Electrostatic Gating of Phosphorene Polymorphs
Fereshteh Mahmoodpouri Malayee, Robabeh Bagheri, Fariba Nazari,* and Francesc Illas*
Cite This: J. Phys. Chem. C 2024, 128, 2997−3010 Read Online
ACCESS Metrics & More Article Recommendations *sı Supporting Information
ABSTRACT: The ability to directly monitor the states of electrons
in modern field-effect transistors (FETs) could transform our
understanding of the physics and improve the function of related
devices. In particular, phosphorene allotropes present a fertile
landscape for the development of high-performance FETs. Using
density functional theory-based methods, we have systematically
investigated the influence of electrostatic gating on the structures,
stabilities, and fundamental electronic properties of pristine and
carbon-doped monolayer (bilayer) phosphorene allotropes. The
remarkable flexibility of phosphorene allotropes, arising from intra-
and interlayer van der Waals interactions, causes a good resilience
up to equivalent gate potential of two electrons per unit cell. The resilience depends on the stacking details in such a way that rotated
bilayers show considerably higher thermodynamical stability than the unrotated ones, even at a high gate potential. In addition, a
semiconductor to metal phase transition is observed in some of the rotated and carbon-doped structures with increased electronic
transport relative to graphene in the context of real space Green’s function formalism.
1. INTRODUCTION
The phenomenon of polytypism, a variant of polymorphism, is
ubiquitous in layered materials.1,2 Polytypes exhibit the same
close-packed planes but with a different stacking sequence in
the third dimension, the one perpendicular to these planes.
Hence, a diverse crystal structure can be obtained by just
changing the layer stacking sequence, while the periodic
structure of each layer is preserved. In fact, only the periodicity
along the growth axis varies from one polytype to another.
Polytypes of a material have analogous structural features as
well as nearly the same internal energies, the simultaneous
occurrence of several similar structures under identical growth
conditions being at the heart of this phenomenon.1,2 Layered
materials also exhibit other interesting properties and, in
particular, have the potential for the development of high-
performance field-effect transistors (FETs).3
Among layered materials, phosphorene is a promising
candidate due to rich geometric structures that is leading to
various polymorphs and polytypes4−27 while having none of
the obstacles exhibited by other two-dimensional materi-
als.28−31 Several structurally different two-dimensional poly-
morphs of phosphorus namely, α-P, β-P, γ-P, δ-P, ε-P, τ-P, η-P,
θ-P, σ-P, ϕ-P, tricycle-type red phosphorene (R-P), square-
octagon phosphorene (O−P) and hexagonal-star phosphorene
(H−P) have been investigated using first principle meth-
ods.32−34 Most of these two-dimensional polymorphic
materials are semiconductors with a band gap in the range of
0.4 to 2.1 eV.7,35−37 We recall that α-P and β-P have been
prepared experimentally, while other allotropes have not yet
been synthesized.38 According to the polytypism definition, the
individual phosphorene allotropes can be coupled through
noncovalent interactions leading to bi/tri/few layer phases up
to the bulk material.39 The resulting stacks can be
characterized into three types: in-plane shifted, in-plane
twisted, and hybrids of the former two polymorphs. In
addition, a new family of 2D materials consisting of
phosphorus and carbon (phosphorene carbide, (PC)) has
been rather recently predicted theoretically.40−43 Interestingly,
the experimental realization of 2D PC allotropes was achieved
by combining the theoretical predictions and previous
experimental observations.44 These studies demonstrated that
various structures in phosphorus carbide can be produced by
considering different atomic ratios of P/C.43−46 Furthermore,
structure, stability and electronic properties of PC monolayers,
namely α-, β-, and γ-PC, have been predicted.45 Rather
recently, Kou et al.47 suggested that polytypism and poly-
morphism in phosphorene play a crucial rule and provide a
fertile landscape to design novel architectures and instructing
new functionalities.
On the other way, field-effect transistors revolutionized the
field of electronics, enabling the development of smaller, faster,
and more efficient devices. FETs work by controlling the flow
of current through a semiconductor channel using an electric
Received: August 31, 2023
Revised: November 14, 2023
Accepted: November 14, 2023
Published: February 9, 2024
Articlepubs.acs.org/JPCC
© 2024 The Authors. Published by
American Chemical Society
2997
https://doi.org/10.1021/acs.jpcc.3c05876
J. Phys. Chem. C 2024, 128, 2997−3010
This article is licensed under CC-BY 4.0
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field, making the device more efficient and less prone to noise,
which is important in high-speed and low-power applications.
FETs consists of a gate (metal), a channel, a source, and a
drain, all of which are made of a given semiconductor material
(Figure 1a). The gate is separated from the semiconductor
channel by a thin layer of an insulating material. When a
voltage is applied to the gate, an electric field is created in the
channel, which controls the flow of electrons between the
source and the drain. The channel of an FET is a key
component that determines the device electrical characteristics
and performance. Recent research on FET channel materials
has focused on improving device performance by optimizing
the channel properties and exploring new materials and
structures.48−51
The channel consists of a region of a semiconductor material
connecting the source and drain terminals of the transistor. It
is the pathway through which the current flows when the
transistor is turned on. The conductivity of the channel can be
controlled by varying the voltage on the gate terminal. The
length and width of the channel also affect the transistor
performance. A shorter channel allows for faster switching
speeds but can lead to an increased leakage current and
reduced reliability. A wider channel can handle higher currents
but may also have a higher capacitance, which can limit the
device performance under high frequency. Summing up, FETs
have their own unique properties and applications, but the
channel constitutes a fundamental component to controlling
the current flow.52−54 The choice of semiconductor material
depends on the specific application requirements, such as the
operating frequency, power handling capability, and thermal
performance. Recent studies have reported high-performance
2D- based FETs with record-high transconductance and low
power consumption, and with high on/off ratio and sensitivity
to light and gas molecules.55−58
There is evidence that field-effect transistors with p-channel
such as phosphorene show higher performance and efficiency
than other nanomaterials.59 This is confirmed by Das et al.60
who showed that in phosphorene the on-to-off current ratio
(ION/IOF) of holes (105) is much larger than that of electrons
(103), which is very desirable in FETs. With this perspective,
we have examined the capability of phosphorene polymorphs
as channel candidates in the field-effect transistor and analyzed
their geometry and electronic properties under the influence of
the gate potential. Hereby, we report a first-principles study
that clarifies the microscopic origin of the band gap variation in
the electrostatic gated polytypes and polymorphs of phosphor-
ene. In addition, we report transport properties of these
structures in the context of real space Green’s function
formalism that have prominent importance for FET’s
technology.
2. COMPUTATIONAL DETAILS AND MATERIALS
MODELS
Calculations reported in the present work have been carried
out in the framework of density functional theory (DFT) using
periodic models, as described below and in the next section.
