Supplemental Information for Sun et al., “Thermally enhanced photo-induced electron
emission from nitrogen-doped diamond films on silicon substrates”

Experimental Details
Prior to growth of the diamond film, the boron-doped Si substrate surface was
sonicated in a nano-diamond slurry for 60 min. The sonication process was followed by
an acetone rinse and nitrogen gas drying. The nucleation step was then followed by the
deposition of a nitrogen-incorporated ultra-nanocrystalline diamond ((N)UNCD) layer
and then a polycrystalline nitrogen-doped diamond (N-diamond) layer. The UNCD layer
was deposited using 10 sccm argon, 100 sccm nitrogen and 20 sccm methane for 35 min.
The N-diamond layer deposition employed hydrogen at 400 sccm, methane at 2 sccm,
and nitrogen at 100 sccm for ~70 min. The diamond films had a total thickness of ~400500 nm as determined by in-situ laser reflectance interferometry. After deposition, the
samples were cooled in a hydrogen plasma (400 sccm hydrogen) for 1 min to obtain Hterminated surfaces. The UNCD layer has a smaller grain size and hence a higher
percentage of sp2 bonds at the grain boundary, which leads to sufficient conductivity for
the diamond film. On the other hand the polycrystalline N-diamond layer provides the
low effective work function through the negative electron affinity and n-type doping.
Electron microscopy images of the diamond samples were acquired with a JEOL
ARM200F aberration corrected scanning transmission electron microscope (STEM) to
examine the diamond/Si interface. The specimen preparation employed a focused ion
beam (FIB) lift-out technique using a FEI Nova 200 NanoLab instrument with an
Omniprobe tip. Electron microscopy of the sample (Fig. S1) indicates a smooth interface
between Si and the (N)UNCD layer. A grain size of less than 10 nm is shown in the
(N)UNCD layer. There is a thin layer between the two materials which has a thickness of
~ 2nm. Energy-dispersive X-ray spectroscopy (EDX) measurements indicate that this
layer is likely a disordered combination of Si, C and a trace amount of oxygen.
In the electron spectroscopy system, a toroidal tungsten coil beneath the sample
provided radiative heating for a temperature range of 20 to 400ºC. The sample
temperature was monitored with a thermocouple located at the center of the coil, and the
S1

sample surface temperature was calibrated with a Mikron M90Q infrared pyrometer
throughout the experiments. The vacuum pressure was maintained between 10-9 to 10-8
Torr. The band pass filters on the filtered Xe lamp have a FWHM of ~10 nm. The photon
flux was estimated by measuring the radiative power density of the filtered light using a
Newport 1916-C optical power meter. During measurements at the same temperature set
point, the monitored temperature showed a variance of less than ±2ºC, and the light
illumination had no observable effect on the measured sample temperature. A Keithley
237 source measuring unit was employed to record the photocurrent from the diamond
sample when photon illumination was provided. The measured photocurrent was
typically in the range of 0.5 to 5 nA depending on the photon energy, which
corresponded to an effective quantum efficiency of ~10-5 to 10-4. Work function of the
hemispherical analyzer is ~ 4.3 eV as calibrated by a standard Au foil. As this value is
higher than the kinetic energy of the emitted electrons, a -10V bias was applied to the
sample surface to overcome the analyzer work function. The spectra were shifted by the
applied bias. Consequently, the electron energy above EF, KE(sample), is given by the
following equation:
KE (sample)  KE (analyzer )  e V   A , (1)

where KE(analyzer) refers to the electron kinetic energy as measured by the analyzer, V
the applied voltage (10V), and ФA the analyzer work function (4.3 eV).
Fig. S2 shows UV photoemission spectra as a function of temperature, collected
from a nitrogen-doped diamond film on the p-type Si substrate. The measurements
employed a He discharge lamp optimized for generation of He I (21.2 eV) photons,
which were delivered to the sample surface through a ~1.5 mm diameter quartz capillary.
As the photon energy is greater than the bandgap of diamond, the photoelectrons are
excited from valence band states close to the diamond surface. The electrons in the
conduction band lead to the photoemission spectra. Thus, the low energy cut-off of the
spectra represents the effective work function ΦW of the N-diamond surface layer. A low
value (~1.9 eV) was observed, which remains approximately constant within the studied
temperature regime.
S2

Modeling Approaches
1) Photon-enhanced thermionic emission (PETE)
The following analysis is based on the work by Schwede et al. [1]. For a
semiconductor which exhibits PETE, the photons with energy above the band gap will
generate electrons in the conduction band and form an enhanced carrier population. This
leads to a shift of the quasi-Fermi level in the semiconductor towards the CBM and
consequently reduces the effective energy barrier for thermionic emission. As a result, the
electron emission intensity may be significantly enhanced with photon illumination. The
PETE coefficient KPETE is given as:

