Si (001) epifilms

Accepted Manuscript Title: Spectroscopic phonon and extended x-ray absorption fine structure measurements on 3C-SiC/Si (001) epifilms Authors: Devki N. Talwar, Linyu Wan, Chin-Che Tin, Hao-Hsiung Lin, Zhe Chuan Feng PII: DOI: Reference:

S0169-4332(17)32266-3 http://dx.doi.org/doi:10.1016/j.apsusc.2017.07.266 APSUSC 36800

To appear in:

APSUSC

Received date: Revised date: Accepted date:

13-4-2017 19-7-2017 28-7-2017

Please cite this article as: Devki N.Talwar, Linyu Wan, Chin-Che Tin, HaoHsiung Lin, Zhe Chuan Feng, Spectroscopic phonon and extended x-ray absorption fine structure measurements on 3C-SiC/Si (001) epifilms, Applied Surface Sciencehttp://dx.doi.org/10.1016/j.apsusc.2017.07.266 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Spectroscopic phonon and extended x-ray absorption fine structure measurements on 3C-SiC/Si (001) epifilms Devki N. Talwar, 1,* Linyu Wan2, Chin-Che Tin3, Hao-Hsiung Lin4, and Zhe Chuan Feng2,# 1

Department of Physics, Indiana University of Pennsylvania, 975 Oakland Avenue, 56 Weyandt Hall, Indiana, Pennsylvania 15705-1087, USA and Department of Physics, University of North Florida, 1 UNF Drive, Jacksonville, Florida 32224, USA 2

Laboratory of Optoelectronic Materials and Detection Technology, Guangxi Key Laboratory for Relativistic Astrophysics, School of Physical Science & Technology, Guangxi University, Nanning, 530004, China 3

Department of Physics, Auburn University, Auburn, Alabama 36849, USA and Department of Materials Engineering, Faculty of Engineering, Tunku Abdul Rahman University College, Jalan Genting Kelang, 53300 Kuala Lumpur, Malaysia 4

Graduate Institute of Electronics and Department of Electrical Engineering, National Taiwan University, Taipei, 106-17, Taiwan *

[email protected]; #[email protected]

Highlights     

Vibrational and structural properties are reported for 3C-SiC/Si (001) epilayers prepared by V-CVD method Phonon characteristics are assessed by Raman scattering and infrared reflectance spectroscopies Local inter-atomic structures are estimated by polarization dependent synchrotron radiation x-ray absorption fine structure Modified 3-component effective medium theory is applied to explicate the observed unusual infrared reflectance features in 3C-SiC/Si (001) Bi-axial stress in 3C-SiC epifilms is estimated to be an order of magnitude smaller while the strains are two-orders of magnitude lower than the lattice misfits of bulk 3C-SiC and Si crystals

Abstract Comprehensive experimental and theoretical studies are reported to assess the vibrational and structural properties of 3C-SiC/Si (001) epilayers grown by chemical vapor deposition in a vertical reactor configuration. While the phonon features are evaluated using high resolution infrared reflectance (IRR) and Raman scattering spectroscopy (RSS) – the local inter-atomic

structure is appraised by synchrotron radiation extended x-ray absorption fine structure (SREXAFS) method. Unlike others, our RSS results in the near backscattering geometry revealed markedly indistinctive longitudinal- and transverse-optical phonons in 3C-SiC epifilms of thickness d < 0.4 m. The estimated average value of biaxial stress is found to be an order of magnitude smaller while the strains are two-orders of magnitude lower than the lattice misfits between 3C-SiC and Si bulk crystals. Bruggeman’s effective medium theory is utilized to explain the observed atypical IRR spectra in 3C-SiC/Si (001) epifilms. High density intrinsic defects present in films and/or epilayer/substrate interface are likely to be responsible for (a) releasing misfit stress/strains, (b) triggering atypical features in IRR spectra, and (c) affecting observed local structural traits in SR-EXAFS. Keywords: Raman scattering spectroscopy; Infrared reflectivity; Synchrotron radiation x-ray absorption fine structure; Chemical vapor deposition; Brugeeman's effective medium theory

PACS: 78.20.-e 63.20.Pw 63.20.D-

1.

Introduction Silicon carbide (SiC) with more than 200 different crystalline structures or polytypes

exhibits many diverse and exceptional properties [1-14]. While these polytypes are formed by choosing special stacking sequence of Si-C bilayers – each arrangement has its explicit set of distinct electrical and vibrational characteristics. A few customary SiC polytypes that are being developed for device applications include the zinc-blende (zb) or cubic (3C-SiC), hexagonal (4H-SiC, 6H-SiC), and rhombohedral (15R-SiC, 21R-SiC) structures. The 3C-SiC polytype with its high electrical breakdown field, high saturated electron velocity, high chemical inertness and good thermal conductivity is regarded as a promising substitute for silicon in a variety of applications such as high-power, high-temperature, high-frequency electronics, optoelectronic devices, micro-electro/nano-electro-mechanical systems (MEMS/NEMS), sensors and detectors. The difficulties of growing [6-11] large size and good quality 3C-SiC material have, however, remained major obstacles for its use in realizing different device applications. The most widely employed substrate for 3C-SiC epitaxial growth is a Si (001) surface. Efforts have been made [12-17] recently for preparing ultrathin 3C-SiC epifilms heteroepitaxially on Si by chemical-vapor deposition (CVD) and/or molecular beam epitaxy (MBE) methods [18-19]. The CVD growth of 3C-SiC on Si substrate is generally achieved at 2

