7
Optical properties of SbI 3 single crystalline platelets Mirosława Ke ˛pin ´ ska , Marian Nowak, Piotr Duka, Michalina Kotyczka-Moran ´ ska, Piotr Szperlich Solid State Physics Section, Institute of Physics, Silesian University of Technology, P.O. Box 221, PL-40019 Katowice, Poland article info Article history: Received 13 January 2011 Received in revised form 26 May 2011 Accepted 7 June 2011 Available online 8 July 2011 Keywords: Thin films Antimony triiodide Anisotropic materials Optical parameters Spectrogoniometry abstract Optical parameters of platelets of crystalline antimony triiodide (SbI 3 ) have been evaluated using spec- trogoniometric interference spectroscopy technique. Spectral characteristics of real parts of refractive indices of radiation with electric vector normal and parallel to the optical c-axis of SbI 3 crystalline plate- lets (i.e. n o , n e – refractive indices for ordinary and extraordinary rays) have been shown. The temperature dependences of spectra of optical parameters (n o and absorption coefficient of radiation with electric vec- tor normal to the optical c-axis) have been presented. The temperature dependences of fitted optical indi- rect allowed energy gap of SbI 3 , Urbach energy and phonons energies are the main findings of the presented work. The obtained results have been compared with literature data. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Metal halides have been the subject of growing interest due to their various industrial applications, for example, in halogen met- allurgy, nanotechnology, semiconductors and in production of hal- ogen lamps for medicine. Antimony triiodide (SbI 3 ) with layered structure is well known [1–5] semiconductor. Crystalline SbI 3 exhibits second-harmonic generation [6]. Photosensitive films of SbI 3 have found applications in solid-state batteries as cathodes [7], in high-resolution image microrecording and in information storage [8]. SbI 3 belongs to the trigonal system with a space group C 2 3i . Unlike alkali halides antimony triiodide has a rhombohedral crystal structure in which the halogen atoms are in almost perfect hexagonal packing. The main properties of SbI 3 have been re- viewed in a few monographs (see e.g. [9,10]). However, the optical properties of this material are still investigated [11,12]. The aim of this paper was to use the recently evaluated spec- trogoniometric interference spectroscopy technique [13] to inves- tigate some of optical properties of SbI 3 crystalline platelets. The value of refractive index of radiation is crucial for optoelectronics application of the investigated material. The main interest is in the determining the type of optical energy gap of SbI 3 and in its temperature dependence. 2. Experimental details The investigated single-crystalline platelets of SbI 3 were grown from a vapor phase. The platelets had area of 5–19 mm 2 and thicknesses in the range from 2 to 22 lm(Fig. 1). Specular trans- mittance measurements in temperature range from 80 K to 343 K and in spectral range from 380 nm to 1050 nm were performed using the experimental set-up presented in Fig. 2. Samples were mounted in 1.33 Pa vacuum in an optical cylindrical chamber placed on the table of GUR-5 (LOMO) goniometer or in the optical D2209 chamber (in the case of perpendicular illumination). The chambers were equipped with R2205 Cryogenic Microminiature Refrigeration II-B System and K20 temperature controller (MMR Technologies, Inc.). Vacuum was obtained by TSH 071E turbomo- lecular drag pumping station (Pfeiffer). The optical transmittance was measured using PC2000 (Ocean Optics Inc.) spectrophotome- ter with master card (600 lines grating, blazed at 500 nm). The spectrophotometer was equipped with appropriate waveguide cables and the deuterium–halogen light source DH2000-FHS from Ocean Optics Inc. The multiple averaged spectral characteristics containing 2048 data points for various wavelengths were regis- tered using the OOI-Base program from Ocean Optics Inc. at con- stant temperature of the sample. The measurements were carried out for angles of light incidence upon a sample from about 60° to 60° with a sampling interval of 0.5°. Using Glan-Thomson pola- rizer (LOT-Oriel) the incoming radiation beam was linear polarized with the electric vector parallel (p) or perpendicular (s) to the plane of incidence. 3. Results Fig. 3 shows typical spectra of optical transmittances (T s and T p ) of SbI 3 crystalline platelet for fixed h i angles of incidence of s and p polarized light. All of them are characteristic for interference of radiation multiply internal reflected in a parallel-sided thin 0925-3467/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2011.06.009 Corresponding author. Tel.: +48 32 603 41 88; fax: +48 32 171 06 58. E-mail address: [email protected] (M. Ke ˛pin ´ ska). Optical Materials 33 (2011) 1753–1759 Contents lists available at ScienceDirect Optical Materials journal homepage: www.elsevier.com/locate/optmat

