Phonon Conductivity Research Articles

Role of compensation in electron-phonon scattering in lightly doped semiconductors

Low-temperature phonon conductivity results of compensated semiconductors such as Ge(P,Ga), Ge(As,Ga), and Ge(Sb,In) have been for the first time interpreted quantitatively on the basis of the theory proposed by Griffin and Carruthers and extended by Kwok. The compensated Ge samples are designated as Ge(donor impurity, compensating acceptor impurity). The basis of the present interpretations are the complete expressions obtained by Suzuki and Mikoshiba in the light of Kwok's theory for the resonance-scattering relaxation rates of phonons by bound donor electrons in Ge. The elastic and inelastic scatterings, both from the donor-electron singlet ground state and the next higher-energy triplet state, separated by $4\ensuremath{\Delta}$, as well as phonon-assisted absorption processes are considered in the present calculations in the temperature range 1-4\ifmmode^\circ\else\textdegree\fi{}K. The effect of compensation by acceptor impurities such as Ga in the case of P- and As-doped ($n$-type) Ge and by indium in the case of Sb-doped Ge is reflected in the variations of $4\ensuremath{\Delta}$ and the donor-electron radius ${a}_{0}$. Compensation in the case of P- and As-doped Ge by gallium reduces the values of $4\ensuremath{\Delta}$ but it almost remains unaffected in the case of Sb-doped Ge when it is compensated by indium. However, the donor-electron radius is reduced in all the cases on compensation.

Ultrasound absorption due to electrons and phonons in alkali liquid metals

The excess longitudinal ultrasonic absorption over and above the classical value in four alkali liquid metals near their melting points has been accounted for by the mechanisms of interaction of sound waves with the conduction electrons and the thermal phonons (Akhieser mechanism), both exhibiting a quadratic dependence on sound frequency. An expression, similar to the Bridgman relation for liquids, for the phonon conductivity in the liquid metals has been developed. This approach briefly reported here yields good results.

Phonon focusing and phonon conduction in orthorhombic and tetragonal crystals in the boundary-scattering regime. II

Striking differences (up to a factor of 100) are predicted in the intensity of phonons propagating ballistically along different directions in certain orthorhombic and tetragonal crystals. The predicted results arise from phonon focusing due to elastic anisotropy, due to the fact that in elastically anisotropic crystals the phonon phase and group velocities are, in general, not collinear. Conditions for the existence of cuspidal edges in group-velocity surfaces are given in symmetry planes along all directions where the phase and group velocities are collinear. Approximate amplification factors have been calculated for phonons of each polarization along symmetry-plane collinear axes. An analytic expression is also given for the nonsymmetry collinear direction for the longitudinal and one of the transverse modes. Calculations have been performed for a number of crystals and demonstrate that the phonon-focusing property can cause differences in the phonon transport in the boundary-scattering regime by more than 80%.

Analysis of lattice thermal conductivity of GaAs at high temperatures

The lattice thermal conductivity of GaAs has been analysed in the entire temperature range 100–800 K in the frame of the Sharma-Dubey-Verma (SDV) model of phonon conductivity, and very good agreement has been found between the calculated and experimental values of the lattice thermal conductivity in the entire temperature range of study. The temperature exponentm(T) for the three-phonon scattering relaxation rate for GaAs has also been calculated in the above temperature range. The separate percentage contributions due to transverse and longitudinal phonons have also been studied.

Influence of internal stress on electron-phonon interaction inn-type germanium and silicon at low temperatures

Expressions for resonance scattering of phonons by the bound donor electrons have been obtained for the first time for $n$-Ge in the presence of strains for the most general situation when, besides the usual valley-orbit splitting of the four-fold degenerate ground state into a singlet state and a triplet state, the triplet state splits into a doublet state and a singlet state due to internal static and dynamic strains present in the crystal. Similarly for $n$-Si, the most general situation is considered when the degeneracy of the donor-electron ground state is completely removed due to internal strains besides the usual valley-orbit splitting of the six-fold ground state into a singlet state and five-gold degenerate state. The expressions obtained for the resonance scattering relaxation rates of phonons by bound electrons for strained $n$-Ge are used to explain the phonon conductivity results of Sb-, P-, and As-doped Ge.

