Structural and optical characteristics of in-situ sputtered highly oriented 15R-SiC thinfilms on different substratesSatyendra Mourya, Jyoti Jaiswal, Gaurav Malik, Brijesh Kumar, and Ramesh Chandra

Citation: Journal of Applied Physics 123, 023109 (2018);View online: https://doi.org/10.1063/1.5006976View Table of Contents: http://aip.scitation.org/toc/jap/123/2Published by the American Institute of Physics

Structural and optical characteristics of in-situ sputtered highly oriented15R-SiC thin films on different substrates

Satyendra Mourya,1,2 Jyoti Jaiswal,1 Gaurav Malik,1 Brijesh Kumar,2

and Ramesh Chandra1,a)

1Thin film Laboratory, Institute Instrumentation Centre, Indian Institute of Technology Roorkee,Roorkee-247667, India2Department of Electronics and Communication Engineering, Indian Institute of Technology Roorkee,Roorkee-247667, India

(Received 29 September 2017; accepted 24 December 2017; published online 12 January 2018)

In this work, we have reported the in-situ fabrication of nanocrystalline rhombohedral silicon

carbide (15R-SiC) thin films by RF-magnetron sputtering at 800 �C substrate temperature. The

structural and optical properties were investigated for the films grown on four different substrates

(ZrO2, MgO, SiC, and Si). The contact angle measurement was performed on all the substrates to

investigate the role of interfacial surface energy in nucleation and growth of the films. The XRD

measurement revealed the growth of (1 0 10) orientation for all the samples and demonstrated bet-

ter crystallinity on Si substrate, which was further corroborated by the TEM results. The Raman

spectroscopy confirmed the growth of rhombohedral phase with 15R polytype. Surface characteris-

tics of the films have been investigated by energy dispersive x-ray spectroscopy, FTIR, and atomic

force microscope (AFM) to account for chemical composition, bonding, and root mean square sur-

face roughness (drms). The optical dispersion behavior of 15R-SiC thin films was examined by vari-

able angle spectroscopic ellipsometry in the wide spectral range (246–1688 nm), including the

surface characteristics in the optical model. The non-linear optical parameters (v3 and n2) of the

samples have been calculated by the Tichy and Ticha relation using a single effective oscillator

model of Wemple and Didomenico. Additionally, our optical results provided an alternative way to

measure the ratio of carrier concentration to the effective mass (N/m*). These investigated optical

parameters allow one to design and fabricate optoelectronic, photonic, and telecommunication

devices for deployment in extreme environment. Published by AIP Publishing.https://doi.org/10.1063/1.5006976

I. INTRODUCTION

Silicon carbide (SiC) has a prodigious potential in harsh

environment, extreme temperature, high-power, and high-

frequency operation regime due to its exceptional physical

and chemical properties, particularly its tunable wide

bandgap (2.3–3.2 eV), excellent hardness (3800 MPa), high

thermal conductivity (5 W/cm-�C), polytypism, super plastic-

ity, high critical breakdown field (5� 106 V/cm), and good

chemical inertness.1–6 Due to these exceptional properties,

SiC may outclass conventional semiconductor (Silicon:Si and

Germanium:Ge) based devices, providing high power output

and better thermal management. As a result, scientific frater-

nity across the globe has accepted this material as a potential

candidate for various research and technological applications.

These include microwave absorbers, high-frequency resona-

tors, bioimaging probes, optoelectronics, integrated optics,

radiation sensors, high-temperature gas sensors, spintronics,

electron devices, very large scale integration (VLSI) technol-

ogy, supercapacitors, and nano/micro electromechanical sys-

tem (NEMS/MEMS) devices.1–3,7–18

Nowadays, optical properties of SiC thin films have

attracted researchers’ attention in many fields such as photo-

diodes, phototransistors, photoconductive switches, solar

cells, extreme ultraviolet (EUV) reflectors, and astrophys-

ics.19–24 The optical dispersion behavior of SiC thin films

must be explored in depth to design and fabricate such opto-

electronic and photonic devices, as the semiconductor mate-

rials are characterized by their unique complex dielectric

functions.

A large number of publications have already been

reported on the determination of the optical constants of dif-

ferent polytypes of SiC.25–31 Kildemo26 has done an exhaus-

tive study on the optical properties of bulk SiC polytypes in

the spectral range of 300–1100 nm and concluded that the

dielectric function is strongly influenced by the polytypism.

Further, Larruquert et al.27 have probed the optical constants

of amorphous SiC thin films by ellipsometry in the spectral

range of 190–950 nm without considering the optical stack

model, whereas Zollner et al.29 have explored the dielectric

properties of the commercially procured hexagonal SiC sub-

strate by ellipsometry in the broad spectral range

(188–1722 nm), including surface characteristics in the opti-

cal stack model. Recently, Qamar et al.25 have studied the

temperature (850–950 �C) dependent optical dispersion

behavior of sputtered 8H-SiC films in the spectral range of

350–900 nm. Hence, on the basis of available literature, we

have concluded that there are still several key challenges

such as polytypism, crystallinity, phase purity, surface char-

acteristics, and broad spectral range pertaining to thea)Author to whom correspondence should be addressed: ramesfic@iitr.ac.in

0021-8979/2018/123(2)/023109/13/$30.00 Published by AIP Publishing.123, 023109-1

JOURNAL OF APPLIED PHYSICS 123, 023109 (2018)

investigation of the optical properties of SiC, which is not

being addressed in detail. Additionally, the effect of sub-

strate on the growth rate and optical properties of the 15R-

SiC film have not been reported yet, since the surface energy

of the substrate is a key parameter which plays an important

role in the minimization of the free energy of the system, as

a criterion for stabilities in the system and forward change in

the growth process. So, it becomes quite interesting to study

the tunability in optical and structural properties of 15R-SiC

thin films grown on a variety of semiconductors and oxide

substrates. The reason for choosing these substrates is to

develop crystalline SiC films for diverse applications to cater

for the need of cutting-edge technology.

