Recent Developments on Silicon Carbide Thin Films for Piezoresistive Sensors Applications

375
When subjected to a mechanical stress, the electrical resistance of the resistors change
leading to a variation of the output voltage, according to the following relationship

()
()
()()
33
44
11 33 22 44
out
s
VRR
RR
VRRRRRRRR
Δ+Δ
+Δ
=−
+Δ + +Δ +Δ + +Δ

(16)
Whereas the four resistors have the same nominal resistance value (
R
1
=R
2
=R

(17)
Given this, the sensitivity of a piezoresistive pressure sensor is determined by

11
out
s
V
R
S
RP V P
Δ
Δ
==
ΔΔ

(18)
where ∆
P is change in pressure.
Whereas, for a piezoresistive accelerometer, the sensitivity is defined as the electrical output
per unit of applied acceleration:

11
out
s
V
R
S
Rg V g
Δ
Δ

376
(Pearson et al., 1957). In addition, the silicon does not support prolonged exposure to
corrosive media. Another important factor that should be considered is that silicon pressure
sensors using p-n junction piezoresistors have exhibited good performance at temperatures
up to 175ºC and the SOI sensors at temperatures up to 500ºC.
Among the semiconductor materials with potential to substitute the silicon in harsh
environments, SiC is the most appropriate candidate because its native oxide is SiO
2
which
makes SiC directly compatible with the Si technology. This signifies that a sensor based on
SiC can be developed following the same steps used in silicon sensors.
On the other hand, the chemical stability that have qualified SiC for harsh environments,
makes it difficult to etch the bulk and to integrate any process step with already established
Si based processes. Furthermore, the high cost of SiC wafer also difficult the development of
“all of SiC” sensors. Faced with these difficulties the use of SiC thin films is quite attractive
because the film can be grown on large-area Si substrates and by the ease of using
conventional Si bulk micromachining techniques (Fraga et al., 2011a).
The second question is: When to use piezoresistive sensors based on SiC?
As already mentioned in the beginning of this section, at room temperature the
monocrystalline silicon has greater
GF than the SiC, i.e. sensors based on silicon operating
on this condition has superior sensitivity. This fact shows that the use of SiC is only justified
for specific applications in four main types of harsh environments, namely:
a. Mechanically aggressive that involve high loads as in oil and gas industry applications
which require sensors to operate in pressure ranges up to 35,000 psi and at
temperatures up to 200°C (Vandelli, 2008);
b. Thermally aggressive that involve high temperatures as in combustion control in gas
turbine engines, where the operating temperatures are around 600°C (Vandelli, 2008)
and in pressure monitoring during deep well drilling and combustion in aeronautical
and automobile engines that require sensors to operate at temperatures ranging

attractive processes for the synthesis of thin films at low temperature as those based on plasma
assisted techniques, such as plasma chemical vapour deposition (PECVD) and plasma
sputtering, which operate at temperatures below 600°C (Rajagopalan et al., 2003; Lattemann et
al., 2003). But SiC films obtained at low temperature processes are amorphous (a-SiC) or nano-
crystallines (nc-SiC) and, thus, can exhibit properties somewhat different from those observed
in crystalline films (Foti, 2001). Because of this, a process usually used to improve the
crystallinity of the a-SiC films is the annealing (Rajab et al., 2006).
Among the techniques used to deposit SiC films, in this chapter only four of them will be
described: CVD, PECVD, magnetron sputtering and co-sputtering. These techniques were
chosen because have been used with success in the deposition of undoped and doped SiC
films for MEMS sensors application. A common point among them is the ease to perform
the “in situ” doping by the addition of dopant gas (N
2
, PH
3
or B
2
H
6
) during the film
deposition.
4.1 Chemical deposition processes: CVD and PECVD techniques
One of the most popular (laboratory) thin film deposition techniques nowadays are those
based on chemical deposition processes such as chemical vapor deposition (CVD) and
plasma enhanced chemical vapor deposition (PECVD) (Grill, 1994; Ohring, 2002; Bogaerts et
al., 2002).
CVD or thermal CVD is the process of gas phase heating (by a hot filament, for example
(Gracio et al., 2010)) in order for causing the decomposition of the gas, generating radical
species that by diffusion can reach and be deposited on a suitably placed substrate. It differs
from physical vapor deposition (PVD), which relies on material transfer from condensed-