Due to our objective of comparing the trends in structural
parameters and electronic properties, we utilized the cost-
effective Perdew−Burke−Ernzerhof (PBE)61 forms of the
generalized gradient approximation (GGA) exchange−corre-
lation functional.62 However, to investigate whether changing
the functional affects the trend of variations, we also employed
the SCAN63,64 functional. Notably, the band gap obtained
from the SCAN functional showed significant similarities to
the band gap results corrected by meta-GGA, confirming our
choice.
The electron density is expanded in plane-wave basis sets
with a cutoff energy of 52 Ry and the interaction between the
valence electrons and ion cores is described through the P.pbe-
n-rrkjus_psl.1.0.0.UPF, C.pbe-n-rrkjus_psl.1.0.0.UPF ultrasoft
pseudopotentials.65 The effect of van der Waals interactions is
taken into account by the DFT-D3 approach due to Grimme
et al.66 To avoid the interaction between the monolayer
(bilayer) structure and its periodically repeated images in the
slab model, a vacuum layer of 30 Å thickness is added. For all
periodic systems, the Brillouin zone is sampled with 4 × 4 × 1
and 15 × 15 × 1 k-point meshes for the structural and
electronic properties, respectively. It should be noticed that
after optimizing the required number of k points along various
directions while considering optimal conditions, we generated
a uniform density of k points. The lattice constants and the
positions of the atoms are optimized until the Hellmann−
Feynman forces are less than 0.001 eV/Å. All calculations were
carried out using the Quantum-Espresso package version qe-
6.567 and the XCrySDen68 and Vesta packages69 were used to
visualize the atomic structures.
Using the experimental lattice parameter that is reported for
black phosphorus (BP)70,71 we have designed the starting
geometry of the unit cell of the different phosphorene
polymorphs. We have classified the studied polymorphs into
five categories: monolayer structures, polytypes, hybrid-
Figure 1. (a) Schematic representation of the Field Effect Transistor
model used in the present work. (b) Sketch of a gated system model
in a periodically repeated unit cell (left), potential energy barrier
(blue), monopole potential (red), and dipole potential (green) in the
Z direction.
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polytypes, rotated polytypes, and PC. Information of the
individual phosphorene allotropes are summarized in Table S1
and Figure S1a in the Supporting Information. We must point
out that to ensure a meaningful comparison; a single cell with
the same number of atoms (4 atoms) has been selected for all
three starting structures (α, β, and γ), and among possible
stable stackings, three high symmetry polytypes of AA, AB, and
AC of α, β, and γ allotropes have been considered (Figure S2).
In addition, hybrid-polytypes were designed by considering
different stacking of two polymorphs. Herein, three hybrid-
polytypes of α/β, γ/β, and α/γ have been investigated (Figure
S3). Rotated polytypes are considered including α↶α, β↶β,
and γ↶γ with rotation angles of 90, 21.79, and 90° for the
upper layer, respectively (Figure S4). The rotated unit cell is
chosen based on minimum mismatch of the top (rotated) and
bottom (unrotated) layers. In addition, less than 100 atoms in
the unit cell were taken into consideration.
Furthermore, we have generated single and bilayer carbon-
doped phosphorene structures considering a constraint,
namely, that in phosphorene with a 50 percent concentration
of carbon, carbon atoms are not placed next to each other.
Note also that, in bilayer structures, it is possible to place the
atoms in two positions, which are represented by m1 and m2
(see Figure S5). For the later doped models, AA, AB, and AC
stacking with m1 and m2 arrangements has also been
investigated.
To evaluate the bond strength of atoms and obtain a
measure of the thermodynamical stability of structures, the
cohesive energy of bare and carbon-doped structures is
calculated using eqs 1 and 2, respectively.
E
E
n
ECoh b
total
P= (1)
E
E
n
E E
1
2
( )Coh c doped
total
P C= + (2)
where Etotal and n are the total energy of the system and
number of atoms in the system, and EP and Ec the energy of
isolated phosphorus and carbon atoms, respectively. The
coefficient of 1/2 in eq 2 is due to the 1:1 carbon/phosphorus
atom ratio in the structures.
2.1. Modeling the Field-Effect Transistor (FET)
Configuration. DFT-based computations can be used for
modeling field-effect transistors due to their ability to predict
the properties of materials and interfaces at the atomic scale
with rather good accuracy. Back in 2014, Brumme et al.72
designed a DFT-based approach to study doping effects in
field-effect devices. Their method allows for calculation of the
electronic structure as well as complete structural relaxation in
a field-effect configuration. Here, we apply their approach to
phosphorene-polytype-based field effect and analyze in detail
the structural changes induced by the electric field. Following
Brumme’s model,72 the phosphorene polytypes are placed in
front of a charged plane or monopole�the location of the
monopole in the unit cell is specified as “zgate” in the quantum
espresso input�which models the gate (Figure 1b). The
phosphorene polytypes layers are charged with an equal and
opposite amount of ndop × A charge where ndop represents the
number of doped electrons per unit area, and A stands for the
area of the unit cell parallel to the surface. Consequently, a
finite electric field is generated in the region between the gate
and the system. To correctly determine the changes in the
electronic structure and geometry for a given field-effect setup,
the electric field within the vacuum region between periodi-
cally repeated images must be zero (the total potential should
be constant). However, due to the dipole generated between
the charged system and the gate, an artificial electric field is
generated between the periodically repeated slabs. To
overcome this effect, we introduce an electric dipole consisting
of two planes of opposite charge located at the vacuum region
adjacent to the monopole�in the quantum espresso input, the
position of the dipole and the unit cell thickness are defined as
“emaxpos” and “eopreg”, respectively. Following previous
work,70 the optimal bipolar size is one-hundredth of the unit
cell length, in line with the definition of dipole in the z-
direction.
The application of an electric field between the gate and the
system alters the atomic structure of the channel in the gate
model, and it is necessary to perform a structural relaxation at
the different fields of interest. Due to the opposing charges of
the gate and the system during the structural relaxation, the
atoms are displaced from their original positions and attracted
to the gate. To prevent the movement of atoms toward the
gate, a barrier potential is added between the system and the
gate, which is equivalent to the dielectric structure placed
between the channel and gate in the real FETs. Technically,
the width and height of the potential barrier are defined in the
quantum espresso input as “block_1”, “block_2”, and “block_-
height”, respectively. “block_1” and “block_2” represent the
starting and ending points of the potential barrier, respectively,
and the difference between these two determines the width of
the barrier potential. The optimal size of the width barrier
potential has been estimated as one-tenth of the unit cell
length in the z-direction.70,71
Finally, the WanT code73 has been used to calculate electron
transport and current−voltage curves. To investigate the
transport properties of the candidate structures, we use the
real space Green function method with the localized-orbital
basis Hamiltonian constructed by using maximally localized
Wannier functions (MLWFs). To this end, for each P and C
atoms in the unit cell, we have positioned four sp3 and three
sp2 hybrid orbitals, respectively, according to the definition of
Wannier90.74 After wannierization, the spatial spread of each
type of orbital is reduced to less than 10−7 Bohr 2. To show the
accuracy of obtained MLWFs, the variation of the Hamiltonian
with distance in the basis of Wannier function is shown in
Figure S6 for the three desired structures in the absence of gate
potential. Obviously, the band structure obtained from the
Wannier functions completely matches the one build from
Bloch functions. These confirm basis transformation has been
carried out properly.