Up to now, significant processes have been made in the

growth of crystalline SiC films, with a special emphasis on

the 6H- and 4H- and 3C polytypes, which require high sub-

strate temperature (1000–1400 �C),3,32–36 causing large

residual stress, micro pinholes, and cracks, resulting in poor

quality SiC thin films.37 These defects are detrimental for

device applications, and to overcome this 15R-SiC thin films

are ideal candidates, as they can be grown at relatively low

temperatures using RF-magnetron sputtering and have a tun-

able wide bandgap (2.8–3.1 eV), which may be useful to

realize short wavelength emitter and detecting devices.

Sch€orner et al.38 have also discussed the improved electrical

properties of the 15R-SiC based MOS device over other pol-

ytypes. So, it becomes important to explore structural and

optical properties of 15R-SiC thin films in detail.

The purpose of this work is to investigate the structural,

optical, and dispersion energy parameters of nanocrystalline

15R-SiC thin films grown in-situ by RF-magnetron sputter-

ing on four different substrates (Zirconia:ZrO2, Magnesium

oxide:MgO, Silicon carbide:SiC, and Silicon:Si) using spec-

troscopic ellipsometry (SE) in the broad spectral range,

accounting the surface characteristics (roughness and com-

position) in the optical stack model. Further, we have corre-

lated the structural and optical properties of the samples

under investigation.

II. EXPERIMENTAL

Highly nanocrystalline 15R-SiC thin films were fabri-

cated on four different substrates, i.e., ZrO2, MgO, SiC, and

Si, maintained at a temperature of 800 �C by RF-magnetron

sputtering, using a 99.99% pure commercial SiC target

(50.8 mm dia. and 5 mm thick) as shown in Fig. 1. The target

is stacked in on-axis sputter-up configuration having 5 cm

distance from the substrate. Initially, all the substrates were

cleaned by the RCA procedure followed by an ultrasonic

acetone clean for 15 min. The custom designed sputtering

chamber (381 mm dia., in-house with Molybdenum (Mo)-

heater) was initially evacuated with the help of a rotary

pump (DUO 10M, PFEIFFER VACUUM, Germany) to a

roughing pressure of 1� 10�2 Torr and further backed by a

turbo molecular pump (HIPace 700, PFEIFFER VACUUM,

Germany) to a base pressure of 1� 10�6 Torr. Before start-

ing the sputtering process, cooling was provided to both gun

and Mo-heater by employing chiller (CKL-20, ESCY

Enterprises Pune, India). When the temperature of Mo-

heater reached 800 �C, the inert argon (Ar) gas (Sigma gases

services, New Delhi, India) was blown into the sputtering

chamber at a flow rate of 20 sccm controlled by a mass flow

controller (mks PR4000B, mks Instruments Deutschland

GmbH, Germany). Finally, the RF power source (Cesar 136,

600 W, 13.56 MHz, Advanced Energy, USA) was employed

to establish the plasma. The optimized sputtering parameters

are listed in Table I. After the deposition, the chamber

remains into vacuum until the room temperature (RT) is

achieved. The 15R-SiC thin films deposited at ZrO2, MgO,

FIG. 1. Schematic diagram of synthe-

sis and characterization for 15R-SiC

thin films on four different substrates.

023109-2 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

SiC, and Si are hereafter abbreviated as SiC@ZrO2,

SiC@MgO, SiC@SiC, and SiC@Si, respectively.

The crystal structure and crystallinity of the representative

samples were investigated using Grazing angle X-ray diffrac-

tometer (GAXRD) (D8 advance, Bruker, USA, with CuKa radi-

ation (40 kV, 40 mA), kCu¼ 1.5406 A˚, step¼ 0.02�, scan

speed¼ 1 s/step) at RT. The polytypism of the samples was

investigated using Raman spectrophotometer (RE 04,

Renishaw, UK) operating at an excitation wavelength of

514 nm (Argon laser). The transmission electron microscope

(TEM) (TECNAI G2, 200 keV, FEI, USA) was employed to

authenticate the crystallinity in the grown films. A field emis-

sion scanning electron microscope (FESEM) (Ultra Plus,

20 keV, Carl Zeiss, Germany), operated in the secondary elec-

tron mode, was used to measure the cross-sectional thickness of

the grown films. Atomic force microscope (AFM) (NATEGRA

Prima, NT-MDT Spectrum Instruments, Russia) having silicon

nitride (Si3N4) coated tip of pyramid type geometry, operated

in tapping mode, was used to analyze the topography of the

representative samples. The compositional analysis of the 15R-

SiC films was done by an energy dispersive x-ray spectroscopy

(EDX) fastened in FESEM. Fourier transform infrared spectros-

copy (FTIR) (NICOLET 6700, Thermo Fisher Scientific,

Germany) analysis was performed in the mid-IR range

(4000–400 cm�1) to fingerprint the Si-C bond in grown films

and data were processed using OMNIC v6.1 software. To mea-

sure the optical properties of the films, nondestructive, univer-

sally accepted and highly reliable method of determining

optical dispersion parameters by using Variable angle spectro-

scopic ellipsometry (VASE) (J. A. Woollam M2000, J. A.

Woollam Co., USA) at an angle of incident of 65� and operat-

ing in the spectral range of 246–1688 nm (step size: 1.5899 nm,

spot size �3 mm) was employed.

