Designing new electronic materials with tailored transport properties

Seminar given at Queen Mary University of London, 2023

Transcript

1. Alex Ganose Imperial College London, UK Virtual Atoms Lab: https:/ /virtualatoms.org Designing new electronic materials with tailored transport properties
2. Thermoelectrics convert waste heat into electrical energy Thermoelectric figure of merit: 𝛼 = Seebeck coefficient 𝜎 = conductivity 𝑇 = temperature 𝑘!"## = lattice thermal conductivity 𝑘$!$% = electrical thermal conductivity Snyder and Toberer, Nat. Mater. 7, 105 (2008)
3. Computational prediction of experimentally verified thermoelectrics is rare Urban; Menon; Tian; Jain; Hippalgaonkar, J. Appl. Phys. 125, 180902 (2019) 2008 2012 2016 2020 Year 0.0 0.4 0.8 1.2 1.6 Exp. ZT n-LiZnSb p-SnS p-NbFeSb p-TmAgTe2 p-YCuTe2 n-Er12 Co5 Bi n-KAlSb4 p-Cd1.6 Cu3.4 In3 Te8 p-TaFeSb n-type p-type
4. Boltzmann transport equation determines carrier transport group velocity (easy) lifetime (hard) energy (easy)
5. Lifetimes determined by matrix elements of scattering processes matrix element overlap
6. τ ... constant lifetime A hierarchy of methods exist for calculating electron lifetimes Pros: – Quick – Widely used Cons: – Fixed lifetime – Arbitrary results
7. τ ... ∝ DOS–1 constant lifetime A hierarchy of methods exist for calculating electron lifetimes Pros: – Quick – Models acoustic phonon scattering Cons: – Still arbitrary – Fixed scattering process
8. τ ... DFPT ∝ DOS–1 constant lifetime A hierarchy of methods exist for calculating electron lifetimes Pros: – First principles matrix elements – High accuracy Cons: – Expensive – Limited to <~20 atoms
9. τ ... DFPT AMSET ∝ DOS–1 constant lifetime Calculate scattering rates but remain computationally efficient close to accuracy of DFPT+Wannier at 1/500th computational cost AMSET is a new framework for calculating transport properties Ganose et al. Nat. Commun. 12, 2222 (2021)
10. All inputs obtained through DFT calculations primary input: uniform band structure calculation Ganose et al. Nat. Commun. 12, 2222 (2021)
11. Electronic structure Fourier interpolated onto dense mesh Fourier interpolation of eigenvalues of group velocities Ganose et al. Nat. Commun. 12, 2222 (2021)
12. Band- and k-dependent scattering rates obtained on dense mesh lifetimes from first principles inputs — no fitting parameters used Ganose et al. Nat. Commun. 12, 2222 (2021)
13. Transport properties obtained from Boltzmann transport eqn calculate mobility, conductivity, Seebeck & thermal conductivity Ganose et al. Nat. Commun. 12, 2222 (2021)
14. Multiple scattering mechanisms incorporated through computationally cheap matrix elements acoustic deformation potential (AD) deformation potential, elastic constant ionized impurity (II) dielectric constant polar optical phonon (PO) dielectric constant, polar phonon frequency Ganose et al. Nat. Commun. 12, 2222 (2021)
15. AMSET provides insights into transport physics First principles inputs No fitting or tuning parameters 10 min runtime on laptop Ganose et al. Nat. Commun. 12, 2222 (2021)
16. AMSET obtains similar mobilities to DFPT Ganose et al. Nat. Commun. 12, 2222 (2021)
17. AMSET shows close agreement to experiment for the mobility across many materials All calculations with PBE functional Comparisons against single crystal measurements Ganose et al. Nat. Commun. 12, 2222 (2021)
18. AMSET is an open-source python package you can run today Docs: https://hackingmaterials.lbl.gov/amset/ Support: https://matsci.org/c/amset Installation pip install amset Usage amset run --static-dielectric 10 ... Can be controlled through the command line or python interface Ganose et al. Nat. Commun. 12, 2222 (2021)
19. Carrier mobility is a key materials property that is relatively independent of carrier concentration how quickly an electron or hole moves when pulled by an electric field µ = σ/en mobility conductivity carrier concentration
20. Temperature dependence of carrier mobility has been used since ~1930 to understand the quantum behaviour of materials First expressions for mobility in semiconductors include a T –3/2 dependence
21. 25 years later, these expressions do remarkably well predicted the transport in n-type Germanium Impressive, since Wilson’s was the first to treat: 1. Valence/conduction bands separated by a gap 2. Impurities as the source of free carriers 3. Lattice vibrations as the source of scattering
22. Since then, the T-dependence of mobility has been used as experimental signature of the dominant scattering mechanism Acoustic/optical deformation µ~T –3/2 Polar optical µ~T –0.75 Alloy µ~T –1/2 Ionized impurity µ~T 3/2
23. Since then, the T-dependence of mobility has been used as experimental signature of the dominant scattering mechanism Acoustic/optical deformation µ~T –3/2 Polar optical µ~T –0.75 Alloy µ~T –1/2 Ionized impurity µ~T 3/2 derived from simplified models in a single parabolic band yet limitations are often forgotten in thermoelectric studies
24. As computational tools have improved/become tractable, theory tells a different picture modern approaches allow transport properties to be predicted quantitatively
25. DFPT+Wannier shows excellent agreement across many materials / 1 341 . ( (3 2 . 2  0 (  . 1 (  . 2 .1 7/ 0 ( .1 7/ . 1 ( .1 7/ . 1 ( .1 7/ Agrees with experiment across - scattering types - band structures - temperatures
26. Tin selenide is the poster boy for thermoelectric materials, long assumed to be limited by acoustic phonons SnSe DFPT+Wannier obtains experimental mobility dependence of T –3/2 BUT polar optical phonons dominate scattering
