Quantifying the Short-Range Order in Amorphous ... - ACS Publications

Article Cite This: Anal. Chem. XXXX, XXX, XXX−XXX

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Quantifying the Short-Range Order in Amorphous Silicon by Raman Scattering Priyanka Yogi,† Manushree Tanwar,† Shailendra K. Saxena,*,‡ Suryakant Mishra,§ Devesh K. Pathak, Anjali Chaudhary, Pankaj R. Sagdeo, and Rajesh Kumar* Material Research Laboratory, Discipline of Physics & MEMS, Indian Institute of Technology Indore, Simrol-453552, India S Supporting Information *

ABSTRACT: Quantification of the short-range order in amorphous silicon has been formulized using Raman scattering by taking into account established frameworks for studying the spectral line-shape and size dependent Raman peak shift. A theoretical line-shape function has been proposed for representing the observed Raman scattering spectrum from amorphous-Si-based on modified phonon confinement model framework. While analyzing modified phonon confinement model, the term “confinement size” used in the context of nanocrystalline Si was found analogous to the short-range order distance in a-Si thus enabling one to quantify the same using Raman scattering. Additionally, an empirical formula has been proposed using bond polarizability model for estimating the short-range order making one capable to quantify the distance of short-range order by looking at the Raman peak position alone. Both the proposals have been validated using three different data sets reported by three different research groups from a-Si samples prepared by three different methods making the analysis universal.

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Si device. Additionally, quantification of the short-range order in amorphous materials may help in identifying any possible scientific information in this gray area, which may lead to great discoveries as in the case of nanoscience. Presence of order, whether short-range or long-range, can be examined by X-ray diffraction (XRD) qualitatively but can not be quantified by this method. Raman scattering,19−21 which has been established as a widely used versatile spectroscopic tool, may prove to be just appropriate for the purpose because of its various scientific merits. The only disadvantage, being a weak phenomenon, has been taken care of in the instrumentation because of the availability of very good source and detectors making it an unmatchable characterization tool used by scientists across all the disciplines. Raman scattering is not only a probe to study the phase identification,22,23 chemical compositions,24,25 and level of doping26,27 but it also has shown a promising potential for acting as a sensitive probe to monitor various physical phenomena taking place at microscopic levels, such as confinement,21,28−31 defect structures, and crystalline nature of materials.32 Because of its immense advantages and broader acceptability, Raman spectroscopy has not lagged behind even in understanding different phenomena in comparatively newer but exceptionally important field of nanosciences and nanotechnology.33,34 At times, Raman spectroscopy has been proved to be superior to other methods

anoscience and nanotechnology has been established as an important area, which makes it equally important to characterize these materials which were considered amorphous for long.1,2 At the junction of the (poly-)crystalline and amorphous, in a particular crystallite size window,3,4 a sizedependent property variation was observed, which marks the domain of the nanoscience.5,6 The length of ordered material7 (in the crystallinity) remained the distinguishing parameter between the three phases of solid,8 crystalline,9,10 nanocrystalline,11 and amorphous,12 with crystalline material having the longest range of order of crystallinity, whereas amorphous material13 has the least. The distance up to which a (poly)crystalline solid maintains the crystallinity defines the degree of order,14 which is quantified by the crystallite size. Though the crystallite size quantifies the degree of order in crystalline materials, ambiguity remains inherently, while quantifying the term in amorphous material as the range of the order is rather “short” and usually not defined even empirically. Whereas, in nanocrystalline materials the crystallite size comparable to the Bohr’s radius15,16 declares the onset of the “nano” regime and can be defined as the distance of the range of order. Such kind of quantification of the degree of order may prove to be of scientific and technological importance and thus needs attention. As an example, it is often observed that efficiency of amorphous silicon (a-Si) solar cells17,18 depends on the method of material preparation though the actual player responsible for this variation is unknown. It is possible to see a correlation between the quantified short-range order and solar cell efficiency thus will be helpful in designing an appropriate a© XXXX American Chemical Society

