RAPID COMMUNICATIONS

PHYSICAL REVIEW B 90, 121302(R) (2014)

Thermally enhanced photoinduced electron emission from nitrogen-doped
diamond films on silicon substrates
Tianyin Sun, Franz A. M. Koeck, Aram Rezikyan, Michael M. J. Treacy, and Robert J. Nemanich*
Department of Physics, Arizona State University, Tempe, Arizona 85287-1504, USA
(Received 18 April 2014; revised manuscript received 20 August 2014; published 15 September 2014)
This work presents a spectroscopic study of the thermally enhanced photoinduced electron emission
from nitrogen-doped diamond films prepared on p-type silicon substrates. It has been shown that photonenhanced thermionic emission (PETE) can substantially enhance thermionic emission intensity from a p-type
semiconductor. An n-type diamond/p-type silicon structure was illuminated with 400–450 nm light, and the
spectra of the emitted electrons showed a work function less than 2 eV and nearly an order of magnitude increase
in emission intensity as the temperature was increased from ambient to 400 °C. Thermionic emission was
negligible in this temperature range. The results are modeled in terms of contributions from PETE and direct
photoelectron emission, and the large increase is consistent with a PETE component. The results indicate possible
application in combined solar/thermal energy conversion devices.
DOI: 10.1103/PhysRevB.90.121302

PACS number(s): 84.60.Jt, 79.40.+z, 79.60.Jv, 81.05.ug

Photons have been employed to generate electron emission
from novel materials through various physical mechanisms
[1,2]. Notably, a new emission mechanism that combines photoexcitation and thermal excitation, namely, photon-enhanced
thermionic emission (PETE), has been proposed to describe
results for Cs-coated p-type GaN [3]. Several theoretical
studies have described possible applications of PETE in concentrated solar-thermionic energy conversion devices [4–11].
In a recent experimental study, photon-enhanced thermionic
emission using a p-type GaAs/p-type AlGaAs heterojunction
interface was explored [12], and the results indicated the spatial
separation of photon absorption and electron emission in a
PETE device. However, these prior results employed notably
unstable cesiated surfaces to indicate the PETE effect. Studies
involving new methods to decrease the emission barrier are
therefore desirable.
Diamond films acquire a negative electron affinity (NEA)
after hydrogen passivation [13–15] where the electron affinity
is defined as the energy required to remove an electron from
the conduction band minimum (CBM) of a semiconductor
into vacuum away from the surface. For NEA diamond films,
conduction band electrons can be readily emitted without
overcoming an energy barrier. For crystalline diamond, n-type
doping has been achieved by incorporation of nitrogen or
phosphorus, with a donor level of nitrogen at 1.7 eV and
that of phosphorus at 0.6 eV below the CBM [16,17]. The
strong upward band bending often observed in n-type doped
diamond can be mitigated in nanocrystalline diamond apparently because of the sp2 bonds at the grain boundaries [18].
As a result, n-type doping of nanocrystalline diamond leads to
lowering of the electron emission threshold, i.e., the effective
work function W , which is defined for NEA materials to
be the energy difference between the CBM and the Fermi
level (EF ). Effective work functions of 1.3 eV with nitrogen
doping and 0.9 eV with phosphorus doping have been reported
for n-type chemical vapor deposited diamond [19,20]. These
low work function surfaces enable visible light photoinduced
electron emission and low temperature thermionic electron
emission from diamond films on metallic substrates [21–23].
*

robert.nemanich@asu.edu

1098-0121/2014/90(12)/121302(5)

Based on these results, in this work we explore a twolayer configuration that combines a nitrogen-doped (n-type),
hydrogen-terminated diamond film and a p-type semiconductor (i.e., silicon) substrate. The advantage of this structure is
that the Si substrate is nearly ideal for absorption of the solar
spectrum and the p-type character will enable a large increase
of the electron quasi-Fermi level. The NEA n-type diamond
film provides a low work function surface with potentially
reduced recombination due to the lack of mobile holes.
A schematic of the emission mechanism is illustrated in
Fig. 1: Photon-enhanced thermionic electrons are generated
in the substrate, transported through the interface towards the
diamond surface and contribute to the emission. Due to the
wide band gap of diamond (5.5 eV at room temperature), it is
presumed that the illuminating photons from the front side will
be absorbed in the substrate. Alternatively, electrons can be
generated directly from valence band states in the Si substrate
and injected into the diamond layer without contributing to
the enhanced population. This Rapid Communication presents
an investigation of the photoinduced electron emission from
nitrogen-doped (n-type) diamond films deposited on p-type
Si substrates and its temperature dependence. The results are
discussed in terms of the emission mechanisms.
The PETE model from the work by Schwede et al.
[3] is based on a balance between photoexcitation and
recombination in a single layer of material, which absorbs
photons and emits electrons through the opposite surfaces. In
a zero-dimensional simplification, the loss of electrons due
to transport between the two surfaces is neglected, which
provides a carrier distribution that is essentially identical to our
front illumination experimental setup. In the following analysis
[24], the fundamental relationships in both the PETE and the
direct photoemission mechanisms are introduced, based on a
single-layer film. To apply the two single-layer models to a
diamond-Si bilayer structure, it is assumed that the emission
threshold is determined by the interface conduction band
barrier. Consequently the electron affinity χ is replaced with
the value of this barrier as experimentally measured in the photoinduced emission spectra. Additionally, recombination due
to the diamond-Si interface is also ignored, and ideal electron
transport properties are assumed. These assumptions may be

