Dielectric Proper,es of Carbon, Silicon and Germanium Based Polymers: A First Principles Study C. C. Wang, G. Pilania, C. S. Liu and R. Ramprasad* Chemical, Materials & Biomolecular Engineering Ins7tute of Materials Science University of Connec7cut
Materials Requirements • Current standard: biaxially-‐oriented polypropylene1 q Breakdown ﬁeld of 700 V/micron (for 10 micron thick ﬁlms) q Low dielectric constant of 2.2 • Next generaOon materials requirements q High dielectric constant q Large band gap q High breakdown strength q Ease of processability q High thermal stability 1, E. J. Sarjeant, etc. IEEE Trans. Magn. 43, 223 (2007)
Our Goal Chemical modiﬁcaOon of polyethylene, to idenOfy promising candidates with large dielectric constant and band gap. q Backbone: C, Si, Ge, etc. q Side chain: H, F, Cl, etc.
Computa,onal Method Density Func,onal Theory (DFT) q DFT is an alternaOve formulaOon of quantum mechanics q Many nuclei-‐many electron problem → one electron problem q DFT as implemented in VASP and FHI-‐ aims is used DFT BOOK CHAPTER: R. Ramprasad, N. Shi and C. Tang, "Modeling the physics and chemistry of interfaces in nanodielectrics", in Dielectric Polymer Nanocomposites (Ed. J. K. Nelson), Springer (2010).
van der Waals (vdW) Interac,ons q Polymer interchain interacOons are controlled by vdW forces a q Labce parameters, volumes and densiOes predicted incorrectly b q Errors carry over to dielectric constants c q ConvenOonal DFT fails to capture vdW interacOons
vdW Interac,ons in DFT q ConvenOonal DFT funcOonals (LDA, PBE) q vdW-‐augmented funcOonals (PBE-‐D2, PBE-‐TS) q Assessment of funcOonals based on geometry predicOons q We consider 10 polymers for which reliable crystallographic informaOon is available
Predic,ons of Geometry a b Root-‐mean-‐ a, b (Å) Volume (Å3) square error c LDA 0.47 25.75 PBE 0.52 30.84 PBE-‐D2 0.29 13.77 PBE-‐TS 0.19 7.65
XY2 Homopolymers q Nine XY2 homopolymers (X = C, Si, Ge, Y= H, F, Cl) q CH2, CF2, SiCl2 occur in the Type A structure q GeF2 occurs in the Type B structure q All nine homopolymers are considered in both Type A and Type B structures and include vdW interacOons.
Dielectric Constant ε(total) = ε(electronic) + ε(ionic) An approximate inverse relaOonship Systems with bridging halogens display between electronic dielectric constant large dielectric constant and large band and band gap gap Ge containing polymers are iden,ﬁed as par,cularly promising, especially GeF2.
An Alternate Fast Method ESTIMATION OF CRYSTAL DIELECTRIC CONSTANT FROM SINGLE-‐CHAIN COMPUTATIONS Supercell Volume deﬁned through charge density cutoﬀ Vpolymer Vsupercell EﬀecOve medium Polymer mixing rules Chain q Amenable to “high-‐throughput” computaOons
Valida,on of Single-‐Chain Approach q In general, the single-‐chain results are either close, or smaller than the crystal results. q Overall, the agreement between the two methods is good, given that interchain interacOons are completely neglected in the single-‐chain computaOons.
Summary q We have studied nine XY2 homopolymers in two types of crystal structures. q Systems containing Ge are idenOﬁed as parOcularly promising for applicaOons requiring insulators with high dielectric constant. q It is desirable to consider heteropolymers composed of GeF2 and CH2 units (to opOmize both the dielectric constant and band gap). q In order to aid in an eﬃcient search of the chemical space spanned by such heteropolymers, a “high-‐throughput” strategy for the rapid computaOon of the dielectric constant is presented and validated.