temperatures higher than 1300 K after the formation of a carbonized buffer layer. However, the Si vapor pressure at higher temperature is largely responsible for causing structural damages that create defects, voids/pits in the epilayers and at the film/substrate interface. Moreover, significant differences in lattice constants (19.8%) and thermal expansion coefficients (8%) between 3C-SiC and Si, also affect the heteroeptaxial growth. These factors usually generate additional stress and strains in the epitaxial films during post-growth cooling process producing high density of intrinsic defects at the 3C-SiC/Si interface and in the epilayers [20-28]. It is, therefore, essential to evaluate biaxial stress in epilayers for further progress in device engineering. Likewise, the identification and disposition of intrinsic defects in 3C-SiC/Si (001) have been the major concerns among the scientific and technological communities [1-11]. While many experimental and theoretical investigations are reported on the electrical, mechanical, elastic, optical, and defect properties – fewer efforts have been made, however, to assess strains, modeling voids/pits, identifying types of intrinsic defects and evaluating local atomic structures in 3C-SiC/Si (001) epifilms. In the electronics industry, the infrared reflectance (IRR) spectroscopy is regarded as one of the fast-turn around methods for establishing optical parameters of semiconductor materials [29-36]. Earlier Holm et al. [36] examined the IRR spectra on 3C-SiC/Si (001) by applying different surface treatments. They emphasized that small pits and bumps on the film’s surface could possibly be the major source of anomalous features (divot) observed at the top of the reststrahlen peak. No theoretical simulations were performed, however, to bolster their assertion. The authors of Ref. [36] also proposed that interfacial roughness might be responsible for the diminishing average reflectance of interference fringe contrasts at higher frequency – yet, their spectral analyses remained rather limited to being qualitative. To assess residual stress in materials, x-ray diffraction (XRD) [37-38] has been frequently used – where one measures strain and then determines the associated stress by using elastic constants assuming linear distortion of appropriate crystal lattice plane. While XRD is insensitive for estimating stress/strains in epitaxially grown ultrathin films – the Raman scattering spectroscopy (RSS) [39-51] has always been preferred. The RSS method is used before to appraise microstrains [41-42] in bulk semiconductors by expending hydrostatic and uniaxial stress. It can be exploited to study biaxial stress/strain [43-48] in thin 3C-SiC/Si (001) epilayers as well. In mapping local atomic structures around selected atoms in semiconductors 3

– SR-EXAFS is considered as one of the most powerful tools. Although limited studies have been made recently on hydrogenated [52], Mn- [53-54] and/or Cr-doped [55] thin SiC films – the SR-EXAFS measurements on different SiC polytypes have largely been overlooked. Given these important issues along with restricted experimental/theoretical studies on the key areas – we find it intriguing to investigate the vibrational traits, evaluate stress/strain and assess structural properties of these technologically important 3C-SiC/Si (001) epifilms. The purpose of this paper is to report the results of comprehensive experimental (cf. Sec. 2) and theoretical (cf. Sec. 3) investigations to assess the dynamical and structural properties of 3C-SiC/Si (001) epifilms grown by CVD method in a vertical reactor (V-CVD) configuration (cf. Sec. 2.1). While phonon characteristics of the material samples are evaluated using RSS and IRR spectroscopy (cf. Secs. 2.2-2.3) the structural traits are assessed by polarization dependent SR-EXAFS measurements (cf. Sec. 2.4). The observed vibrational features (cf. Secs. 3 - 3.2) are meticulously explicated in terms of classical methodologies by incorporating phonons from a realistic lattice dynamical model [60]. To appraise residual stress/strain in 3CSiC epifilms, we have integrated the observed RSS phonon shifts of longitudinal and transverse optical (LO and TO) modes in the conventional (cf. Sec. 3.1) elastic deformation theory [4348]. Atypical vibrational features observed in the IRR spectra of 3C-SiC/Si (001) samples are analyzed (cf. Sec. 3.2.1) judiciously by using self-consistent [61-67] Bruggeman effective medium theory (BEMT). For examining the SR-EXAFS data we have performed comprehensive simulations exploiting commercially available IFEFFIT software package consisting of ATOMS, ATHENA, AUTOBK, ARTEMIS programs [52-59]. Theoretical results have offered (cf. Sec. 3.3) valuable information on the structural characteristics of 3C-SiC/Si (001) material systems. Small discrepancies in Si-C and Si-Si bond lengths are attributed to the possibility of intrinsic defects/disorder present on the surface/interface of 3C-SiC/Si (001) epifilms. Theoretical simulations of phonon/structural properties are carefully assessed by comparing and contrasting them against the experimental results with concluding remarks presented in Sec. 4.