III. RESULTS AND DISCUSSION

Figure 2 exhibits the XRD diffractogram of 15R-SiC

thin films deposited on four different substrates, i.e., ZrO2,

MgO, SiC, and Si. The XRD analysis reveals a single peak

centered on 2h¼ 35.37� corresponding to the crystallo-

graphic orientation (1 0 10), which indicates the formation of

single nanocrystalline SiC with a rhombohedral structure

[Ref. JCPDS-ICDD no. 00–002–1042]. The highly ordered

growth of the film along the crystallographic orientation (1 0

10) is due to minimization of surface energy for this plane

under optimized deposition conditions.39–41 Further, it has

been observed that the full width at half maxima (FWHM) of

crystallographic orientation (1 0 10) of the films changes

with the change in substrates. This may be attributed to the

different interfacial energies (i.e., surface energies) for dif-

ferent substrates. Moreover, the XRD diffractogram (Fig. 2)

of the films deposited on Si and MgO substrates shows the

lowest and highest values of FWHM (listed in Table II) for

the crystallographic orientation (1 0 10), respectively, which

indicates the variation in crystallite size and crystallinity of

the films. The average crystallite size (t) of the representative

samples was calculated using Scherer’s formula42 and is

listed in Table II. Inset of Fig. 2 shows the FESEM cross-

section image of the sample SiC@Si. It is difficult to

measure the cross-sectional image for other samples, as the

substrates on which they have been grown are hard enough

and require a motorized cutting machine to cut them, result-

ing in a poor film-substrate interface, which is very hard to

resolve using SEM. Further, SE is employed to determine

the film thickness of all the samples (tabulated in Table II)

and well corroborated with the FESEM result. We have

found different average crystallite sizes and film thicknesses

for the sample deposited on different substrates. The highest

and smallest average crystallite size was found for the sam-

ples deposited at Si and MgO, respectively, and the film

thickness has also followed the same trend. This may be

explained with the help of the thin film growth mechanism,

i.e., the thermodynamics of adsorption and the grain growth

kinetics. Noticeably, as per the basic theory of nucleation

and growth of thin films, an optimized minimum free energy

leads to maximum number of nucleation sites.43,44

To validate this hypothesis, we have determined the sur-

face energy of all the substrates, i.e., ZrO2, MgO, SiC, and

Si using water contact angle measurement. As shown in Fig.

3(a), the observed water contact angle (hw) varies with the

substrates. We have found highest and lowest hw values for

the substrates MgO and Si, respectively. Wenzel45 proposed

a relation between hw and interfacial energies, i.e., solid-

liquid (csl), liquid-vapor (clv) and solid-vapor (csv) for rough

surfaces given by the following equation:

TABLE I. The sputtering parameters for the deposition of nanocrystalline

15R-SiC thin films.

Sputtering parameters

Target SiC

Substrates ZrO2, MgO, SiC, and Si

Base pressure 2 � 10�6 Torr

Working pressure 5 mTorr

Deposition power 150 W

Deposition time 2 h

Substrate temperature 800 �C

Target-substrate distance 5 cm

Gas used Ar (20 sccm)

FIG. 2. XRD spectra of 15R-SiC thin films fabricated at various substrates

and the inset shows the cross-section image of the sample grown at Si

substrate.

023109-3 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

coshw ¼ rwcsv � csl

clv

� �; (1)

where hw and rw are the water contact angle and the rough-

ness factor, respectively. The surface energy of all the sub-

strates was determined by using the Owens-Wendt and Wu

method.46,47 It has been observed [Fig. 3(b)] that the surface

energy csv of all the substrates calculated by both methods

follows the same trend. Highest and smallest csv was found

for Si and MgO substrates, respectively. In order to under-

stand the physics of substrate-dependent growth of the 15R-

SiC films, the growth rate r (ratio of film thickness to deposi-

tion time) and average crystallite size t in terms of csv have

been displayed in Figs. 3(c) and 3(d), respectively. It exhibits

a linear dependence on csv and concludes that there exists a

trend in which average crystallite size and film thickness

increase with an increase in substrate’s surface energy.

Further, a simple model (linear fit) can be developed to

explain the obtained functional csv–t and csv–r relationship

for 15R-SiC films and yields a good linear fit.

On the other hand, a close analysis of XRD diffracto-

gram revealed a trivial shift in the XRD peak position of the

15R-SiC films fabricated on different substrates, which

indicates the expansion or contraction of lattice correspond-

ing to the left and right shift, respectively. These peak shifts

may be ascribed to the presence of lattice strain in the sam-

ples.43,48 To gain further insight into structural properties,

the lattice strain (e) of the 15R-SiC thin films was calculated

using the formula [Eq. (2)]

e ¼ d � d0

d0

; (2)

where d is the interplanar spacing of the strained 15R-SiC

films obtained from XRD analysis and d0 is the interplanar

spacing in ideal conditions extracted from XRD database

(JCPDS-ICDD No. 00-002-1042). The calculated d values

are listed in Table II, and it was found that d changes with

the substrates used. The values of e are computed using the

above relationship and summarized in Table II. The value of

the lattice strain was found both positive and negative in our

case, which indicates tensile and compressive nature of

stress, respectively.49 It is noticeable from Table II that there

exists an inverse linear relationship between t and magnitude

of e; i.e., the film having highest average crystallite size is

the most oriented due to minimum lattice strain.

TABLE II. The structural and morphological properties of 15R-SiC thin films fabricated at various substrates.

Sample t (nm)

D (�nm) d (A)

e (%)

drms (�nm)

FWHM (deg) d (1011 line/cm2)SE FESEM XRD TEM AFM SE

SiC@ZrO2 15.9 1635 2.538 0.31 1.66 1.73 6 0.28 0.535 3.95

SiC@MgO 10.9 1520 2.559 1.14 3.12 2.99 6 0.11 0.774 8.41

SiC@SiC 16.4 1650 2.524 �0.23 1.28 1.57 6 0.05 0.518 3.71

SiC@Si 17.7 1690 1720 2.535 2.519 0.19 1.10 1.41 6 0.15 0.482 3.19

FIG. 3. The variation of water contact

angle hw (a) and the calculated surface

energy csv values using both Wu and

Ownes and Wendt method (b) with

four different substrates, i.e., ZrO2,

MgO, SiC, and Si. The growth rate r(c) and average crystallite size t (d)

variation as a function of substrate’s

surface energy csv.