where the species are created (see Figure 3b). Here, we focused the rf discharge because it is
the configuration more used in research and industry. The rf PECVD reactor essentially
consists of two electrodes of different areas, where the substrate is placed on the smaller
electrode, to which the power is capacitively coupled. The rf power creates a plasma
between the electrodes. Due to the higher mobility of the electrons than the ions, a sheath is
created next to the electrodes containing an excess of ions. Hence, the sheath has a positive
space charge, and the plasma creates a positive voltage with respect to the electrodes. The
electrodes therefore acquire a dc self-bias equal to their peak rf voltage (self-bias electrode).
The ratio of the dc self-bias voltages is inversely proportional to the ratio of the squared
electrode areas, i.e., V
1
/V
2
= (A
1
/A
2
)
2
(Lieberman & Lichtenberg, 2005). Fig. 3. Schematic diagram of CVD (a) and PECVD (b) systems.

Recent Developments on Silicon Carbide Thin Films for Piezoresistive Sensors Applications

379
Therefore, the smaller electrode acquires a larger bias voltage and becomes negative with
respect to the larger electrode. The negative sheath voltage accelerates the positive ions
towards the substrate which is mounted on this smaller electrode, allowing the substrate to

Silicon Carbide – Materials, Processing and Applications in Electronic Devices

380
4.2 Physical deposition processes: Magnetron sputtering and co-sputtering
techniques
The physical deposition process comprise the physical sputtering and reactive sputtering
techniques. Basically, these techniques differ when a neutral gas (physical sputtering) is
added together with a reactive gas (reactive sputtering). In physical sputtering, ions (and
atoms) from the plasma bombard the target, and release atoms (or molecules) of the target
material. Argon ions at 500–1000 V are usually used. The sputtered atoms diffuse through
the plasma and arrive at the substrate, where they can be deposited (Bogaerts et. al., 2002).
In reactive sputtering, use is made of a molecular gas (for example, N
2
or O
2
). Beside the
positive ions from the plasma that sputter bombard the target, the dissociation products
from the reactive gas will also react with the target. Hence, the film deposited at the
substrate will be a combination of sputtered target material and the reactive gas (Bogaerts et
al., 2002; Berg, 2005; Lieberman & Lichtenberg, 2005). The sputter deposition process is
schematically presented in Figure 5. Fig. 5. Schematic of sputtering process.
Basically the steps of sputtering process are the following: (i) the neutral gas is ionized by a
external power supply, producing a glow discharge or plasma; (ii) a source (the cathode,
also called the target) is bombarded in high vacuum by gas ions due to the potential drop
acceleration in the cathode sheath; (iii) atoms from the target are ejected by momentum
transfer and diffuse through the vacuum chamber; (iv) atoms are deposited on the substrate
to be coated and form a thin film.

Deposition of SiC films by the Magnetron Sputtering technique is performed generally using
a SiC target in Ar atmosphere or a silicon target with precursor gases Ar plus CH
4
(Stamate
et al., 2008). The dual magnetron (or co-sputtering) method also has been used to deposit
SiC films. In this technique, the films are produced by co-sputtering of carbon and silicon
targets (see Figure 7) with Ar as precursor gas (Kikuchi et al., 2002; Kerdiles et al., 2002). The
co-sputtering technique offers as main advantage to obtaining of SiC films with different
electrical, structural and mechanical properties by the variation of C/Si ratio in the film
deposited (Kikuchi et al., 2002). Using this technique, it is possible to obtain a range of SiC
film compositions by applied different power on each target (Medeiros et al., 2011).
5. Requirements of SiC films for piezoresistive sensors application
In order to develop piezoresistive sensors with high performance based on SiC films is
necessary to optimize the properties of the SiC thin-film piezoresistors to maximize their
sensitivity with the minimum temperature-dependent resistance variation (Luchinin &
Korlyakov, 2009).
The first step for this optimization is the choice of the technique to deposit SiC films onto an
insulator on Si substrates. Silicon dioxide (SiO
2
) is the most used insulator material for this
purpose, but some studies have showed silicon nitride (Si
3
N
4
) or aluminum nitride (AlN) as
alternative materials. In general, good results have been achieved with the SiO
2
, although this
material has a coefficient of thermal expansion (
CTE) significantly lower than the SiC, giving

