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44036-AC10
Intrinsic Lattice Thermal Conductivity of Nanostructured Semiconductor Systems

David A. Broido, Boston College

The central focus of this research is to develop accurate theoretical approaches to calculate the intrinsic lattice thermal conductivity, k⁽ⁱ⁾, of bulk and nanostructured materials.  Historically, most theories used to calculate k⁽ⁱ⁾ in crystalline semiconductors have been based on approximate solutions to the Boltzmann transport equation (BTE) for phonons.  This equation describes the heat flow in a material resulting from an applied temperature gradient.  The approximate treatments of the BTE introduce ad hoc parameters, which are adjusted to fit existing experimental data.  Such approaches have limited predictive power, so they cannot be used to provide guidance to experimental thermal transport studies nor can they aid in the design of new materials tailored for specific applications.  We have implemented an exact solution of the linearized BTE for phonon transport.  This solution incorporates explicitly the normal and umklapp phonon-phonon scattering processes necessary to calculate thermal resistance.  A central feature of our work is the inclusion of an accurate description of the harmonic and anharmonic interatomic forces (IFCs).  We are calculating these using two methods:

(i) The adiabatic bond charge model (ABCM).  This model employs only a small number of physically motivated parameters to obtain the harmonic IFCs and phonon dispersions and modes.  We have constructed an ABCM for both bulk semiconductors and for SiGe and GaAs/AlAs quantum well superlattices.  Calculated phonon dispersions show excellent agreement with those measured for many elemental and compound semiconductors.  The anharmonic forces are parametrized by taking first nearest neighbor interactions and matching calculated thermal conductivities to measured bulk values.  For bulk semiconductors, we demonstrated the inverse relationship between our calculated phase space for phonon-phonon scattering with measured thermal conductivities of a broad array of semiconductors.  Anomalous behavior seen in InP, GaP and AlSb because these materials have large energy gaps between acoustic and optic phonon branches.  These large gaps prevent heat-carrying acoustic phonons from being scattered by optic phonons.  The corresponding reduction in scattering phase space leads to an increase in measured thermal conductivity.  For superlattices, we have calculated growth axis k⁽ⁱ⁾ of 2x2 and 4x4 structures as a function of the mass ratio of the constituent atoms.  With inicreasing mass ratio, reductions in k⁽ⁱ⁾ arise because the average decrease in phonon group velocity.  We find that simple models based on the relaxation time approximation and the Keating model for the interatomic forces give lower thermal conductivities than our full ABCM based results because the ABCM model more accurately represents the flattening of the transverse acoustic branches and because of the decreased phonon-phonon scattering obtained from the full BTE solution, which occurs with increasing mass ratio.  These differences highlight the need to provide accurate representations of phonon dispersions and of obtaining complete solutions of the BTE in calculations of superlattice thermal conductivity.

(ii)  ab initio Calculations   ab initio models based on density functional perturbation theory (DFPT) that accurately calculate the harmonic IFCs and phonon dispersions and modes in a host of bulk semiconductors are available from standard packages (we use the Quantum Espresso package).  A description of the anharmonic forces needed to evaluate the phonon-phonon scattering rates requires the extension of DFPT to include nonlinear response.  We have implemented a recently developed ab initio approach to calculate these.  The real space anharmonic IFCs, which describe triplet interactions between atoms, are computed out to seventh nearest neighbors.  The ab initio based approach to calculate k⁽ⁱ⁾ requires no adjustable parameters.  We have applied this approach to obtain the anharmonic IFCs for silicon and germanium, and we find excellent agreement with the measured values over a wide range of temperatures (from 100K to 300K).  Consideration of other materials and systems is now underway.

Two graduate students have been supported on this grant during the past year.  Both have presented results of their research at a national conference and both have submitted papers for publication based on this work.

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