023109-4 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

Furthermore, TEM analysis was also performed to con-

firm the crystallinity as well as to determine the lattice

parameters. We have prepared TEM sample of the 15R-SiC

film deposited on the Si substrate only because TEM sample

preparation for other substrates used in this article is very

arduous, as they are very hard to grind and polish. The high

resolution (HR) TEM and selected area electron diffraction

(SAED) images are shown in Figs. 4(a) and 4(b), respec-

tively. The SAED image consists of three diffraction rings,

confirming the crystalline behavior of the grown 15R-SiC

thin film. These rings correspond to crystal orientations (1 0

10), (1 0 12), and (1 0 58). In addition, no diffraction ring

was observed for the native oxide formed on the top of the

grown film; this may be ascribed to its glassy nature. A char-

acteristic interplanar spacing of 2.519 A has been observed

corresponding to the (1 0 10) crystallographic plane. Figures

4(c)–4(f) show the EDX spectra of the 15R-SiC thin films

grown on various substrates. It reveals the presence of Si and

C in the films having good stoichiometry. A little atomic per-

centage (<4%) of oxygen has been detected in all the

samples, which indicate the presence of native oxide on the

film surface. No other elements were detected as an impurity,

which indicates the formation of high purity 15R-SiC thin

films.

Raman spectroscopy is considered to be the most power-

ful tool to find out the useful information about the crystal-

line phases and quality, crystal symmetry, local lattice

distortion, dislocation density, and the presence of impurity

phases.50,51 Figures 5(a)–5(d) manifest the Raman spectra of

15R-SiC thin films grown on different substrates. It has been

observed that all the samples show a typical 15R-SiC trans-

verse optical (TO) phonon mode peak, located in the range

of 750–800 cm�1.52,53 Additional Raman peaks appearing at

571 and 580 cm�1 corresponding to the films grown on ZrO2

and MgO substrates can be assigned to the fundamental

Raman active longitudinal acoustic (LA) mode of rhombohe-

dral phase of 15R-SiC as given in Table III. However, the

shoulder peaks at 925 and 932 cm�1 for SiC and Si substrates

match well with the longitudinal optical (LO) phonon mode

of 15R-SiC.52 A little shift in TO peak towards lower wave-

number for the film grown on MgO substrate is observed

compared to ZrO2 and Si substrates, which may be attributed

to the increase in tensile strain for the film grown on MgO

substrate. As, it is well known that the bond length between

atoms decreases with either decreasing tensile or increasing

compressive strain; consequently, the force constant and the

vibrational frequencies increase.49 This also indicates poor

crystallinity of the film grown on MgO substrate, which is in

good agreement with the XRD analysis. Additionally, suffi-

cient broadening and reduction of the TO peak intensity of

all the samples indicate the presence of various defects

including lattice vacancies, local lattice disorder, and dislo-

cations. Further, the existence of impurities is confirmed by

the presence of shoulders, like one observed at 650 cm�1 for

the film grown on Si substrate. It may be attributed to the

interdiffusion of sputtered atoms into the Si substrate at such

high deposition temperature. Furthermore, the lowest value

of FWHM for TO peak in the case of Si substrate authenti-

cates this film to be the best crystalline and is well corrobo-

rated by XRD and TEM results. The shoulder appearing at

703 cm�1 for SiC substrate is difficult to define and remains

unassigned.

IR absorption of the synthesized 15R-SiC thin films was

measured using FTIR spectroscopy to identify the chemical

bonding and nature. Figure 6 illustrates the FTIR spectra of

all the samples having broad and strong absorption bands

with shallow interference fringes. This may be ascribed to

the existence of a graded refractive index in the system (sub-

strates, films, and air), which leads to a contrast in the refrac-

tive index between the film and the substrate.54 In addition,

the FTIR spectroscopy exhibited two absorption peaks at

672 and 1054 cm�1, which correlate with the transverse opti-

cal (TO) phonon and stretching vibration mode of Si-C and

Si-O, respectively.55,56 The 15R-SiC absorption band (Si-C)

is observed at a lower wave number 672 cm�1 than those for

the 3 C-SiC phonon mode (780 cm�1). It may be attributed to

the difference in the absorption properties of different poly-

types of SiC. However, the Si-O absorption band is attrib-

uted to the native oxide layer formed on the top of the film

FIG. 4. HRTEM image (a) and SAED pattern (b) of the film grown at Si

substrate. (c)–(f) EDX spectra of the films grown at four different substrates,

i.e., ZrO2, MgO, SiC, and Si.

023109-5 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

surface and has good concurrence with EDX results. The

FTIR transmission peak of the film prepared at Si substrate

is narrower than the peak of the films prepared at other sub-

strates, which is a comprehensible evidence in the enhance-

ment of bonding uniformity within the film. Further, it is

interesting to discuss the variation in the intensity of FTIR

spectra of the investigated films. The highest intensity indi-

cates more and more formation of 15R-SiC and is highly

dependent on nucleation thermodynamics, i.e., substrate to

film interfacial surface energy, and is well corroborated with

XRD and surface energy measurements.55

Knowing the fact that root mean square surface rough-

ness (drms) plays a vital role in determining the unique opti-

cal constants (refractive index n and extinction coefficient k)

of the grown samples,40,57 we have performed the AFM mea-

surement to determine drms. A scanning area of 5� 5 lm was

selected for all the samples with tapping mode of scan.

Figures 7(a)–7(d) present 3D AFM micrograph of 15R-SiC

thin films deposited on various substrates, showing spherical

ball like regular features of nanometer size grains. Further,

the drms was calculated from the AFM micrographs and tabu-

lated in Table II. The value of drms was found to be in the

range of 1.1–3.12 nm, lowest and highest for the films grown

on Si and MgO substrates, respectively. This kind of varia-

tion in drms may be ascribed to the variation in the average

crystallite size40 and is well corroborated with the XRD

results. Such fabricated smooth (i.e., low roughness) 15R-

SiC thin films may favor the calculation of unique optical

properties using SE. It may also be used as a potential candi-

date for protective coatings.

The thickness and optical constants of the grown 15R-

SiC films were probed by variable angle spectroscopic ellips-

ometry (VASE), regarded as a non-destructive optical tech-

nique. A relative change in phase and amplitude of the

linearly polarized monochromatic light incident upon the

sample surface after oblique reflections was measured by

FIG. 5. Raman spectra of the 15R-SiC

thin films fabricated at four different

substrates, i.e., ZrO2, MgO, SiC, and

Si.