Optical properties of SbI3 single crystalline platelets

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Page 1: Optical properties of SbI3 single crystalline platelets

Optical Materials 33 (2011) 1753–1759

Contents lists available at ScienceDirect

Optical Materials

journal homepage: www.elsevier .com/locate /optmat

Optical properties of SbI3 single crystalline platelets

Mirosława Kepinska ⇑, Marian Nowak, Piotr Duka, Michalina Kotyczka-Moranska, Piotr SzperlichSolid State Physics Section, Institute of Physics, Silesian University of Technology, P.O. Box 221, PL-40019 Katowice, Poland

a r t i c l e i n f o a b s t r a c t

Article history:Received 13 January 2011Received in revised form 26 May 2011Accepted 7 June 2011Available online 8 July 2011

Keywords:Thin filmsAntimony triiodideAnisotropic materialsOptical parametersSpectrogoniometry

0925-3467/$ - see front matter � 2011 Elsevier B.V. Adoi:10.1016/j.optmat.2011.06.009

⇑ Corresponding author. Tel.: +48 32 603 41 88; faxE-mail address: [email protected] (M. K

Optical parameters of platelets of crystalline antimony triiodide (SbI3) have been evaluated using spec-trogoniometric interference spectroscopy technique. Spectral characteristics of real parts of refractiveindices of radiation with electric vector normal and parallel to the optical c-axis of SbI3 crystalline plate-lets (i.e. no, ne – refractive indices for ordinary and extraordinary rays) have been shown. The temperaturedependences of spectra of optical parameters (no and absorption coefficient of radiation with electric vec-tor normal to the optical c-axis) have been presented. The temperature dependences of fitted optical indi-rect allowed energy gap of SbI3, Urbach energy and phonons energies are the main findings of thepresented work. The obtained results have been compared with literature data.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction thicknesses in the range from 2 to 22 lm (Fig. 1). Specular trans-

Metal halides have been the subject of growing interest due totheir various industrial applications, for example, in halogen met-allurgy, nanotechnology, semiconductors and in production of hal-ogen lamps for medicine. Antimony triiodide (SbI3) with layeredstructure is well known [1–5] semiconductor. Crystalline SbI3

exhibits second-harmonic generation [6]. Photosensitive films ofSbI3 have found applications in solid-state batteries as cathodes[7], in high-resolution image microrecording and in informationstorage [8]. SbI3 belongs to the trigonal system with a space groupC2

3i. Unlike alkali halides antimony triiodide has a rhombohedralcrystal structure in which the halogen atoms are in almost perfecthexagonal packing. The main properties of SbI3 have been re-viewed in a few monographs (see e.g. [9,10]). However, the opticalproperties of this material are still investigated [11,12].

The aim of this paper was to use the recently evaluated spec-trogoniometric interference spectroscopy technique [13] to inves-tigate some of optical properties of SbI3 crystalline platelets. Thevalue of refractive index of radiation is crucial for optoelectronicsapplication of the investigated material. The main interest is inthe determining the type of optical energy gap of SbI3 and in itstemperature dependence.

2. Experimental details

The investigated single-crystalline platelets of SbI3 were grownfrom a vapor phase. The platelets had area of 5–19 mm2 and

ll rights reserved.

: +48 32 171 06 58.epinska).

mittance measurements in temperature range from 80 K to 343 Kand in spectral range from 380 nm to 1050 nm were performedusing the experimental set-up presented in Fig. 2. Samples weremounted in 1.33 Pa vacuum in an optical cylindrical chamberplaced on the table of GUR-5 (LOMO) goniometer or in the opticalD2209 chamber (in the case of perpendicular illumination). Thechambers were equipped with R2205 Cryogenic MicrominiatureRefrigeration II-B System and K20 temperature controller (MMRTechnologies, Inc.). Vacuum was obtained by TSH 071E turbomo-lecular drag pumping station (Pfeiffer). The optical transmittancewas measured using PC2000 (Ocean Optics Inc.) spectrophotome-ter with master card (600 lines grating, blazed at 500 nm). Thespectrophotometer was equipped with appropriate waveguidecables and the deuterium–halogen light source DH2000-FHS fromOcean Optics Inc. The multiple averaged spectral characteristicscontaining 2048 data points for various wavelengths were regis-tered using the OOI-Base program from Ocean Optics Inc. at con-stant temperature of the sample. The measurements were carriedout for angles of light incidence upon a sample from about �60�to 60� with a sampling interval of 0.5�. Using Glan-Thomson pola-rizer (LOT-Oriel) the incoming radiation beam was linear polarizedwith the electric vector parallel (p) or perpendicular (s) to theplane of incidence.