3. RESULTS AND DISCUSSION
As already mentioned, polytypism applies to close-packed or
layered materials, where polytypes are characterized by
constituent layers with identical structures but different
periodicities perpendicular to the layer plane (i.e., different
stacking). Since layered materials have weak van der Waals
(vdW) like interlayer interactions, polytypism is commonly
observed and constitutes a highly relevant form of poly-
morphism for multilayer 2D materials.75 On the other hand,
we recall that the main objective of the present work is to
explore the FETs model of the phosphorene polymorphs
which makes use of the flexibility and anisotropy of the
phosphorene family in line with the need to use flat structures
in the design of electronic devices.76 To this end, we make use
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of candidate structures in the gate model of the simple yet
realistic FET model which is described in the previous section.
The beta phosphorene and phosphorene carbide structures
are more stable than the other structures; their stability is in
the range of −3.713, −5.483 eV per atom and −4.720, −5.176
eV per atom, respectively.
Interestingly, according to the literature, phosphorene
carbide structures have the lightest electrons and holes
effective mass11,45 leading to a high mobility of charge carriers
in these structures.77 The stability and high mobility of charge
carriers of phosphorene carbide suggest that this material may
have good performance as a channel in the gated model, which
can reveal details about the structural and electronic properties
not easily accessible by experiments on FET. One of the key
factors in the present FET model is the stability of the channel
material in the different ranges of electric field because it is
related to its FET performance as it is discussed in the
following sections.
3.1. Geometric and Electronic Properties of Bare
Phosphorene Polymorphs. As mentioned in the computa-
tional section, the studied structures include the α, β, and γ
polymorphs (monolayer), homogeneous bilayers with different
stacking, heterogeneous bilayers (α/β, α/γ, β/γ), and rotated
bilayers (α↶α, β↶β, and γ↶γ). The unit cells of all
monolayers and bilayers with three different stacking are
shown schematically in Figures S1a, S2, S3, and S4.
Numerous theoretical and experimental data regarding
structural and electronic properties for monolayer phosphor-
ene, its allotropes and some of its bilayer structures have been
reported.78−80 The present results of our systematic study on
the three stable allotropes, namely, α, β, and γ, are summarized
in Figure S1a and Table S1. A comparison with previous work
shows good agreement between both sets of results81−83 and
supports the use of these computational parameters in the
calculations reported in the following subsections.
Phosphorene sheets have two types of P−P bonds in the
relaxed structures. We marked the bonds parallel to the
puckered layer as dpd1‑pd2 (bottom surface) and d′pd1‑pd2 (upper
surface) as shown in Figure 2, while the bonds tilted to the
two-dimensional in-plane directions are marked as dpd2‑pd3
(bottom surface) and d′pd1‑pd3 (upper surface), respectively,
with the bond lengths for all structures reported in Table S2. In
the monolayer structures, the largest dpd1‑pd2 (2.31 Å) and dpd1‑pd3
(2.26 Å) bond lengths belong to γ and β allotrope, respectively.
In all homogeneous bilayer structures, the dpd1‑pd2 and dpd2‑pd3bond
lengths in the top layer and d′pd1‑pd2 and d′pd2‑pd3 bonds lengths
from the top and bottom layers coincide. The maximum and
minimum of buckling height (2.11 and 1.24 Å; see Table S1)
correspond to the α and β allotropes, respectively, while the γ
allotrope exhibits an intermediate value of 1.49 Å. Among α, β
and γ allotropes, β is the most stable one. According to the
results reported for phosphorene,57 all bilayers are more stable
than their constituent monolayers. This is also the case for
heterogeneous structures.
For all stacking possibilities of homogeneous bilayers of α
and β allotropes, the bonds parallel to the puckered layer
remain the same as in the monolayer structure. But in the AA
stacking of the homogeneous γ bilayer, there are noticeable
changes with respect to the γ monolayer allotrope; −0.06,
−0.01 Å in dpd1‑pd2 for the AA stacking and 0.03 Å in dpd2‑pd3 in the
AC one. A noteworthy point in the obtained data for
homogeneous rotated bilayer structures, where the top layer
is rotated at a certain angle with respect to the bottom layer
(α↶α (90°); β↶β (21.79°); γ↶γ (90°)) is that dpd1‑pd2 and
d′pd1‑pd2 as well as dpd2‑pd3 and d′pd2‑pd3 increased. The details of the
changes for three rotated structures are respectively as follows:
α↶α: 0.45% (0.45%) and 0.00% (−0.44%), d (4.26%). β↶β:
0.44% (0.44%) and 0.44% (0.88%), d (0.00%). γ↶γ: 3.46%
(2.16%) and 1.77% (0.88%), d (26.17%). These are compared
to those of the monolayer structures (Table S2, Figure S7).
In the α/β heterogeneous bilayer structure, the mutual
interaction of the two layers affects the bond length in the beta
layer while the structure of the α layer remains unchanged. The
mutual interaction effect in the α/γ heterogeneous bilayer
structure causes changes in the bond length of the two
constituent layers. Besides, in α/β and β/γ heterogeneous
bilayers, the structure of the β allotrope becomes altered.
Indeed, among the investigated allotropes, β is not only the
most stable one but also induces the largest effect in
heterogeneous bilayer structures. In all homogeneous bilayer
stacking that involves the β allotrope, the buckling height of
the individual layers remains almost the same as in the β
allotrope. This is not the case for stacking involving α- and γ-
allotropes, where a change in the buckling height is observed.
In any case, in the homogeneous bilayer structures, the change
is small and does not show a specific trend. It is noteworthy
that the buckling height in the rotated bilayers is slightly
changed compared with the constituent monolayers. In the
heterogeneous bilayer structures, mutual interactions of
constituent monolayers cause a change in the buckling height
of both, top and bottom, layers. Distortion of buckling height
of the α layer in the α/β and α/γ is 4.7% and 9.9%,
respectively. Likewise, in the other layers of heterogeneous
bilayers, the buckling height of constituent β and γ layers
changes by 0.8% and 2.0%, respectively. Furthermore, for the
β/γ heterogeneous bilayer, the buckling height of the γ layer
remains unaltered, while the buckling height of the β layer
Figure 2. Schematic side view of the α phosphorene bilayer with the
parameters defining the buckling layer in the z-direction, the distances
between two top and bottom layers (D), and the different distances
between atoms. Light and dark spheres represent the top and bottom
atoms in each layer, respectively.
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experiences a mere 1.6% change compared to that of the
monolayer structure.