K PETE 

kBT
exp[  / kBT ] , (2)
2 mn*

where kB stands for the Boltzmann constant, mn* the electron effective mass, and T the
emitter temperature. Only the cross-gap recombination through black-body type radiation
is considered here by simplification, which has a coefficient KBB of:
K BB 

2
3 2
h c neq peq

(h ) 2 d (h )
EG exp  h / kBT  1 , (3)


where h stands for the Planck constant, ν the photon frequency, c the speed of light, and
neq and peq the equilibrium electron and hole concentrations. Auger recombination, while
neglected here, can become more significant as the electron population increases, and
will need to be included for a more complete analysis.
Within the constraints of this model, the equilibrium between generation and
recombination leads to the following relationship:

0  ( P  K PETE neq )  ( K PETE  K BB (neq  peq ))dn  K BB dn2 . (4)
Here ΓP represents the photon flux, dn the enhanced electron population in the conduction
band, and χ the emission barrier height with respect to the CBM. To express the analysis
in a more familiar form, the photon-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[(  ( EF ,n  EF )) / kBT ]  e  neq  dn 

kBT
exp[  / kBT ] , (5)
2 mn*
S3

2) Direct photoemission
Direct photo-electron generation in a semiconductor focuses on a non-equilibrium
process, where the photo-electrons transport across the interface barrier before thermal
relaxation. This emission mechanism can be simulated by employing an internal photoemission model [2, 3], which describes the quantum yield as a function of the energy of
the illuminating photons:


Y (h ) 

h  EG

0

T ( E ) S ( E , h ) N c ( E ) N v ( E  h )dE



h  EG

0

N c ( E ) N v ( E  hv)dE

, (6)

where Nc and Nv are the conduction band and valence band density of states (DoS) in the
absorbing substrate, respectively. The energy zero is referred to the CBM. The emitted
electron function, T(E), with kinetic energy E that exceeds the energy barrier χ is given
by Fowler’s assumption [3, 4] as:
T (E) 

1

1 
 , E   ; T ( E )  0, E   . (7)
2
E

The absorption function S(E, hν) is given in the form of:

S ( E , h ) 

 (h ) L( E )
, (8)
1   (h ) L( E )

which involves α(hν), the frequency dependent optical absorption coefficient of the
substrate, and L(E), the electron inelastic mean free path (IMFP). As Si has an indirect
band gap of 1.12 eV, its optical properties in the UV and visible wavelength regimes
show a significant temperature dependence. For instance, the absorption coefficient (α) of
Si as a function of temperature for 400 nm light has been measured experimentally, and
an empirical equation in Ref. [5] is employed in this work:

4
c


7.946


 0.0805  exp  3.1893  3.6482  h 2 2  



, (9)


T
 exp 

 369.9  exp  12.92  5.509  h  

 (h ) 

S4

where c is the speed of light, T is in the unit of ºC and hν in eV. The IMFP of low kinetic
energy electrons is usually difficult to determine, and thus in this model it is assumed to
be a constant ~100 nm in Si. Assuming parabolic DoS for Si and diamond, and
substituting Eq. (6) and (7) into Eq. (5), the direct photo-generation spectrum using the
specific diamond properties is obtained through a numerical calculation.
References
[1] J.W. Schwede, I. Bargatin, D.C. Riley, B.E. Hardin, S.J. Rosenthal, Y. Sun, F.
Schmitt, P. Pianetta, R.T. Howe, Z.X. Shen, N.A. Melosh, "Photon-Enhanced
Thermionic Emission for Solar Concentrator Systems", Nat. Mater. 9 (2010): 762-767.
[2] N.B. Kindig, W.E. Spicer, "Band Structure of Cadmium Sulfide - Photoemission
Studies", Phys. Rev. 138 (1965): A561-576.
[3] R.J. Powell, "Interface Barrier Energy Determination from Voltage Dependence of
Photoinjected Currents", J. Appl. Phys. 41 (1970): 2424-2432.
[4] R.H. Fowler, "The Analysis of Photoelectric Sensitivity Curves for Clean Metals at
Various Temperatures", Phys. Rev. 38 (1931): 45.
[5] G.E. Jellison, F.A. Modine, "Optical Functions of Silicon at Elevated Temperatures",
J. Appl. Phys. 76 (1994): 3758.

S5

Fig. S1 High resolution electron microscopy image of the diamond/Si interface, showing
the (N)UNCD layer on the top and single crystal Si substrate on the bottom.

S6

Fig. S2 UV (21.2 eV) photoemission spectra of a nitrogen-doped diamond film on a ptype Si substrate. Data were acquired with a ~0.02 eV resolution. An effective work
function of ~1.9 eV was observed which was relatively independent of temperature.

S7