3. Results

Fig. 3 shows typical spectra of optical transmittances (Ts and Tp)of SbI3 crystalline platelet for fixed hi angles of incidence of s and ppolarized light. All of them are characteristic for interference ofradiation multiply internal reflected in a parallel-sided thin

Page 2: Optical properties of SbI3 single crystalline platelets

Fig. 1. Image of one of the investigated SbI3 crystalline platelets.

Fig. 2. Schematic illustration of the experimental set-up for measurements ofangular dependencies of the spectra of optical transmittance (DH-2000 – lightsource; W1 – waveguide; L – lens; P – Glan–Thomson polarizer; ? representincident and transmitted light; S – sample; G – goniometer; VC – vacuum chamber;JTR – Joule–Thomson refrigerator; W2 – waveguide on moving arm of goniometer;PC2000 – PC plug-in spectrometer; IBM PC – computer).

Fig. 3. Spectra of optical transmittance of SbI3 crystalline platelet (T = 298 K)illuminated under different angles by plane polarized light with electric vectornormal (a) and parallel (b) to the incidence plane; arrows show the shift of thepeaks of constant interference order with increasing angle of light incidence uponthe sample.

1754 M. Kepinska et al. / Optical Materials 33 (2011) 1753–1759

sample. One can observe the strong influence of hi upon the posi-tion of interference extrema in spectral characteristics of SbI3

transmittance. The arrows indicate shifts of a typical interferencefringe to shorter wavelengths with increasing value of hi. Fig. 4 pre-sents angular dependences of spectral positions of some extremain transmittance spectra of the investigated SbI3. It should be no-ticed that these angular dependences are different for variouslypolarized light.

Fig. 5 presents spectral dependences of optical transmittance ofSbI3 crystalline platelet at different temperatures (hi = 0). It shouldbe underlined that only some of the experimental data are shownin the figure to make them clearer. The shift of the absorption edgeto longer wavelengths with increasing of temperature is due to thechange of the energy gap of the investigated material. Extrema ofoptical transmittance are shifted mainly due to the temperaturechange of the real part of SbI3 refractive index.

Fig. 4. Influence of polarization of light on the angular dependences of the spectralpositions of selected extrema in transmittance of SbI3 crystalline platelet (blank andfilled signs – data for s and p polarized light; solid and dashed curves represent theinterpolation of the data; , , , – points representing angles hk0 (description inthe text) for k0 = 675 nm, 665 nm, 654 nm, and 645 nm, respectively.

4. Discussion

Interference of radiation internally reflected in parallel-sidedsamples affects characteristic extrema in spectral distributions ofoptical transmittance (To(k)) and reflectance (Ro(k)). The main fea-ture distinguishing them from absorbance extrema is correlationbetween maxima and minima in To(k) and Ro(k). The other featureconsists in the relation between positions ðkm; kmþ1Þ of the extrema

Page 3: Optical properties of SbI3 single crystalline platelets

;

Fig. 5. Spectral dependences of optical transmittance of SbI3 crystalline platelet atdifferent temperatures: solid line – 80 K, dashed line – 200 K, dotted line – 320 K(hi = 0�, w = 2.73(2) lm).

Fig. 6. Influence of the wavelength and polarity of radiation on the square functionof the sine of the angle of light incidence upon the SbI3 crystalline platelet versusthe square of the interference order of extrema; - k0 = 700 nm, -k0 = 687 nm, - k0 = 675 nm, - k0 = 665 nm, - k0 = 654 nm, -k0 = 645 nm; blank and filled signs represent data for s and p polarized light; solidand dashed lines show the least square fitted functions (4a) and (4b), respectively.