The present results indicate that αAB, βAA, and γAA stacking
exhibit the largest cohesive energy of −3.737, −3.746, and
−3.897 eV per atom, respectively, (Table S2), in agreement
with values in the literature.50,84 The largest cohesive energy
for the γAA homogeneous bilayer is consistent with the fact that
the γ monolayer is the less stable one. It is noteworthy that all
rotated bilayer structures α↶α, β↶β, and γ↶γ show
remarkable stability along with more (∼46%) (Table S2)
cohesive energy as compared to the most stable unrotated
counterparts. Another intriguing observation is the enhanced
stability of α↶α compared to the other two rotated bilayers
(β↶β and γ↶γ), even though its constituent allotropes are not
individually the most stable ones. As previously mentioned, the
heterogeneous α/β, α/γ, and β/γ bilayers exhibit higher
stability than both the constituent monolayers and the
homogeneous bilayers. The observed order of stability for
heterogeneous bilayers is as follows: α/β> α/γ > β/γ. Although
the cohesive energy for α and β monolayer is larger than that
of the γ monolayer allotrope, the cohesive energy of α/β is
larger than that of α/γ and β/γ with the values of 1.95% and
2.3%, respectively. As a result, the allotropes containing γ
allotrope are less stable. Another valuable point is that, in
general, heterogeneous bilayers are about 4% (Table S2) more
stable than the homogeneous bilayers (Figure S7).
At the utilized computational level, α, β, and γ monolayers
exhibit band gap values of 0.91, 1.9, and 0.43 eV, respectively.
Analysis and comparison of band structures for homogeneous,
heterogeneous, and rotated bilayers of phosphorene allotropes
show that by adding a layer, the band gap decreases.
Essentially, it has been reported that the interlayer stacking
pattern plays a crucial role in determining the gap values.47
The present results (Figure S7) show that the largest band gap
change occurs in all stacking structures involving the less stable
allotrope (γ), which has zero gap. The band gap of structures
involving the α allotrope is altered by at least 50% and at most
∼78%. The minimum variation of band gaps corresponds to
the different stacking of the β allotrope, which is placed in the
range of 12.6%. to 22%. The band gap is also reduced in the
studied heterogeneous bilayers. As a conclusion of this part, in
addition to the effect of increasing the number of layers on the
band gap, a clear dependency appears of the band gap variation
on the intrinsic properties of the constituent layers of the
heterogeneous bilayer structures. For example, in the α/β and
γ/β heterogeneous bilayers, sharing the β layer, the second
layer is composed of other allotropes (α and γ), the band gap
decreases from 1.66 eV (homogeneous bilayer (βAA)) to 0.52
eV (α/β) and 0.74 eV (γ/β). This means that creating multiple
layers of different allotropes can be a means of controlling the
band gap (Table S2 and Figure S7).
3.2. Structural and Electronic Properties of Bare
Phosphorene Carbide. In recent decades, numerous stable
two-dimensional allotropes of monolayer PC were theoretically
predicted.45,85 Afterward, few-layer two-dimensional PC was
synthesized successfully via a novel carbon doping technique.86
In this section, we present findings concerning the stability and
electronic structure of PC models for the α, β, and γ
phosphorene polymorphs as well as the homogeneous bilayers
(Figures S8−S11). Related structural details and binding
energies are summarized in Table S3.
The structural optimization of α, β, and γ phosphorene
layers doped with C in a one-to-one ratio results in a single
shared structure hereafter referred to as CPCS (common
phosphorene carbide structure) and displayed in Figure S8.
This structure has a configuration similar to that of the bare β
allotrope. Moreover, similar to those of other phosphorus
carbide monolayers,44,45 CPCS has zero band gap. It is 29.38%,
28.96% and 33.27% more stable than the undoped α, β, and γ
structures, respectively (Tables S2 and S3). The bonds lengths
and angles obtained for CPCS monolayer are in good
agreement with the reported values45,52,53 of carbon-doped
phosphorene structures.
Although the carbon-doped α, β, and γ monolayer structures
were all optimized to a CPCS, the doping of homogeneous
bilayer structures of α, β, and γ with carbon according to the
conditions that we mentioned earlier leads to distinct
structures for each of the allotropes. In the homogeneous
bilayer of αc structures, including αPC‑m1AA , αPC‑m2AA , αPC‑m1AC ,
αPC‑m2AC , and αPC‑m2AB , a new interaction with covalent bond
characteristics appears (see Figure S9). In the αPC‑m1AA structure,
the mentioned covalent interaction involves carbon and
phosphorus atoms from two constituent layers, resulting in
the formation of six-member rings. However, in the αPC‑m2AA ,
αPC‑m1AC and αPC‑m2AB structures, a new strong interaction forms
between two phosphorus atoms of the constituent layers. This
leads to the formation of similar ten-member rings in the
αPC‑m2AA and αPC‑m1AC structures, while in the αPC‑m2AB structure, four-
membered rings are formed (see Figure S9).
Except for βPC‑m2AC , in the homogeneous bilayer of the βc
structures, the situation is different. In these structures, due to
the high interlayer distance, no covalent bond is formed
between the two constituent layers. In the βPC‑m2AC structure, due
to the arrangement of the atoms, a covalent bond is formed
between P and C atoms from top and bottom layers, which led
to 6-member rings in these structures (see Figure S10).
The characteristic feature of γc homogeneous bilayer
structures is the formation of four, six, eight, and ten-member
rings (Figure S11). Covalent bond forms between the two
constituent layers in all structures of these doped allotropes. In
the γPC‑m1AA , γPC‑m1AC and, structures, the rings are made up of six
atoms. It should be noted that the optimization of γPC‑m1AA and
γPC‑m1AC structures leads to a shared single structure. The strong
interactions between C and P atoms, enabled by the sliding of
vertically stacked layers, facilitate the formation of eight-
membered and four-membered rings in the structure γPC‑m1AA
and γPC‑m1A structures. In theγPC‑m1AB structure, the covalent bond
formed between the carbon and phosphorus atoms from
constituent layers leading to the formation of six-member rings
in these structures. Typically, the covalent bond length
between the two constituent layers falls within the 1.83−2.22
Å range. All structural parameters related to the examined
structures are reported in Table S3.
3.3. Properties of Gated Monolayer and Polytypes.
To assess the suitability of the phosphorene monolayer and
polytypes for application in field-effect transistor channels, the
monolayers and bilayers were placed at the center of the region
as in Figure 1, with a constant external electric field. To
minimize interactions between bilayers in neighboring super-
cells, a large supercell size of 30 Å was chosen. The
arrangement of structures in the gate model follows a similar
grouping as in the geometric and electronic studies section.
Since the change in the structural parameters affects the
electronic properties, electron transport and performance of
the structures as FET channel, we first examine the electronic
structure details in the presence of the gate and subsequently
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discuss the electronic properties including the details of the
band structure, charge density distribution and electron
transport. To this end, single and bilayer systems with different
doping hole levels ranging from 0.05 to 2 holes per unit cell
with increment of 0.5 were selected. Hole doping was
considered because, as mentioned in the computational part,
the potential of the gate is equal to the charge of the system
with the opposite sign. Furthermore, we recall that in field-
effect transistors with p-type channels, the gate potential must
be negative, otherwise the transistor will not perform
properly.87 The criterion for selecting this range for the hole
loading to the system was the stability of the system versus the
loading amount. As a measure of the stability of the systems,
the resistance of phosphorene to tension was chosen.
