PHYSICAL REVIEW MATERIALS
8
, 104602 (2024)
Valleytronics and negative differential resistance in cubic boron nitride: A first-principles study
Benjamin Hatanpää
and Austin J. Minnich
*
Division of Engineering and Applied Science,
California Institute of Technology
, Pasadena, CA, USA
(Received 20 August 2024; accepted 23 September 2024; published 8 October 2024)
Cubic boron nitride (c-BN) is an ultrawide-bandgap semiconductor of significant interest for high-frequency
and high-power electronics applications owing to its high saturation drift velocity and high electric breakdown
field. Beyond transistors, devices exploiting the valley degree of freedom or negative differential resistance are
of keen interest. While diamond has been found to have potential for these applications, c-BN has not been
considered owing to a lack of knowledge of the relevant charge transport properties. Here, we report a study
of the high-field transport and noise properties of c-BN using first-principles calculations. We find that c-BN
exhibits an abrupt region of negative differential resistance (NDR) below 140 K, despite the lack of multivalley
band structure typically associated with NDR. This feature is found to arise from a strong energy dependence
of the scattering rates associated with optical phonon emission. The high optical phonon energy also leads to
an intervalley scattering time rivaling that of diamond. The negative differential resistance and long intervalley
scattering time indicate the potential of c-BN for transferred-electron and valleytronic devices, respectively.
DOI:
10.1103/PhysRevMaterials.8.104602
I. INTRODUCTION
Ultrawide-bandgap (UWBG) semiconductors are the sub-
ject of intense study owing to their utility in power electronics
and related device applications [
1
,
2
]. Cubic boron nitride (c-
BN), with a wide bandgap of 6.4 eV [
3
], has long been of
interest for electron devices and other applications owing to its
competitive mechanical, thermal, and electrical properties. c-
BN has a high hardness of 30–43 GPa [
4
], thermal conductiv-
ity that is second only to diamond [
5
], excellent oxidation re-
sistance, and high chemical and thermal stability. In addition,
c-BN also has a high electric breakdown field of 4 MV cm
−
1
,
comparable to those of diamond and GaN; and a high pre-
dicted saturation drift velocity of 4
.
3
×
10
7
cm s
−
1
, which is
the highest of any semiconductor [
6
]. These properties lead
to the prediction of among the highest figure-of-merits (such
as Johnson, Baliga, and Keyes figures-of-merit) for high-
frequency and high-power applications [
1
,
6
,
7
].
In addition to transistor-based devices using UWBGs,
other device types such as transferred-electron and val-
leytronic devices are of interest. For instance, diamond
exhibits a region of negative differential resistance (NDR)
below room temperature [
8
], enabling the realization of Gunn
oscillators [
9
]. Further, the large intervalley time of 300 ns
[
10
] allows for the manipulation of electrons by their valley
degree of freedom, for instance, in a valleytronic transistor
[
11
]. However, diamond has long-standing challenges, in-
cluding the difficulty realizing n-type doping [
12
–
14
] and
synthesis of high-quality thin films.
c-BN has the potential to overcome some of these diffi-
culties. c-BN can be doped both n- and p-type [
15
–
18
], has
a higher oxidation temperature than diamond, and is more
thermally and chemically stable [
19
]. However, c-BN films
face various challenges in synthesis, including formation of
*
Contact author: aminnich@caltech.edu
nanocrystalline films, growth of the hexagonal crystal struc-
ture rather than the desired cubic structure [
20
], and high
compressive stresses [
21
]. As a result, devices based on c-BN
are still rare. Most devices are limited to
p
−
n
junctions
[
22
] fabricated from doped or intrinsic c-BN thin films [
23
].
Diodes [
24
] and ultraviolet emitters [
25
] have been realized
in c-BN. In addition, deep-ultraviolet photodetectors based
on c-BN have been fabricated [
26
–
28
] and are of interest for
extreme-environment applications.