M. Kepinska et al. / Optical Materials 33 (2011) 1753–1759 1755

in optical characteristics and the changes in phases (Cm, Cm+1) ofthe beam on traversing the film of thickness 2w:

Cm � Cmþ1 ¼ 2p ð1Þ

where m and m + 1 represent orders of extrema,

Cm ¼4pwkm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12ðn2 � j2 � n2

0 sin2 hiÞ þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi14ðn2 � j2 � n2

0 sin2 hiÞ2 þ n2j2

rs

ð2Þ

n and j are the real and imaginary parts of the refractive index ofthe investigated material, n0 is the refractive index of the mediumin which there is the sample.

Sometimes Eq. (1) is used for estimation of sample thickness orrefractive index of materials. However the exact description ofthese parameters needs more sophisticated approach. Recentlythe interference spectrogoniometric method of material investiga-tions was proposed [13]. The observed (see e.g. Fig. 3) angulardependences of spectral positions of extrema in transmittancespectra of the investigated SbI3 agree with the predictions of[13]. In the case of negligible absorption of radiation the positions(kext) of interference extrema are described by [13–15]

mkextðTÞ ¼ 2n?ðTÞ �wðTÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� sin2 hi

n2?ðTÞ

sð3aÞ

for s polarized radiation and

mkextðTÞ ¼ 2n?ðTÞ �wðTÞ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� sin2 hi

n2jjðTÞ

vuut ð3bÞ

for p polarized radiation, where symbols n\ = no and njj ¼ ne de-scribe values of refractive indices of plane polarized light with elec-tric field perpendicular and parallel to the c-axis of the investigatedSbI3, i.e. refractive indices of ordinary and extraordinary rays.

The wavelengths (kext) of interference extrema decrease withincreasing the angle of light incidence and with increasing the or-der of interference fringes (Figs. 3 and 4). Values of kext depend onpolarity of the used light (Fig. 4). Interpolation of angular depen-dences of kext allows find angles (hk0) of light incidence for whichextrema of transmittance can be observed for a fixed wavelengthof light (k0) and different orders of interference (see Fig. 4).

As it was presented, e.g. in [13], Eqs. (3) are simply transformedinto linear formulae:

sin2 hk0 ¼ �as �m2 þ bs ð4aÞ

sin2 hk0 ¼ �ap �m2 þ bp ð4bÞ

Using these dependences one can determine refractive indicesand sample thickness from the linear dependence of sin2 hk0 onthe square of the order of interference

n?ðk0Þ ¼ ðbsðk0ÞÞ1=2 ð5aÞ

njjðk0Þ ¼ ðbpðk0ÞÞ1=2 ð5bÞ

wðk0Þ ¼k0

2ðasðk0ÞÞ1=2 ð6aÞ

wðk0Þ ¼k0njjðk0Þ

2n?ðk0Þðapðk0ÞÞ1=2 ð6bÞ

It should be underlined that uncertainties of Dn\, Dn|| and Dw canbe very easily calculated (see [13]).

As the main problem is the using of appropriate interference or-der in the presented formulae, one can use the method presentedin [13] to calculate m. That method is based on the fact that forgood assigned value of m the calculated thickness is independenton the wavelength of radiation [13]. In the presented case, the bestvalue of w = 2.73(2) lm was obtained taking m0 = 14 (at kext

= 1.011 lm). The values of m0 from 10 to 20 have been taken intoaccount. Fig. 6 presents such normalized square functions of thesine of hk0 for variously polarized light of different wavelengthsversus the square of the interference order of extrema. Solid anddashed lines in Fig. 6 represent the least square fitted dependences(4a) and (4b). The values of the least square fitted parameters as, bs,ap and bp were used to evaluate the values of refractive indices ofordinary and extraordinary beam in the investigated material forthe appropriate wavelength of light. Fig. 7a presents the goodagreement of the obtained results with the data presented in[4,16–18].

According to formula (3a), in the case of perpendicular illumi-nation of the sample

Page 4: Optical properties of SbI3 single crystalline platelets

Fig. 7. Spectral dependences of real part of refractive index of SbI3 platelet. (a)Comparison of the results obtained for ordinary (no, ) and extraordinary (ne, )rays at T = 298 K with the literature data: - [4], - [16], - [17], - [18]; (b)influence of temperature on real parts of refractive indices for ordinary rays –80 K, – 320 K. Solid curves represent the least square fitted Cauchy formula (8).Values of the fitted parameters are given in Fig. 8.

