Investigation of zinc oxide thin film by spectroscopic ellipsometry

Transcription

1 VNU Journal of Scence, Mathematcs - Physcs 24 (2008) Investgaton of znc oxde thn flm by spectroscopc ellpsometry Nguyen Nang Dnh 1, Tran Quang Trung 2, Le Khac Bnh 2, Nguyen Dang Khoa 2, Vo Th Ma Thuan 2 1 College of Technology, VNU, 144 Xuan Thuy, Hano, Vetnam 2 Unversty of Natural Scences, Vetnam Natonal Unversty Ho Ch Mnh Cty, 227 Nguyen Van Cu, 5 Dstrct, Ho Ch Mnh Cty, Vetnam Receved 4 January 2008; receved n revsed form 26 March 2008 Abstract. ZnO flms were deposted on glass substrates by magnetron RF-sputterng. An accurate determnaton of the optcal constants of these flms s extremely mportant pror to ts applcaton n optcal devces and spectroscopc ellpsometry provdes a reasonably accurate method for the determnaton of optcal constants of thn flms. In ths study, we present the results ganed by analyzng spectroscopc ellpsometry of ZnO thn flm combned wth comparson of transmsson spectroscopy measured on a UV-VIS-NIR spectrophotometer. Ellpsometry data have been ftted wth a model ncludng a glass substrate and a ZnO flm plus a surface vod layer on top. From ths fttng the refracton ndex (n), extncton coeffcent (k) and thckness (d) of the sputtered ZnO flms were determned. By usng the ganed n, k and d values the transmsson spectrum was theoretcally calculated and compared wth the expermentally obtaned transmsson one. As a result of the combned spectroscopc ellpsometry and transmsson analyss, there was the good correlaton n comparson. Keywords: Thn flm, ellpsometry, transmsson spectrum, refracton ndex, extncton coeffcent. 1. Introducton Although ellpsometry theory was well-known for a long tme ago, untl 70s of the XX century ellpsometry has not been commonly used, because of ts sophstcated mathematcal technque. Snce the computer scence has strongly developed, ellpsometer systems become popularly used n laboratores for charactersaton of materals, and for optc thn flms n partcular. The theory for ellpsometrc analyss s based on the change n the polarzaton state of lght when the lght transmts or reflects from an optc sample. In both the case of a sngle layer and a multlayer of the thn flm whch are coated on a glass substrate, after the transmson and/ or reflecton through/ from the sample, the lght s polarzed dependng on the thckness and the refracton ndex of the flm. From the ellpsometry spectra of the samples one can fnd out the optc constants and optcal propertes of the flms. Ths work presents new nvestgaton results on znc oxde (ZnO) thn flm deposted on glass substrate by usng spectroscopc ellpsometer wth a wavelength range from 350 nm to 1100 nm. The Correspondng author. E-mal: dnhnn@vnu.edu.vn 16

2 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) measured ellpsometrc data are ftted wth theoretcal spectra generated assumng approprate models regardng the sample structures. The fttng has been done by mnmzng the squared dfference (χ 2 ) between the measured and calculated values of the ellpsometrc parameters (ψ and ) and accurate nformaton has been derved regardng the thckness and optcal constants of the dfferent layers. 2. Expermental ZnO flms were deposted on glass substrates by a magnetron Rf-sputterng. A ZnO ceramc target wth dameter of 75 mm was used. The sputterng pressure of the Ar/O 2 mxture gases was mantaned at P = 8 x 10-3 Torr, the densty of the sputterng current was kept at I 60 ma/cm 2 wth the bas voltage of V = 350 V. The deposton tme was of about 70 mn and the average deposton rate was evaluated as 1.5 Å/s. The ellpsometrc measurement s normally expressed n terms of a polarzaton angle Ψ [1, 2], as follows: tan( Ψ)e rp = ρ= (1) r where ρ s the complex rato as a functon of wavelength, = δ p - δ s s the phase dfference (as well as an ampltude rato), r p and r s are the complex Fresnel reflecton coeffcents of the sample, respectvely for p- (n the plane of ncdence) and s- (perpendcular to the plane of ncdence) polarzed lght, as shown n Fg Lnearly polarzed lght p s Ψ s ϕ o 3 - Ellptcally polarzed lght 2 - Reflect off sample Fg. 1. Schematc dagram of ellpsometer system. The ellpsometrc spectra were measured n a spectroscopc phase modulated ellpsometer (Model UVISEL HR 460, Jobn Yvon) n the wavelength range from 280 nm to 1700 nm. On ths measurement system, the modulated sgnal to detector takes the general form as follows: I(t) = I[I o + I s snδ(t) + I c cosδ(t)] (2) where I o, I s, I c are complcated trgonometry functons related to the measurement condtons (e.g. the angle of polarzaton mrrors and modulators) and parameters of flm (, Ψ). The measurement confguraton s chosen for the purpose of smplfyng the calculaton of trgonometry functons. In the present set of measurement, M = 0 o, P = 45 o, A = 45 o, so that,