2.

Experimental

2.1 V-CVD Growth of 3C-SiC/Si (001) epifilms

4

The 3C-SiC/Si (001) samples used in the RSS (cf. Sec. 2.2), IRR (cf. Sec. 2.3), and SREXAFS (cf. Sec. 2.4) spectroscopic measurements were grown on Si substrates under normal atmospheric pressure environment by CVD method in a vertical reactor configuration (VCVD). The V-CVD system utilizes a rotating SiC-coated susceptor heated by a radio-frequency (RF) induction power supply – it can be operated both at the atmospheric and low pressure modes. The vertical configuration has many advantages including substrate rotation to produce large-area, thickness uniformity, enabling in-situ monitoring of substrate parameters, and easy implementation of various growth enhancement procedures. The specimens were produced following three main steps according to the procedures of 3C-SiC heteroepitaxial growth on Si (001) substrate reported in details elsewhere [17]. The 3C-SiC/Si (001) epilayers were made at an ambient pressure (1 atm) and 1360 oC with source ratio of Si/C (~ 0.33). The growth time

was varied between 2 m to 5 h. The growth rate was ~3.2 ± 0.1 m h-1 and the film thickness d, ranged from ~ 0.1 m to ~16.0 m. Four relatively thicker [S1 ( 3.2 m), S2 ( 5.6 m), S3 (12.8 m), S4 ( 16.0 m)] and two thinner [S01 ( 0.4 m) and S02 ( 1.6 m)] samples are used in the present study. Although, we have employed 25 mm diameter Si wafers as substrates – our reactor is capable of scaling up to handle 76 mm diameter Si substrates for growing 3CSiC epifilms. The set of single-crystalline 3C-SiC films used here show uniformly smooth and mirror-like surfaces without macro-cracks – even in the thinnest possible epifilm.

2.2

Raman scattering Raman scattering is a valuable tool for probing local strain, composition, thickness, doping,

defects and crystallographic orientations in many ionic and partially ionic materials. For SiC, in particular, the Raman efficiency is quite high due to strong covalent bonding between Si-C atoms. We have performed RSS measurements at room temperature (RT) on several V-CVD grown 3C-SiC/Si (001) samples in the near backscattering x(y',y') x geometry to assess he crystalline quality and stress/strains in 3C-SiC films. A T64000 Jobin Yvon triple advanced spectrometer equipped with electrically cooled CCD detector is employed with Kr+ 406 nm laser as an excitation source by adjusting its power level to 100 mW for avoiding thermal damage to the material samples. For collecting the scattered light we used a triple monochromator with conventional photon counting electronics.

2.2.1 Stress-induced phonon shifts 5

Figure 1 shows the Raman spectra recorded at RT in the near back-scattering geometry for ″as grown″ 3C-SiC/ Si (001) sample # S3 (of thickness 12.8 m) with no processing done after V-CVD growth [Fig. 1 a)] and the self-supported ″free-standing″ 3C-SiC film by removing Si substrate with KOH etching solution [Fig. 1 b)]. We believe that the observed optical phonon feature from ~930 cm-1 to 1000 cm-1 is associated with the second-order Raman scattering band from Si substrate. The characteristic optical modesTO andLO at ~794 cm-1 and ~970 cm-1 affirms that the film consists of a cubic polytype of SiC. While the TO phonon structure exhibited full width at half maximum (FWHM) of about ~ 8 cm-1 – its asymmetric broadening is likely to be induced by the effect of a minor crystal quality. No second-order phonon trait of Si substrate is noticed in the “free standing” film [see: Fig. 1 b)] – the LO mode became, however, symmetric and narrower. By examining several “as-grown” 3C-SiC/Si (001) samples (not shown here) we acknowledge perceiving the second-order phonon feature of Si substrate only in a few cases and certainly not in the “free-standing” films. Again, we have observed

LO [TO] phonon mode shifting by nearly ~2.0 cm-1 [~1.0 cm-1] towards higher energy side (see: Table 1) after etching away the Si substrate. The observed shifts of optical phonon frequencies are incorporated in a classical elastic deformation theory (cf. Sec. 3) for assessing [43-48] the biaxial stress and strains in 3C-SiC films. It is worth mentioning that the secondorder phonon feature of Si observed in “as-grown” samples has neither affected LO, TO frequencies nor it changed our stress and strain calculations.