According to a report by Wei et al.,88 α-phosphorene polytype
exhibits a tensile strength of 30% in the armchair direction.
Further application of tension can result in a structural change.
Subsequently, we compared the collected data with the results
obtained after applying potential gates up to 2 holes per unit
cell. The findings revealed that hole doping exceeding 1.5 holes
per unit cell on α-phosphorene led to a decrease in the
cohesive energy compared to the state in which a 30% tension
was applied to it. Hereupon, we have limited the amount of
doping up to 2 holes per unit cell. We have included data for
doping 2 holes per particle to show the instability of the
structures and its effect of the different properties. It is worth
mentioning that the degree of effectiveness of the systems by
the created electrical field between the system and gate
depends on the potential value of the gate as well as the
distance of the system from the gate.
3.4. Atomic Structures within the Channel of Field-
Effect Transistors. Since, for homogeneous bilayer polytypes
with different stackings (αAA, αAB, αAC, βAA, βAB, βAC, γAA γAB,
and γAC), the geometric changes for the monolayer closer to
the gate in the optimized bilayer structures are the same as the
changes of the bare monolayer of allotropes in the gated
model, we present only the results of optimization for the
homogeneous bilayers of αAA, βAA and γAA. We recall that the
increase of the layer number causes to stability of the
structures.
In all homogeneous bilayer structures, van der Waals
interaction between the layers led to the increase of the top
layer distance from the gate. Moreover, bilayer structures
contain a higher number of atoms within the same surface area
compared with their monolayer counterparts. Consequently,
the top layer in all bilayer structures is less affected by the gate
potential than the bottom layer (closer to the gate). The
results show that the general arrangement of atoms in bilayer
structures of homogeneous βAA, βAB, βAC, γAA γAB, and γAC
remains the same as their monolayer structures under the gate
potential and there is no change by increasing the potential.
But in the αAAand αAB bilayer structures, increasing the gate
potential changes the structure of the layer closer to the gate,
as for the bare phosphorene monolayer, and its thickness
increases. In the presence of a gate potential, the αAC stacking
bilayer has enhanced stability when compared to αAA and αAB
stacking. In the αAA structure, the interlayer distance decreases
as the gate potential increases, so that at the potential of 2
holes per unit cell, the interlayer distance decreases by ∼9%,
compared to that of the bare structure. The distance decrease
between layers causes the upper layer to be closer to the gate,
the closer to the gate the more affected by the gate potential.
At a 2 hole per unit cell potential, the thickness of the
mentioned monolayer (d′) increases by 1.10%. The effect of
the potential on the layer closer to the gate is an ∼34%
increase in the thickness of this monolayer (d) at a potential of
2 holes per unit cell compared to a bare counterpart. In the αAB
and αAC cases, with the continued increase in the gate
potential, the interlayer distance begins to expand. Specifically,
at a potential of 2 holes per unit cell, there is an increase in the
distance between the layers within the structures αAB andαAC
by ∼14.18% and ∼13%, respectively, compared to that of the
bare structures. In both αAB and αACstructures, the thickness of
the layer (d′) far from the gate remains unchanged by applying
the gate potential, but in the layer closer to the gate, as in the
αAA bilayer, the thickness of the monolayer (d) increases by
increasing the gate potential (Figure S12). It is worth noting
that the αAC structure exhibits a lower increase in monolayer
thickness (d) compared to αAAand αAB. This distinction in the
trend of variation of structural parameters is the only difference
observed. In the βAAand βAB bilayers, the interlayer distance
(D) decreases by increasing the gate potential, while in the
βACstructure, it increases by ∼30%, compared to that of the
bare state. Bilayers of βAA, βAB, and βAC are different from
homogeneous alpha phosphorene bilayers; as the gate potential
increases, the thickness of the layer closer to the gate decreases
with a trend similar to that of the β monolayer. Also, by
applying the gate potential, bond lengths in these three
structures decrease. In all studied stackings of the γ bilayer, all
bond lengths in the layer closer to the gate decrease and those
of in layer further away the gate increase.
In heterogeneous bilayer structures, the bond lengths and
bond angles experience slight alterations while the overall
atomic arrangement of the structures. However, by increasing
the gate potential up to 2 holes per unit cell in the β/α
structure, the thickness of the β layer (d) decreases by 4.16%
and that of the α layer increases by 1.33% compared to those
of the bare states. In the γ/α structure, the thickness of the γ
(d′) decreases by 0.66% and that of in α increases by 2.10%
and in the structure β/γ thickness of β decreases by 4.20% and
that in γ increases by 0.66%. The layers’ distance in β/α, γ/α,
and β/γ decreases by 2.48%, increases by 0.6%, and decreases
by 3.48%, respectively.
The obtained results from the relaxation of the atoms in the
primary unit cell of α↶α show that the in-plane bond length is
increased by 0.44% in both layers compared to that of the
phosphorene monolayer. The thickness of phosphorene
monolayers (d) in this structure has increased by ∼4%
compared to that of the phosphorene monolayer. This increase
is attributed to the angle changes observed in this structure
compared to those in the phosphorene monolayer.
The phosphorene monolayer has anisotropy89−91 and this
feature plays an important role in the properties of the rotated
homogeneous bilayers and results in different characteristics
from the homogeneous bilayers. For this reason, the structural
changes caused by applying the gate potential are less in the
rotated homogeneous alpha−alpha bilayer compared to the
homogeneous bilayer and monolayer of phosphorene. In the
90° rotated bilayer γ↶γ, the thickness of each monolayer
increases by 20.74% and 25.78% for the bottom top layer,
respectively, compared to that of monolayer γ-phosphorene.
The thickness of the bottom and top layer as well as the
distance between the two layers in the β↶β structure at the
gate potential of 2 holes per unit cell decreases by 3.33%,
3.07%, and 2.22% compared to those of the bare structures,
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respectively. In rotated structures, the overall arrangement of
the structures does not change by applying the gate potential.
Summing up, while all three phosphorene allotropes, α, β,
and γ, possess an identical number of electrons and atoms in
the primary unit cell, they display varying structures as well as
distinct electron density distributions within these structures.
(Figure S1). Therefore, different trends and ratios of changes
in the bond lengths and angles were found in these structures
under application of the gate potential. Upon closer
examination of the data, it becomes apparent that in α and
γ-phosphorene structures, three types of bonds exist that
exhibit varying degrees of effectiveness in response to the gate
potential. This is because of the different positions of atoms
and their structure. In α-phosphorene, the longer out-of-plane
P−P (dpd1‑pd2) bond length than the in-plane (dpd1‑pd2) bond length
causes easier bond breaking by increasing the gate potential.
