1. T H Heat flow across a SiO2 layer EXAS TEC
Motivation
Si|SiO2 interfaces are ubiquitous in Si technology.
How does heat generated by a CPU in Si interact with this layer?
Our study: ‘first-principles’ theory
Existing theoretical studies: all are empirical [1-5]
Experiment: focus on the ‘interface boundary resistance’ [8-10]
Interface vibrational modes
ΔT 1
ΔT 2 𝑇0
𝑇ℎ𝑓
𝑇0 = background T
𝑇ℎ𝑓= heat front T as it reaches the interface
ΔT 1 = ‘low-T’ window
ΔT 2 = ‘high-T’ window
Result: monitoring heat flow
Theory
Electronic structure: SIESTA[7]
valence regions: DFT (LDA)
core regions: ab-initio pseudopotentials
Nuclei classical
Host material
H-saturated Si nanowire in a large 1D-
periodic box (strictly microcanonical)
Non-equilibrium MD:
‘supercell preparation’ technique [6]
NO thermostat or thermalization runs
excellent T control
t=0: distribution of normal vibrational
modes with random phases
averaging: microstates
Physics Department T
EXAS TEC H
U N I V E R S I T Y
Christopher M. Stanley and Stefan K. Estreicher
Heat flow across a SiO2 layer
Result: oxide layer is a barrier to heat flow
With an oxide: considerably more time needed to equilibrate
With oxide: time constant increases by factors of 2.4 (low-T window) to 2.3 (high-T window)
Difference between the T windows: due to
difference in thermal conductivity of nanowire at different temperatures
With Oxide
Without Oxide
Oxide construction: a-SiO2 layer
Simulate experimental approach
repeat steps 1-3
remove self-interstitial when needed
coordinates relaxed by CG
one O2 molecule added at a time
Construction Summary
Typical initial position O2
final structure: Si230O54H56
Set up a T gradient at t=0
A slice of the nanowire is heated above background temperature (T0) at t=0
MD run: the heat initially flows only to the right
Temperature gradients are chosen based on frequency range of oxide-related vibrational modes
[1] B. Deng et al., J. App. Phys. 115, (2014).
[2] S.S .Mahajan et al., Therm. Thermomech. Phenom. Ele. Sys (2008)
[3] E. Lampin et al., Appl. Phys. Lett. 100, (2012)
[4] J Chen et al. J. App. Phys. 112, (2012)
[5] S. Munetoh et al., Comput. Mater. Sci. 39, 334 (2007)
[6] T.M. Gibbons et al., J. App. Phys. 118, (2015)
[7] J.M. Soler, et al., J. Phys. Cond. Matt. 14, 11 (2002)
[8] D.H. Hurley et al. J. App. Phys. 109, (2011)
[9] R Kato et al. Int J Thermophys. 29, p (2008)
[10] S.M. Lee. J. App. Phys. 81, p (1997)
References
Oxides:barriers to heat flow
The heat generated in the Si (e.g. by a CPU) finds it harder to escape
The results point towards the possibility of non-propagating vibrational modes, which cannot be explained by conventional models of heat flow.
Conclusions