34th annual international conference on ......arxiv:1506.01522 poster pb002 2. si/ge alloys 34th...

THERMAL CONDUCTIVITY IN THE KINETIC COLLECTIVE MODELF.X. Alvarez, P. Torres, A. Shakouri, C. de Tomas, A. Lopeandia,

A. Mohammed and X. Cartoixà

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS (ICT 2015)

June 28 - July 2, 2015, Dresden

Summary

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS


1. Motivation

2. Predictions for Si – Group IV materials and SiGe alloys

3. Collective behaviour in graphene

4. Phonon Spectra in KCM

5. Combination with abinitio calculations

1. Motivation



Obtain the simplest thermal conductivity model able to predict the largest number of materials

1. Kinetic and Collective regimes



( )∫ Σ+Σ−= colvkinvtot vCvC ττκ 2213

1

Thermal conductivity splitted in two contributions: Kinetic and Collective

( ) TBTTB NHDNLN

1

)/3exp(1

123

1 +Θ−−

=−

ωτ

( ))/3exp(1

)/exp(4

1

DU

UU TTB

T

Θ−−Θ=−

ωτ

ωωπτ DV MI21

6Γ=−

L

vB =−1τ

Scattering Rates

Non-Resistive Resistive




( )∫ Σ+Σ−= colvkinvtot vCvC ττκ 2213

1

Thermal conductivity splitted in two contributions: Kinetic and Collective

1111 −−−− ++= IUBR ττττ

Scattering Rates

Mathiessen Rule

Kinetic

( ) 1/1 −+=Σ RN ττ

Switching Factor

Collective

Rkin ττ =1

111

−−

−−

==

∫∫

v

Rv

RcolC

C τττ




Kinetic

CollectiveRkin ττ =

11

11

−−

−−

==

∫∫

v

Rv

RcolC

C τττ

( ))/3exp(1

)/exp(4

1

DU

UU TTB

T

Θ−−Θ=−

ωτ

ωωπτ DV MI21

6Γ=−

L

vB =−1τ

2. Prediction for natural and isotopically rich silicon



ωωπτ DV MI21

6Γ=−

Prediction for isotopically rich materials calculating the mass variability.

Good fitting to natural silicon

JAP 115, 164314 (2015)

L

vB =−1τ

2. Reduced size samples



Prediction for reduced size samples using the effective length.

JAP 115, 164314 (2015)

2. Group IV materials



( ) TBTTB NHDNLN

1

)/3exp(1

123

1 +Θ−−

=−

ωτ

( ))/3exp(1

)/exp(4

1

DU

UU TTB

T

Θ−−Θ=−

ωτ

SiUNxBUxUN BfB )/()/()/( =

( )( )Si

xxBU MvV

MvVf

5

5

)/( /

/

γγ=

Prediction for group IV materials calculating B factors with material properties

Proc. Roy. Soc. A 420, 20140371 (2014)

2. Si/Ge Alloys



ωωπτ DV totI21

6Γ=−

Including lattice volume and strenght variability

arXiv:1506.01522 Poster PB002

RvMtot Γ+Γ+Γ=Γ 2



Size effects destroy thermal conductivity

2. Si/Ge Alloys


2. Si/Ge Alloys



Alloy samples are purely kinetic


3. Collective behavior on Graphene



3. Phonon spectra in KCM



Collective transport. Normal scattering dominates for bulk at 300K.

Kinetic transport. Boundary scattering dominates for NW at 30K.




1)/exp(

1

−+=

TTkf

B δω

1)/)·exp((

1

−+=

Tkf

Bquω

δT depends on τkin

u depends on τcol

xq

yq

xq

yq

Kinetic regime

Collective regime




KCM Similar phonon mfp spectra than abinitio calculations

Vermeersch et al. PRB 91, 085202 (2015)

5. Combination with abinitio calculations



KCM can be used starting from force constants (IFC)

6. Conclusions



• Thermal conductivity can be splitted in two different regimes with very different properties: kinetic and collective

• Collective regime is important when normal phonon-phonon scattering is dominant

• KCM can be combined with other approaches like abinitio or lattice dynamics IFC calculations

Future work



• Study materials with other crystal structure and composition (any proposal?)

• Study the influence role of collective transport in thermoelectricity

Thank you for your attention

[email protected]

and

Think in collective!



mailto:[email protected]

34th annual international conference on ......arxiv:1506.01522 poster pb002 2. si/ge alloys 34th...

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