Considering that diamond thin films are considered
promising for Gunn oscillators and valleytronic transistors
[
9
,
11
], it is natural to consider c-BN as well given the sim-
ilarities in electronic band structure. However, experimental
data regarding the transport properties of c-BN, especially
at high electric fields, are scarce. The low-field mobility has
been reported experimentally [
16
,
29
–
31
], with values varying
by several orders of magnitude. The low-field mobility of
c-BN has been computed with ab initio methods [
32
–
34
],
but investigations at higher fields are limited to Monte Carlo
methods with semi-empirical inputs [
35
–
37
]. The proper-
ties relevant for transferred-electron and valleytronic devices,
namely the occurrence of negative differential resistance and a
sufficiently long intervalley scattering time, have not yet been
assessed in c-BN.
Here, we report first-principles calculations of the high-
field electron transport properties and noise characteristics of
c-BN. We find a pronounced region of negative differential
resistance below 140 K. This feature occurs due to the strong
dependence of the electron scattering rates associated with
optical phonon emission. The high optical phonon energy in
c-BN also leads to intervalley scattering times rivaling those
of diamond. We identify how these predictions could be ex-
perimentally tested via a non-monotonic trend in the spectral
noise current density versus the electric field. These properties
suggest that c-BN is a promising contender in novel electron-
ics applications, such as valleytronics or Gunn oscillators.
2475-9953/2024/8(10)/104602(7)
104602-1
©2024 American Physical Society
HATANPÄÄ AND MINNICH
PHYSICAL REVIEW MATERIALS
8
, 104602 (2024)
II. THEORY AND NUMERICAL METHODS
The approach used here to compute the high-field trans-
port and noise properties of electrons has been described
previously [
38
–
41
]. In brief, the Boltzmann transport equa-
tion (BTE) for a nondegenerate and spatially homogeneous
electron gas subject to an applied electric field is given by
q
E
̄
h
·∇
k
f
k
=−
∑
k
kk
f
k
.
(1)
Here,
q
is the carrier charge,
E
is the electric field vector,
f
k
is the distribution function describing the occupancy of
the electronic state indexed by wavevector
k
,
f
k
is the
perturbation to the equilibrium electron distribution function
f
0
k
, and
kk
is the linearized collision matrix arising from
Fermi’s golden rule given by Eq. 3 of Ref. [
38
]. Here, we
assume that only one band contributes to charge transport, as
the minimum of the next-lowest energy band is calculated to
be 4.32 eV above the conduction band minimum, far higher
than the electronic states occupied at the highest fields used in
this work, and thus we neglect the band index in our notation.
The formulation of the BTE we use here is applicable to
arbitrarily high fields [
39
], so long as the electron gas remains
nondegenerate.
Beyond the low-field regime, the reciprocal space deriva-
tive of the total distribution function must be evaluated
numerically. Here, we use a finite difference approximation
given in Refs. [
42
,
43
]. The BTE then takes the form of a linear
system of equations (Eq. 5 in Ref. [
38
]), which can be solved
using numerical linear algebra:
∑
k
kk
f
k
=
∑
γ
qE
γ
k
B
T
v
k
,γ
f
0
k
.
(2)
Here,
E
γ
and
v
k
,γ
are the electric field and electron drift ve-
locity along the
γ
-Cartesian axis, and the relaxation operator
kk
is defined as
kk
=
kk
+
∑
γ
qE
γ
̄
h
D
kk
,γ
,
(3)
where
D
kk
,γ
is the momentum-space derivative repre-
sented in the finite-difference matrix representation given by
Eq.24inRef.[
42
]. Once the steady-state distribution function
is obtained by solving the linear system, various transport
properties can be calculated via an appropriate Brillouin zone
sum. For instance, the drift velocity in the
β
direction is
given by
V
β
=
1
N
∑
k
v
k
,β
f
k
,
(4)
where
N
=
∑
k
f
k
is the number of electrons in the Brillouin
zone. Similarly, the total intervalley scattering rate
k
of a
state
k
can be expressed as
k
=
∑
k
k
k
(1
−
δ
k
k
)
.