Received: March 26, 2018 Accepted: June 1, 2018

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DOI: 10.1021/acs.analchem.8b01352 Anal. Chem. XXXX, XXX, XXX−XXX

Article

Analytical Chemistry

Figure 1. (a) Raman spectra of a-Si of samples AS1 (Reproduced from ref. 49 with permission from the PCCP Owner Societies) and AS2 (Reproduced from ref 42 with permission from The Royal Sciety of Chemistry), discrete data points show the experimentally obtained Raman spectra whereas solid line corresponds to theoretical fitting (eq 1). Left and right insets in panel a shows the theoretical Raman line shapes of c-Si and n-Si (2 nm) respectively. (b) Illustration for depicting various Raman processes involving the scattering from c-Si, n-Si, and a-Si.

positions in the range of 475−482 cm−1 and yield three different size parameter and has been quantified as the distance of short-range order. This is validated by another established model, the bond polarizability model (BPM)48 yielding an empirical relation between the Raman peak position and the size parameter or the short-range order distance. An inverse size dependent on power ∼2.2 between the size and Raman peak position is observed for a-Si showing a short-range order of less than one nanometers which is very small to be called a nanomaterial.

for quantification of various physical parameters, such as size,35,36 level of doping,27,31 electron−phonon interaction,37 etc., of Si by theoretically calculated Raman line shape and fitting it with the experimentally observed data. The theoretical Raman line shape may prove to be a superior module for the quantification of short-range order present in amorphous materials as well. It is worth mentioning here that light scattering phenomenon also plays an important role for studying the structure of disordered or quasi-disordered systems,38−40 it can be used to quantify the distinction between the crystalline lattice and messy lattice (the lattice having disordered nature, amorphous materials), which again is more qualitative in nature. On the other hand Raman spectral line-shapes can be explained explicitly by theoretically modeled line-shape functions for crystalline (a sharp and symmetric spectrum) and nanocrystalline materials (a broader and asymmetric spectrum), especially Si. Such a line-shape function for representation of experimentally observed Raman spectra from amorphous material is not available. Lack of such an analysis forces one to use Gaussian function to fit the observed spectra23,38 making it an unrealistic approach. A successful quest for finding a Raman spectral line-shape for representation of Raman spectra from amorphous material will not only make the Raman spectral line-shape study complete but may also enable one to quantify the short-range order of the amorphous solids. As an example, the Raman spectra of a-Si41−44 has a broad band around 480 cm−1 with a hump around 350 cm−1. However, in case of crystalline Si (c-Si), the sharp, as well as symmetric, peak is observed at ∼520 cm−1 attributed to the participation of zone centered phonons.45−47 An in-depth study of Raman spectra from amorphous material may help in quantification of the short-range order present, which makes the basis of this paper. In the existing study, Raman scattering has been used to quantify the disorders present in the a-Si by analyzing the existing modified phonon confinement model (MPCM) generated spectral line-shape function, which contains a size parameter and represent the crystallite size for nanomaterials. The line-shape function is then compared with the Raman scattering data from three different a-Si prepared by different research groups. Raman spectra from the three samples show Raman peaks at different

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MATERIALS AND METHODS Three different sets of experimental Raman scattering data of aSi has been used in the present study out of which two data sets have been taken from two reports from Lopez T. et al.42 and Al-Salman R. et al.49 The third Raman scattering data has been obtained from a-Si sample prepared by ion-implantation. The recipe of a-Si sample fabricated by ion implantation is as follows. First a 500 nm thick film of crystalline Si, prepared by routine chemical vapor deposition (CVD) technique, on sapphire was used as starting point. The above c-Si thin film was implanted with phosphorus ions with a fixed fluence of 5 × 1015 ions/cm2 and energy of 150 keV. The resultant film, obtained after ion implantation, was characterized using X-ray diffraction and Raman spectroscopy to validate the amorphous nature as will be discussed in detail later on appropriately. The Raman spectrum has been recorded using a SPEX-1403 double monochromator with HAMAMATSU (R943-2) photomultiplier tube with laser excitation wavelength of 514.5 nm. Philips X’pert, pro PW 3,040 X-ray diffractometer was used for recording the XRD pattern in glancing angle geometry with glancing angle of 2°. The Raman line shape analysis has been carried out to measure the short-range order present in these samples. The Raman spectra taken from previous literature have been used to validate the present study.