2.2.2 Thickness dependent Raman spectra Additional RSS measurements reported in the near back-scattering geometry (see: Figs. 2 ac) for “as-grown” 3C-SiC/Si (001) samples of different thickness d (~0.4 m to ~16.0 m) have revealed changes in the relative peak intensities and lineshapes of Si o mode (substrate) and of 3C-SiC LO, TO phonons (epifilm). The perusal of Figs. 2 a) and 2 b) reveals that as the film thickness increases from ~0.4 m (sample # S01) to ~1.6 m (sample # S02) the intensity of the Si phonon mode o (~ 520 cm-1) decreases while that of the 3C-SiCLO, TO modes (near ~ 970 cm-1, ~ 794 cm-1) increases. Our RSS results of o mode and LO, TO phonon frequencies are found in very good agreement with the inelastic neutron-scattering [68] dispersions of the

6

bulk Si crystal and the inelastic x-ray scattering (IXS) [69] as well as Raman scattering [70] data for 3C-SiC, respectively. In our sample # S2 the observed broad LO phonon feature of nearly ~50 cm-1 FWHM is most probably caused by amorphous Si-C vibrations [Fig. 2 c)] – indicating damage in the crystalline structure of the epilayer. In thicker sample (# S4) of d ~ 16 m, however, one would expect relatively less penetration of laser light through 3C-SiC into Si substrate to inflict decrease in the intensity of o (not shown here) and rise in intensity of LO [see: Fig. 2 c)] phonon with respect to TO mode. This observation has clearly indicated an improvement in the crystalline quality of thicker samples prepared with increased growth time . Unlike others, our RSS measurements have revealed [51] strikingly indistinctive 3C-SiC LO, TO optical phonon features [see: Fig. 2 a)] for samples having thickness smaller than 0.4 m.

2.3

Infrared reflectance Infrared spectroscopy is one of the most important methods [43-52] for determining optical

parameters in ionic/partially-ionic materials. Many semiconducting ultrathin epifilms grown on different substartes were characterized [43-49] earlier by examining their IRR spectra for evaluating film thickness, carrier concentartion and crystalline quality. More recently, extensive studies have been conducted to understand the unusal spectral features [29-31] observed in 3C-SiC/Si (001) samples prepared under different growth conditions.

2.3.1 Anomalous reflectivity In Fig. 3, we have displayed our IRR spectra at near normal incidence (i ~ 8 o) for one of the V-CVD grown 3C-SiC/Si (001) epifilms (sample # S1 growth time  ~1 h). The spectra was recorded over the wavelength (frequency) range of 1.54 m – 50 m (200 cm-1 – 6500 cm-1) by using a nitrogen purged Perkin Elmer 2000 spectrometer having ~2 cm-1 spectral resolution. The IRR spectra has clearly revealed unusual characteristics – a dip in the flat reststrahlen region (near ~895 cm-1) along with damping in the interference fringes away from the maximum phonon frequency m (~ 970 cm-1) of 3C-SiC. By examining the reflectivity data of 3C-SiC films with different surface treatments, Holm et al. [36] emphasized earlier that small pits and bumps on the surface (surface roughness) can create not only anomalous features (divot) at the top of the reststrahlen band but also abate the interference fringe contrasts at 7

higher frequency. The authors [36] gave no theoretical explanation to bolster this assertion and their spectral analyses remained rather limited to being qualitative. In Sec. 3.2 we have carefully appraised the observed atypical IRR spectra (see: Fig. 3) by exploiting Bruggeman’s effective medium theory [61-67].

2.4

EXAFS measurements Ever since the availability of broadly tunable sources – the SR-EXAFS spectroscopy is

recognized as a versatile structural characterization tool to study the local atomic environments [52-59] in both crystalline and amorphous (glasses) materials [52-55]. The information offered by SR-EXAFS in solids include average interatomic distances and number of chemical identities of neighbors within 5 to 6 Å. For V-CVD grown 3C-SiC/Si (001) samples (# S1 - S4) – the polarization dependent SREXAFS measurements were carried out at Si K absorption edge using a double-crystal monochromator beam line 16 A at the National Synchrotron Radiation Research Center (NSRRC) in Hsinchu, Taiwan. In fluorescence mode, the absorption spectra for each sample was recorded with applied incident x-ray photon flux covering the energy range E between ~1800 eV – 2700 eV. While the intensity of the incident photon flux was monitored by N2 filled ionization chamber – the fluorescence emitted from each sample was assessed with an argon filled Stern-Heald-Lytle type detector. A filter was inserted between the sample and detector window for reducing the noise from scattering and improving the spectrum quality. All SR x-ray absorption spectral (XAS) measurements at RT were carried out with spectra normalized to the intensity of incident Io photon flux. In 3C-SiC/Si (001) epifilms, the XAS coefficient μ as a function of E [cf. Sec. 3.3 and see: Fig. 4 a)] revealed sharp rise in intensity at the Si K absorption edge – initiating almost a step-like function with weak oscillatory wiggles beyond several hundred eV above the edge. The region closer to the absorption edge is often dominated by strong scattering processes including local atomic resonances. We focused our attention here on the region of EXAFS oscillations covering x-ray photon energy E from nearly tens of eV above the absorption edge (i.e., ~1839 eV). It is a common practice to convert the x ray energy to photoelectron wave number k   

 2m e ( E  E ) o  for evaluating (k) – the prime 2 

quantity of EXAFS to measure the oscillations in the absorption coefficient. By carefully 8

extricating oscillating signals [cf. Sec. 3.3 and see: Figs. 4 b-e)] from the raw absorption data and using fitting programs from the IFEFFIT package [52-59] – the EXAFS features are converted into Fourier transform spectra over the wave number range of 1 - 15.0 Å-1 to obtain the radial distribution function of atoms. The structural information i.e., nearest-neighbor (NN), next-nearest-neighbor (NNN) bond lengths, coordination numbers etc., is acquired by modeling the spectra after Fourier filteration and using XRD data as a reference for 3C-SiC.