383
The most used technique to determine the value of GF of a piezoresistor is the cantilever
deflection method. In this method, the piezoresistor is glued near to the clamped end of a
cantilever beam and on the free end of the beam different loads are applied. The value of GF
is obtained by monitoring the resistance change when the resistor is subjected to different
applied stress. Once determined the
GF, the TCR and the TCGF are determined to evaluate
the influence of the temperature (see details on topic 2).
Table 2 summarizes the main requirements that SiC film should present to be successfully
used in the development of piezoresistive sensors. As can be seen, the resistivity of the SiC
thin film should be low (preferably of the order of m
Ω.cm) because its thickness in general
less than 1.0
μm. As the depth of the SiC thin-film piezoresistor is equals the thickness film,
it is necessary a low resistivity film to form low electrical resistance piezoresistors.

Electrical and Mechanical Characteristics Requirement
Elastic modulus The greater
Residual stress The lower
Resistivity The lower
GF The greater
TCR The lower
TCGF The lower
Table 2. Main requirements of SiC films for piezoresistive sensor applications.
6. Examples of piezoresistive sensors based on SiC films
Among the many silicon-based microsensors, piezoresistive pressure sensors are one of the
widely used products of microelectromechanical system (MEMS) technology. This type of
sensor has dominated the market in recent decades due to characteristics such as high
sensitivity, high linearity, and an easy-to-retrieve signal through bridge circuit. The main
applications of Si-based piezoresistive pressure sensors are in the biomedical, industrial and

N
4
film as etch mask. It is also necessary to grow SiO
2
or Si
3
N
4
on the front side of
the wafer to perform the electrical insulation of the SiC thin-film piezoresistors from the
substrate. Generally, the SiC thin-film piezoresistors are produced by RIE (reactive ion etching).
Figure 9 illustrates two piezoresistive pressure sensors based on SiC films: one with six
PECVD a-SiC thin-film piezoresistors, configured in Wheatstone bridge, on a SiO
2
/Si square
diaphragm with Ti/Au metallization (Fraga et al., 2011b) and the other with phosphorus-
doped APCVD polycrystalline 3C-SiC piezoresistors on Si
3
N
4
/3C-SiC diaphragm with Ni
metallization (Wu et al., 2006). Fig. 9. Schematic illustration of piezoresistive pressure sensors based on SiC films.
Another sensor type that has been developed based on SiC is the accelerometer. However,
for now, the studies are still focused on piezoresistive accelerometers based on 6H-SiC bulk
substrate (Atwell et al., 2003) or on SiC thin-film capacitive accelerometers (Rajaraman et
al., 2011).
This occurs because the capacitive accelerometer is usually more sensitive than

crystalline and amorphous SiC films which have enabled the development of sensors
appropriate for harsh environments with costs lower than those based on SiC bulk.
This chapter reviewed the concepts of piezoresistivity, presented a brief survey on the
studies of piezoresistive properties of SiC films, described the main techniques that are
being used to deposit SiC films for MEMS sensor applications, discussed when and why to
use SiC and what are the requirements that SiC films must attain to be applied successfully
in piezoresistive sensors. Futhermore, it was shown examples of SiC film based pressure
sensors and accelerometers.
8. Acknowledgments
The authors acknowledge the financial support of Brazilian agencies: program PNPD-
CAPES (process number 02765/09-8), CNPq (process number 152912/2010-0) and AEB. We
also would like to thank the institutions that have provided their infrastructure for the
experiments: Plasma and Processes Laboratory of the Technological Institute of Aeronautics,
Microfabrication Laboratory of the Brazilian Synchrotron Light Laboratory (LMF-LNLS)
,
Institute for Advanced Studies (IEAv), Center of Semiconductor Components (CCS-
UNICAMP), Faculty of Technology of São Paulo (FATEC-SP) and Associate Laboratory of
Sensors (LAS-INPE)
.
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0
Opto-Electronic Study of SiC Polytypes:
Simulation with Semi-Empirical
Tight-Binding Approach
Amel Laref
1
and Slimane Laref
2
1
Department of Physics and Astronomy, King Saud University,
Riyadh 11451, Saudi Arabia
and Department of physics, National Taiwan University, Taipei 106
2
Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, Institut de Chimie de
Lyon, Laboratoire de Chimie, Lyon
1
Taiwan
2
France
1. Introduction
The recent growing scientific and technological interest on silicon carbide (SiC) arises from
its peculiar physical properties, i.e., its mechanical, and chemical stability. Moreover, SiC
is considered to be a promising material for electronic and optical devices. Microelectronic

