Thermoelectrics of Cu2Se:Organic-Inorganic Hybrid Approaches to zT

Enhancement

David Brown, Tristan Day and Dr. G. Jeffrey Snyder

High Temperature Phase• Phonon Liquid (low κ)• High ion conductivity • Anti-fluorite structure

Room Temperature Phase• Lower ion conductivity• Ion-ordered stucture

– Crystallography unresolved

Copper(I) SelenideMixed ion-electron conductor (MIEC)

Copper interstitials

Obviously there is a phase transition in between. (≈410K)The sub-lattice melts (1st order transition)The ions disorder (2nd order transition)

Mixed Ion Electron Conductors

Materials that conduct both ions and electronsLow thermal conductivities due to unstable structure

Separate out ion and electron contributions Gated Seebeck and hybrid thermoelectrics

H. Liu, et al., Nat Mater 11, 422 (2012)

Near the Phase Transition

80% increase in thermopower over 40 Kelvin

Tk

SZT

2

1st Order Transition• i.e. melting• Sudden structural transition• Enthalpy of formation• 1st order discontinuity

2nd Order Transition• i.e. ferromagnetism• “gradual” transformation• Critical power law behavior

• 2nd order discontinuity

1st versus 2nd Order Transitions

Plot: Water enthalpy with temperature

Critical Scattering

Follow critical power laws below the transitionGo rapidly to zeroPossible critical enhanced scattering

Critical Exponent: .80

Critical Exponent: .32

Temperature Resolved pXRD

Continuous TransformationObserved

Heat Capacity

DSC Heat Capacity With PPMS to 400K

Continuous “Lambda” Transition

Rigid Band Thermopower

Degenerate rigid band model

Below 360K: Below 385K rigid band model fits

There is extra thermopower

Carrier concentration changes at 360K360K to 420K ion ordering range

Resulting zT Enhancement

Why do Seebeck and zT increase?

Thermopower and EntropyS* Entropy transported per carrier

Increase entropy transported Increased efficiency

Ji are transport integrals i.e. Kubo or Boltzmann integral

How much does entropy change when a carrier is added?Can we increase it?

Quasi-equilibrium term:

The “presence” thermopower term

Degrees of FreedomDegree of Freedom

Entropy per Carrier

Scale

Configurational

≈ 86 uV/K kb

Configurational

Spin Entropy

W. Koshibae et al., Phys Rev B 62 6869 (2000)

Degree of Freedom

Entropy per Carrier

Scale

Configurational

≈ 86 uV/K kb

Spin state[1] ≈ 86 uV/K kb

Degree of Freedom

Entropy per Carrier

Scale

Configurational

≈ 86 uV/K kb

Spin state[1] ≈ 86 uV/K kb

2nd order transition

50,000 uV/K

10 J/(mol K∙ )

Analogously, we suggest that structural entropy of a phase transformation may be coupled to transport in Cu2Se.

-200

-150

-100

-50

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1

10 spaces100 spacesHiekes formula

See

beck

Coe

ffici

ent

(µV

/K)

Fractional Concentration

Entropy and Thermopower

6

Near a phase transition:

Tc is the critical temperature m is the order parameter

Expand the presence term

Tc depends on copper concentration[1]Copper ions thermally diffuse ordering component migratesHoles couple to Cu+ electrically

[1] Z. Vučić, O. Milat, V. Horvatić, and Z. Ogorelec, Phys Rev B 24, 5398 (1981)

Organic/Inorganic Hybrids

heat

Charge transfer to NC film

S

S2Semiconductors Metals

Carrier concentrationDTA of various Cu2-xSe

Organic Ligands

Donate charge carriers Dope sampleStructure unchanged

Z. Vucic and Z. Ogorelec, Philos Mag B 42, 287 (1980)

Gated Seebeck

Gate

T1 T2

Semiconductor

Gate dielectric

Source Drain

Degenerate Si with SiO2

Change carrier concentrationDon’t alter structure or chemistry

Perfect way to probe this effect

Thin Film Cu2Se

film thickness: 270 nmroughness average: 2.5 nmroot mean square: 3.2 nm

1 inch diameter hot-pressed disk Made at CaltechPLD at 300°C and 10-6 mBar

Danish Technical University

Initial Data on Cu2Se

250 300 350 400 450 500 550 6000

1

2

3

4

5

6

Temperature (K)

Con

duct

ivity

(10

3 S*c

m)

Cu2Se 1 micron Thin Film

Heating 1

Cooling 1Heating 2

Cooling 2

Initial measurement unstableBehavior atypical of the bulkElectromigration?

Soon we will have:PPMS running (DC Hall measurements 4K-400K)Lower current Hall chamber (80K – 450K)Position resolved Seebeck data

Conclusions

The phase transition enhances the thermopower and zT

New method for zT enhancement

Study fundamentals of transport Thrust 3: Understand and engineer

Gate

T1 T2

Semiconductor

Gate dielectric

Source Drain

Degenerate Si with SiO2

heat

Charge transfer to NC film

Acknowledgments

Yunzhong Chen & Nini PrydsKasper Borup & Bo B. IversenHuili Liu, Xun Shi & Lidong Chen

Alex Z. Williams & NASA JPL

Caltech Thermoelectrics Group

Seebeck Stability

Figure S5. The sample was held at an average temperature of 390 K and a temperature difference of 16 K for 13 hours. The measured thermopower, 152 µV/K, varied by less than 1% during this time period.

More Transport Data

More Transport Data

Seebeck Methodology