(5)
Here,
δ
k
k
=
1if
k
and
k
are in the same valley, and
δ
k
k
=
0 if they are in different valleys. We do not make any
distinction between valleys on the same axis as the minima
in c-BN are at the
X
point, meaning that such valleys are
connected across the Brillouin zone edges. There thus exist
three distinct valley types: (100), (010), and (001). We then
define the average intervalley scattering time
τ
int
as
τ
int
=
1
N
∑
k
k
f
k
.
(6)
The current noise, characterized by the power spectral den-
sity (PSD), can also be computed using the BTE. As derived
in Ref. [
38
], the current PSD
S
j
α
j
β
can be calculated at angular
frequency
ω
as
S
j
α
j
β
(
ω
)
=
2
(
2
e
V
0
)
2
[
∑
k
v
k
,α
∑
k
(
i
ω
I
+
)
−
1
kk
(
f
s
k
(
v
k
,β
−
V
β
)
)
]
,
(7)
where
j
α
and
j
β
are the current densities along axes
α
and
β
, and
I
is the identity matrix. In the limit
ωτ
1, where
τ
is a characteristic relaxation time,
S
j
α
j
β
is proportional to
the diffusion coefficient, a relation known as the fluctuation-
diffusion relation [
44
]. We can thus compute the diffusion
coefficient from Eq. (
7
), and for simplicity, we refer to the
quantity defined in Eq. (
7
) as the diffusion coefficient.
The numerical details are as follows. For all calculations,
the electron-phonon matrix elements and electronic structure
are computed on a coarse 12
×
12
×
12 grid using DFPT and
DFT in Q
UANTUM
E
SPRESSO
[
45
]. The PBE functional was
used for the DFT calculations. A wave-function energy cutoff
of 80 Ryd was used for all calculations. A relaxed lattice
parameter of 3.623 Å was used, which overestimates the ex-
perimental value by only 0.22% [
46
]. The electronic structure
and electron-phonon matrix elements were then interpolated
to a fine grid using P
ERTURBO
[
47
]. For all temperatures, a
fine grid of 160
×
160
×
160wasusedwitha5meVGaus-
sian smearing parameter. Increasing the grid size to 180
×
180
×
180 led to a maximum change of 3.3% in the mobility
and a maximum change of 8.0% in the diffusion coefficient.
An energy window of 383 meV was used. Increasing this
energy window to 437 meV led to a maximum change of
0.16% in the mobility and a maximum change of 4.0% in the
diffusion coefficient. The linear system of equations used to
compute the high-field transport properties was then solved by
a Python implementation of the GMRES method [
48
]. For all
calculations and temperatures, the Fermi level was adjusted to
yield a carrier density of 4
×
10
13
cm
−
3
. For all calculations
of the diffusion coefficient, a frequency of 1 GHz was used,
selected to ensure that
ωτ
1 (where
τ
is a characteristic re-
laxation time), while avoiding too-low frequencies that result
in numerical instabilities.
III. RESULTS
We begin by examining the dependence of the electron
drift velocity and mobility on the electric field at various
temperatures. We first compare our computed low-field mo-
bility with other reported values. At 300 K, we compute
a low-field mobility of 1860 cm
2
V
−
1
s
−
1
. When includ-
ing two-phonon scattering in the framework described in
Refs. [
39
,
40
], the value decreases to 1136 cm
2
V
−
1
s
−
1
.c-BN
has an experimentally reported Hall mobility value of
104602-2
VALLEYTRONICS AND NEGATIVE DIFFERENTIAL ...
