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RESEARCH PAPERS: Radiative Properties

Near-Field Radiation Calculated With an Improved Dielectric Function Model for Doped Silicon

[+] Author and Article Information
S. Basu

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

B. J. Lee

Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15261

Z. M. Zhang1

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332zhuomin.zhang@me.gatech.edu

1

Corresponding author.

J. Heat Transfer 132(2), 023302 (Nov 30, 2009) (7 pages) doi:10.1115/1.4000179 History: Received September 18, 2008; Revised March 16, 2009; Published November 30, 2009; Online November 30, 2009

This paper describes a theoretical investigation of near-field radiative heat transfer between doped silicon surfaces separated by a vacuum gap. An improved dielectric function model for heavily doped silicon is employed. The effects of doping level, polarization, and vacuum gap width on the spectral and total radiative transfer are studied based on the fluctuational electrodynamics. It is observed that increasing the doping concentration does not necessarily enhance the energy transfer in the near-field. The energy streamline method is used to model the lateral shift of the energy pathway, which is the trace of the Poynting vectors in the vacuum gap. The local density of states near the emitter is calculated with and without the receiver. The results from this study can help improve the understanding of near-field radiation for applications such as thermophotovoltaic energy conversion, nanoscale thermal imaging, and nanothermal manufacturing.

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Figures

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Figure 2

Predicted dielectric function of n-type silicon for different doping concentrations at 400 K: (a) real part and (b) imaginary part

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Figure 3

Contour plot of s(ω,β) for doping concentration of 1020 cm−3 in both the emitter (at 400 K) and receiver (at 300 K) when the vacuum gap width d=10 nm. Note that the angular frequency is shown in the range from 1014 rad/s to 4×1014 rad/s and the parallel wavevector component is normalized to the frequency. The dashed curves represent the two branches of the surface-polariton dispersion.

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Figure 4

Graph of s(ωm,β) as a function of β for different vacuum gap widths

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Figure 5

Spectral energy flux for different doping levels at (a) d=100 nm and (b) d=10 nm

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Figure 6

Net energy flux between medium 1 at 400 K and medium 2 at 300 K at different doping levels versus gap width. The dash-dotted line refers to the net energy transfer between two blackbodies maintained at 400 K and 300 K, respectively.

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Figure 7

Effect of doping on the net energy transfer between two doped Si plates separated by 1 nm vacuum gap

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Figure 8

Contribution of TE and TM waves to the net energy transfer for (a) 1020 cm−3 and (b) 1021 cm−3 doped Si at different gap widths

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Figure 9

Graphs of s(ωm,β) and lateral shift versus β for 1020 cm−3 doped Si media with a gap width of 10 nm. The lateral shift δ is normalized with respect to d.

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Figure 10

Local density of states for 1020 cm−3 doped Si plates separated by a 10 nm vacuum gap: (a) spectral variation in LDOS at z=0.01d, z=0.6d, and z=d (b) spatial variation in LDOS at ωm=2.67×1014 rad/s

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Figure 1

Schematic for near-field radiation between two closely placed parallel plates at temperatures T1 and T2 separated by a vacuum gap of width d. The random motion of the dipoles, represented as ellipses in the figure, result in a space time-dependent fluctuating electric field.

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