27. Does the T-dependence tell us anything about the dominant scattering mechanism?
28. Does the T-dependence of mobility give insight into the dominant scattering mechanism Review of all DFPT+Wannier studies (60+ materials) No correlation between T- dependence and scattering type Ganose et al. submitted (2022) arXiv.2210.01746
29. Does the T-dependence of mobility give insight into the dominant scattering mechanism Review of all DFPT+Wannier studies (60+ materials) No correlation between T- dependence and scattering type Not safe to assume scattering type based on T-dependence alone Ganose et al. submitted (2022) arXiv.2210.01746
30. τ ... DFPT AMSET ∝ DOS–1 constant lifetime Calculate scattering rates but remain computationally efficient close to accuracy of DFPT+Wannier at 1/500th computational cost AMSET is a new framework for calculating transport properties Ganose et al. submitted (2022) arXiv.2210.01746
31. Using AMSET calculations, we find the primary factor controlling T-dependence are the phonon frequencies Calculations on a single parabolic & isotropic band Phonon frequencies have large impact Ganose et al. submitted (2022) arXiv.2210.01746
32. Using AMSET calculations, we find the primary factor controlling T-dependence are the phonon frequencies / 1 341 . ( (3 2 . 2  0 (  . 1 (  . 2 .1 7/ 0 ( .1 7/ . 1 ( .1 7/ . 1 ( .1 7/ Ganose et al. submitted (2022) arXiv.2210.01746
33. / 1 341 . ( (3 2 . 2  0 (  . 1 (  . 2 .1 7/ 0 ( .1 7/ . 1 ( .1 7/ . 1 ( .1 7/ Using AMSET calculations, we find the primary factor controlling T-dependence are the phonon frequencies Phonon frequencies control T-dependence irrespective of scattering type Ganose et al. submitted (2022) arXiv.2210.01746
34. Band structure features minimally affect T-dependence non-parabolicity anisotropy Ganose et al. submitted (2022) arXiv.2210.01746
35. Dielectric tensors ~8,000 Polar freqs ~8,000 Deform potentials ~3,000 Elastic tensors ~11,000 Band structures 24,000 Mobility database 24,000 We performed 24,000 mobility calculations using AMSET with machined learned materials parameters Ganose et al. submitted (2022) arXiv.2210.01746
36. Average T-dependence for polar and acoustic phonon scattering are very similar across the full dataset Ganose et al. submitted (2022) arXiv.2210.01746
37. Mobility dependence has been used to justify unphysical materials properties Material Fitted SnSe 24 eV PbTe 22 eV BiCuSeO 24 eV Calc 10 eV 7 eV 4 eV
38. Can we use AMSET for materials discovery and optimisation?
39. We have applied AMSET to many emerging energy materials Sb2 Se3 Wang et al., ACS Energy Lett. 7, 2954–2960 (2022) BaBi2 O6 Spooner et al., Chem. Mater. 33, 7441–7456 (2022) ZnSb2 O6 Jackson et al., ACS Energy Lett. 7, 3807–3816 (2022)
40. … and lots of other groups are using AMSET too
41. Discovering new p -type transparent conductors Transparent conductors are a vital technology n-type materials dominate: In2 O3 , SnO2 , ZnO p-type TCs needed for fully-transparent technologies
42. Needs to be conductive Dopable (>1020 cm–3 carriers) High mobility (>50 cm2/Vs) Needs to be transparent Wide bandgap (>3.2 eV) What do we need in a p - type transparent electrode? valence band conduction band Eg > 3.2 eV
43. The picture is more complicated – must consider matrix elements symmetry-forbidden transitions can widen the optical bandgap
44. We performed a high-through search for p- type conductors with forbidden optical transitions 18,000 candidates Woods-Robinson et al. Matter, 2023 (accepted)
45. Calculated optical absorption for all 18,000 materials – most materials have forbidden transitions ”forbidden energy difference”: Woods-Robinson et al. Matter, 2023 (accepted)
46. Database of optical properties screened for plausible p- type candidates with large forbidden energy difference 579 candidates Woods-Robinson et al. Matter, 2023 (accepted)
47. Hybrid DFT used to obtain a better bandgap and filter the candidates further 184 candidates Woods-Robinson et al. Matter, 2023 (accepted)
48. Many materials would have been missed by conventional screening based on bandgap alone Would be excluded in conventional screening (184 candidates) Would be included in conventional screening Woods-Robinson et al. Matter, 2023 (accepted)
49. Final stage is to evaluate dopability and mobility In2 O3 & SnO2 emerge from n- type study validating the approach final candidates Woods-Robinson et al. Matter, 2023 (accepted)
50. 6 promising p- type candidates were identified and validated through high-level calculations BeSiP2 has the potential to be doped n- or p- type Woods-Robinson et al. Matter, 2023 (accepted)
51. What do we need in a p-type transparent electrode BAs is strongly p- type Woods-Robinson et al. Matter, 2023 (accepted)
52. Both are highly conductive with high mobilities due to their small effective masses Even at degenerate doping mobility is ~100 cm2/Vs Woods-Robinson et al. Matter, 2023 (accepted)
53. Conclusions Access to cheap and accurate mobility calculations through AMSET is proving insights into the electronic behaviour of materials challenged long-held assumptions on T-dependence of mobility enabling the screening of novel optoelectronics including TCs
54. Acknowledgements Funding EPSRC DOE ECR Program Computing NERSC ARCHER2 MMMHub and you for your attention! Electron transport Anubhav Jain Junsoo Park Transparent conductors Rachel Woods-Robinson Yihuang Xiong Jimmy-Xuan Shen