PHYSICAL REVIEW MATERIALS
8
, 104602 (2024)
FIG. 1. Computed drift velocity versus electric field at (a) 300 K,
(b) 200 K, (c) 130 K, and (d) 77 K, with field applied along the [100]
direction (orange line) and [111] direction (blue line).
825 cm
2
V
−
1
s
−
1
[
16
] (although much lower values have
been reported [
29
–
31
]). The variations in the experimental
values likely originate from the varying quality of the sam-
ples. A significant density of threading dislocation lines may
lead to a large reduction in the low-field mobility, for in-
stance [
36
]. Previously computed ab initio values range from
1230 cm
2
V
−
1
s
−
1
[
34
] to 1610 cm
2
V
−
1
s
−
1
[
32
]. Considering
that ab initio values of mobility vary by around 10–20%
depending on choices of exchange-correlation functionals, as
well as other choices, our computed one-phonon mobility
value is thus in reasonable agreement with prior computed
results at the same level of theory.
For the rest of this work, we consider only one-phonon
scattering. We find that adding two-phonon scattering de-
creases the mobility at all temperatures by roughly 40%,
and the qualitative features of the mobility and diffusion
coefficient versus electric field are generally retained. These
findings are similar to those in Refs. [
39
,
40
]. Therefore, to
reduce computational cost, we consider only one-phonon scat-
tering, as is typically assumed.
Next, we examine the drift velocity versus the electric field
at 300 K in Fig.
1(a)
. At sufficiently high electric fields, we
observe an anisotropy in the drift velocity despite the cubic
symmetry of the crystal, with the drift velocity in the [100]
direction being less than that in the [111] by around 4% at
3kVcm
−
1
. This anisotropy is present with greater magnitude
at 200 K, as seen in Fig.
1(b)
. We also note that, as the
temperature decreases, the onset of a discernible difference
in drift velocity between the two directions occurs at a lower
field. The anisotropy arises due to differences in the average
energy of the electron distribution function between the
longitudinal and transverse valleys [
49
,
50
], as discussed in
more detail below.
At 130 K, a qualitative change in the [100] drift velocity
characteristics is seen in Fig.
1(c)
as an abrupt decrease in
drift velocity above
≈
500 V cm
−
1
. The effect is even more
pronounced at 77 K, with the drift velocity dropping 25%
within only 20 V cm
−
1
. The decrease in drift velocity with
increasing field is known as negative differential resistance
(NDR). The effect is well-known in semiconductors such as
GaAs, forming the basis for Gunn diodes which provide mi-
crowave power from a DC bias [
51
,
52
]. For these materials,
NDR is caused by intervalley scattering of electrons, from the
primary, high-mobility valley at
to a satellite valley with
higher effective mass, such as the
L
valley in GaAs. However,
this explanation is not applicable in c-BN, as we calculate
that the next-lowest-energy satellite valley in the same band
is 2.44 eV higher than the conduction band minimum. This
energy is sufficiently large enough that this satellite valley
plays a negligible role in the transport in the electric field
range used in this work, which indicates that the usual NDR
mechanism does not apply to c-BN.
In diamond, NDR has been experimentally observed when
the electric field is oriented along the [100] direction, despite
lacking the two-valley band structure required for the conven-
tional NDR mechanism [
8
]. In this case, NDR was attributed
to the onset of intervalley scattering associated with zone-
edge longitudinal acoustic phonon emission, which causes
an abrupt repopulation from valleys transverse to the electric
field to those parallel to it [
8
]. This repopulation occurs only
at a high enough electric field value where the threshold for
longitudinal acoustic intervalley phonon emission is reached.
As c-BN has a similar band structure to diamond with six
equivalent conduction band minima, we hypothesize that a
similar explanation is applicable. To test the hypothesis, we
compute the energy dependence of the electron-phonon scat-
tering rates. The result at 77 K is shown in Fig.