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PHYSICAL REVIEW B 90, 121302(R) (2014)

FIG. 1. (Color online) Band schematics of the proposed
diamond-Si structure showing electrons being excited in the absorbing substrate and contributing to the photon-enhanced emission
through the low work function surface.

reasonable since recombination at Si interfaces is typically low
and diffusion lengths of electrons in n-type diamond may be
expected to be long due to the lack of free holes.
We first summarize the PETE model [3]. It is assumed that
all photons with energy above the semiconductor band gap are
absorbed and converted into conduction band electrons which
follow a thermally stabilized Maxwell-Boltzmann distribution,
and the enhanced emission current density is given in a form
similar to the Richardson-Dushman relationship for “pure”
thermionic electron emission:
J = A∗ T 2 exp{−[W − (EF,n − EF )]/kB T }

kB T
exp[−χ /kB T ],
= e(neq + dn)
2π m∗n

(1)

where A∗ is the Richardson constant of the emitter, T is the
emitter temperature, EF,n is the electron quasi-Fermi level,
kB is the Boltzmann constant, m∗n is the electron effective
mass, neq is the equilibrium electron concentrations, dn is
the enhanced electron population in the conduction band, and
χ is the emission barrier height with respect to the CBM.
Consequently, the PETE current intensity J can be found by
solving dn and substituting into Eq. (1). We also note that
a recent publication employed a modified PETE model that
achieved good correspondence with experimental data [25].
It should be noted that recent considerations of the PETE
model have focused mostly on p-type substrates. This is due
to the fact that the enhancement in PETE is most significant
when dn is significantly larger than neq , as shown in Eq. (1).
For an n-type material, as electrons are the majority carriers,
the relative enhancement from photon illumination will be
considerably smaller compared to a p-type material under the
same illumination conditions.
Direct photoelectron generation in a semiconductor, on the
other hand, focuses on a nonequilibrium process, where the
photoelectrons transport across the interface barrier before
thermal relaxation. This calls for a separate analysis. This
emission mechanism can be simulated by employing an

FIG. 2. (Color online) Simulation results of the two models on
an ideal electron emitter, which has a band gap of 1.12 eV, electron
affinity of 0.5 eV, and is under illumination of 400 nm light with a
photon flux of 1015 cm−2 per second. The thermionic contribution
is obtained by calculating the emission current with no photon
illumination.

internal photoemission model [26,27], which describes the
quantum yield as a function of the energy of the illuminating
photons:
 hν−EG
T (E)S(E,hν)Nc (E)Nv (E − hν)dE
Y (hν) = 0
, (2)
 hν−EG
N
(E)N
(E
−
hv)dE
c
v
0
where Nc and Nv are the conduction band and valence band
density of states (DOS) in the absorbing substrate. T (E)
and S(E,hν) are the electron emission function and optical
absorption function, respectively. The energy zero is the
CBM. Assuming parabolic DOS for Si and diamond, the
direct photogeneration spectrum using the specific diamond
properties is obtained through a numerical calculation.
As an example, Fig. 2 shows the results of individually applying the two models to an ideal single-layer electron emitter
based on p-type Si. The structure includes a constant emission
threshold of 0.5 eV above the Si CBM (i.e., χ = 0.5 eV),
and is illuminated with 400 nm photons at a flux of 1015 cm−2
per second. We note that in both models the emission current
is approximately proportional to the photon flux in the tested
temperature range. Like other studies, the calculation uses
the ideal Richardson constant of 120 A/cm2 K2 . The results
contain the net current density, and the components contributed
by both the “pure” thermionic emission and the photoinduced
emission mechanisms, respectively. A comparison between the
two models shows different features: The direct photoemission
is relatively constant within the tested temperature range,
while the PETE-induced charge distribution is affected by
temperature, and consequently the PETE model results in
a more significant temperature dependence. For the specific
barrier values employed here, the PETE model shows a
much stronger increase of electron emission than the direct
photoemission model. We note that under these conditions
EF,n is positioned at 0.78 eV above the valence band