Fig. 8. Temperature dependences of Cauchy parameters n00 (a), a2 (b) and a4 (c) ofSbI3 crystalline platelet for plane polarized radiation with electric vector normal tothe optical c-axis; h – Cauchy parameters determined at room temperature.

1756 M. Kepinska et al. / Optical Materials 33 (2011) 1753–1759

n?ðTÞ ¼m2

kextðT; hi ¼ 0�ÞwðTÞ ð7Þ

Neglecting (in the first approximation) the temperature depen-dence of the platelet thickness and taking into account the deter-mined thickness of the sample and the order of interference foreach of the extrema one can use (7) to calculate the temperaturedependences of n\ (Fig. 7b).

Solid curves in Fig. 7 represent the fitted dispersions of the ob-tained refractive indices described by Cauchy formula:

nðkÞ ¼ n00 þa2

k2 þa4

k4 ð8Þ

Fig. 9. Temperature dependences of real part of refractive index of radiation withelectric vector normal to the optical c-axis of investigated SbI3 crystalline plateletfor selected wavelengths: – 570 nm, – 600 nm, – 650 nm, – 700 nm, –750 nm, – 800 nm, – 900 nm.

Values of the fitted parameters are given in Fig. 8. For theextraordinary ray at room temperature n00=2.20(4), = 2.20(4),a2=1.1(4)�10 = 1.1(4) � 10�15 m�2, a4 = 2.7(2) � 10�26 m�4. Addi-tional calculations were performed taking into account thermalexpansion of the investigated sample. The values of thermal expan-sion coefficients of layered GaSe and GaS [19] have been used inthese calculations due to the lack of data for SbI3. The performedcalculations have shown that the assumed constant thickness of asample is a quite good approximation for determining refractiveindices of the investigated material.

The presented spectra of real part of refractive indices (Fig. 7)prove the normal dispersion of radiation in the investigated SbI3.The fitted parameters n00, a2 and a4 of Cauchy dependence(Fig. 8) can be used for interpolation of the determined spectraland temperature dependence of n?ðkext ; TÞ. Fig. 9 shows suchevaluated temperature dependences of real parts of refractiveindex of radiation with electric vector normal to the optical c-axisof investigated SbI3 crystalline platelet. The values of no decreasewith increasing temperature (Figs. 7b and 9). Therefore the inves-tigated SbI3 belongs to the materials with negative thermo-optic

Page 5: Optical properties of SbI3 single crystalline platelets

M. Kepinska et al. / Optical Materials 33 (2011) 1753–1759 1757

coefficients. One can calculate values of the thermo-optic coeffi-cients for different temperatures and wavelengths using the datapresented in Fig. 8.

Some of determined spectral and temperature dependences ofoptical parameters of single crystalline SbI3 platelets, i.e. the ne(k;N = 298 K) (Fig. 7a), no(k; 80 K 6 N 6 320 K) (Figs. 7 and 9) werenever reported for this material. Therefore, only a few of the deter-mined parameters can be compared with literature data. However,one can see that the presented results are in good agreement withliterature data [4,16–18] on no (k, N = 298 K).

There are many techniques applied to determine the value of arefractive index. However, all of them feature various limitationsand disadvantages. We have applied one of the simplest methodsthat can be used for determining spectra of refractive indices inthin anisotropic films. It is based on the evaluation of the ordersof extrema in interference spectra of optical transmittance thatwas measured for various angles of light incidence. The interfer-ence of light is characteristic for thin films. It can be applied ininvestigations of SbI3 because the single crystals of this semicon-ductor grow as parallel sided, thin plates with c-axis perpendicularto their surface. The transmittance spectra of SbI3 plates exhibitwell resolved interference maxima and minima due to multiplereflection of radiation at the boundary surfaces of the samples. Itis important that the used method of investigations enables us todetermine spectra of ordinary and extraordinary refractive indicesindependently. The uncertainties of the determined values ofrefractive indices are very simple for reliable determining.

