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

June 28 - July 2, 2015, Dresden

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

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

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

1. Kinetic and Collective regimes

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

( )∫ 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

1. Kinetic and Collective regimes

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

( )∫ 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

1. Kinetic and Collective regimes

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

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

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

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

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

Prediction for reduced size samples using the effective length.

JAP 115, 164314 (2015)

2. Group IV materials

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

( ) 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

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

ωωπτ DV totI21

6Γ=−

Including lattice volume and strenght variability

arXiv:1506.01522 Poster PB002

RvMtot Γ+Γ+Γ=Γ 2

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

Size effects destroy thermal conductivity

2. Si/Ge Alloys

arXiv:1506.01522 Poster PB002

2. Si/Ge Alloys

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

Alloy samples are purely kinetic

arXiv:1506.01522 Poster PB002

3. Collective behavior on Graphene

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

3. Collective behavior on Graphene

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

3. Collective behavior on Graphene

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

3. Phonon spectra in KCM

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

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

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

3. Phonon spectra in KCM

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

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

4. Phonon spectra in KCM

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

4. Phonon spectra in KCM

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

KCM Similar phonon mfp spectra than abinitio calculations

Vermeersch et al. PRB 91, 085202 (2015)

5. Combination with abinitio calculations

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

KCM can be used starting from force constants (IFC)

6. Conclusions

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

• 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

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden

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

• Study the influence role of collective transport in thermoelectricity

Thank you for your attention

xavier.alvarez@uab.cat

and

Think in collective!

34TH ANNUAL INTERNATIONAL CONFERENCE ON THERMOELECTRICS

June 28 - July 2, 2015, Dresden