3 18 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) I o = 1 (3) I s = sn2ψsn (4) I c = sn2ψcos (5) Ellpsometrc data have been analyzed by Delta Ps software (Jobn Yvon Co.). Fg. 2 shows ellpsometer spectra I s (λ), I c (λ) of a ZnO flm. Transmsson spectra of the sample were measured on a Jasco. UV-VIS-NIR V530 spectrophotometer, n a wavelength range from 190 nm to 1100 nm (Fg. 3). From the transmsson spectra, one can note that the ZnO spectrum qute appears n the same transparent regon of the substrate. Ths means, the glass substrate dd not affect to the shape of transmsson spectrum of coated ZnO flm. From ths spectrum one can also determne the optcal band gap (E g ) of the znc oxde flm whch was found to be E g 3.33 ev. a. b. Fg. 2. Polarzed spectra of ZnO sample, wth I s = sn2ψsn (a) and I c = sn2ψcos (b). Fg. 3. Transmttance spectra of glass substrate and ZnO flm.

4 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) Results and dscusson 3.1. Modelng and fttng I s, I c spectra Ellpsometry does not drectly measure flm thckness or optcal constants; t measures the changes n polarzaton expressed as Ψ and [4]. To extract useful nformaton about a materal structure, t s necessary to perform a model dependent analyss of ellpsometrc data. A model for the optcal structure of the sample was desgned wth ntal estmates of the parameters. Intally, we have started wth the smplest model; t ncluded a glass substrate and a sngle flm on the surface. By regularly ncreasng complexty, we have constructed more complcated model, for nstant, ncreasng the amount of possble flms or the possble elements exst n flm structure, predctng dfferent thcknesses, changng the knd of substrate materal. Through these steps, we fnally could fnd out the best model whch has the most sutable structure n compare wth the real sample. The ntal guesses of the model parameters were transformed fnally nto true parameters of the sample, such as thckness and optcal constants. In the process of fttng parameters of model and sample, by usng the Marquardt Levenberg algorthm [5] one can get the dfference between the expermental values (from the measurement) and calculated values (from the model). The Mean Square Error (MSE) χ 2 s used to qualfy the dfference between the expermental and predcted data. ( Mes ) 2 1 Th χ = N N 2 = 1 σ where σ s the standard devaton of the -th data pont N s the number of data ponts Mes s the -th expermental data pont Th s the -th calculated data pont from assumed theoretcal model MSE s dfferent n each model. A smaller MSE mples a better model ft to the data. MSE wll exhbt a mnmum value when the model matches the expermental data as closely as possble. 2 (6) Fg. 4. The frst fttng model of ZnO sample.

5 20 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) From the measurement I s, I c spectra were plotted as a functon of wavelength. Next, a model for the optcal structure of the sample have been constructed. Ths frst model ncluded a glass substrate and a sngle flm ZnO on surface wth 1000 nm predcted thckness (Fg. 4). The fttng results of model 1 have been presented n Fg. 5 and Table 1. Wth ths model the MSE has been found to be of 133.6, ths means that by model 1 there was a bg dfference between the measured I s, I c spectra wth the calculated I s, I c spectra. a. b. Fg. 5. Measured data (dark curve) and smulated data (lght curve) of ZnO sample n model 1 for Is (a) and Ic (b). In ths case, t was hard to accept ths model Comparson of theoretcal and expermental transmsson spectra To evaluate the results from analyzng polarzed spectra there was a comparson between the calculated transmsson spectrum and the expermental transmsson spectrum. By applyng the algorthm from [6] we have used ftted ellpsometrc data (n, k, d) to calculate the transmsson spectrum of ZnO sample. After that, we have made a compare between ths calculated spectrum and the measured spectrum of ZnO sample. Fg. 6 shows the dfference of these two spectra, one s the transmsson spectrum calculated from resultng ft parameters, whch have ganed from analyzng I s, I c spectra (calculated spectra), n model 1 and another s the transmsson spectrum measured from experments (measured spectrum). It shows that the model dd not adequately represent the true structure, the model needed to be reformulated.