3.

Theoretical In order to comprehend the ″stress-dependent″ vibrational properties in zb materials, it is

possible: (i) to apply ″hydrostatic stress″ in bulk samples by using diamond anvil cell, (ii) perform ″uniaxial-stress″ on large size specimens, and (iii) examine ″biaxial-stress″ in thin films prepared on mismatched substrates. In each case the ″stress″ is considerd as a perturbation. By adopting a conventional elastic deformation theory, we have derived expressions [46] for the three cases in terms of the Raman-stress coefficients and optical mode frequency shifts to empathize the experimental data. 3.1

Esimating stress and strain in 3C-SiC/Si (001) The characterization of 3C-SiC epilayers grown on Si (001) substrate by transmission

electron microscopy (TEM) and high-resolution x-ray diffraction (HR-XRD) [47] revealed biaxial in-plain strain – caused by changes in their lattice constants and thermal expansion coefficients. An accurate evaluation of stress X and strain in 3C-SiC films – crucial for engineering MEMS and/or NEMS devices [1-11] – can be achieved from the optical phonon shifts observed by RSS. In the back-scattering geometry, the singlet (s) and doublet (d ) modes relative to the unstrained phonon frequency o of 3C-SiC can be expressed in terms of X by [46]:

 2   s   o    S  2 H  X ,  3 

(1a)

1   d   o    S  2 H  X , 3 

(1b)

and

where the two stress  S ,  H coefficients

9

 S  o S (S11  S12 ) and  H  o o (S11  2S12 )

(2)

are linked to the elastic compliances Sij, hydrostatic Grüneisen constant  o , shear deformation parameter  s and o. It is customary to add superscripts LO, TO on  , o for classifying the singlet and doublet [cf. Eqs. 1 (a-b)] modes i.e., 2

 LO   oLO     S  2 H  X  3  1

 TO   oTO    S  2 H  X 3 

,

,

(3a) (3b)

Subtracting Eq. (3 b) from Eq. (3 a) one can express  S X :

 S X  (oLO   LO )  (oTO   TO ) ,

(4)

in terms of the observed Raman phonon (Table 1) frequencies (  LO ,  TO ,  oLO and  oTO ). By integrating hydrostatic stress coefficients  HLO ,  HTO known [41-42] from the hydrostatic pressure dependent RSS experiments in Eqs. [3 (a-b)] one can get two values of X using:

and

X = [(  oTO   TO ) +

1  S X]/( 2 HTO ) , 3

(5)

X = [(  oLO   LO ) -

2  S X]/( 2 HLO ) . 3

(6)

By taking an average of the two X values and assigning error bar, one can appraise both the in-plane  ||  ( S 11  S 12 ) X  and normal    2 S 12 X  strains in 3C-SiC films (see: Table 1). The elastic constants used here are obtained by fitting the IXS data of phonon dispersions [69] by exploiting a realistic lattice dynamical model [60]. Our simulations of X,  || and   provided results in very good agreement with those reported by different research groups [39-46]. In 3CSiC films, while the appraised average value of the biaxial stress X (~ 0.581 GPa) is an order of magnitude smaller – the strain estimates are found, however, two-order of magnitudes lower than the lattice misfits between the bulk 3C-SiC and Si materials. Although this result is quite intriguing – it has provided strong corroboration to our recent study of impurity vibrational modes based on an average-t-matrix Green’s function theory [71] implying that there exists a

10

high density of intrinsic defects at the 3C-SiC/Si interface which are possibly responsible for releasing misfit stress and strains in 3C-SiC films. 3.2

Infrared reflectance In an ideal situation for preparing epifilms on nearly lattice matched substrates – one

assumes the growth to be perfectly uniform with all interfaces optically sharp and parallel. In such cases one generally exploits a Drude-Lorentz (DL) method and follows multilayer optics using transfer-matrix formalism [35, 36] to simulate the IRR spectra by adopting a three-phase (vacuum/ film/substrate) model. In 3C-SiC/Si (001) system, however, the roughness in the forms of lumps and pits on the surface/interface have been suggested [36] as the leading cause of dips or divots within the reststrahlen band as well as damping observed in the interference fringes at higher (> m) frequency. Thus, the IRR analysis of the anomalous reflectivity spectra by classical DL model has remained inadequate. 3.2.1 Bruggeman effective medium theory Earlier Berreman [63] modelled the microscopic surface roughness in ionic solids by considering hemispherical shaped bumps and pits. More recently, many quasi-static theories have been developed to treat optical properties of epitaxially grown materials with different surface roughness features of size smaller than the wavelength of light [64-67]. Here, we have adopted the BEMT methodology and simulated the anomalous IRR spectra of 3C-SiC epifilm (sample # S1) by considering an effective dielectric function < > of the material system comprising of three different constituents (viz., micro-crystalline, intergranularandpores) distributed homogenously with corresponding volume fractions f1, f2, and f3. The effective dielectric function < > is evaluated from the self-consistency condition [67]: 3

 i 1

fi

i      0 with i  2   

3

f

i

=0

.

