tunneling process ( 25 , 26 ). In this model, tun-
neling is a multistep process that results from
the absorption of a photon in an occupied state
near the Fermi energy of the metal followed
by subsequent field-enhanced tunneling into
an unoccupied state of the silicon leading to
a small direct photocurrent. A similar time-
reversed process occurs in the semiconductor,
resulting in a backflow current into the metal.
The resulting direct current is due to the dif-
ference in these currents, which arises from
the difference in effective mass for electrons
in the metal and the semiconductor. This sim-
ple picture accurately predicts the temper-
ature transitions and current-voltage (IV)
dependence on temperature for measured
rectenna power generation. The full perturba-
tive dynamic current model predicts a non-
linear expansion of the PAT current in terms
of nonlinear conductance in analogy with
nonlinear susceptibilities in conventional
nonlinear optics.Photon-mediated charge pumping
PAT and the spatially varying confined opti-
cal field in the tunnel barrier suggest a newly
devised means for thermal photovoltaic con-
version from a low-grade thermal source in the
temperature range of 100° to 400°C (Fig. 1A).
An interdigitated bipolar pn junction array
under the tunneling gate electrode acts as a
charge pump moving electrons from p-type
region to n-type well in a half period of the
optical field. Figure 1B shows a schematic of
multiple periods of a bipolar grating-coupled
tunnel diode. The underlying band structure
and associated charge wells are also shown.
An instantaneous electron particle current,JT,
shown in Fig. 1B leads to charge separation
into the n and p wells. An optical micrograph
of the fabricated three-terminal bipolar device
is shown in Fig. 1C. The simulated instanta-
neous enhanced transverse field at the grating
resonance is shown in Fig. 1D, which can be
translated into a spatially varying voltage across
the grating-metal width. At maximum current,
the metal-n+ and metal-p+ tunnel diodes are
both forward-biased tunnel junctions. After
a half cycle of the optical field, a minimal
backflow current occurs owing to the reverse
biasing of the two tunnel junctions. This is
analogous to photovoltaic conversion in a pn
junction, except that the device current does
not arise from square-law generation in the
depletion region but from ultrafast PAT in
the two metal-oxide-semiconductor tunnel
diodes and subsequent charge pumping. The
interdigitated p and n regions are separately
contacted, and power generation is measured
across a variable external load resistance,R,
that shorts the pn junction. As will be dem-
onstrated, the advantage of using multiple
pn junctions is that the open-circuit voltage,
Voc, is not limited by the induced alternating
current (ac) infrared voltage on the tunnel
diode. This effective diode voltage multiplier
circuit results in orders-of-magnitude improve-
ment in electrical power generation compared
with direct rectification approaches ( 20 ).Device modeling
A device model for thermal photovoltaic con-
version in an ideal bipolar antenna-coupled
tunnel diode rectifier consists of a buried
symmetric pn junction under an equilibrium
MOS metal gate, as shown in Fig. 2A. The
model development proceeds by considering
the confined and enhanced electric field in the
tunnel barrier, which gives rise to a spatially
varying voltage across the metal gate. The de-
vice is illuminated by a thermal source mod-
eled as a blackbody broadband emitter. The
enhanced and confined transverse field in
the gap is obtained from the incident field,
Emax(w)=g(w)E 0 (w), wheregis the ENZ en-
hancement factor andE 0 (w) is the incident
field. The power per unit area emitted from a1342 20 MARCH 2020•VOL 367 ISSUE 6484 SCIENCE
Fig. 1. Bipolar grating-coupled tunnel diode thermal photovoltaic device.(A)Illustration of thermal
illumination of a bipolar thermal photovoltaic device in a vacuum radiometry setup. Device is packaged
and mounted on a chilled stage with temperature stabilized at 20°C. (B) Schematic of multiple periods of bipolar
thermal photovoltaic device, illustrating the charge-pumping mechanism.E, energy; h+, holes; e−, electron.
(C) Image of actual bipolar grating-coupled tunnel diode at resonance with front-side contacting scheme. (Grating
area is 60mm by 60mm.) (D) The modeled transverse spatial field profile in a thin tunnel barrier at peak field
confinement. This confined field leads to the driven photon-assisted tunneling. (E) The model IV tunneling
characteristic for the n+ MOS tunnel diode.Rnandrnare the diode resistances in forward and reverse bias and
the rectification of the tunneling current. (Model p+ MOS leads to similar IV characteristics.)
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