2(a)
. Indeed,
we observe that below the optical phonon energy of 150 meV,
the scattering rates have a relatively weak dependence on
energy, while the scattering rates abruptly increase above the
optical phonon energy (
∼
150 meV).
The strong energy dependence of the scattering rates has
consequences for the relative occupation in the various valleys
and, ultimately, the transport properties. Below the threshold
field, few electrons have sufficient energy to scatter to an
inequivalent valley, and the [100], [010], and [001] valleys
react to the electric field largely independently. In addition,
owing to the lower effective mass of the transverse valleys
relative to longitudinal ones (0
.
36
m
0
versus 0
.
95
m
0
for trans-
verse and longitudinal, respectively), transverse valleys have
a higher effective carrier temperature than the longitudinal
valleys at a given field, as shown in Fig.
2(b)
. The effective
valley temperatures are defined by computing the average
energies of the steady distributions at the given field and
identifying the temperature of a Boltzmann distribution with
the same average energy. The valley temperature is a measure
of the average energy of the distribution, rather than a ther-
modynamic temperature. As the field increases, the transverse
valleys achieve a higher steady-state temperature owing to
their lower effective mass. The higher electron temperature of
the transverse valleys also leads to the drift velocity anisotropy
between [100] and [111] directions shown in Fig.
1
.
104602-3
HATANPÄÄ AND MINNICH
PHYSICAL REVIEW MATERIALS
8
, 104602 (2024)
FIG. 2. (a) Electron scattering rate versus energy. (b) Valley
temperature versus electric field for [100] type valleys (blue), and
[010]
+
[001] type valleys (orange). (c) Population fraction versus
electric field for c-BN for [100] type valleys (blue) and the sum of
the [010] and [001] type valleys (orange). (d) Average intervalley
relaxation time versus electric field. All calculations are at 77 K with
the electric field applied in the [100] direction. The intervalley time is
on the order of microseconds at low fields, rivaling that of diamond.
At the threshold field, electrons in the transverse valleys
gain enough energy to emit optical phonons and undergo an
intervalley transition to the longitudinal valleys. This repop-
ulation effect is shown in Fig.
2(c)
at 77 K, which plots the
population of the [100]-type valleys in comparison to the sum
of the [010]- and [001]-type valleys versus the electric field,
with the field applied in the [100] direction. At zero field, all
valleys have the same population. As the field increases from
zero, there is little population redistribution due to the absence
of a significant intervalley scattering by phonon emission and
the weak absorption-mediated scattering at 77 K. Even at
500 V cm
−
1
, the [100]-type valleys have less than 40% of
the population. However, once the threshold field is reached
(
≈
560 V cm
−
1
), a redistribution to the [100] longitudinal val-
leys occurs. Because the longitudinal mass is higher than the
transverse mass, the drift velocity abruptly decreases. This
repopulation effect occurs at all temperatures when the field
is applied in any cubic axis, but NDR only manifests in the
transport properties when phonon-absorption intervalley scat-
tering is negligible compared to emission-mediated scattering,
in this case at temperatures below around 140 K.
The high optical phonon energy in c-BN has consequences
for intervalley scattering, which must be mediated by zone-
edge modes due to momentum conservation. For sufficiently
low fields, most electrons do not have sufficient energy
to scatter via an intervalley phonon emission process. Fur-
ther, the high optical phonon energy of c-BN leads to low
thermal occupation even at 300 K, relative to conventional
semiconductors like GaAs. As a result, both absorption and
emission-mediated intervalley scattering are weak in c-BN,
FIG. 3. Computed electron diffusion coefficient versus electric
field at (a) 300 K and (b) 77 K, with field applied along the [100]
direction (orange line) and [111] direction (blue line). A pronounced
peak in the [100] diffusion coefficient is observed at 77 K, which is
attributed to intervalley diffusion.
and so the corresponding average intervalley relaxation time
is expected to be long in comparison to other semiconductors
with lower phonon energies.
In Fig.