(7)

i 1

The optical frequencies LOi, TOi with appropriate volume fractions fi – required to simulate the IRR spectra of 3C-SiC/Si (001) sample # S1 are listed in Table 2. Theoretical results of the IRR spectra displayed in Fig. 3 compared reasonably well with the experimental

11

data. Moreover, the epifilm thickness d (= 3.37 m) required in our simulations agreed satisfactorily with the V-CVD growth time (see: Table 1) of sample # S1. As compared to TO1 frequency of the micro-crystalline SiC material – the calculation required higher value ofTO2 for the intergranular SiC with a lower volume fraction f2 ~ 0.5 % in providing the reasonably accurate depth of the divot observed near ~895 cm-1 within the reststrahlen band region. It is to be noted that we did not include the effects of pores – as its impact in the process of fitting the infrared reflectance spectra of sample # S1 offered least to negligible contributions. 3.3

Analyzing the EXAFS results To explore the SR-EXAFS data for 3C-SiC/Si (001) epifilms, we are primarily concerned

here with the observed oscillations in the XAS coefficient  – well above the Si K edge (i.e., ~1839 eV) – where the single scattering dominates. The energy-dependent EXAFS function

(E) is defined as:

 ( E) 

 ( E )   o ( E) ,  o ( E )

(8)

where the term μ(E) in Eq. (8) is the experimentally measured absorption coefficient; μo(E) is a smooth background function representing the absorption of x-ray by an isolated atom and μo(E) is the measured jump (edge-step) in the absorption at the threshold energy (the binding energy of the core-level electron) Eo. Since the EXAFS is best described by the wave behavior of photoelectron created in the x-ray absorption process – it is a common practice to convert the x-ray energy E to k which is the wave number of the photoelectron in dimensions of Å-1. Thus in analysing the EXAFS data – the required key quantity is (k). Extraction of the EXAFS modulation function (k) has been achieved from the raw absorption data (cf. Sec. 2.4) by following standard procedures [52-59]. The fitting program from IFEFFIT package is used converting the oscillating features of absorption coefficients into Fourier transform spectra. The AUTOBK code is exploited for removing the background contributions from k-space signals. As the EXAFS region above the absorption threshold is oscillatory and decays rapidly with k – it is customary to multiply the (k) data by powers of k to emphasize oscillations. Weighting (k) with lower power of k highlights the oscillations in the low k-region and higher power of k stresses oscillations in the high k-region. In Fig. 4 b) 12

[Fig. 4 c)], we have displayed the Si K edgekweighted EXAFS oscillations of the V-CVD grown 3C-SiC/Si (001) samples for k ranging between ~1 Å-1 – 14.5 Å-1 [~1 Å-1 – 13.0 Å-1]. Similar to other zb materials [72] our results for 14.5 Å-1 > k > 9 Å-1 reveal higher noise level [see: Fig. 4 b)] in the EXAFS oscillations which become significantly lower for k ≤ 11.0 Å-1. Improvements in the (k) oscillations are shown in Fig. 4 d) for sample # S1 by adjusting background removal contributions to minimize noise level with different choice of k values. The information on local atomic structures [see: Fig. 4 e)] including the first and second coordination shells (see: Table 3) is obtained for 3C-SiC/Si (001) samples by utilizing FEFF 8.2 program implemented in the ARTEMIS software. Our results of the NN Si-C and NNN Si-Si bond lengths are found in good agreement with the existing data from the XRD measurements.

4.

Concluding remarks Comprehensive experimental and theoretical studies are performed to assess the vibrational

and structural properties of V-CVD grown 3C-SiC/Si (001) epilayers. Samples of different thickness are prepared keeping Si/C ratio at ~ 0.33 by varying growth times between 2 min to 5 h. Dynamical and structural traits are evaluated using high resolution RSS, IRR and SREXAFS spectroscopies. Unlike others [51] our RSS measurements [see: Figs. 2 a-c)] in the near-backscattering geometry revealed markedly indistinctive 3C-SiC like LO, TO phonons in samples with film thickness d < 0.4 m. Conventional elastic deformation [46] theory is used incorporating optical phonon shifts of “as-grown” and “free-standing” films to appraise the crystalline quality of material samples and estimating stress/strains in 3C-SiC films. The simulated average biaxial stress (X~ 0.581 GPa) is found an order of magnitude smaller (see: Table 1) while strains are projected two-orders of magnitude lower than the lattice misfits of 3C-SiC and Si crystals. These intriguing results provided strong corroborations to our recent study [71] of impurity vibrational modes implying the presence of high density intrinsic defects in 3C-SiC films and/or epilayer/substrate interface – responsible for releasing stress/strains in epilayers. By deliberating the Bruggeman methodology with a self-consistent effective dielectric <  > function of homogenously distributed structures and including appropriate film thickness, we have successfully explicated (see: Fig. 3) atypical IRR features having dip in the reststrahlen band as well as diminishing interference fringe contrasts at  > m observed in 3CSiC/Si (001) sample # S1. In the Si K edge EXAFS spectroscopy – the oscillating signals for 13

