013115-3
Teii, Matsumoto, and Robertson
Appl. Phys. Lett. 92, 013115 ͑2008͒
duction band of cBN by tunneling, thermalization to the con-
duction band minimum ͑CBM͒, and subsequent emission
from the CBM to the vacuum by tunneling ͑ii͒. The origin of
emission from the CBM has explained the field-emission en-
ergy distribution from cBN powders coated on Mo tips.12
This process lowers ⌽ by at most ϳ3 eV in comparison to
the aforementioned ͑i͒ for a positive electron affinity surface
and no longer depends upon the surface roughness for a
NEA surface. The band bending over ϳ3 eV is required to
lower the CBM of cBN below the Fermi level of sp2BN and
enable electron injection into the conduction band of cBN.
An experimental study has confirmed this condition,12 but a
theoretical study has not clearly yet.13 If the film has a p-type
character, the larger band bending is required.
FIG. 4. ͑Color online͒ Energy-band diagram for the sp2BN/cBN layered
structure. CBM: conduction band minimum, VBM: valence band maximum,
EF: Fermi level, Evac: vacuum level, PEA: positive electron affinity, and
NEA: negative electron affinity.
Finally, a slope decrease in the high field region of the
FN plot is attributed to depletion of available trapped elec-
trons to be emitted. This degradation may be caused by the
high potential barrier height for electron injection into the
conduction band of cBN or the high resistance of the initial
sp2BN layer.
The relationship among the slope of the FN plot ͑⌬͒, the
effective potential barrier height ͑⌽͒, and the field enhance-
ment factor ͑͒ is expressed as ⌬=−6840⌽3/2/, where ⌬
and ⌽ are in V/m and eV, respectively. For td=15 min, ⌬
is about −230 in the low field region, which is steeper than
about −40 in the high field region. This transition is attrib-
uted to different emission mechanisms as argued later. Here,
we focus on the change of ⌬ in the low field region. For
td=3 and 8 min, ⌬ is about −390 and −330, respectively. A
decrease in the magnitude of ⌬ with td means a decrease in
the ⌽3/2/ ratio. For td from 3 to 8 min, ⌽ decreases since 
usually decreases with decreasing surface roughness. This
indicates some that ⌽ decreases fundamentally by the forma-
tion of cBN. For td from 8 to 15 min, ⌽ changes a little,
while  increases with increasing surface roughness and the
emission site density increases with increasing island density.
The energy-band diagram for the sp2BN/cBN layered
structure is depicted in Fig. 4. Band bending is caused by
field penetration or space charge in the film. Band gaps
of 6.0 and 6.2 eV are adopted for sp2BN and cBN,
respectively.3 The Fermi level is assumed in the middle of
the band gap. The electron transport mechanism for undoped
sp2BN and cBN is most likely hopping conduction at defect
levels such as grain boundaries and dangling bonds near the
Fermi level. There are two possible emission processes from
cBN surfaces. One consists of hopping at defect levels from
sp2BN to cBN and subsequent emission from the defect lev-
els to the vacuum by tunneling ͑i͒. This process is believed to
be typical of the emission from sp2BN surfaces.11 The other
consists of hopping at defect levels, electron injection from
the defect levels near the sp2BN/cBN interface into the con-
One of the authors ͑K.T.͒ acknowledges the financial
support from the Murata Science Foundation.
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