Role of oxygen atoms in the phonon conductivity of Si containing 5 ×1017oxygen atoms percm3

The reduction in the phonon conductivity of silicon crystals containing 5 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ oxygen atoms per ${\mathrm{cm}}^{3}$ near the maximum is interpreted on the basis of the phonon scattering by clusters of oxygen atoms, each atom forming an isosceles triangle with two neighboring silicon atoms at its lattice site. Klemens's theory for the scattering of phonons by clusters of substitutional impurities is assumed for interstitial impurities and is used to explain the results. The scattering of phonons by clusters is negligible in the case of samples containing less than 5 \ifmmode\times\else\texttimes\fi{} ${10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ oxygen atoms.

Electron–phonon interaction and phonon conductivity of the n‐type semiconductors Mg2Ge and Mg2Sn at low temperatures

AbstractIt is shown that the expressions obtained by Singh for the relaxation rates of the resonance scattering of phonons by donor electrons for n‐type zemiconductors in presence of internal static and dynamic strains in the crystal can account very well for phonon‐conductivity results for the n‐type semiconductors Mg2Ge and Mg2Sn at low temperatures.

Role of resonance scattering of phonons in the phonon conductivity of strainedn-Si: Application to Li-doped Si

It has been established in the present work that the expression obtained by Singh and Verma for the relaxation rates of the resonance scattering of phonons by bound donor electrons in the presence of internal strains can account very well for phonon-conductivity results for Li-doped silicon at low temperatures.

Peripheral phonons and phonon conductivity of the doped semiconductor

The percentage contribution of the peripheral phonons towards the total phonon conductivity of P-doped Ge has been studied with the help of the Ziman expression of the electron-phonon scattering relaxation rate and the Callaway integral of the lattice thermal conductivity. It is found that the percentage contribution of the peripheral phonons increases with the increase of temperature. The entire study is limited to the temperature range 1–5 K.

Role of Electron—Phonon Interaction and Peripheral Phonons in the Lattice Thermal Conductivity of Doped Semiconductor at Low Temperatures. Application to Phosphorus‐Doped Germanium

AbstractThe role of the electron—phonon scattering and the peripheral phonons are studied by calculating the lattice thermal conductivity of phosphorous doped Ge in the temperature range 1 to 5 K. The temperature and the carrier concentration dependences of the reduced Fermi potential (η*) and of the density of states effective mass (m*) of electrons are also studied at low temperatures. The entire study is made using the Ziman expression of the electron—phonon scattering relaxation rate and the Callaway integral of the lattice thermal conductivity. The contribution of the peripheral phonons in the total phonon conductivity of the P‐doped Ge is also studied. A good agreement is found between the calculated and experimental value of the phonon conductivity for five different samples of P‐doped Ge having different carrier concentrations of 1.2 × 1017 to 1.1 × × 1018 cm−3 in the entire temperature range 1 to 5 K. The analytical expressions are also obtained for the phonon conductivity of the doped semiconductor in the low temperature approximation.

Boundary Scattering and Phonon Conductivity: Application to GaAs

Boundary Scattering and Phonon Conductivity: Application to GaAs

The thermal conductivity and Lorenz function of the tin-lead alloy system Sn x Pb1 ? x (x = 0.85, 0.7 0.5 0.3)

The thermal conductivity and electrical resistivity of the tin-lead alloy system Sn x Pb1 − x (x = 0.85, 0.7 0.5 0.3) were measured in the temperature range 7–300 K. The thermal conductivity λ was analyzed at temperature T ≤20K, assuming 1/λ≡α/T+βTn, where α, β, and n are constants. The analysis shows that n < 2, and not n ≥ 2, which would be expected for a normal pure metal. The electrical resistivities could be represented by a T 5 relation for temperatures up to about 60 K. The characteristic temperature θ R appears to decrease with increasing weight percent of lead. The total Lorenz functions were high, indicating the presence of phonon conductivity. The phonon conductivity λ g appears to vary with T, and can be represented by λg=a/Tn (a > 0) and n≈2.