3C-SiC/Si (001) epifilms with extracted modulations in the k- and R-spaces are used to acquire (see: Table 3) the first or NN shell (Si-C) and second or NNN shell (Si-Si) distances with respect to the Si core. The small discrepancies in our EXAFS study with respect to the bulk 3CSiC NN Si-C (1.89 Å) and NNN Si-Si (3.08 Å) bond lengths is attributed to the possibility of intrinsic defects and/or disorder on the surface/interface in our 3C-SiC/Si (001) epifilms.

ACKNOWLEDGEMENTS The author (DNT) wishes to thank Dr. Deanne Snavely, Dean College of Natural Science and Mathematics at Indiana University of Pennsylvania for the travel support and the Innovation Grant that he received from the School of Graduate Studies making this research possible. We acknowledge Dr. Ling-Yun Jang for his support and help in the performance of synchrotron radiation x-ray absorption spectroscopy measurements on our samples. The work at Guangxi University was supported by National Natural Science Foundation of China (NO.61367004) and Natural Science Foundation of Guangxi Province (No.2013GXNSFFA019001).

14

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20

Figure captions Fig. 1 Raman spectra in the near back-scattering geometry for a V-CVD grown 3C-SiC/Si (001) sample # S3 prepared with an approximately ~ 4 h growth time . A Kr+ 406 nm line is used as the excitation source while keeping the laser power level adjusted to 100 mW. (a) The magenta color line represents our results for the sample on Si substrate (″as-grown″), and (b) the cyan color line indicates our results for the film without Si substrate (″free-standing″). Fig. 2 Thickness dependent Raman spectra in the near back-scattering geometry for four VCVD “as-grown” 3C-SiC/Si (001) samples, where the growth time  is varied from 8 min sample # S01 (Fig. 2 a), 30 min sample # S02 (Fig. 2 b) and between 1 h to 5 h (Fig. 2 c). The y-axis intensity in (Fig. 2 a) and (Fig. 2 b) is scaled up ten times. Clearly in (Fig. 2 a) the o Si phonon band intensity near ~520 cm-1 is strong while LO, TO modes of 3C-SiC near ~970 cm-1, ~794 cm-1 are nearly indistinctive (see text). In (Fig. 2 b) as the growth tme increases the o Si phonon band intensity near ~520 cm-1 decreases while those of LO, TO modes for 3C-SiC near ~970 cm-1, ~794 cm-1 increase (see: text). Fig. 3 Comparison of the simulated (blue color line) and experimental infrared reflectance spectra (red color square □ ) for sample # S1 (see: text). Theoretical calculation is performed using Bruggeman effective medium theory (BEMT) with parameter values from Table 2. Fig. 4 (a) Si K edge EXAFS absorption coefficient (E) versus x-ray photon energy for four V-CVD grown 3C-SiC/Si (001) samples (# S1, # S2, # S3 and # S4). (b) Normalized oscillating parts of EXAFS spectra: k2(k) versus k between 1-14.5 Å-1 for VCVD grown 3C-SiC/Si (001) samples (# S1, # S2, # S3 and # S4). (c) Normalized oscillating parts of EXAFS spectra: k2(k) versus k between 1-8.5 Å-1 for VCVD grown 3C-SiC/Si (001) samples (# S1, # S2, # S3 and # S4). (d) Fourier transformed EXAFS spectra: (R) versus R between 0 – 10 Å for different choice of k to improve exceptional noise in sample (# S1). (e) Fourier transformed EXAFS spectra: (R) versus R between 0 – 10 Å for V-CVD grown 3C-SiC/Si (001) samples. Experimental results for #S1 ●, # S2 , # S3 □ and # S4 ○ are shown by symbols and fitted data by similar colored lines.

21

Raman intensity (arb. units)

V-CVD 3C-SiC 300 K 12.8 m

LO ()

+

406 nm Kr #S

without substrate with Si substrate

(b)

LO ()

(a)

3

TO ()

TO () -1

794.2 cm 750

800

850

-1

970.3 cm

900 -1

Frequency (cm ) Fig. 1

22

950

1000

Raman intensity (a.u.)

V-CVD 3C-SiC/Si (001) #S

a)

01

3C-SiC

LO

TO

-1

Si 520 cm 400

500

600

700

800

900 -1

Frequency (cm )

23

1000 1100 1200

LO

Raman intensity (a.u.)