It should be noticed that the applied method of investigationsallows one to evaluate thickness of investigated sample and in con-sequence to determine the spectra of absorption coefficient oflight. The latter ones are necessary to establish the mechanism oflight absorption and to determine optical energy gap of the inves-tigated semiconductor. The interference transmittance spectros-copy [20] was used to evaluate absorption coefficients (a of theSbI3 single-crystalline platelet from the spectra of optical transmit-tance measured at different temperatures (see e.g. Fig. 5). In theseevaluations platelet thickness and values of no(k, T) determined bythe spectrogoniometric method were taken into account. Fig. 10presents such determined spectral dependences of a for planepolarized radiation with electric vector normal to the optical c-axisof SbI3 crystalline platelet at different temperatures. Using themethod presented in [20] the standard deviation of the platelet

Fig. 10. Spectral dependences of absorption coefficient of plane polarized radiationwith electric vector normal to the optical c-axis of SbI3 crystalline platelet atdifferent temperatures: – 80 K, – 160 K, – 240 K, – 320 K. Lines representthe fitted theoretical dependence (9). The insert shows fitted Urbach’s absorption(a2) for different temperatures. Values of the fitted parameters are described in thetext and shown in Figs. 11 and 12.

thickness over the illuminated sample area rw = 30 nm wasestablished.

Various mechanisms of absorption of electromagnetic radiationcan be observed in semiconductors, furthermore some of them cancoexist in the same spectral range. Therefore, the absorption spec-tra of SbI3 (Fig. 10) have been least square fitted with theoreticaldependence appropriate for the sum of the following mechanismsof absorption: (a1) indirect allowed absorption with absorption/emission of phonons without excitons [21,22], (a2) Urbach ruledabsorption [23], and (a3) constant absorption term [24]

a ¼ a1 þ a2 þ a3 ð9Þ

where

a1 ¼ 0 hm 6 EgIa � Eph ð10aÞ

a1 ¼ A50 �ðhm�EgIaþEphÞ2

expEphkBT

� ��1

for EgIa � Eph < hm 6 EgIa þ Eph ð10bÞ

a1 ¼ A50 �ðhm� EgIa þ EphÞ2

exp Eph

kBT

� �� 1

þhm� EgIa � Eph� �2

1� exp � Eph

kBT

� �24

35 for hm

> EgIa þ Eph ð10cÞ

a2 ¼ AU � exphmEU

� �ð11Þ

a3 ¼ A0 ð12Þ

EgIa represents the indirect allowed energy gap, Eph – the energyof emitted/absorbed phonon, EU is the Urbach energy, kB – Boltz-mann’s constant, and A50, AU are constant parameters. The fittingpresented in Fig. 10 is rather good. Temperature dependences ofthe fitted parameters that describe the energy gap of SbI3 are givenin Fig. 11. Fig. 11 presents the good agreement of these results withenergy gaps and phonon energy reported for T = 95 K and T = 293 Kin [21].

The temperature dependence of EgIa (T) has been least squarefitted (see the solid curve in Fig. 11) with the following equation[25]:

Fig. 11. Temperature dependences of optical indirect allowed energy gap ( , EgIa),Urbach energy ( , EU), and energy of phonons emitted/absorbed ( , Eph) in SbI3

crystalline platelet for ordinary ray; , – EgIa and Eph reported in [21]; solidcurves represent the fitted theoretical dependences (13) and (14). The fitted valuesof parameters are given in the text. Horizontal line represents value and uncertaintyof the average energy of effective phonons determined from the fitting oftemperature dependence of steepness parameter (Fig. 12) with Eq. (16).

Page 6: Optical properties of SbI3 single crystalline platelets

1758 M. Kepinska et al. / Optical Materials 33 (2011) 1753–1759

EgðTÞ ¼ Egð0Þ �Kg

expðHET Þ � 1

ð13Þ

where Eg (0) is the energy gap extrapolated to 0 K, Kg is proportion-ality factor, HE is so-called Einstein temperature that equals 3/4 ofDebye temperature [25]. The following values of parameters havebeen obtained: Eg (0) = 2.28(1) eV, Kg = 0.48(11) eV, HE = 423(60) K.