Moreover, the atom closer to the gate moves toward the gate
and leads to the increment of roughly 35% in thickness
compared to that of the bare state and hence an overall change
in α-phosphorene structure (Figure 3). In contrast to the α-
phosphorene structure, the overall arrangement in γ-
phosphorene remains unchanged even when a gate potential
is applied. This is attributed to the nonplanarity of the γ-
phosphorene structure in the z-direction (Figure 3). In the β-
phosphorene structure, similar to the results found for α- and
γ-phosphorene structures, the positions of the atoms differ
from each other. However, due to the buckled structure and
high symmetry of β-phosphorene, all three bonds occupy the
same position relative to the gate potential, resulting in equal
changes in bond lengths. Additionally, the increase in angles of
β-phosphorene caused by the application of the gate potential
leads to a decrease in thickness.
In the CPCS structure, with an increase in the gate potential,
the closer in-plane phosphorus−carbon bond length to the
gate potential decreased. The thickness (d) of the CPCS
structure decreases by increasing the gate potential and reaches
its minimum value at the gate potential of 1.5 holes per unit
cell (151.22% decrease compared to that of the bare state). At
the gate potential of 2 holes per unit cell, the thickness
increases compared to 1.5 holes per unit cell, but at the end,
the thickness of the CPCS structure at the gate potential of 2
holes per unit cell is still lower compared to that of the bare
state.
The results in this subsection demonstrate that the gate
potential causes formation of a quasi-flat structure and results
in a CPCS which has similar structure to graphene. A
comparison of the structural data for undoped and doped
counterparts shows that the effectiveness of doped bilayers by
the gate potential is larger than in the undoped structures, in
such a way that by applying the gate potential, to most of the
doped bilayers their overall structures are changed. This
indicates that the range of gate potential for no structural
change is lower in the doped structures compared to undoped
ones.
The overlap between phosphorus and carbon atoms in the
doped structures led to the formation of modified structures.
However, it is important to note that this overlap is not as big
(size and difference in energy levels) as the overlap between
phosphorus atoms in phosphorene or carbon atoms in
graphene. This heightened sensitivity leads to substantial
structural modifications. These changes are so significant that
they trigger a phase transition within the material. This
characteristic proves to be advantageous for these structures,
particularly in the presence of an applied potential.
To close this subsection, note that the cohesive energy
results show that, after applying the gate potential, the stability
of the structures tends to decrease. The order of the highest
reduction percentage of cohesive energy in α and its bilayers is
as follows: α > αAB > αAA > αAC. The same trend was found for
β and γ allotropes except that the structural stability reduction
percentage is lower than that of α-phosphorene. In the carbon-
doped structures, the application of gate potential reduces the
cohesive energy. It is noteworthy that by applying the
maximum gate potential (in our work), the cohesive energy
of the carbon-doped monolayer structure is greater than that of
the initial α-phosphorene while maintaining the overall
arrangement.
3.5. Electronic Structure within the Channel of Field-
Effect Transistors. Previous experimental and theoretical
studies on graphene and MoS2 have shown that it is possible to
tune the band gap by applying an external electric field.92−97
Therefore, it is interesting to know how the band gaps of the
phosphorene family introduced in this study change with
application of the gate potential.
Apart from the alterations in electronic structure induced by
the gate potential, the results obtained indicate that even the
smallest gate potential applied to the studied structures can
cause a phase transition from a semiconductor to a conductor.
Conversely, structures that are inherently conductive maintain
their phase and retain their conductivity when the gate
potential is applied. With the exception of the CPCS structure
and of γPC‑md1AB , γPC‑md2AC , αPC‑md2AB , and αPC‑md1AA bilayer structures, which
undergo two phase changes in their band structure with
varying gate potential, other phosphorene polymorphs
transition occurs from being semiconductors to conductors.
As the gate potential increases, the valence bands in these
structures shift above the Fermi level. Moreover, as the gate
Figure 3. Structures of α, β, and γ phosphorene from the top and side views in the absence of the gate potential (ndop= 0) and in the presence of a
gate potential (ndop= 2 hole per unit cell).
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potential continues to increase, the displacement of the valence
band also increases.
The specifics of the changes in the band structures of the
studied structures are outlined below.
Figure 4. Averaged potential (a, e), averaged charge density (c, g), difference between the potential (b, f) and difference between the charge density
(d, h) of the doped and undoped αAA and βAA bilayers as a function of the z-direction.
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From the band structure of α and αAA at different gate
potentials, it can be concluded that at a 2 hole per unit cell
potential, the band structure qualitatively changes compared to
small changes at lower potentials. In monolayer, homogeneous
bilayers, and rotated bilayers of beta phosphorene, like alpha
phosphorene, the semiconductor phase changes to metallic
phase by applying the gate potential. Bilayers of gamma
phosphorene, unlike alpha and beta structures and their
bilayers, retain their phase in the presence of the gate potential
and the phase remain metallic. As mentioned, the CPCS
structure is intrinsically conductive and it remains as so at gate
potentials up to 1.5 hole per unit cell. However, at a potential
of 2 holes per unit cell, the electronic structure changes from
conductor to a semiconductor with an indirect band gap of
2.15 eV (Figure S13). In the bilayers of alpha phosphorene
carbide, αPC‑md1AA , and αPC‑md2AB , which are conductive in the
absence of a gate potential, the conductive character remains
by applying a gate potential up to 1.5 hole per unit cell, but at a
potential of 2 hole per unit cell their character changes from
conductor to semiconductor, respectively, with a direct band
gap of 1.52 and 1.17 eV. In the β-phosphorene carbide bilayer
structures, the application of the gate potential causes the band
gap to close, and it remains metallic in the whole range of
applied potentials. In the bilayer structures of gamma
phosphorene carbide, γPC‑md1AB , and γPC‑md2AC structures, which are
intrinsically semiconducting, become conductive under the
application of a gate potential. However, by further increasing
the gate potential up to 2 holes per unit cell they change from
conductors to semiconductors with indirect band gaps of 1.14
and 0.68 eV, respectively.
To further investigate the effect of the gate potential in the
electronic structure of phosphorene polymorphs, we analyze
the electron density distribution, which is one of the
characteristics of any material. In addition, by considering
structure phosphorene as a suitable reference,98 the electron
density difference (Figure S14), and chemical intuition, are
proper tools to extract the structural changes.
Due to the physical arrangement of P atoms and the quasi-
two-dimensional structure of these materials, the electron
density of α, β, and γ phosphorene monolayers have two, one,
and one peak(s), respectively. The so-called phosphorene
polymorphs have two half-plane structures. The double-peaked
electron density in α indicates that the density of electrons
between these two half-planes is lower than inside the half-
planes, which is a reason for the dpd2‑pd3 being longer than dpd1‑pd2
(in-plane bond). The single peak of the electron density
diagram of β and γ phosphorene indicates that, unlike in the α
one, the accumulation of electrons between the two half-planes
is larger than in the half-planes inside, and this is a reason for
the shorter dpd2‑pd3 distance compared to that of dpd1‑pd2 in the
mentioned structures. The results obtained from the
calculation of the electron density and potential energy at
different gate potentials show that the gate potential changes
the density distribution of electrons in different structures,
Figure 4.