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RESULTS AND DISCUSSION In contrast to the Raman spectrum of c-Si, a symmetrical Lorentzian Raman line shape35 with peak at ∼520.5 cm−1 and full width at half maximum (fwhm) of ∼4 cm−1, a-Si shows a rather broad Raman spectrum with peak around 480 cm−1, which is also accompanied by another small peak near 150 B


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Analytical Chemistry cm−1,44,49 making the spectrum a distribution of Raman scattering signal spread asymmetrically across a wide range of energy. Another typical nature of Raman spectrum from a-Si is inconsistency in its peak position as can appear between any value between 475 and 490 cm−1,49−51 depending on the method of preparation giving rise to a different phonon spectrum at microscopic level in a given sample. This behavior makes it difficult to define the Raman spectral line-shape for aSi, which has been attempted here by taking three experimental data sets, two from already reported Raman spectra42,49 and third one by performing Raman spectroscopy on prepared sample using ion implantation as mentioned above. Figure 1a shows Raman spectra from a-Si as reported by AlSalman R. et al.49 and Lopez T. et al.42 shown as discrete points for samples AS1 and AS2, respectively. The broad band around 480 cm−1 dominates in Raman spectra of a-Si in both the samples with Raman peaks appearing at 477 and 480 cm−1 respectively for sample AS1 and AS2 if to be mentioned precisely and a fwhm of ∼100 cm−1. For comparison, typical Raman line-shapes from c-Si and nanocrystalline Si are shown in the insets. It can be appreciated from the insets that a welldefined Raman line-shape functions can define the Raman scattering profile from crystalline and nanocrystalline Si as given in the Supporting Information. Just to mention, a pure Lorentzian function (eq S1) represents the Raman line-shape from c-Si, whereas a rather comprehensive equation, obtained by incorporating various factors that affect the Raman scattering including nanocrystallite size, is used to explain the asymmetric Raman line-shape for nano-Si (Figure S1). Both these equations are well established and provided as eqs S1 and S2 and have been discussed at length somewhere else,30,31,35,52 using a phonon confinement model (PCM). To understand the line-shape of the broad Raman spectrum from a-Si (Figure 1a), prior to represent it in the form of a line-shape function, it will be important to understand the rather well-understood Raman line-shape from c-Si and nano-Si. The symmetric Raman lineshape from c-Si (left inset, Figure 1a) originates because of Raman scattering of single phonon with single frequency (ωc) equal to the zone center phonon (ω0). This can be seen pictorially in Figure 1bI, where a photon of frequency ωi results in another photon of frequency ωs after undergoing Raman scattering from single-frequency (ωc) phonons corresponding to zone center phonon of frequency ω0. On the other hand, a nanocrystalline material allows all phonons, arranged throughout the phonon dispersion curve,45 to participate in Raman scattering thus resulting in a line-shape as shown in right inset of Figure 1a. Raman scattering of a photon from these arranged phonons in a poly/nanocrystalline Si is shown pictorially in Figure 1bII, where ωn represents the integral sum of all phonons available on the phonon dispersion curve with all possible wave-vectors (k).45,53,54 Unlike c-Si or nano-Si, a-Si does not contain phonons with well-defined wave vectors and thus the phonons are not ordered rather are random with no assigned momentum vector to it. This disorder is expected to get reflected in Raman scattering and the corresponding spectral line-shape will be a manifestation of the average sum of all these random phonons present in a-Si. This process is represented pictorially in Figure 1bIII, where ωa represents the summation (of all random phonons available) sign, in contrast with the integral sign in Figure 1bII, is used to represents the random phonons. As a consequence to this, the Raman spectra from a-Si is not usually represented through a line-shape function, like the one for c-