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THERMALLY ENHANCED PHOTOINDUCED ELECTRON . . .

maximum (VBM) at 300 K, and as the temperature is increased
to 650 K it is reduced to 0.14 eV at 650 K due to increased
recombination. At higher temperatures the thermal excitation
of conduction band electrons become more significant than the
photoinduced change of EF,n .
In the experimental setup [24], the nitrogen-doped diamond
films were deposited on boron-doped ([B]∼1019 cm−3 ) single
crystal Si(100) substrates by microwave plasma enhanced
chemical vapor deposition. The combined photoinduced and
thermionic electron emission spectra were recorded as a
function of temperature, using a VSW HA50 hemispherical
electron analyzer positioned normal to the sample surface and
operated at 0.1 eV resolution. The electron emission spectra
were referenced to the Fermi level (EF ) of the metallic sample
holders which was calibrated with a gold foil. A −10 V bias was
applied to the sample to overcome the analyzer work function
and the spectra were corrected for the applied bias. The photon
source was a focused Oriel 100W Xe arc lamp with associated
bandpass filters to provide visible light photons, at an angle of
35° to the normal direction.
Figure 3 shows photoinduced components of the emission
spectra collected while the sample was illuminated by selected
wavelength photons. When measured at elevated temperatures,

PHYSICAL REVIEW B 90, 121302(R) (2014)

the sample also exhibited thermionic emission without photon
illumination, which is shown in Fig. 3(d). The thermionic
emission spectra (TE, “light-off”) were subtracted from
the combined emission (“light-on”) to obtain the displayed
photoinduced component. Note that the TE component was
only significant at the highest temperature, where it was still
substantially less than the photoinduced emission component.
In contrast to the UV (21.2 eV) photoemission results, the
visible light photoinduced emission spectra exhibited a higher
threshold energy which decreased at elevated temperatures. At
400 °C where thermionic emission started to be significant,
this threshold was found to be approximately the same as the
surface work function (1.9 eV). This decrease in low energy
cutoff is possibly due to an interface barrier that becomes less
significant for transport at elevated temperatures.
Figure 4 shows the temperature dependence of the integrated spectral intensities for the various illuminating
wavelengths. In this measurement series, the sample was
illuminated with 400 to 450 nm (3.10 to 2.76 eV) photons at
a flux of ∼1015 cm−2 per second, and the thermionic emission
contribution was subtracted from the combined emission
spectrum. At low temperatures, the intensity increases with
increasing photon energy, as expected for photoemission.

FIG. 3. (Color online) Photoinduced emission spectra from nitrogen-doped diamond films on a p-type doped Si substrate, obtained by
subtracting the thermionic emission contribution from the combined emission spectra. The corresponding photon energies are labeled with solid
lines relative to EF . The “pure” thermionic emission spectra are shown in (d), and were collected at each temperature without illumination.
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PHYSICAL REVIEW B 90, 121302(R) (2014)

Integrated Intensity (a.u.)

40000

30000

Experimental:
400 nm
430 nm
450 nm
Thermionic emission
400 nm, Mo/diamond

400 nm
430 nm
450 nm
ΦW = 1.9 eV
15

-2

ΓDirect = 10 cm
20000

15

-2

ΓPETE = 2×10 cm

10000

0
300

400

500

600

700

Temperature (K)
FIG. 4. (Color online) Temperature dependence of integrated
photoinduced emission spectral intensity and thermionic emission
intensity, obtained from a nitrogen-doped diamond film on a p-type
doped Si substrate, showing results with different excitation energies.
Results obtained from an N-doped diamond film on a Mo substrate
[20] are also included for comparison. Combined curves of the two
models are shown for the three wavelengths respectively.