Although there is a correlation between the changes in
different regions of the α studied structures and different parts
having a mutual effect on each other, this change is larger in
the layers and atoms closer to the gate than in the layer and
atoms further away from the gate. To better show the changes
trend of electron density and potential energy, the variation of
these features is shown in Figure 4 for the α and β allotropes
which belong to the most unstable and stable structures in the
presence of the gate potential, respectively. As shown in Figure
S14, changes in potential energy and electron density in the
βAA structure are insignificant, and the arrangement of atoms
remains similar to that of bare AA staking of the β allotrope.
However, in the αAAstruture, in the layer closer to the gate,
potential and electron density changes are noticeable, which
causes a change in the arrangement of atoms and, as a result,
induces changes in the properties of the related structures.
Figure 4 compares the potential energy and electron density
at different gate potentials for the isolated structures. The
disparity in potential energy and electron density increases
with increasing gate potential. In the α allotrope, the difference
from the isolated structure is much larger in the layer closer to
the gate. The later trend has also been found for the β allotrope
but the magnitude of changes in both layers is the same and
symmetrical.
In bilayer α phosphorene structures, the trend of changes in
structural and electronic properties induced by the presence of
the gate potential is similar to that observed in the
phosphorene monolayer, but compared to bilayers of other
allotropes, the changes in electron density and potential energy
in the α bilayer induced by the presence of the gate potential
are larger. In addition, in the gated bilayer structures of all
studied allotropes, increasing the gate potential causes an
increase in the electron density between the two layers, and as
a result, an increase in the potential between the two layers of
AA and AB stackings. However, in the AC staking of all three
allotropes, the electron density between the two layers
decreases when the gate potential. It is therefore clear that
the layers close to the gate are more sensitive to the presence
of the applied potential than the layers far from the gate.
Nevertheless, understanding the electronic and structural
changes in the bilayer induced by the presence of the gate
sheds light on several complications in estimating the behavior
of the layer in the presence of the gate potential. For example,
the comparison of the αAA and βAA structures in the presence
of the gate potential shows that in the βAA structure, unlike the
αAA structure, the layer farthest from the gate potential is not
affected by the gate potential. While there is effectiveness in
the farthest αAA layer and the bond length, bond angle and
layer thickness change by 0.88%, 0.35% and 1.1%, compared to
the values for the bare structure (Figure S14 and Table S3).
Another noteworthy point is the symmetric or asymmetric
effectiveness of the gate potential for the nearer layer. As can
be seen in the Figure S12, in the layer close to the gate
potential, the angles and bond lengths in the βAA structure are
symmetrically affected by the gate potential. In such a way that
symmetrical changes, in the direction of an increase in one
section and a decrease in the other part, in different parts of the
layer close to the gate eliminate the effect of the gate potential
on the structural deformation. In other words, the resulting
average of the variations due to gate potential does not show a
change in the structure, and the overall arrangement of the
structure is preserved. On the other hand, in the αAA structure,
the atoms and thus the bond angles and lengths are
symmetrically unaffected by the gate potential. For this reason,
the effect of the potential in different parts of the layer near the
gate is different, and this has caused a general change in the
structure.
As stated in the structural properties section, doping
phosphorene bilayer allotropes with 50% carbon atom does
not change the stability trends of bare bilayer allotropes. In this
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regard, in α phosphorene carbide structures, the effect of the
gate potential on the electron density and potential energy of
these structures is as high as in the undoped α phosphorene
bilayers. Consequently, in some of these structures, the
electron density and potential energy change significantly.
Analysis of the electron density and potential energy of β
phosphorene carbide structures shows that the gate potential
effect in AB and AC stackings is such that the electron density
and, as a result, the interaction between the two layers
decreases and the distance between the two layers increases. In
the AA arrangement of this group, the gate potential causes a
slight change in the arrangement of atoms closer to the gate,
increases the electron density and interaction between the
layers, and decreases the distance between the layers. Except
for γPC‑md2AA and γPC‑md2AB structures, the changes of electron density
and potential energy of γ phosphorene carbide structures are
the same as for the β phosphorene carbide. In the two γPC‑md2AA
and γPC‑md2AB structures, the electron density in the layer farthest
from the gate does not change, although in the layer of both
mentioned structures closer to the gate, there are significant
changes leading to an overall structural change.
We can summarize and explain the shift of energy levels and
changes in the band widths based on structural alterations and
their impact on the electron density distribution. Modifications
to the structural characteristics of materials can have a
profound impact on their electronic properties. In the specific
case of the phosphorus family, these alterations can
significantly influence the distribution of electron density
within these structures. On the other hand, electron density
distribution plays a crucial role in determining various
electronic properties, such as conductivity and resistivity.
When the distances, angles, buckling, and overall structure of a
material like the phosphorene family are modified, they can
directly affect how electrons are distributed within the material.
By understanding the changes in electron density distribution
resulting from structural modifications, we can gain a deeper
understanding of the material’s electronic properties (Figure
S14). The direct impact of these changes in the structures is
observed in the electronic band structure, including variations
in bandwidth and band shifts.99 Consequently, in the
mentioned structures, the valence band has shifted toward
positive energies.
According to this part, it is interesting to notice that the
CPCS structure displays case desirable attributes such as a
phase transition from a conductor to a semiconductor,
enhanced stability compared to other studied allotropes
through carbon atom doping, reduced buckling in the structure
upon applying a gate potential, and the obtained graphene-like
structure with favorable properties100−102 in the presence and
absence of the gate potential.
3.6. Quantum Transport. The quantum description of the
electronic conductance is a complex nonequilibrium problem,
and electric transport and FET characteristic of the pristine
and C-doped phosphorene’s should be investigated by
nonequilibrium Green’s function (NEGF) method. Hence,
the present work constitutes the first step in focusing on
structural and electronic properties. Thus, real space Green’s
function formalism based on the Landauer approach is taken
into consideration for the initial assessment. Accordingly, the
electron transport and electric current of the α (low stability)
and β phosphorene (high stability) and of CPCS among doped
structures with desirable attributes are examined and
compared.
The results of electron transport calculations for the
mentioned structures are summarized in Figure 5 and those
for current−voltage in Figures 6 and 7. In the absence of gate
potential, phosphorene does not exhibit electron transport and,
consequently, electronic current either in both armchair or
zigzag directions at the Fermi level.83
The CPCS has electron transport at gate potentials of 0 and
1.5 holes per unit cell (Figure 5c) which is due to the density
of the electronic states in the Fermi level of this structure. This
structure has the highest amount of electron transport and
Figure 5. Comparison of the electron transport in armchair and zigzag directions for α (left), β (middle) phosphorene, and CPCS (right).
