Thermal conductivity of isotopically enriched 28Si: revisited

Abstract

The thermal conductivity of isotopically enriched 28 Si (enrichment better than 99.9%) was redetermined independently in three laboratories by high precision experiments on a total of 4 samples of different shape and degree of isotope enrichment in the range from 5 to 300 K with particular emphasis on the range near room temperature. The results obtained in the different laboratories are in good agreement with each other. They indicate that at room temperature the thermal conductivity of isotopically enriched 28 Si exceeds the thermal conductivity of Si with a natural, unmodified isotope mixture by 10±2 %. This finding is in disagreement with an earlier report by Ruf et al. At ∼26 K the thermal conductivity of 28 Si reaches a maximum. The maximum value depends on sample shape and the degree of isotope enrichment and exceeds the thermal conductivity of natural Si by a factor of ∼8 for a 99.982% 28 Si enriched sample. The thermal conductivity of Si with natural isotope composition is consistently found to be ∼3% lower than the values recommended in the literature. PACS: 66.70.+f, 63.20.Mt, 74.25.Fy, 65.40.Ba, 65.90.+i Keywords: silicon, stable isotopes, thermal conductivity INTRODUCTIONPhonon scattering due to the presence of different isotopes in an otherwise pure crystal (no chemical defects or dislocations) has been identified as a mechanism that strongly affects the thermal conductivity κ [1−3]. The availability of larger quantities of highly isotope-enriched materials recently revived the interest in this effect in order to study the mechanisms underlying the thermal conductivity and possibly to improve material properties [4−8].Recently, the observation of a significantly enhanced thermal conductivity of isotopically enriched 28 Si near room temperature by Capinski [9] and Ruf et al. [10] has generated large interest. In these studies, it was found that the thermal conductivity of isotopically enriched 28 Si is enhanced by about 60% over that of silicon with natural isotopic composition. This rather high isotope effect attracted considerable attention concerning both, fundamental physics and applications. For technical applications, a significantly enlarged thermal conductivity at room 2 temperature would be of interest for high performance electronic devices. [11]. From the fundamental physics aspect, the experimental results were unexpected since the observed isotopic effect was significantly larger than the prediction of simple theoretical estimates [10−13] and more advanced model calculations [14]. On the other hand, theoretical papers [15−17] were published with the results supporting the data of refs. [9,10]. A large isotopic effect at room temperature is in principle only possible if normal phonon-phonon scattering processes play an important role in determining the formation of the non-equilibrium distribution function of phonons at these temperatures.The large room temperature isotope effect was questioned following the results of an experimental study by Gusev et al. [18] which indicate that th...

The physical principles of terahertz silicon lasers based on intracenter transitions

“…When the silicon crystal was mounted on the cold finger of the cryocooler, which has a limited heat-extraction capacity, the maximal achieved duty cycle was 2 Â 10 À5 for pumping with a CO 2 laser. Lasing from Si:P silicon crystals with natural isotopic composition ceases at a repetition rate of the CO 2 laser higher than 10 Hz, while it remains constant up to the highest repetition rate of the CO 2 laser (20 Hz) for lasers made from isotopically enriched 28 Si:P crystals, apparently due to higher thermal conductivity of monoisotopic silicon crystals [77]. The roll-off of the laser emission with increasing temperature occurs due to an increase of the lattice temperature caused by a slow extraction from the silicon of low-energy thermal phonons, which in turn is the result of the decay of nonequilibrium high-energy phonons.…”

Dispersion considerations affecting phonon-mass impurity scattering rates

“…(6) is used with only the Normal and Umklapp scattering times and fit with the coefficients A N,j and A U,j to data from measurements on isotopically pure Si ( 28 Si) from 100 -350 K (this high temperature range available in the experimental data is chosen for the fit to avoid any complication from boundary scattering); 12 In this fit, θ is slightly adjusted to achieve a better fit over the temperature (θ = 635 K). This is in excellent agreement with the textbook values of the Debye temperature of Si (θ = 625 -645 K).…”

“…(6) is then fit to the measured thermal conductivity on natural Si (n-Si). 12 For this fit, the prefactor in Eqs. (4) and (5) is iterated to achieve a best fit using the two different scattering rates.…”

“…11 For example, the naturally occurring isotopes in Si create phonon scattering events that can lower the thermal conductivity from that of isotopically pure Si by 14% at room temperature. 12,13 This type of phonon-mass impurity scattering process can be used to systematically reduce the thermal conductivity in alloys, 13,14 which has immense importance for thermoelectric applications in which controlled reduction of phonon thermal conductivity is crucial for increasing thermoelectric material efficiency. 15 Clearly, the ability to accurately predict the effects of phononmass impurity scattering is of utmost importance for understanding and engineering thermal transport processes in a wide array of material systems.…”

Validation of thermal models for a prototypical MEMS thermal actuator.

“…Measurements of the thermal conductivity of crystalline silicon are available from a large number of studies over a wide temperature range, from below 100 K to the melting point at 1683 K (e.g., Holland and Neuringer, 1962;Hull, 1999;Kremer et al, 2004). These values agree to a reasonable accuracy for temperatures higher than approximately 200 K, where sample-size effects are unimportant for millimeter-scale samples.…”