Germanium

Measurements of the infra-red Faraday effect have been made in n-type, p-type and intrinsic germanium. The Faraday rotations observed are interpreted as being due to free electrons in n-type germanium, valence to conduction band transitions in intrinsic germanium, and light and heavy holes and intervalence band transitions in p-type germanium. The rotations obtained for variously doped n-type specimens are used in conjunction with Hall effect measurements on the same specimens to evaluate the Hall scattering constant as a function of the impurity content. In p-type material the rotations obtained are used to estimate the relative population of the light and heavy hole states.

Cyclotron Resonance of Hot Electrons in Germanium

Cyclotron Resonance of Hot Electrons in Germanium

Imaginary Part of X-Ray Scattering Factor for Germanium. Comparison of Theory and Experiment

The imaginary part of the x-ray scattering factor for germanium is calculated from dispersion theory and individual Hartree-Fock electron scattering factors and is compared with Hunter's experimental values measured with anomalously transmitted x rays. The agreement is quite good and verifies the treatment of anomalous transmission by the dynamical theory of diffraction. It is shown that the imaginary part of the scattering factor can be related directly to the form factor of the L electrons in germanium and it is concluded that their charge distribution in the solid is essentially the same as in the free atom.

Variational Treatment of Warm Electrons in Nonpolar Crystals

Deviations from Ohm's law in nonpolar crystals are treated for weak fields by the variational method. A simple band structure is assumed. Scattering by both acoustical and optical phonons, and ionized impurities is included. It is shown that the influence of optical phonons on the field dependent mobility (${E}^{2}$ term where $E$ is the electrostatic field) is maximum for a temperature which corresponds approximately to the optical phonon energy. The field dependent mobility is highly sensitive to ionized impurity scattering as in the case of acoustical phonons alone. Finally, the convergence of the variational method is established in limiting cases using as a representation a set of polynomials which are orthonormal with respect to the collision operator. Extensive calculations are given for electrons in germanium and comparison with experiment is discussed.

The Anisotropy of the Conductivity of Hot Electrons and their Temperature in Germanium

By making certain simplifying assumptions a method of analysing the anisotropy of the conductivity of electrons in germanium at high electric fields is presented. The method is applied to Koenig's data on a specimen having a free carrier concentration of 6.5 × 1014 cm-3. The electron temperatures in each valley are obtained and the mobility and population of carriers within the valleys are calculated. These electron temperatures are compared with electron temperatures calculated from an energy balance equation applied to each valley as though it existed independently of the other valleys. The comparison shows that there is interaction between electrons in different valleys. Estimates are made of the rate of energy transfer between valleys.

GFactor of Electrons in Germanium

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