Figure 6. Current−voltage (I−V) curves for, graphene, α
phosphorene, and pristine and charged CPCS at ndop= 1.5 and
ndop= 2 hole per unit cell.
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electronic current at a potential of 1.5 hole per unit cell in both
directions in comparison with graphene. The calculated CPCS
band structure (Figure S13) shows a band gap at potential
equal to 2 holes per unit cell, which implies the absence of
available density of electronic states with concomitant zero
electron transport and electronic current at the later potential.
In the absence of gate potential, the composition and
arrangement of C and P atoms in the CPCS structure lead to a
higher passing current through this structure than in graphene.
The comparison of the band structure and Fermi energies
indicates that in the CPCS structure, there is no band gap, and
the Fermi energy is lower compared to graphene. The reason
for these changes can be attributed to the charge transfer from
phosphorus atoms to carbon atoms (∼0.1) and the inherent
potential of carbon atoms in this structure to accept charge.
This results in reduced charge accumulation on phosphorus
atoms, leading to decreased repulsion, increased overlap, and
consequently flattening of the structure. In other words, the
structure under consideration exhibits behavior similar to
graphene, except for the higher value of electron density per
unit surface area.
Applying an electric field increases the current passing
through the CPCS structure in such a way that in an electric
field equal to 1.5 holes per unit cell, the electric current reaches
its highest value compared to current values in other gate
potentials. The higher current observed in CPCS structures
compared with graphene can be attributed to the value of
electron density per unit surface area. This higher electron
density in CPCS structures translates to a more efficient flow
of the electric current through the material. Due to the fact that
the application of an electric field equivalent to 2 holes per unit
cell changes the phase of this structure from conductor to
semiconductor with a band gap of 2.15 eV, the current passing
through the CPCS structure in this field (2 holes per unit cell)
is largely reduced. Consequently, by changing the electric field,
it is possible to control the current passing through CPCS-
based devices in different conditions.
According to the present I−V curves (Figures 6 and 7) and
in agreement with previous studies,84,103 the current passing
through graphene is high. But in the β phosphorene structure
(Figure 5 and Figure 7), the electron transmission and passing
current is larger than that predicted for graphene and
phosphorene. Although gated β phosphorene has a reduced
current through this surface in higher gate potential, the
current is still higher than that of graphene. Increasing the
electric field does not have a great effect on the current value in
this structure.
4. CONCLUSIONS
Understanding the principles of 2D field-effect transistors is
important for solving practical manufacturing problems. It has
been claimed that a deeper understanding of the discoveries of
these transistors at the fundamental level will strengthen their
market value.104 In the present work, a fresh and
comprehensive picture of the phosphorene polytypes and
their carbon-doped counterparts has been presented and their
properties related to a possible use in FET have been
discussed.
The α, β, and γ structures of phosphorene allotropes have
the same number of electrons and atoms in the designed unit
cell. However, due to their placement in different regions of
the potential energy surface minima, they exhibit different
structural and electronic properties with respect to each other.
In this respect, the structural properties of the homogeneous
bilayers and the rotated bilayer for each allotrope resemble the
monolayer structure of each of them.
The doping of carbon atoms to the bilayer structures of
phosphorene allotropes causes significant changes in the
positions of atoms and the interlayer distance compared with
the original bilayers. These fundamental changes lead to the
formation of a new type of covalent bonding between the
layers in several PC structures.
The monolayer and bilayer structures of β phosphorene
have the highest band gap compared to those of other
structures. Doping with carbon atoms in the structures leads to
a fundamental change in the band structure due to the
alteration of the structural properties. So in CPCS and bilayer
structures, the band gap is closed and conductivity is induced
in these structures.
Using the studied structures as channel materials in field-
effect transistors causes the structural properties of the systems
to change upon application of the gate potential. The extent of
the structural property changes increases with an increase in
the gate potential. The sensitivity of the monolayer and bilayer
structures with different stacking arrangements of α phosphor-
ene and several related structures is higher compared with
other arrangements. The results of the structural stability
analysis indicate that bilayer formation, including different
stacking arrangements, layer mismatch, layer rotation relative
to each other, and substitution of carbon atoms with a 1:1 ratio
of phosphorene atoms in the structures, enhances their
stability.
Furthermore, the present results obtained from periodic
calculations using density functional based methods, predict
that in the presence of an electric field of up to 2 hole per unit
cell, the CPCS and β structures are more stable than the α and
γ polymorphs in good agreement with the results reported by
Zhen et al.105 Moreover, in the β and CPCS structures, the
electron transport is also larger than that predicted for the
other studied systems. Therefore, applying the gate potential
induces an increase of the current passing through CPCS and
it reaches its highest value, compared to other fields, at the gate
potential of 1.5 holes per unit cell. Finally, a phase transition
from conductor to semiconductor in the CPCS structure,
induced by the presence of an electric field equivalent to 2
Figure 7. Current−voltage (I−V) curves for graphene and pristine
and charged α and β phosphorene.
The Journal of Physical Chemistry C pubs.acs.org/JPCC Article
https://doi.org/10.1021/acs.jpcc.3c05876
J. Phys. Chem. C 2024, 128, 2997−3010
3007
holes per unit cell, causes significant electric current reduction.
Consequently, it is possible to tune and control the current
passing through CPCS-based devices under different con-
ditions by changing the electric field. The present work
suggests that CPCS and β structures are promising 2D
materials for channels in FET devices.
■ ASSOCIATED CONTENT
*sı Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.jpcc.3c05876.
Structural information on all studied systems, relevant
band structures and charge density plots (PDF)
■ AUTHOR INFORMATION
Corresponding Authors
Fariba Nazari − Department of Chemistry, Institute for
Advanced Studies in Basic Sciences, Zanjan 66731, Iran;
Center of Climate Change and Global Warming, Institute for
Advanced Studies in Basic Sciences, Zanjan 45137-66731,
Iran; Email: nazari@iasbs.ac.ir
Francesc Illas − Departament de Cieǹcia de Materials i
Química Física & Institut de Química Teor̀ica i
Computacional (IQTCUB), Universitat de Barcelona, 08028
Barcelona, Spain; orcid.org/0000-0003-2104-6123;
Email: francesc.illas@ub.edu
Authors
Fereshteh Mahmoodpouri Malayee − Department of
Chemistry, Institute for Advanced Studies in Basic Sciences,
Zanjan 66731, Iran
Robabeh Bagheri − Department of Chemistry, Institute for
Advanced Studies in Basic Sciences, Zanjan 66731, Iran
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.jpcc.3c05876
Notes
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
F.N. is grateful to the Institute for Advanced Studies in Basic
Sciences for financial support through research Grant
No.G2022IASBS32604. The research carried out at the
Universitat de Barcelona has been supported by the Spanish
MCIN/AEI/10.13039/501100011033 PID2021-127957NB-
I00, TED2021-132550B-C21, PID2021-126076NB-I00, and
María de Maeztu CEX2021-001202-projects, funded partially
by the European Union (FEDER).
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3010