2(d)
, we show the intervalley time versus elec-
tric field along the [100] direction at 77 K. At low field
(
≈
1Vcm
−
1
), the intervalley relaxation time is calculated to
be 5
.
3 μs. For comparison, we also computed the intervalley
relaxation time in diamond, obtaining a value of 2
.
4μs. c-BN
thus has an intervalley relaxation time at low fields nearly
100% larger than that of diamond. We note that the value
decreases with increasing electric field as electrons can emit
zone-edge phonons and scatter to other valleys. However, the
relatively long intervalley time suggests that c-BN may be
promising in valleytronic applications.
Experimental tests of these predictions are challenging
owing to the difficulties in preparing high-quality thin films
of c-BN. We suggest an approach to mitigate this challenge
based on measurement of the current noise power spectral
density (PSD), or equivalently in the low-frequency limit, the
diffusion coefficient. Due to the long intervalley scattering
time in c-BN, we expect a clear intervalley noise contribution
arising from electrons scattering between valleys with distinct
effective masses when the electric field is applied in the [100]
direction. Intervalley noise manifests in experiments as an
anisotropy in the diffusion coefficient, with the value being
larger along the direction with inequivalent valleys relative
to the case in which all valleys are equivalent [
53
,
54
] ([100]
valleys versus [111] valleys, respectively, for c-BN).
More precisely, the general expression for the intervalley
diffusion coefficient is given by
D
int
=
n
1
n
2
(
v
1
−
v
2
)
2
τ
int
.
(8)
Here,
n
1
and
n
2
are the fractions of electrons in valleys of
types 1 and 2,
v
1
and
v
2
are the drift velocities in valleys
of types 1 and 2, and
τ
i
is the intervalley relaxation time
[
55
]. In the present case, the valley types refer to longitudinal
and transverse valleys defined by the field direction. Thus,
intervalley noise will manifest as an increase in the [100]
diffusion coefficient over the [111] diffusion coefficient, with
the precise amount depending on the quantities in Eq. (
8
)at
each field.
In Fig.
3
, we show the electric field dependence of the
diffusion coefficient for 300 K and 77 K. At 300 K in Fig.
3(a)
,
104602-4
VALLEYTRONICS AND NEGATIVE DIFFERENTIAL ...
PHYSICAL REVIEW MATERIALS
8
, 104602 (2024)
we observe that the diffusion coefficient monotonically de-
creases with an increasing field along the [111]. This behavior
is similar to what is seen in n-Si [
56
], and it occurs when the
scattering rates increase sufficiently strongly with increasing
energy [
38
,
55
,
57
]. For the [100] direction, however, we see a
higher diffusion coefficient value and a non-monotonic trend
with the electric field. At 300 K in Fig.
3(a)
, we observe
that the diffusion coefficient peak when the electric field is
applied in the [100] direction leads to a non-monotonic trend,
with a peak around 2% higher than the equilibrium value.
We attribute this peak to the contribution of intervalley noise,
although the magnitude of the peak may be difficult to detect
experimentally.
Figure
3(b)
shows the corresponding results at 77 K. Along
the [111], a non-monotonic trend is observed despite the
expected absence of intervalley noise. This feature can be
explained using an approximate generalization of the Einstein
relation applied to high fields,
D
=
(2
/
3)
μ
(
E
)(
/
e
), where
μ
(
E
) is the electric field-dependent mobility and
the av-
erage electron energy [
58
]. Due to the weak dependence of
scattering rates on energy below the optical phonon energy
as seen in Fig.
2(a)
, the average electron energy exhibits a
stronger dependence on the electric field than the mobility. As
a result, the diffusion coefficient initially increases with the
increasing field.