Phonon conductivity of InSb and GaAs

AbstractThe new expression for the three‐phonon scattering relaxation rate τ = (BN + BUe−θ/αT) × × g(w) Tm proposed by Dubey and Misho is used to calculate the lattice thermal conductivity of InSb and GaAs in the entire temperature range 2 to 300 K and 2 to 800 K, respectively and very good agreement is obtained between experimental and calculated values of the phonon conductivity of both the samples, InSb and GaAs, in the entire temperature range investigated. The reduced contribution due to transverse and longitudinal phonons are also studied by calculating the separate contribution due to each mode of phonons. The percentage contributions of three‐phonon normal and three‐phonon umklapp processes are studied. A comparative study of present results with the results obtained by previous workers is also made for both of the samples.

Phonon scattering and effect of dislocations on the low‐temperature phonon conductivity in Ge

AbstractIt is shown that the theory, which is based on the scattering of phonons by bound dangling electrons associated with the dislocation core, gives excellent agreement between the theoretical and experimental results of phonon conductivity for deformed germanium. No adjustable physical parameter is used in the calculation except the difference of energy splitting. From a comparison of theory and experiment is found that the density of dangling electrons is directly proportional to the dislocation density.

Heat transfer at low temperatures: Application to sapphire

It is found that at low temperatures, the Callaway expression for the lattice thermal conductivity of a sample having dislocations reduces to the expression obtained by Dubey based on the nonlinear heat transfer theory. The obtained expression is used to explain the measurements of Wolfimeyer and Dillinger of phonon conductivity of sapphire in the temperature range 0.4–4 K.

A relationship between phonon conductivity and seismic parameter ? for silicate minerals

The relationship between the phonon conductivity at room temperature (K N ) and the seismic parameter (Φ) for silicate minerals is suggested. The considerations are based on the Debye model of thermal energy transport phenomena in solids and on the ‘seismic equation of state’ for silicates and oxides given byAnderson (1967). The semiempirical relationship is the formK N = 0.43Φ0.82 where Φ is in km2/s2 andK N in mcal/cm s K, and the empirical relationship isK N =(0.528±0.006)Φ −(8.18±2.11). The laboratory data on thermal and elastic properties for several silicates were taken fromHorai andSimmons (1970).

Heat transfer in solid HD at low temperatures

The lattice thermal conductivity of solid HD has been calculated in the temperature range 0.2–4°K. The important scatterers of phonons are found to be boundary walls of the crystal, isotopic impurities, phonons and molecules of ortho hydrogen and para deuterium. The presence of molecules of ortho hydrogen and para deuterium in solid HD which act as rotational impurities, are responsible for one and two phonon scattering processes in the system. The entire study is based on the Callaway model of the lattice thermal conductivity of an insulator. Excellent agreement is found between calculated and experimental values of phonon conductivity. The extra lattice thermal resistivity due to the presence of the ortho hydrogen and para deuterium is also calculated.

Three‐phonon scattering relaxation rate and phonon conductivity. Application to Mg2Ge

AbstractThe new expression τ = g(ω) (BN + BUe−θ/αT) Tm is proposed for the three‐phonon scattering relaxation rate taking into consideration normal and umklapp processes. Incorporating the above expression, the phonon conductivity of Mg2Ge is calculated in the entire temperature range 4 to 1000 K and good agreement is found between calculated and experimental values of phonon conductivity of the sample in the entire temperature range of investigation. Analytical expressions are reported to calculate an approximate value of lattice thermal conductivity. The role of four‐phonon processes is also included in the present study. Using the expression for τ proposed by Joshi and Verma and Sharma et al. the phonon conductivity of InSB and Mg2Ge is calculated to compare the results obtained using the proposed expression for the three‐phonon scattering relaxation rate.

Phonon conductivity of sapphire

Phonon conductivity of sapphire

Thermal resistance at metal/diamond interfaces in relation to the mounting of microwave diodes

The thermal resistances of samples with various kinds of metal/diamond interface have been measured at about 400K with a radiation detector. The results are analysed in terms of series resistances due to the change from electron to phonon conduction and due to the non-ideal thermal compression bonding technique. The first of these is at least five times smaller than previously thought and is in accordance with the practical improvements obtained in the use of diamonds as heat sinks.