TABLE III. Comparison of Raman band frequencies obtained for 15R-SiC thin film grown at different substrates with reported literature for different poly-

types of SiC bulk crystals. The boldface values that appear in the table are the experimentally observed Raman bands of the 15R-SiC thin films fabricated at

different substrates.

Experimentally observed Raman frequencies of 15R-SiC thin films (cm�1) 571, 580, 703, 797, 794, 800, 806, 925, 932

SiC PolytypeRaman band positions (cm�1)

TA LA TO LO

3C (b) 796 972

2H (a) 264 764 799 968

4H (a) 196 204 266 610 776 796 838 964

6H (a) 145 150 236 241 266 504 514 767 789 797 889 965

15R (a) 167 173 255 256 331 337 569 577 767 789 797 800 932 938 956

023109-6 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

this technique. The SE measurement yields the angles w (azi-

muth) and D (phase change), given by the following

equation:55,59

q ¼ rp

rs¼ tanwexp iDð Þ; (3)

where rp and rs represent the complex reflection coefficients

of the polarized light (polarization occurs perpendicular and

parallel to the plane of incidence). The experimental data

were fitted to the Tauc-Lorentz dispersion model to extract

optical dispersion behavior of 15R-SiC thin film and given

by the following eqution:60

e2 Eð Þ ¼ ALE0C E� Egð Þ2

E2 � E2o

� �þ C2E2

:1

E

" #; (4)

where E0 and Eg represent the resonance energy and bandgap

energy, E stands for photon energy, and C, AL is the repre-

sentation of the broadening coefficient and amplitude of e2

peak, respectively. It is very important to remember the

direct relationship between the complex dielectric function

and optical constants (refractive index n and extinction coef-

ficient k), i.e., e1 ¼ n2 � k2; e2 ¼ 2nk in the linear regime.

We need to construct an optical stack model of the repre-

sentative samples to fetch significant physical and optical

parameters from raw SE data, which usually accounts for a

number of distinct layers having individual optical dispersion.

In addition, refraction and reflection also occur at the interfa-

ces between these layers (optical boundaries) as per the

Fresnel relations. Figure 8(a) represents the schematic of opti-

cal stack model of the samples SiC@Si and SiC@SiC, having

an air ambient, a surface roughness layer, surface oxide layer

(SiO2 containing C species), a SiC film, and a surface interface

(SiO2 for Si; SiO2 containing C species for SiC) on Si and SiC

substrates. However, Fig. 8(b) exhibits the schematic of optical

stack model of the samples SiC@ZrO2 and SiC@MgO, hav-

ing an air ambient, a surface roughness layer, a surface oxide

layer (SiO2 containing C species), and a SiC film on ZrO2 and

MgO substrates. To fit the experimental data accurately, the

surface roughness and surface interface layers were considered

in the optical model. The thickness of surface interface layer

was assumed to be 1.6 nm (Ref. 61) and 1 nm (Ref. 62) for Si

and SiC substrates, respectively. Further, we have also consid-

ered the native oxide layer63 on the top of the grown films, as

EDX and FTIR results have also ensured the existence of oxy-

gen on the sample surface. Furthermore, a recipe of each layer

has been defined before fitting the experimental SE data, i.e.,

the surface roughness was modeled as per effective medium

approximation (EMA) theory, which is a 50:50 model (a mix-

ture of 50% surface material and 50% voids) and its dispersive

function is referred from Bruggeman.57,58 The optical disper-

sion of the surface oxide layer (SiO2 containing C species) on

SiC film is also considered as per the Bruggeman EMA theory.

The complex dielectric function of SiC is framed by the most

appropriate general oscillator model along with the Tauc-

Lorentz dispersion model. Two Lorentz oscillators are consoli-

dated in this model. The thickness of the substrates is kept

fixed in the optical stack model 0.50, 0.50, 0.25, and 0.67 mm

corresponding to ZrO2, MgO, SiC, and Si, respectively.

The wavelength dependent SE parameters, w and D,

determined for 15R-SiC thin films grown at various sub-

strates can be fitted with the above discussed appropriate

optical stack model to evaluate film thickness and unique

optical constants (n and k), as shown in Figs. 9(a)–9(d). The

obtained results of 15R-SiC thin films (Fig. 9) indicate a

good match between the exp. and simulated data. The mean-

squared error (MSE) in the simulation was minimized using

a Levenberg-Marquardt regression algorithm given by the

following equation:

MSE¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2N�M

XN

i¼1

wexpi �wcalc

i

rexpwi

!2

þ Dexpi �Dcalc

i

rexpDi

!28<:

9=;

vuuut ;

(5)

where wcalci , Dcalc

i and w expi , D exp

i are the calculated and

experimental ellipsometry functions, respectively, N repre-

sents the total number of w, D pairs measured, M indicates

the total fitted parameters in the optical model, and r standsFIG. 7. AFM micrographs of the 15R-SiC thin films fabricated at various

substrates (a) ZrO2, (b) MgO, (c) SiC, and (d) Si.

FIG. 6. FTIR spectra of the 15R-SiC thin films fabricated at four different

substrates, i.e., ZrO2, MgO, SiC, and Si.

023109-7 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

for standard deviation in the experimental data. The experi-

mental and simulated W and D exhibit an excellent fit in the

wide spectral range, which is evident from Figs. 9(a)–9(d).

The fitting parameters within the parametric dispersion

model yielded thickness and surface roughness of the sam-

ples fabricated at various substrates ZrO2, MgO, SiC, and Si

about 1635, 1520, 1650, and 1690 nm, and 1.73 6 0.28,

2.99 6 0.11, 1.57 6 0.05, and 1.41 6 0.15 nm, respectively,

which are in good agreement with measured FESEM cross-

section image (inset of Fig. 2) and AFM data (Fig. 7), sug-

gesting a reliable fitting procedure. These calculated values

from SE are tabulated in Table II, for comparison with the

values obtained from other characterization tools. In addi-

tion, the thickness of native oxide was found to be

1.01 6 0.04, 0.91 6 0.01, 1.01 6 0.06, and 1.21 6 0.04 nm in

accordance with samples deposited on different substrates

ZrO2, MgO, SiC, and Si, respectively, which have good

agreement with previously reported results.62

Figure 10(a) depicts the dispersion of refractive index (n)

in the measured wavelength (k) range of 246 to 1688 nm for

15R-SiC thin films grown on various substrates. As depicted

by the spectra, n decreases with the increasing wavelength.