In the [100] direction, the peak is markedly larger com-
pared to the [111] case, with the peak value of the [100]
diffusion coefficient at
≈
700 V cm
−
1
being nearly 300%
larger than the equilibrium value. The effect is much larger
at 77 K than at 300 K. Such large peaks in the diffusion
coefficient have been observed experimentally for other ma-
terials such as GaAs [
59
–
61
] but have not been seen in
first-principles calculations [
39
] until now. Monte Carlo calcu-
lations of the diffusion coefficient in diamond at 300 K have
found a slight increase of the diffusion coefficient with the
electric field [
62
], similar to what is observed here in c-BN
at 300 K. The magnitude of the peak at low temperatures is
sufficiently large enough to be discerned easily in an exper-
iment, and its detection would support the prediction of the
long intervalley time in c-BN.
IV. DISCUSSION
Our first-principles calculations have predicted that c-BN
exhibits a region of NDR and a long intervalley lifetime rival-
ing that of diamond. These properties may be useful in device
applications. In materials with a pronounced NDR region,
instabilities in electric current will lead to the formation of
charged domains [
52
], which can be utilized in Gunn oscilla-
tors for various microwave applications. As a Gunn oscillator
has been constructed with diamond thin films [
9
], it is possible
that such devices could be realized in c-BN. We note that in
both cases, the devices would need to operate below room
temperature.
Experimental characterization of the NDR region can also
provide insight into the role of 2ph scattering in c-BN. While
in this work we have employed the 1ph level of theory,
2ph scattering was found to reduce the predicted mobil-
ity by
≈
40%, in line with the reduction reported for other
semiconductors [
40
,
63
,
64
]. The 2ph scattering also shifts the
electron distribution to lower energies at a given field, which
in turn would cause the threshold field for NDR to occur at
≈
1120 V cm
−
1
, rather than the 560 V cm
−
1
obtained with the
1ph level of theory. If sufficiently pure samples were available,
the difference in threshold field should be discernible.
For valleytronics, electrons within a valley must remain
there long enough to perform the desired function [
65
]. For c-
BN, at equilibrium, our calculated intervalley time of 5
.
3
μ
sat
77 K is significantly greater than the 300 ns value for diamond,
calculated from Monte Carlo simulation [
10
] and the value of
2
.
4 μs we computed. We note that the Monte Carlo study was
based on a semi-empirical treatment of the electron-phonon
interaction using a deformation potential, while our ab initio
approach treats the electron-phonon interaction throughout
the Brillouin zone within the framework of DFT and DFPT.
We therefore expect the ab initio approach to give a more
accurate intervalley lifetime. The intervalley time of c-BN
also greatly exceeds the intervalley time of typical semicon-
ductors; for instance, we compute the intervalley time of n-Si
to be only 149 ps at the same temperature. However, due to the
strong decrease of the intervalley time with increasing field
seen in Fig.
2(d)
, some optimization may be required to use
c-BN in valleytronic applications. The intervalley relaxation
time may be increased further by leveraging the compressive
strain present in most c-BN thin films. Strain would break
the degeneracy of the six equivalent valleys, further inhibiting
intervalley scattering and leading to an increase in intervalley
relaxation time.
V. SUMMARY
We have computed high-field transport properties and the
diffusion coefficient of c-BN from first principles from 77 –
300 K. We find that below 140 K, c-BN exhibits a region
of negative differential resistance arising from the strong en-
ergy dependence of the scattering rates around the optical
phonon energy. The calculated intervalley time is comparable
to that of diamond, suggesting that c-BN could be a promis-
ing material for valleytronic applications. We also show that
our predictions can be tested by identifying a non-monotonic
trend of the diffusion coefficient versus the electric field. Our
work highlights the potential electron device applications of
c-BN beyond conventional power electronics, stimulating a
further experimental investigation into the synthesis and elec-
trical transport properties of c-BN thin films.
ACKNOWLEDGMENTS
B.H. was supported by a NASA Space Technology Grad-
uate Research Opportunity. A.J.M. was supported by AFOSR
under Grant No. FA9550-22-1-0286.
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