Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Abstract

Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.

Ab initio study of mode-resolved phonon transmission at Si/Ge interfaces using atomistic Green's functions

“…[24]. This method requires knowledge of the harmonic force constants of the system, which we obtain from first principles using the temperature-dependent effective potential method (TDEP) [26][27][28].…”

“…1. We assume identical interactions between Si and Ge atoms based on the ab initio force constants of bulk silicon [28]. The mass mismatch between the two materials is considered as the key parameter for phonon reflection and transmission at the interface [20].…”

Thermal expansion in insulating solids from first principles

“…Many techniques have been developed for going beyond the quasiharmonic approximation and while this Tutorial will not discuss them in depth, we refer the reader to the relevant literature for further details. [23][24][25][26][27][28][29][30][31][32][33]…”

A systematic study of the negative thermal expansion in zinc-blende and diamond-like semiconductors

“…Material undergoing expansion upon heating and contraction upon cooling is a common expectation. However, some materials are discovered to demonstrate a contraction upon heating, known as negative thermal expansion (NTE) [1][2][3][4][5][6][7]. Such NTE materials have attracted considerable attention for use as thermal-expansion compensators by mixing with a 'normal' material which expands on heating to fabricate composites with tailored expansivity, which have a range of potential engineering, mechanical, ferroelectric and chemical applications [8][9][10][11][12][13].…”