As the sample temperature was increased to 400 °C, the
emission exhibited an intensity increase by a factor of 7.3 to
18.4 for the different excitation energies. In contrast, this strong
temperature dependence was not observed from diamond
films deposited on metal substrates (also shown in Fig. 4).
The diamond-metal samples have shown relatively constant
photoinduced emission intensity [21,22], which is consistent
with the conventional Fowler-DuBridge model [2,28] that only
involves direct photoemission. These results are consistent
with the model discussed here, since PETE is not expected
from a metal substrate.
The modeling results of this N-doped diamond on p-type Si
sample are represented by the curves in Fig. 4. The numerical
calculations show the sum of emission intensities obtained
from the two models, and are based on the temperatures and
wavelengths used for the measurements. A photoemission barrier of 1.9 eV was employed in the simulations. The collection
efficiency of the system was varied to fit the results obtained
from the different methods. We found that with a photon
flux ratio of 1:2 between the direct photoemission model
and the PETE model, the simulation presented a temperature
dependence that was similar to the experimental results.
The measurements were repeated for several samples prepared under different conditions. All samples showed similar
results with variations in work function and enhancement
factors. The samples were also found to show degradation
after measurements at high temperature, and the photon enhancement was substantially reduced in repeated experiments.
This could be related to changes of the interface properties and
needs further study.
The key question of this study is whether PETE is observed.
Most significantly, the diamond on Si showed a substantial
increase in intensity as the temperature was increased, while
for diamond on metals the intensity was approximately

constant with temperature [21,22]. This comparison indicates
that the PETE mechanism is consistent with the emission
intensity increase for diamond films on Si substrates.
Meanwhile, there is also evidence that suggests the significance of emission mechanisms other than PETE. At lower
temperatures (below 200 °C) photoinduced emission can be
observed, although the PETE model predicts negligible emission under such conditions. Also, while showing significant
temperature dependence, the photoinduced spectra of the
diamond-Si samples still show similarities to the results
collected from diamond films deposited on metal substrates.
For instance, the spectral intensity shows a dependence on the
photon energy, where the maximum electron kinetic energy in
the spectrum approximately corresponds to the energy of the
illuminating photons. Previously it was concluded that these
high-energy electrons are from direct excitation of states near
EF [21]. For the PETE mechanism, however, the emission
spectra are expected to be almost independent of photon energy
[3], since the photoelectrons are thermally stabilized into a
Maxwell-Boltzmann distribution regardless of the excitation
energy. This supports the direct-generation model, as EF in a
heavily doped p-type Si wafer is close to the VBM. Therefore,
direct generation of photoelectrons should be considered in the
observed photoinduced electron emission.
The role of defects in both photogeneration and transport
has not yet been considered in the models discussed above.
Moreover, the actual generation and transport of photoelectrons can be a complex process. In our recent study of N-doped
diamond on metal substrates [23], it was concluded that the
photoelectrons may be generated in the substrate or in the
nucleation layer which has a higher density of sp2 bonds in
the grain boundaries. The photon energy dependence shown
in Fig. 4 may also be related to smaller optical absorption in
the Si substrate for lower-energy photons, so that electrons
generated deeper in the substrate may contribute less to the
observed emission. These results indicate the complexity of the
emission process that the two simplified models we examined
cannot independently describe. A more advanced model would
be necessary to better assess the specific mechanisms of the
more complex double-layer structure.
The relative significance of the PETE and direct-generation
processes may be related to the properties of the absorbing
substrate material. The material will more likely exhibit PETE
if forming a quasiequilibrium population of photoexcited
electrons is more favorable than direct injection of the electrons
across the barrier. Additionally, an optimal band gap of the
substrate is required to absorb a wide solar spectrum, and it
is necessary to limit surface and bulk recombination. We have
assumed that a semiconductor with an indirect band gap (e.g.,
Si) will enable PETE-type emission, due to reduced cross-gap
recombination and a longer electron relaxation time. These
properties, and the NEA of diamond surfaces, lead to the
proposed structure in this work. Theoretically, the optimal
band gap for PETE materials has been predicted to be 1.4 eV
[3,6], and candidate substrates including GaAs and InGaN
may be appropriate. To develop high efficiency PETE devices,
it is important to understand the transport and recombination
properties of these materials.
To conclude, a significant increase of photoinduced electron
emission at elevated temperatures has been observed from

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PHYSICAL REVIEW B 90, 121302(R) (2014)

nitrogen-doped diamond films on p-type silicon substrates.
The results differ from previously reported features of
diamond emitters on metal substrates, where a relatively
constant photoinduced emission was observed. The results
are consistent with PETE, which involves generation of an
enhanced electron population and lowering of the emission
barrier due to the diamond film. Computer-based modeling
is employed to compare different physical mechanisms,
and the results appear to indicate a complex generation
process. As significant enhancement of electron emission
is shown through combined excitation from heat and light,

such diamond emitters could potentially be applied in concentrated solar collection systems for solar-thermionic energy
conversion. Examination of different substrate candidates to
optimize the PETE contribution will be important in the
future.

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We gratefully acknowledge the LeRoy Eyring Center for
Solid State Science at Arizona State University for the use of
the aberration corrected microscope. This work is supported
through the Office of Naval Research under Grant No. N0001410-1-0540.

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