availability, most measurements were on 6H-SiC and 3C-SiC (54)-(57). Very recently, some
measurements on 4H-SiC have also been reported (58)-(61). There are considerable variations
in the measured optical properties mainly because the photon energy is limited to less than
6.6 eV using the popular ellipsometry technique. The use of vacuum-ultraviolet (VUV)
spectroscopy can extend the energy range significantly and so far has only been carried out on
6H-SiC (57). Recent advances in crystal growth of SiC have allowed the study of the optical
properties of different polytypes (54)-(60). In addition, tight-binding (TB) method has proven
to be very useful for the study of both semiconductors and metallic systems, especially in
systems which are too large to be studying via ab-initio techniques. This method is about 2 or
3 orders of magnitude faster than the ab initio formulations, and at the same time it describes
with suitable accuracy the electronic structure of the systems. The computational efficiency of
the TB method derives from the fact that the Hamiltonian can be parametrized. Furthermore,
the electronic structure information can be easily extracted from the TB hamiltonian, which,
in addition, also contains the effects of angular forces in a natural way. In order to use a more
realistic method, we present a TB model with sp
3
s* basis, representing exact curvatures of
lowest conduction bands. The TB approach is standard and widely used for the electronic
properties of a wide variety of materials. In the present contribution we overview our
most recent results on the electronic structures and optical properties of SiC polytypes
(62). Hence, the SiC polytypes can be considered as natural superlattices, in which the
successive layers consist of Hexagonal SiC material of possibly different width. Our TB
model can treat SiC polytypes as superlattices consisting hexagonal bulk-like blocks. We
have investigated to which extent it is acceptable approximation for existing polytypes when
various of nH-SiC crystal are used to present polytype superlattices. Indeed, this is an
accurate approximation by building blocks consist of n-layers of nH-SiC. By representing
in general the polytypes as superlattices, we have applied our recent TB model (62) that
can treat the dimensions of the superlattice. Within this model we take for each sublayer
linear combination of atomic orbitals of hexagonal SiC which are subsequently matched at the
interfaces to similar combinations in the adjacent sublayers by using the boundary conditions.

now being that the manufacturing of different electronic devices becomes feasible. The wide
band-gap semiconductor SiC, with its excellent thermal conductivity, large breakdown fields,
and resistance to chemical attack, will be the material of choice for these applications. Realized
prototype power devices of SiC, like rectifier diodes, and junction field-effect transistors,
show indeed encouraging performance results under extreme conditions (54)-(66). In the
optical device arena, the ever increasing need for higher density optical storage and full
color display technologies are driving researchers to develop wide band-gap semiconductor
emitting technologies which are capable of shorter wavelength operation. Since the different
energy gap values of SiC all happen to lie in the visible range of the spectrum, SiC is an
interesting optical device material. Indeed, blue light emitting diodes were the first electronic
SiC devices which found a good sale. Some SiC polytypes are in addition most promising
as photodetective material sensitive to ultraviolet radiation. SiC is a good candidate for a
short wave length diode laser. Prototype transistors have been fabricated from SiC, and the
microwave and high temperature performance of SiC transistors have been studied. Devices
like field effect transistors, bipolar storage capacitors, and ultraviolet detectors have been
fabricated (57)-(64). SiC has a relatively high atomic bonding energy which is responsible for
its mechanical strength and chemical stability at high temperatures. This material can without
major difficulty, be crystallized in several polytypes, primarily due to similar geometric
structures and atomic bonds (1)-(11). The different stacking of C-Si bilayers remarkably
influences the properties of SiC. The most pronounced example concerns their electronic
structure. Hence, a controlled epitaxial growth of different polytypes on each other would
lead to high-quality heterostructures of chemical identical material with a locally adjustable
band gap (7)-(14). Meanwhile, growth of heterocrystalline structures seems to be possible (4),
but exhibits problems with the reproducibility and the crystal quality. Another possibility
to create a combination of two polytypes is a solid-solid phase transition, which transforms
one polytype into another one (6)-(8). However, polytypism also gives some advantages for
constructing electronic devices, for example homo-material heterostructures. Quantum wells
can be made by embedding a SiC polytype in another polytype with a wider gap(55)-(60).
Among the SiC polytypes, 6H is most easily prepared and best studied, while the 3C and
4H polytypes are attracting more attention for their superior electronic properties. The very