Si31,46 and n-Si,27,30,36 rather a Gaussian line-shape50,51 is used to represent it. As a result, lot of information, lying under the envelop of spectral line-shape, remains hidden and unexplored. However, phonons can be thought of being confined in a-Si like the ones in n-Si, but this hypothesis driven line-shape equation obtained using PCM does not explain the broad asymmetric Raman line-shape from a-Si, thus requiring an alternative lineshape function as it fails to yield a broad asymmetric Raman line-shape for very low sizes of nanoparticle as can be seen in Figure S1. Alternatively, the modified PCM (MPCM)28,29,33,40 was tried for the same as given by eq 1. 2π + 1

1 I(ω , D) = ρ(ω) 3 × πD

∫

4πQ

2

2

(Q2 )

sin

3

π 3Q (4π 2 − Q 2)

[ω − ω′(Q )]2 +

( Γ2 ) 2

( Γ2 )

dQ

2π − 1

(1) 2⎞

⎛ where, ω′(Q ) = 521⎜1 − 0.23 ⎝

( 2QaπD ) ⎠ ⎟

is the dispersion

n(ω) + 1

relation, ρ(ω) ∼ ω is the Bose−Einstein occupation function, Γ is the line width of the Raman line shape, D is the crystallite size, and a is the lattice constant of Si. It is worth mentioning here that the MPCM is not correct enough to explain the Raman spectra from low dimensional Si in to as it fails completely to explain the size dependent asymmetry31,55−58 as has been discussed somewhere else58 and a size dependent spectral behavior is given in Figure S2. Equation 1, has been used to fit the data in Figure 1a by appropriately choosing the value of ‘D’ and is shown as solid lines (Figure 1a). The best fit lines in Figure 1a is obtained for samples AS1 and AS2 when D of 8.3 and 8.8 Å, respectively, as summarized in Table 1 below along with other Raman spectral parameters. Table 1. Raman Parameters Calculated from Fitting of Raman Spectra of AS1, AS2, and AS3 Used in Existing Studya Raman spectra ref and present work

Raman peak position (cm−1)

fwhm (Γ) (cm−1)

short range order D (Å)

short range order D (Å) calculated by eq 2 (uncertainty in %)

AS1 (AlSalman R. et al.)49 AS2 (Lopez T. et al.)42 AS3 (present work sample)

477

108

8.3

8.5 (2.4)

480

100

8.8

8.8 (0.0)

482

80

9.3

9.0 (3.2)

a

The uncertainty values of D is estimated by taking the difference between fitted value and estimated value using eq 2 displayed in the parentheses in column five.

A good agreement between the experimental data and theoretical line-shape indicates that eq 1 may be used for spectral line-shape representation for Raman scattering data from a-Si. Another very significant advantage of using eq 1 is related to the quantification of disorder in the sample and will be discussed later. To further validate the above-mentioned agreement, Raman spectrum obtained from a-Si sample prepared by ion implantation (sample AS3) is also fitted using eq 1 as shown in Figure 2 which shows broad spectra centered at 482 cm−1 and an fwhm of 80 cm−1, representing a C


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Another important observation from the above analysis is the dependence of Raman peak position on the size parameter D as evident from the right inset of Figure 2. This behavior is similar to the size dependent red shift observed from nano-Si when analyzed within the framework of BPM48 as given by eq 2. Figure 3 shows the theoretically generated curves using eq 2, at

Figure 2. Discrete data points shows the experimentally acquired Raman spectra of P+ ion implanted sample (AS3) of a-Si and solid line corresponds to the theoretically calculated Raman line shape (eq 1) . Left inset shows the XRD pattern of ion implanted sample and right inset shows the theoretically calculated short-range order present in AS1, AS2, and AS3, respectively, along with their Raman peak positions. Figure 3. Theoretically simulated curves of Raman shift vs size for Si sphere, column, and a-Si. The red, green, and blue data points correspond to the calculated results for column, sphere, and a-Si, respectively. The pictorial representation corresponds to the shape used to calculate the curve of a-Si.

