The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals

Kuleev, I. G.; Kuleev, I. I.

doi:10.1134/1.1513821

Cited by 7 publications

(13 citation statements)

References 18 publications

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“…For this reason the experimental data on the isotope effect in thermal conductivity is used commonly to validate different theoretical models of heat conduction in crystals. They include various modifications of the Callaway theory [16] based on the Boltzmann transport equation and formulated within a single-mode relaxation time approximation [5,8,[16][17][18][19], new ab initio Boltzmann transport approaches [20][21][22][23][24][25]. In theoretical calculations the estimation of the phonon-phonon scattering processes is an especially challenging task (see, for example, Refs.…”

Section: Introductionmentioning

confidence: 99%

Ultrahigh thermal conductivity of isotopically enriched silicon

Inyushkin

Талденков

Ager

et al. 2018

Journal of Applied Physics

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Most of stable elements (about eighty) have two and more stable (non-radioactive) isotopes. The physical properties of materials composed of such elements depend on the isotopic abundance in some extent. Remarkably strong isotope effect is observed in the phonon thermal conductivity, the principal mechanism of heat conduction in nonmetallic crystals. An isotopic disorder due to random distribution of the isotopes in the crystal lattice sites results in a rather strong phonon scattering and, consequently, in a reduction of thermal conductivity. In this paper we present new results of accurate and precise measurements of thermal conductivity κ(T) for silicon single crystals having three different isotopic compositions at temperatures T from 2.4 to 420 K. The highly enriched crystal containing 99.995% of 28 Si, which is one of the most perfect crystal ever synthesized, demonstrates the thermal conductivity about 450 W cm −1 K −1 at 24 K, the highest measured value among bulk dielectrics, which is ten times greater than one for its counterpart nat Si with the natural isotopic constitution. For highly enriched crystal 28 Si and crystal nat Si the measurements were performed for two orientations [001] and [011], a magnitude of the phonon focusing effect on thermal conductivity was determined accurately at low temperatures. The κ(T) measured in this work gives the most accurate approximation of the intrinsic thermal conductivity of single crystal silicon which is determined solely by the anharmonic phonon processes and diffusive boundary scattering over a wide temperature range.

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Section: Introductionmentioning

confidence: 99%

Ultrahigh thermal conductivity of isotopically enriched silicon

Inyushkin

Талденков

Ager

et al. 2018

Journal of Applied Physics

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“…We use the method of Kuleev and Kuleev [7] to obtain different relations for the thermal conductivity from the solutions of phonon Boltzmann equation [3]. The phonon conductivity relation finally obtained is…”

Section: Lattice Thermal Conductivitymentioning

confidence: 99%

“…Morelli et al [6] have later analysed the effect of isotopes on the thermal conductivity of group IV and III-V semiconductors by extending Callaway's model [3] to consider the contribution of transverse and longitudinal phonons separately. Recently, Kuleev and Kuleev [7] have considered the effects of normal phonon-phonon scattering processes on the thermal conductivity of Ge crystals with different isotopic compositions, by taking into account the redistribution of phonon momentum due to normal processes to each phonon oscillation branch [8] and between different phonon oscillation branches [9]. They observed that the redistribution between longitudinal and transverse phonons as described by Herring [9] leads to a significant suppression of drift motion and hence a drop in thermal conductivity.…”

Section: Introductionmentioning

confidence: 99%

Effect of normal processes on thermal conductivity of germanium, silicon and diamond

Saikia

Kumar

2008

Pramana - J Phys

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The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch -KK-S model and (b) between different phonon branches -KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.

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“…We adopt the method of Kuleev and Kuleev [8,9] to obtain different relations for the thermal conductivity from the solutions of phonon Boltzmann eqs. [10,11] written as (1) where the effect of electron-phonon interaction is neglected.…”

Section: Lattice Thermal Conductivitymentioning

confidence: 99%

“…The Boltzmann equation is solved to get a generalized expression by relaxation time approximation method [8][9][10] and this generalized expression is used to calculate the thermal conductivity of CoSb 3 for the entire temperature range 1-1000 K.…”

Section: *Corresponding Authormentioning

confidence: 99%

Lattice thermal conductivity of skutterudite compounds

Saikia

Borthakur

2010

Indian J Phys

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A generalized expression is used on the basis of relaxation time approximation to facilitate calculation of lattice thermal conductivity of dielectric materials as well as skutterudite family consists of compounds of the form AB 3 . It is assumed that phonon scattering processes are independent and is represented by frequency dependent relaxation times. The contributions of normal three phonon scattering processes are included explicitly as redistribution of phonon momentum between two oscillation branches is considered. Magnitudes of relaxation times are estimated from the experimental data. The result for CoSb 3 is in reasonably good agreement with the experimental result in the temperature range 1-1000 0 K. It is observed that redistribution of phonon momentum between two oscillation branches leads to a significant suppression of thermal conductivity maximum and it is observed that for unfilled skutterudite the main dominant mechanism at the thermal conductivity maximum is three phonon normal scattering process.

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The effect of normal phonon-phonon scattering processes on the maximum thermal conductivity of isotopically pure silicon crystals

Cited by 7 publications

References 18 publications

Ultrahigh thermal conductivity of isotopically enriched silicon

Ultrahigh thermal conductivity of isotopically enriched silicon

Effect of normal processes on thermal conductivity of germanium, silicon and diamond

Lattice thermal conductivity of skutterudite compounds

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