This decreasing nature of the n shows the normal dispersion

behavior of the representative samples. Further, a substrate-

dependent variation in the n has been observed. The values of

the substrate-dependent refractive index of 15R-SiC films at

different k (540.0 and 632.8 nm) are tabulated in Table IV.

From Table IV, it is evident that the films deposited on Si sub-

strate have the highest value of refractive index compared to

the films deposited on ZrO2, MgO, and SiC, i.e., nSi > nSiC

> nZrO2> nMgO which may be attributed to the increase in the

structural order, improved crystallinity, reduced lattice strain,

and lowest dislocation density d (quantitative measure of

imperfection in crystal) of the film and is in well agreement

with the XRD results (Table IV). This fact leads to the fabri-

cation of 15R-SiC film on the cubic crystalline Si substrate

having lowest defects compared to the films deposited on

crystalline cubic ZrO2, cubic MgO, and hexagonal SiC sub-

strates, as confirmed by dislocation density and lattice strain

calculation using XRD data (Table IV).

Figure 10(b) depicts the wavelength dependent extinc-

tion coefficient k of 15R-SiC thin films grown at various

FIG. 8. Schematic of optical stack

model of 15R-SiC thin films on (a) Si

and SiC, and (b) ZrO2 and MgO sub-

strates, used to analyze the spectro-

scopic ellipsometry data.

FIG. 9. Experimental (circle with solid

line; red and green) and best match

model fitted (solid lines; black) W and

D spectra at an incidence angle of 65�

for 15R-SiC thin films deposited at

various substrates (a) ZrO2, (b) MgO,

(c) SiC, and (d) Si.

023109-8 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

substrates. It can be concluded from Fig. 10(b) that the kvalue of the 15R-SiC thin films also decreases with the

increase in wavelength, which also indicates the normal dis-

persion behavior of the representative samples. The value of

the extinction coefficient k is consistently close to zero in the

higher wavelength region of the spectrum, indicating losses

occurring due to absorption. However, a sudden increase in

the k value in the UV region is attributed to the fundamental

FIG. 10. (a) Refractive index n, (b)

extinction coefficient k, (c) optical

bandgap Eg and corresponding inset

shows the variation of Eg with average

crystallite size t, (d) optical dispersion

behavior 1= n2 � 1ð Þ against h�ð Þ2,

and (e) nonlinear refractive index n2

variation as a function of t for 15R-SiC

thin films fabricated at various

substrates.

TABLE IV. Obtained results of optical and dispersion energy parameters of the 15R-SiC thin films grown at different substrates.

15R-SiC thin films prepared at different substrates

Optical properties SiC@ZrO2 SiC@MgO SiC@SiC SiC@Si

Refractive index, n at k ¼ 540.0 nm 2.7289 2.6588 2.7450 2.7707

at k ¼ 632.8 nm 2.6975 2.6282 2.7134 2.7389

Optical bandgap, Eg (eV) Tauc 3.1489 3.1411 3.1551 3.1595

WDD 3.7884 3.7805 3.7945 3.7990

Oscillator energy, Eo (eV) 7.5768 7.5611 7.5891 7.5980

Dispersion energy Ed (eV) 44.4381 41.7210 45.1257 46.1800

The static refractive index, n1 2.6201 2.5530 2.6355 2.6604

The dielectric constant, e1 6.8650 6.5178 6.9460 7.0779

The susceptibility, v 1ð Þ (esu) 0.46696 0.43932 0.47341 0.48391

The susceptibility, v 3ð Þ (10�12 esu) 8.0828 6.3324 8.5391 9.3219

Nonlinear refractive index, n2 (10�10 esu) 1.1623 0.9346 1.2208 1.3202

(10�17 m2/W) 1.8588 1.5338 1.9408 2.0793

Carrier concentration to the effective mass, N/m* (1049 kg�1 cm�3) 5.2655 5.0117 5.3204 5.4656

Plasma frequency, xp (cm�1) 792.89 793.88 792.35 795.57

023109-9 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

absorption around the band edge. Further, it has been

observed that the k values of the films change with substrates

used, leading to the lowest k values for the film deposited at

Si substrate. This behavior may be associated with the larger

crystallite size, lowest defects, and improved packing den-

sity, which is corroborated by XRD result and AFM micro-

graphs. The substrate-dependent k values may also validate

the variation in optical bandgap Eg.

The bandgap Eg of 15R-SiC thin films has been investi-

gated and correlated with the structural properties. It is a well-

known fact that the optical absorption exhibits an exponential

characteristic below Eg. According to the interband absorption

theory, the absorption follows a power law above the charac-

teristic absorption edge,64 given by the following equation:

ah� ¼ A h� � Egð Þm; (6)