V-CVD 3C-SiC/Si (001) #S

b)

02

TO

Si -1

520 cm 400

500

600

700

800

900 -1

Frequency (cm )

24

1000 1100 1200

#S 4 #S 3 #S 2 #S

Raman intensity (arb. units)

V-CVD 3C-SiC/Si (001) +

Kr 406 nm

TO = 794.5 cm

-1

1

-1

LO = 970.2 cm

c) -1

TO= 794.3 cm TO= 794.2 cm

-1

-1

TO= 794.0 cm 700

800

900

LO = 970.3 cm

-1

LO= 970.5 cm 1000 -1

Frequency (cm )

Fig. 2

25

-1

1100

1200

1.0 -1

895 cm

SiC (Cryst.)

SiC (Intergr.) -1

Reflectance

0.8

V-CVD 3C-SiC/Si (001) #S

0.6

1

d = 3.37 m

TO = 794 cm LO = 973 cm

-1

-1

-1

TO = 940 cm

LO = 980 cm

-1

TO = 6.5 cm

TO = 25.0 cm

f

f

1

= 99.5 %

2

-1

= 0.5 %

Exptl. Calc.

0.4

0.2

0 500

1000

1500

2000

2500 -1

Frequency (cm ) Fig. 3

26

3000

3500

X-ray absorption coefficient,  (arb. units)

V-CVD 3C-SiC/Si(001)

a)

#S 1 #S 2 #S 3 #S 4

1800

1900

2000

2100

Energy (eV)

27

2200

2300

2400

18 V-CVD 3C-SiC/Si (001)

4

10

-2

k (k) (Å )

14

#S 1 #S 2 #S 3 #S

b)

2

6 2 -2 -6 2

3

4

5

6

7

8

9

10 11

12

13

14

-1

k (Å )

V-CVD 3C-SiC/Si(001)

#S 1 #S 2 #S 3 #S

c)

2

-2

k (k)(Å )

4

0

2

4

6

8 -1

k (Å ) 28

10

12

V-CVD 3C-SiC/Si (001) #S

3

k = 2.1 - 10.9 k = 2.1 - 10.1 k = 2.1 - 9.6 k = 2.1 - 8.9 k = 2.1 - 8.3

d)

-3

(R)(Å )

1

2

1

0 0

1

2

3

4

5

6

7

8

9

10

R (Å)

3.0 V-CVD 3C-SiC/Si (001)

2.5 2.0 -3

 (R) (Å )

# S (Fit) 1 # S (Fit) 2 # S (Fit) 3 # S (Fit) 4 # S (Exp.) 1 # S (Exp.) 2 # S (Exp.) 3 # S (Exp.)

e)

1.5 1.0

4

0.5 0 1

2

3

4

5

6

7

R(Å)

Fig. 4 29

8

9

10

Table 1. Comparison of the Raman scattering data on optical phonons (cm-1) used for assessing the stresses and strains in V-CVD grown 3C-SiC/Si (001). The elastic compliance values used here (S11 = 3.074 x 10-13 cm2/dyn and S12 = -0.787 x 10-13 cm2/dyn) are obtained by fitting the IXS data of phonon dispersions [69] of 3C-SiC by exploiting a realistic lattice dynamical model [60]. 3C-SiC/Si (001) d m

TO cm-1

S1

3.2

796.0

S2

5.6

S3

Sample #

LO cm-1

 || (%)

 (%)

Ref.

0.598±0.060

0.137

-0.094

[our]

970.3

0.575±0.058

0.132

-0.091

[our]

794.2

970.3

0.563±0.057

0.129

-0.089

[our]

794.0

970.5

0.587±0.059

0.134

-0.092

[our]

972.4

794.3

969.9

0.575±0.058

0.132

-0.091

[46]

972.4

793.1

971.1

0.622±0.063

0.142

-0.098

[46]

973.6

793.1

970.3

1.138±0.115

0.260

-0.179

[46]

972.8

794.3

969.9

0.810±0.082

0.185

-0.127

[46]

TO cm-1

LO cm-1

972.3

794.5

970.2

795.7

972.4

794.3

12.8

795.5

972.5

S4

16.0

795.5

972.5

487*

4.0

795.5

475 B*

4.5

795.1

462*

6.0

796.3

475*

7.0

796.3

30

X (GPa)

Table 2. The parameters of Bruggeman effective medium theory used in simulating the infrared reflectance spectra of V-CVD grown 3C-SiC/Si (001) sample # S1 (see text).

Sample # S1

Parameters

Volume fraction

TO (cm-1)

LO (cm-1)

Crystalline SiC

f1 = 99.5 % 794

973

Intergranular SiC

f2 = 0.5 %

973

943

31



6.7

6.0

 TO (cm-1)

Thickness (m)

8.5

3.37

25

Table 3. Fitting results from the EXAFS data of four different thickness 3C-SiC/Si (001) samples for extracting local atomic structures [i.e., nearest-neighbor (R1) and next-nearestneighbor (R2) bond lengths in Å]

Sample Local structure R1 R2

# S1

1.88 3.09

# S2

# S3

1.85

1.86

3.07

3.08

32

# S4

1.91 3.06