sequence is repeated, is combined with the letter representing the Bravais lattice type: cubic
392
Silicon Carbide – Materials, Processing and Applications in Electronic Devices
Opto-Electronic Study of SiC Polytypes: Simulation with Semi-Empirical Tight-Binding Approach 5
Fig. 2. Three-dimensional perspective views of the primitive hexagonal unit cells of the
3C-(zinc-blende), 2H-(wurtzite), 4H-, 6H-, and 8H-SiC polytypes. The stacking sequences
ABC
(3C),AB(2H), ABCB (4H), ABCACB (6H) and ABCAB ACB (8H) are also indicated.
(C) or hexagonal (H). With reference to figure 2, if the first Si-C layer is labelled A, the next
layer that can be placed according to a closed packed structure will be placed either on B or
C. The different polytypes are constructed by permutations of these three positions. In figure
2 the stacking sequence is shown for the most common polytypes, 3C, 2H, 4H, 6H, and 8H,
which are very interesting for their technological applications. Three-dimensional perspective
views of the primitive hexagonal unit cells of the 2H-, 3C-, 4H-, 6H-, and 8H-SiC polytypes. In
the case of SiC, the basic units are tetrahedrons with a C(Si) atom at the center, surrounded by
four Si(C) atoms covalently bonded: these units are periodically repeated in closed-packed
hexagonal layers, whose stacking sequence gives rise to the different polytypes. Though
being different in the long range order, the several polytypes show a similar local chemical
environment for both the carbon and silicon species; in particular each Si(C) atom is situated
above the center of a triangle of C(Si) atoms and underneath a C(Si) atom belonging to the next
layer in a tetrahedral coordination. The SiC-polytypes consist of double silicon-carbon layers
which are stacked on top of each other in the c-axis direction. A local arrangement of three
consecutive double layers is called hexagonal, if it is like the arrangement of double layers
in wurzite. It is called cubic, if the stacking arrangement is the same as for the zinc-blende
structure. The basic structural elements is the SiC bilayer composed of one Si [0001] plane and
the adjacent C[0001] plane. The SiC polytypes are differentiated by the stacking sequence of
the tetrahedrally bonded SiC bilayers, such that the individual bond lengths and local atomic
environments are nearly identical, while the overall symmetry of the crystal is determined by
the stacking periodicity. Each SiC bilayer, while maintaining the tetrahedral bonding scheme
of the crystal, can be situated in one of three possible positions with respect to the lattice.

and hexagonal bonds, while 6H
−SiC is two-thirds cubic. Despite the cubic elements, each has
overall hexagonal symmetry. All these polytypes have higher periodicity (more Si-C bilayers)
along the c-axis than 2H-SiC and they are in general called α -SiC together with 2H-SiC. 4H-
and 6H-SiC are the most common polytypes, and single crystal wafers of these polytypes are
currently available and hence all recent research for making commercial devices out of SiC are
focused on these polytypes.
3. Empirical tight-binding model for hexagonal and n-hexagonal systems: General
formalism of the tight-binding model for (0001) wurtzite:
The tight-binding approximation for band structure calculations uses atomic energy
parameters and the expansion of the electron wave functions in terms of a linear combination
of atomic orbitals (LCAO). In the LCAO method, the basic problem is to find the Hamiltonian
matrix elements between the various basis states, as in the original paper of Slater and
Koster (70); the matrix elements can be written for the basis functions sp
3
considering
various possible interactions. In our recent calculations, a standard semi-empirical sp
3
s*
tight-binding method (71) has been employed and the matrix elements are parametrized in
order to reproduce the principal features to know the band structures.
The general form of the Hamiltonian is (72).
H
(
k
)
=
∑
bb