typical Raman spectrum from a-Si.59 It can be appreciated from Figure 2 that the shape and spectral width of Raman spectrum of AS3 is in consonance with the previous literatures,22,33 as well as the data in Figure 1a. The XRD and Raman spectroscopy are the most widely used techniques for phase identification of materials and the same has been utilized here for this purpose. The XRD pattern, from sample AS3, has been recorded in glancing angle geometry with glancing angle of 2° as displayed in the left inset in Figure 2 showing absence of any diffraction peak, a signature of amorphous materials as reported by Shabir Q. et al.59 and others. The XRD pattern from sample AS3 has been compared with that of c-Si sample and has been shown in Figure S3. XRD pattern from c-Si (Figure S3) shows couple of diffraction peaks due to crystallinity, which is not present for sample AS3 indicating the amorphous nature of sample AS3. The XRD pattern and Raman spectrum from sample AS3 (Figure 2 and S3) validates the presence of a-Si in sample AS334,35 The solid line in Figure 2, representing the best fit of the experimental data, is obtained from eq 1 with D = 9.3 Å. This has also been tabled along with the other two data in Table 1 for comparison. It is very conclusive from Table 1 and Figures 1 and 2 that eq 1 can successfully represent three different Raman data sets obtained from three a-Si samples prepared by three different methods by three different researchers. It can be appreciated from Table 1 that the Raman peak shifts as a function of the size parameter D as can be seen in the right inset of Figure 2. One should be very cautious in interpreting the term D by saying it the “nanocrystallite size”, as it is traditionally named, may be a misleading term in the context of amorphous materials. Since the amorphous materials are characterized by the term short-range order and the Raman spectrum obtained is a resultant of scattering from the phonons existing within this short-range order distance it would be appropriate to use the term D for this distance. In other words, the term D, obtained from Raman spectral analysis, can be used to quantify this short-range order in a-Si.

different values of δ (as mentioned below) showing the Raman shifts due to the confinement for different Si structures as a function of size of Si. ⎛ a ⎞δ Δω = −ξ⎜ ⎟ ⎝D⎠

(2)

where a is the lattice parameter and D is the nanocrystallite size for nano-Si and δ governs the size dependence of red shift in term of peak position as compared to the c-Si counterpart and depends on the shape of the nanoparticles. Zi et al.48 proposed a value of δ as 1.08 and 1.44 for columnar and spherical Si nanoparticles, respectively. The parameter, ξ, is used to explain the confinement of phonons and takes the value of 20.92 and 47.41 cm −1 for columnar and spherical nanocrystals, respectively.48 The behavior of eq 2 is shown in Figure 3 for the columnar (red curve) and spherical (green curve) nanoparticles whereas the dotted straight line is shown to represent a Raman shift value of 480 cm−1 around which the typical Raman peak lies for a-Si. If one hypothesizes that the short-range order is having a spherical or columnar shape, a (pseudo)crystallite size of 6.1 and 2.9 Å respectively will be obtained. It means that if this (pseudo)crystallites are columnar in shape, its size will be only 2.7 Å which will only be able to fit couple of Si atoms (nearest distance ∼156 pm) whereas for spherical crystallite the size will be 5.6 Å which is only sufficient to fit a single unit cell of Si (lattice constant ∼5.4 Å). Both of these situations lead to a thermodynamically impossible conclusions thus proving the hypothesis wrong.60−63 It means that the ξ and δ values proposed by Zi et al.48 cannot be used if one wants to estimate the size of (pseudo)crystallite or the distance of short-range order present in a-Si using Raman peak position. Looking at the similarity between the size dependent D


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Figure 4. Theoretically obtained Raman line shapes for (a) c-Si, (b) SiNSs, and (c) a-Si displayed in the different circles. The schematic (blue, green, and red line on the top of Raman line shape) shows the abrupt transition from c-Si to a-Si.

