Strain game revisited for complex oxide thin films: Substrate-film thermal expansion mismatch in ${\mathrm{PbTiO}}_{3}$

Strain game revisited for complex oxide thin films: Substrate-film thermal expansion mismatch in ${PbTiO}_{3}$

Ethan T. Ritz and Nicole A. Benedek

Phys. Rev. Materials 4, 084410 – Published 25 August 2020

Abstract

The sensitivity of materials properties, particularly those of perovskite oxides, to epitaxial strain has been exploited to great advantage to create materials with new or enhanced properties. Although it has certainly been recognized that mismatch in the thermal expansion coefficients of the bulk and substrate material will contribute to the misfit strain, the significance of this contribution for ferroelectric perovskite thin films has not been systematically explored. We use first-principles density functional theory and the example of ferroelectric ${PbTiO}_{3}$ thin films on various substrates to show that ignoring the thermal expansion of the substrate (that is, assuming that the in-plane lattice parameter of the film remains roughly constant as a function of temperature) results in ferroelectric transition temperatures and structural trends that are completely qualitatively different from calculations in which thermal expansion mismatch is properly taken into account. Our work suggests that the concept of a misfit strain defined as a single number is particularly ill defined for ${PbTiO}_{3}$ and invites further study of the interplay between thermal expansion mismatch and structural and functional properties in other thin-film materials.

Received 10 July 2020
Accepted 11 August 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.084410

Physics Subject Headings (PhySH)

Ferroelectricity First-principles calculations Thermal expansion

Complex oxides Thin films

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ethan T. Ritz

Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853, USA

Nicole A. Benedek ^*

Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, USA

^*nbenedek@cornell.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 4, Iss. 8 — August 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Variation in lattice parameters of ${PbTiO}_{3}$ thin films with temperature and substrate compared to bulk ${PbTiO}_{3}$ from our first-principles calculations. Open circles represent data for the $a$ axis (experimental data for ${SrTiO}_{3}$ , ${DyScO}_{3}$ , and LSAT [41, 42, 43]), whereas closed squares represent data for the $c$ axis (predicted from our QHA calculations for each value of $a$ ).
Reuse & Permissions
Figure 2
Variation in thermal expansion coefficients of ${PbTiO}_{3}$ thin films with temperature and substrate compared to bulk ${PbTiO}_{3}$ from our first-principles calculations. Open circles represent data for thermal expansion along the $a$ axis ( $α_{a}$ ), whereas closed squares represent data for thermal expansion along the $c$ axis ( $α_{c}$ ). For the ${PbTiO}_{3}$ thin films, the $α_{a}$ values are those of the substrates and have been extracted from experimental data [41, 42, 43]. All $α_{c}$ values were calculated for this work using the QHA.
Reuse & Permissions
Figure 3
Variation in lattice parameters of ${PbTiO}_{3}$ thin films with temperature when the lattice mismatch is held fixed at its 300 K value [open symbols, $ε_{a}^{T = 300 K}$ term of Eq. (2)] compared with lattice parameters calculated allowing for thermal expansion of the substrate (closed symbols, $ε_{a}^{T = 300 K} + ε_{a}^{thermal}$ ). Squares denote $c$ -axis lattice parameters from our QHA calculations, circles denote $a$ -axis lattice parameters (experimental data [41, 42, 43]).
Reuse & Permissions
Figure 4
Variation in ferroelectric transition temperature and $c$ -axis behavior of ferroelectric ${PbTiO}_{3}$ thin films as a function of misfit strain and substrate coefficient of thermal expansion ( $α_{a}$ ) from our QHA calculations. The color chart for $T_{c}$ has white set to the bulk $T_{c}$ of 760 K. Blue (red) squares indicate a strain and $α_{a}$ combination that produce films with a lower (higher) $T_{c}$ than bulk. Triangles indicate combinations of strain and $α_{a}$ that produce films in which the $c$ axis continues to grow with temperature and $T_{c}$ is suppressed. All other combinations of strain and $α_{a}$ produce films in which the $c$ axis shrinks with temperature and $T_{c}$ is finite. Note that the films with the highest transition temperatures may exceed 1600 K or even be completely suppressed. The letters ‘L,’ ‘S,’ and ‘D’ denote the strain and $α_{a}$ conditions corresponding to growth on LSAT, ${SrTiO}_{3}$ , and ${DyScO}_{3}$ .
Reuse & Permissions
Figure 5
Variation in in-plane misfit strains as a function of temperature for ${PbTiO}_{3}$ thin films on ${DyScO}_{3}$ , ${SrTiO}_{3}$ , and LSAT from our QHA calculations.
Reuse & Permissions
Figure 6
Judicious combinations of initial lattice mismatch (defined at 300 K) and substrate coefficient of thermal expansion ( $α_{a}$ ) can produce ${PbTiO}_{3}$ thin films with zero thermal expansion along the $c$ axis with temperature. Circles represent data for the $a$ axis whereas squares represent data for the $c$ axis. Black: $- 1.46 %$ misfit strain (300 K), $α_{a} = 1.01 \times 10^{- 5} K^{- 1}$ . Red: $- 1.21 %$ misfit strain, $α_{a} = 0.85 \times 10^{- 5} K^{- 1}$ . Blue: $- 0.70 %$ misfit strain, $α_{a} = 0.60 \times 10^{- 5} K^{- 1}$ . Green: $- 0.18 %$ misfit strain, $α_{a} = 0.27 \times 10^{- 5} K^{- 1}$ .
Reuse & Permissions

Physical Review Materials

Strain game revisited for complex oxide thin films: Substrate-film thermal expansion mismatch in PbTiO3

Ethan T. Ritz and Nicole A. Benedek

Phys. Rev. Materials 4, 084410 – Published 25 August 2020

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Strain game revisited for complex oxide thin films: Substrate-film thermal expansion mismatch in ${PbTiO}_{3}$