6 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) Fg. 6. Measured and calculated transmttance spectra n Model Bruggeman effectve medum approxmaton (EMA) model In the case of composte layers, consstng of more than one materal, or materal(s) and vod, the calculaton for the effectve optcal constants have been done usng EMA model, whch descrbes a composte of aggregated phases or random mxture mcrostructure. Delectrc functon ε of the composte s descrbed by the follow equaton: ε ε f = 0 ε 2ε + (7) where ε s the delectrc functon of th component n the composte. f s the volume fracton for th component n the composte. Fg. 7. The second fttng model of ZnO sample. In the second fttng, we have assumed a new model by addng a surface vod layer to the ZnO flm, called model 2. To model ths addtonal layer we have used BEMA wth a 50 50% mxture of ZnO and vod, layer thckness has been predcted about 20nm (Fg. 7). The ft results for a more

7 22 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) complex model are shown n Fg. 8 and Table 1. And the resultng ft MSE was χ 2 = 7.2; t was reduced by an order of magntude. Addtonally, n model 2 the calculated spectra I s, I c were well matched wth expermental spectra. Ths shows that model 2 s much better than model 1 for gettng a good agreement n fttng. a. b. Fg. 8. Measured data (dark curve) and smulated data (lght curve) of ZnO sample n model 2. for Is (a) and Ic (b). The second model s n good agreement wth the expermental data. Table 1. The resultng ft parameters of constructed models Model χ 2 Parameters 1. Wthout vod d ZnO(a) = ± 17.8nm 2. Vod on top 7.2 d ZnO(a) = ± 45.1nm; d vod ZnO(a) = 23.2 ± 2.1nm %ZnO vod = 65.0 ± 3.4 There was a good match between the calculated and measured transmsson spectra (Fg. 9). The mnmum and maxmum wavelength values of nterference frnges were well ft. From that, model 2 and ts ft parameters are acceptable, n good agreement wth the true structure of the sample. Besdes MSE (χ 2 ), thckness and mxture rato, the fttng results also gave the dependence of refractve ndex n and extncton coeffcent k on wavelength of ZnO flm, llustrated n Fg. 10. The ZnO flm refractve ndces n the wavelength range of 500 nm 1100 nm were found to be from 1.94 to The extncton coeffcent k equals to zero for wavelengths greater than 500 nm and suddenly ncreased hgher n the range from 350 nm to 500 nm, ths corresponds to an absorpton edge whch the transmsson spectrum obtaned.

8 Nguyen Nang Dnh et al. / VNU Journal of Scence, Mathematcs - Physcs 24 (2008) Fg. 9. Measured and calculated transmttance spectra n model 2. Fg. 10. The wavelength dependence of reflectve ndex n and extncton coeffcent. 4. Conclusons ZnO flms, deposted on glass substrate by magnetron sputterng process, have been analyzed based on spectroscopc ellpsometry n compare wth transmsson spectroscopy from a UV-VIS system. Ellpsometry data have been ftted wth a model ncludng a glass substrate and a ZnO flm plus a surface vod layer on top. From ths fttng the refracton ndex (n), extncton coeffcent (k) and thckness (d) of the ZnO flms were determned. By usng the ganed n, k and d values the transmsson spectrum was theoretcally calculated and compared wth the expermentally obtaned transmsson one. As a result of the combned spectroscopc ellpsometry and transmsson analyss, there was the good correlaton n comparson. Acknowledgements. The Natonal Program for Basc researches n Natural Scence of Vetnam s acknowledged for provdng fnancal support n 2007 (Project No ). References [1] H.G. Tompkns, W.A. McGahan, Spectroscopc Ellpsometry and Reflectometry A User s Gude, A Wley-Interscence Publcaton [2] R.M. A Azzam, N.M. Bashara, Ellpsometry and Polarzed Lght, North Holland Press, Amsterdam, Fourth Impresson [3] O.S. Heavens, Optcal Propertes of Thn Sold Flms, Dover Publcaton, Inc, New York [4] B. Johs, J.A. Woollam, C.M Herznger, J. Hlfker, R. Synowck, C.L Bungay. Overvew of VASE, Part I: Basc Theory and Typcal Applcatons; Overvew of VASE, Part II: Advanced Applcatons, SPIE Proc. CR [5] G.E. Jellson. Spectroscopc ellpsometry data analyss: measured versus calculated quanttes, Thn Sold Flms (1998) 33. [6] R. Swanepoel, Ellpsometry data for some thn flm samples, J. Phys. E: Sc. Instrum., 16 (1983) [7] Jobn-Yvon, Horba Group Ellpsometry Presentaton 2001.