constant (520 cm−1), for nano Si it ranges from 520 to 510 cm−1 and for a-Si shows transition from 480 to 470 cm−1 respectively. Thus, a spectral line-shape (eq 1) and empirical relation (eq 2) will empower one to quantify the distance up to which the order of crystallinity is intact in an a-Si. As mentioned earlier, this can be of technological use because it is observed that the short-range order in a-Si has an effect on the efficiency of a-Si solar cell and may have similar effect on other technological important properties of amorphous materials in general and a-Si in particular.

peak shift behaviors of n-Si and a-Si, a third set of ξ and δ value is proposed here to be used exclusively for a-Si. The size dependent Raman shift function (eq 2) with ξ = 117 cm−1 and δ = 2.21 is also plotted in Figure 3 (blue curve). The estimated size using these values comes out to be 8.8 Å for Raman spectrum centered at 480 cm−1, which is approximately equal to the size obtained by fitting for sample AS2. This size is reasonable as it may contain more than 160 unit cells of Si making it thermodynamically viable. Similarly, sizes have been estimated for samples AS1 and AS3 and obtained to be 8.5 and 9.0 Å, respectively, which is in the same range as obtained using the fitting (Table 1). A comparison between the sizes estimated using the two approaches, the fitting with the line-shape and the empirical equation, reveals that eq 2 can be used universally to estimate short-range order present in a-Si by looking at the peak position of the Raman spectra. This will help in quantifying the disorder present at microscopic level in a-Si prepared by any method. The above-mentioned discussion can be summarized in a nut shell by consolidating the line-shape representations for Si in it is crystalline, nanocrystalline and amorphous phases as follows. Raman line-shape from c-Si is a typical Lorentzian function and represented by one to result in a sharp symmetric line-shape centered at zone centered phonon frequency and show no size dependent peak shift as represented in Figure 4a, along with the equation (eq S1). A shape- and size-dependent Raman lineshape asymmetry, red-shift, and broadening is a typical behavior of Raman spectra obtained from nano-Si as represented by a spectral line-shape functioned worked out within the framework of PCM as shown in Figure 4b (eq S2). Above mentioned two regimes of Si phases are well discussed in contrast to the aSi phase in the context to Raman spectral line-shape representation. An asymmetric Raman line-shape obtained from a-Si can be successfully represented by MPCM and can be used to estimate short-range order distance and phonon lifetime using eq 1 as shown in graphics in Figure 4c. In other words, Figure 4 depicts that phonon frequency for c-Si is

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CONCLUSIONS A Raman line-shape function proposed within the formulation of MPCM can be used to successfully represent experimental Raman spectrum obtained from a-Si. The line-shape thus obtained is validated by fitting three different sets of a-Si Raman scattering data obtained by three different research groups from a-Si samples prepared by three different methods. The Raman peak position is observed to be depending on a size parameter and has been used to quantify the distance of short-range order present in a-Si. As an extension, an empirical relation between the short-range order and Raman peak position has been proposed to be used as a handy tool for quantification of shortrange order. This relation, obtained based on BPM, seems to be universal in nature for quantification of short-range order and can be used by a-Si prepared by any method. The line-shape fitting followed by proposed empirical relation allows one to have a complete set of Raman line-shape functions for the whole range of Si phases from crystalline to amorphous via nanocrystalline phase.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.8b01352. E


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Theoretical Raman line-shapes obtained using PCM and MPCM, XRD and Raman experimental data with background (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Shailendra K. Saxena: 0000-0001-7156-3407 Suryakant Mishra: 0000-0002-9331-760X Pankaj R. Sagdeo: 0000-0002-2475-6676 Rajesh Kumar: 0000-0001-7977-986X Present Addresses ‡

S.K.S.: National Institute for Nanotechnology, University of Alberta, Edmonton, Canada. § S.M.: Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel Author Contributions †

P.Y. and M.S. contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Authors acknowledge useful discussions with Dr. H.S. Mavi (IIT Delhi), Dr A.K. Shukla (IIT Delhi), and Dr. J. Jayabalan (RRCAT, Indore, India). D. K.P. acknowledges financial assistance from Council of Scientific and Industrial Research (CSIR). Authors acknowledge MHRD and DST, Govt. of India for providing funding.

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