Effect of Evanescent Waves on the Dark Current of Thermophotovoltaic Cells

ABSTRACT

The output power of thermophotovoltaic (TPV) cells may be greatly increased when the gap between the emitter and cell is reduced to submicron distances (near-field regime), at which photon tunneling due to evanescent waves becomes important. Accurate modeling of TPV cells in these conditions is crucial for the design and optimization of near-field TPV systems. The conventional or standard modeling method uses the summation of the dark current and the short-circuit current, while the direct method applies the photon chemical potential. It has been shown that the two methods are linked through a modification of the direct method using Wien’s approximation. By contrasting different modeling approaches, we quantitatively analyze the effects of evanescent waves on the TPV cell performance parameters, especially the dark current, for different emitter and cell materials in the near-field regime. Our results show that the saturation current by radiative recombination is strongly affected by evanescent waves and the bandgap energy. The current-voltage characteristics calculated by different modeling methods are displayed to demonstrate that a constant saturation current typically used in the standard method could cause substantial error in the near-field regime. For a TPV system with an emitter operating at relatively low temperatures, we show that it is necessary to include the photon chemical potential in the computation of the net radiative heat transfer between the emitter and receiver.

KEYWORDS:

• Dark current
• diode
• evanescent waves
• near-field thermophotovoltaic

Nomenclature

$c_0$	=	Speed of light in vacuum, m s−1
$D$	=	Diffusion coefficient, m s−2
$E_{\mathrm{g}}$	=	Bandgap energy, $\mathrm{\hslash }{\omega }_{\mathrm{g}}$, J
$e$	=	Elementary charge, C
$\mathrm{\hslash }$	=	Reduced Planck constant, J s
$i$	=	$\sqrt{-1}$
$J$	=	Current (density), A m−2
$J_0$	=	(reverse) saturation current, A m−2
$J_{\mathrm{d}\mathrm{a}\mathrm{r}\mathrm{k}}$	=	Dark current, A m−2
$J_{\mathrm{s}\mathrm{c}}$	=	Short-circuit current, A m−2
k	=	Magnitude of wavevector, m−1
$k_{\mathrm{B}}$	=	Boltzmann constant, J K−1
$N_{\mathrm{A}},N_{\mathrm{D}},\mathrm{o}\mathrm{r}{N}_{\mathrm{i}}$	=	Acceptor, donor, or intrinsic concentration, m−3
$P_{\mathrm{e}\mathrm{l}\mathrm{e}}$	=	Output power (per unit area), W m−2
$P_{\mathrm{r}\mathrm{a}\mathrm{d}}$	=	Net radiant power received by the TPV cell (per unit area) or net heat flux, W m−2
$T$	=	Temperature, K
$V$	=	Voltage, V
$V_{\mathrm{o}\mathrm{c}}$	=	Open-circuit voltage, V

Greek symbols

β	=	Parallel wavevector component, m−1
γ	=	Perpendicular wavevector component, m−1
ε	=	Relative permittivity
ε0	=	Electric permittivity of vacuum, F m−1
η	=	Energy conversion efficiency
Θ	=	Mean energy of Planck’s oscillator, J
μ	=	Photon chemical potential, J
ξ	=	Mode transmission coefficient
τ	=	Relaxation time, s
Φ	=	Spectral transmission coefficient
Ψ	=	Modified Bose-Einstein distribution function
ω	=	Angular frequency, rad s−1
${\omega }_{\mathrm{g}}$	=	Frequency corresponding to the bandgap, rad s−1

Subscripts

0,1,2	=	Medium 0, 1, 2
b	=	Blackbody
diff	=	Minority carrier diffusion
e, h	=	Electron, hole
rad	=	Radiative recombination
scr	=	Space charge region

Additional information

Funding

D.F. and Z.M.Z. would like to thank support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences (DE-SC0018369). E.J.T. acknowledges support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1650044. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Department of Energy and the National Science Foundation.