where A is the constant which depends on the property of the

material, Eg represents the bandgap of the material, h� is the

energy of the incident photon, m is the transition coefficient

which denotes the nature of transition, and a is an absorption

coefficient having a relation with k, i.e., a ¼ 4pk/k. The vari-

ation of (ah�)1/2 as a function of the h� has been plotted in

Fig. 10(c). The Eg of the samples was extracted by extrapo-

lating the linear part of the curve to zero absorption, i.e.,

(ah�)1/2¼0. The bandgap Eg tunability of the grown samples

was observed and tabulated in Table IV. The highest Eg was

found for the film deposited at Si substrate compared to films

deposited on ZrO2, MgO, and SiC, i.e., (Eg)Si > (Eg)SiC

> (Eg)ZrO2 > (Eg)MgO. To understand this, we have plotted

the variation of Eg as a function of crystallite size as depicted

in an inset of Fig. 10(c). It has been found that the change in

Eg is not significant but increases linearly with increase in

the average crystallite size t. This rather small shift in the Eg

is due to the effect of both lattice strain and dislocation den-

sity, i.e., defect states. For lattice strain, we have found a

trend in which it decreases with an increase in the average

crystallite size (Table IV). The relationship indeed shows

that for a smaller strain, the bandgap is larger, and for a

higher one, the bandgap is smaller. While we have noticed

that there also exists a trend in which average crystallites

increase in size with a decrease in dislocation density (Table

II). The relationship indeed shows that for fewer defect

states, the bandgap is larger, and for a higher one, it is

smaller. However, the quantum confinement effect has not

been witnessed in this case because the average crystallite

size is greater than the Bohr radius (�1–6 nm) of SiC nano-

crystals65,66 for all the samples, as confirmed by XRD

results. Finally, it is apparent from the SE measurements that

the linear optical properties, i.e., n, k, and Eg of 15R-SiC thin

films are strongly substrate-dependent.

Moreover, we have also determined the dispersion

energy parameters, which play a vital role in determining the

optical characteristics of any material. They allow us to cal-

culate the required parameters for designing optical commu-

nication and spectral dispersion devices. We have used a

Wemple and Didomenico (WDD) single effective oscillator

model to explore the dispersion of the refractive index and

given by the following equation:67

n2 ¼ 1þ EdEo=E2o � h�ð Þ2; (7)

where Ed is the optical dispersion energy and has the direct

correlation with the structural properties of the samples. The

energy Eo is the single oscillator energy.

Figure 10(d) shows the plot of optical dispersion behavior

{1= n2 � 1ð Þ vs : h�ð Þ2} of the 15R-SiC thin films. By fitting

the curve [Fig. 10(d)], a straight line to the points, we have

extracted the oscillator parameters Eo and Ed. The slope depicts

(EoEd)�1 and the intercept represents the value of Eo/Ed. The

values of Eo and Ed are deduced and listed in Table IV. The

highest Ed value is observed for the sample prepared at Si sub-

strate, which indicates the improvement in the structural order

of the film because Ed is directly related to the atomic order. It

has been previously reported that the highly ordered materials

have the large dispersion energy.67 Further, WDD showed that

Eg < Eo, and Eo has a direct correlation with Eg, Eo � 2Eg, as

stated by Tanaka,68 which is in good agreement with experi-

mentally calculated Eg value (Tauc) using SE. We can note the

slight difference between Eg (Tauc) and Eg (WDD); however,

obtained Eg from Tauc and WDD follows the same trend with

different substrates. This could be explained by the WDD

model as it estimates the lowest bandgap energy.67

Furthermore, a close investigation of the 1= n2 � 1ð Þ vs : h�ð Þ2results in the static refractive index (i.e., long wavelength

refractive index, n1) using the following equation:67

n1 ¼ 1þ Ed=Eoð Þ1=2: (8)

The calculated values of the static refractive index n1and high-frequency dielectric constant ðe1 ¼ n2

1Þ are listed

in Table IV. Additionally, we have calculated the nonlinear

refractive index (n2) using linear optical parameters. It is well

known that when the materials are subjected to strong electric

fields, the linear relationship of polarization with the electric

field vanishes and the change in polarizability becomes equal

to the square of the electric, i.e., Dn¼ n2 hE2i, where n2 is the

nonlinear refractive index and hE2i is the time-averaged elec-

tric field of the optical beam.69

To investigate the n2 and third-order nonlinear suscepti-

bility v(3), a number of theoretical models have been reported

by various research groups, out of which Tichy and Ticha’s

model was implemented (using WDD parameters, n and Eg)

for assessment of nonlinear properties of the samples under

investigation.70 The accuracy of the models has already been

tested by concurring theoretical values with experimental

findings for more than hundred samples.70 The relation

between the linear susceptibility v(1) and third-order nonlin-

ear susceptibility v(3) in the long wavelength region is

approximately equal to the fourth power of v(1). Further, v(1)

and v(3) can be correlated analytically using Miller’s general-

ized rule as given in [Eq. (9)]70

v 3ð Þ ¼ B v 1ð Þ� �4

; (9)

where B¼ 1.7� 10�10 esu and the value of v(1) can be calcu-

lated in the long wavelength region using the following rela-

tion [Eq. (10)]:70

023109-10 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

v 1ð Þ ¼ n21 � 1

� �4p

: (10)

The substrate-dependent linear and third-order nonlinear

susceptibility of investigated films is tabulated in Table IV.

The obtained values of v(3) were compared with the pub-

lished data and found to have a good agreement.67 A large

value of v(3) is obtained for the 15R-SiC film fabricated at Si

substrate compared to films deposited on ZrO2, MgO, and

SiC, i.e., (v(3))Si> (v(3))SiC> (v(3))ZrO2> (v(3))MgO. It may be

attributed to the higher crystallinity, improvement in the

structural order, lowest lattice strain, and diminution of

defect states and well corroborated with the optical disper-

sion energy Ed and XRD results. Further, the nonlinear

refractive index n2 is calculated by using a Tichy and Ticha

relation, which is a mathematical relationship between

Miller’s generalized rule and n1, which is given by the fol-

lowing equation:70

n2 ¼ 12pv 3ð Þ=n1: (11)

The numerical value of n2 for all the samples is calcu-

lated from Eq. (11) and listed in Table IV. It is very obvious

to get largest values of n2 for the 15R-SiC film fabricated at

Si substrate because of improvement in structural properties.