’s (SL geometry),
we can construct the Hamiltonian matrix and diagonalize it directly for the eigensolutions.
In our recent study, we have performed a TB method with an sp
3
s
∗
basis set (71). We used the
nearest-neighbor TB parameters with a basis of five orbitals (s, p
x
, p
y
, p
z
, and s*) per atom.
We have derived a TB Hamiltonian pH (p
= 2,4, 6, 8, ) for different polytypes of SiC from
the wz TB model. The label pH (p
= 2, 4, 6, 8, ) is the hexagonality for different polytypes.
Consider a TB Hamiltonian of two different alternating wz crystals labelled ”ca” in (0001)
394
Silicon Carbide – Materials, Processing and Applications in Electronic Devices
Opto-Electronic Study of SiC Polytypes: Simulation with Semi-Empirical Tight-Binding Approach 7
direction, where c and a are labelled cation and anion atoms. The pH (p = 2, 4, 6, 8, ) contains
2
(2n) atoms in a unit cell at R
i
with five orbitals each; |αj >, where α denotes the s, x(= p
x
),
y

α
, R
l
> (2)
Here ξ is a quantum number that runs over the basis orbitals s, s*, p
x
, p
y
, and p
z
on the
different types of sites α in a unit cell. The N wave vectors k lie in the first BZ with the origin
of the lth unit cell at R
l
, and r
α
represents the positions of the atoms in this unit cell.
The electronic eigen-states of the pH (p
= 2, 4, 6, 8, ) are expanded as :
|k, λ > =
∑
ξ,α
< ξ, r
α
, k|k, λ > |ξ, r
α
, k > (3)
=
∑
ξ,α

λ
(
k
)
δ
ξξ

δ
αα


< ξ, r
α
, k|k, λ >= 0 (4)
Therefore, we obtain the Hamiltonian matrix for pH (p
= 2, 4, 6, 8, ).
12 3 n
−1 n 12 3 n
(5)
H
=
1
2
3
4
n
−1
n
1
2

0
ca
Hc H
0
ac
Ha
Hc
.
.
.
Ha
Hc H
0
ac
Ha Hac
Hc H
0
ac

Ha Hac
Hc
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥


aac
ac
+
c

, H
0ac
=

aa ac
ca cc

(6)
395
Opto-Electronic Study of SiC Polytypes: Simulation with Semi-Empirical Tight-Binding Approach
8 Silicon carbide
Fig. 3. Brillouin zones of (a) cubic (b) hexagonal structures.
The diagonal elements H
(j = a, and c) correspond to intra-site energies, and the others
contain the nearest atomic interactions in the same layer (H
ij
) or between two neighbor
layers (H
0ij
) perpendicular to the (0001) direction. The terms a and c are regarded as
the anion and cation atoms of the SiC semiconductor. The intra-material elements in the
Hamiltonian can be formed uniquely by using the corresponding bulk parameters. Our TB
parameters (62) give the correct indirect and direct gap in comparison with Ref.(73) and are
checked for their transferability to all considered structures by calculating the optoelectronic

global CBM to be very flat along the ML line and the CBM resides at some place on the line,
resulting in six equivalent CBMs (22), (25), (78),(79). This has been confirmed experimentally
from the Raman scattering measurement by Colwell et al. (80). However, the exact location of
the CBM and the detailed shape of conduction band affecting the determination of effective
electron mass are not yet well-established, either experimentally or theoretically. There are
similarities between the band structures of the hexagonal polytypes, both in the valence
and the conduction bands, especially between 4H, 6H and 8H-SiC structures. A significant
difference between 2H and the other three hexagonal polytyes is that in 2H-SiC the two lowest
conduction bands have an intersection along MK line and that the lowest band at K point has
a one-dimensional representation (in the single group representation). Both in 4H, 6H and
8H-SiC the two lowest conduction bands at K point are degenerate. The intersection in 2H-SiC
makes it possible for the second lowest band at the M point to provide a global conduction
band minimum at the K point with C
3v
symmetry whereas the minimum for 4H-SiC is at
M(C
2v
) and for 6H-, and 8H-SiC along the ML line (also C
2v
symmetry), 44 % out from M
towards L. The variation in band energy gaps is coming from the different locations of CBMs.
This is related with the stacking and period of each polytype. Interestingly, it is predicted
theoretically that the offsets of VBMs among different polytypes are quite small, at most
0.10-0.13 eV for the case of 2H and 3C (11),(14). In other words, the VBMs of all polytypes
are similarly located in energy. This means that the considerable variation of band gap for
different polytypes is mainly due to the difference of CBM location.
Another interesting point to note in the conduction band structures of SiC polytypes is the
location of second CBM. According to the calculation done by Persson et al. (26),(38), the
second CBM of 3C-SiC is at the same symmetry point (X) as the first one with 2.92 eV higher
in energy and this was confirmed experimentally from optical absorption measurements