The temperature dependence of Urbach energy of SbI3 has beenleast square fitted (see the solid curve in Fig. 11) with the followingequation [26]:

EUðTÞ ¼ EUð0Þ þKU

expðHET Þ � 1

ð14Þ

The following values of parameters have been obtained: EU

(0) = 0.15(3) eV, KU = 0.30(43) eV, HE = 330(320) K.The Urbach’s rule is also presented in the forms [27–29]:

a2 ¼ A � expBðhm� CÞ

kBT

� �ð15aÞ

a2 ¼ A00 � exp �~Eg � hm

EU

" #ð15bÞ

Fig. 12 presents the temperature dependence of steepness parame-ter B for SbI3 crystalline platelet illuminated with ordinary ray.These values of B have been determined from the least-square fit-ting of the absorption spectra of SbI3 (Fig. 10) with formula (9) inwhich a2 was given by Eq. (15a). On insert in Fig. 10 one can seethe characteristic point of the intersections of Urbach’s characteris-tics evaluated for different temperatures of the investigated SbI3.The value of C = 2.36(2) eV has been determined. It represents thecharacteristic parameter of this material [30]. Sometimes (e.g., in[29]) this parameter and parameter A are so-called optical bandgap and the absorption coefficient at the band-gap but these namesare misleading due to the temperature dependence of the opticalenergy gap of a semiconductor.

The temperature dependence of steepness parameter is ex-pressed by the following function [30]:

B ¼ B0 �kBThmp

� �� tanh

hmp

2kBT

� �ð16Þ

in which B0 and hmp stand for the high-temperature steepnessparameter and the average energy of effective phonons, respec-tively. The solid curve in Fig. 12 is the least-squares fit of Eq. (16)

Fig. 12. Temperature dependence of steepness parameter B in SbI3 crystallineplatelet for ordinary ray; solid curve is the least-squares fit according to Eq. (16).The fitted values of parameters are given in the text.

to the temperature dependence of B, with B0 = 0.111(5) andhmp = 37.2(35) meV.

Such determined value of the average energy of effectivephonons is in accordance with the energies of emitted/absorbedphonons evaluated from the fitting of spectral dependence ofabsorption of light at different temperatures (Fig. 11) with formula(10) describing indirect allowed absorption at temperatures from80 K to 225 K.

Applying Eq. (15b) to the description of the registered Urbach’srule one obtains: ~Eg = 2.36(2) eV and the values of A00 ¼A � expð�BC=kBTÞ. Unfortunately, in contrary to the case of directband-gap [27], the relation between the steepness of theabsorption tail A00 and the Urbach’s energy EU in indirectband-gap semiconductors is not available.Some of the determinedspectral and temperature dependences of absorption parameters ofsingle crystalline SbI3 platelets, i.e. the temperature dependencesof indirect allowed energy gap EgIa(80 K 6 N 6 320 K, phonon en-ergy Eph(80 K 6 N 6 320 K and Urbach energy EU(80 K 6 N 6 320 K(see Fig. 11) and steepness parameter B(80 K 6 N 6 320 K) (seeFig. 12), have never been reported for this material. Therefore, onlya few of the determined parameters can be compared with litera-ture data. However, one can see that the presented results are ingood agreement with literature data [21] on EgIa(T = 95 K),EgIa(T = 293 K), Eph(T = 95 K) and Eph(T = 293 K).

It should be noticed that the applied measurements of opticaltransmittance are simpler than investigations of optical reflectanceor ellipsometry, and can be easily performed at different tempera-ture. The applied method of investigations needs rather cheapexperimental set-up. It does not require sophisticated computeriteration techniques, either. It is possible to use the applied spec-trogoniometric technique also for other materials.

5. Conclusions

The spectrogoniometric and interference spectroscopy tech-niques are convenient and reliable methods that have alloweddetermining of spectral and temperature dependences of opticalparameters of single crystalline SbI3 platelets.

Spectral characteristics of real parts of refractive indices of radi-ation with electric vector normal and parallel to the optical c-axisof SbI3 crystalline platelets (i.e. no, ne – refractive indices for ordin-ary and extraordinary rays) have been shown. The temperaturedependences of spectra of optical parameters (no and absorptioncoefficient of radiation with electric vector normal to the opticalc-axis) have been presented. The temperature dependences of fit-ted optical indirect allowed energy gap of SbI3, Urbach energyand phonons energies are the main findings of the presented work.Some of them are reported for the first time for SbI3.

The presented material characteristics of SbI3 platelets shouldbe useful in optimisation of optoelectronic devices based on thismaterial.

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