In order to understand the influence of average crystallite

size (t) on nonlinear optical properties of the 15R-SiC films,

the n2 variation of the films with t is shown in Fig. 10(e). It

has been observed that n2 exhibits a linear dependence on t,i.e., nonlinear refractive index improves with an increase in

the crystallite sizes and is well agreed with the previously

reported literature.71,72 The change in nonlinearities with the

crystallite size may be attributed to the lattice defects, which

leads to light-induced changes in the refractive index causing

optical distortion, phase modulation, Bragg scattering, and

green-induced infrared absorption. Consequently, this

decreases the efficiency of nonlinear interactions when the

crystal is subjected to an intense visible radiation. Thus, the

higher defects present in the film lead to the small value of

the nonlinear refractive index. Here, it can be noted from

Table II that there is a trend in which crystallites decrease in

size with an increase in lattice defects. As a result, for larger

crystallites, the defects are smaller and therefore there is an

improvement in nonlinearities. This accomplished nonlinear

interaction is remunerative for emphatic optical confinement,

which enables compact circuit design, enhanced optical

intensities, and low power devices for telecommunication

applications at high-temperature, high-frequency, and harsh

environment.

Being a semiconducting material, it is very important to

determine the ratio of the carrier concentration to the effec-

tive mass (N/m*) for 15R-SiC thin films. In general, the elec-

trical properties of SiC are excellent for harsh environment,

as might have been expected from the low background impu-

rity concentrations. The free carrier concentration is an

important parameter to extract meaningful electrical charac-

teristics of semiconductor devices. Therefore, to address the

electrical applicability of grown 15R-SiC films, we have

determined the free carrier concentration per unit effective

mass (N/m*) by using the following relationship between nand N/m* as given in the following equation:73

n2 ¼ e1 �e2

4p2e0c2

� �:

N

m�

� �k2; (12)

where e¼ 1.6021� 10�19 C is the electronic charge and E0

is the permittivity of free space (8.854� 10�12 F/m). From

the plots of n2 vs. k2 as shown in Fig. 11, the value of N/m*

can be calculated with the help of the slope of the linear

part of the curve at a higher wavelength, while the extrapo-

lation to k2¼ 0 enables to determine E1. It is evident from

Table IV that all N/m* values are in the range of

1049 kg�1 cm�3 which indicate the extrinsic behavior of

grown films under investigation. It may be noticed that the

samples are not intentionally doped, but ionic and nitrogen

impurities added during the fabrication process resulted in

N/m* values in the range of 5.26–5.46� 1049 kg�1 cm�3 for

all the samples. The calculated value of N/m* was found to

be highest for the 15R-SiC film deposited at Si substrate.

This may be ascribed to the defect states present in the

films; however, the defect states in the film are related to

the dislocation density, i.e., the lowest value of the disloca-

tion density will correspond to the lowest defect states.

Therefore, the sample SiC@Si having the lowest value of

dislocation density resulted in the highest value of N/m*

(Table IV) because few carriers get trapped in case of low

dislocation density. A good electrical property also

demands low defects (point-defects and dislocations)

because these electrically active defects act as shallow and

deep trapping centers for free carriers. The mobility of the

free carriers gets reduced along threading dislocation

because filled traps lines act as Coulomb scattering centers.

Additional mobility reduction occurs at SiC film-substrate

interface due to scattering at dislocations and defects.

At this point in time, it may be very interesting to dis-

cuss the plasma frequency of our samples for the develop-

ment of high-temperature and high-frequency plasmonic

devices. As per the Drude’s theory for the dielectric materi-

als, the plasma frequency (xp) is given as follows:74

FIG. 11. The variation of the square of refractive index n as a function of

the square of wavelength k for 15R-SiC thin films fabricated at various

substrates.

023109-11 Mourya et al. J. Appl. Phys. 123, 023109 (2018)

x2p ¼

N

m�:

e2

e0e1; (13)

where e0 is the absolute permittivity, e is the electronic

charge, m* is the effective mass of the electron, and N is the

free carrier concentration. Therefore, using Eq. (13) and hav-

ing the quantitative value of the N/m* and e1, the plasma

frequency (xp) can be deduced. The estimated values of xp

for 15R-SiC thin films are listed in Table IV.

IV. CONCLUSION

In summary, highly ordered crystalline 15R-SiC thin

films have been fabricated on four different substrates, i.e.,

ZrO2, MgO, SiC, and Si using RF-magnetron sputtering at a

temperature of 800 �C. It has been observed that the sub-

strate’s surface energy plays a crucial role in the nucleation

and growth of 15R-SiC thin films resulting in tunable micro-

structural and optical properties. Single crystal orientation (1

0 10), maximum average crystallite size (�17.7 nm), lowest

surface roughness (�1.10 nm), minimum strain (0.19%), and

lowest dislocation density (�3.19� 1015) were observed in

the sample grown at Si substrate, which also confirmed the

fabrication of high quality 15R-SiC film having minimum

defects. Additionally, the lowest value of FWHM and the

peak shift of TO mode in Raman spectra for the sample

SiC@Si authenticate the best crystallinity with minimum

defects and this result is also validated by FTIR measurement.

The optical properties of 15R-SiC thin films were probed in

the broad spectral range (246–1688 nm) considering the sur-

face characteristics (roughness and composition) in the optical

stack model using SE, and it is expected that these results pro-

vide new and unique optical constant data for the 15R-SiC

thin film. Further, the film thickness and surface roughness

obtained from SE data are well corroborated with SEM and

AFM measurements, respectively. The highest optical and dis-

persion energy parameters were observed for the sample

deposited at Si substrate, i.e., refractive index (n¼ 2.7707 at

k¼ 540 nm), bandgap (Eg � 3.1595 eV), oscillator energy

(Eo¼ 7.5980 eV), dispersion energy (Ed¼ 46.1800 eV),

dielectric constant (e1 ¼ 7.0779), third order susceptibility

(v(3) � 9.3219� 10�12 esu), nonlinear refractive index (n2

�2.0793� 10�17 m2/W), carrier concentration to the effective

mass (N/m*¼ 5.4656� 1049 kg�1 cm�3), and the plasma fre-

quency (xp¼ 795.57 cm�1), allowing this sample to be a

promising candidate for optoelectronics, photonics, and tele-

communication applications at elevated temperature and harsh

environment.

ACKNOWLEDGMENTS

One of the authors, Satyendra Mourya, would like to

thank the Ministry of Human Resource and Development

(MHRD), Government of India, for providing the financial

assistance.

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