Dispersion and Fundamental Absorption Edge Analysis of Doped a-si:h thin Films I : p-type

Transcription

1 Egypt. J. Slids, Vl. (31), N. (), (8) 191 Dispersin and Fundamental Absrptin Edge Analysis f Dped a-si:h thin Films I : p-type 1 Assem Bakry Physics Dept., Faculty f Science, Ain-Shams Univ., Cair, Egypt The refractive indices and the extinctin cefficients f Al dped a-si:h films are determined frm their transmittance spectrgrams ver a wide energy range, ev. Analysis f the refractive index data yields the values f the lng wavelength dielectric cnstant, the average scillatr wavelength, average scillatr strength, average scillatr energy, dispersin energy, and lattice energy. The change f the absrptin edge versus phtn energy shws the transitin t be f the indirect type and gives as well the Urbach energy. The real and imaginary parts f dielectric cnstant are used t calculate the free carrier plasma resnance frequency, ptical relaxatin time and the rati f free carrier cncentratin t the free carrier effective mass. 1. Intrductin The suitability f hydrgenated amrphus silicn (a-si :H) fr phtvltaic devices has stimulated great interest in the preparatin and characterizatin f this material. Since the first a-si:h slar cell was made by Carlsn et al. [1] the technlgy has imprved tremendusly, leading t reprted initial cnversin efficiencies exceeding 15% []. Fr ptelectrnic devices, an accurate determinatin f the ptical cnstants such as bandgap, absrptin cefficient, refractive index, extinctin cefficient with dping cncentratin and wavelength f semicnductr thin films are imprtant t precisely mdel their spectral respnse. The ptical cnstants als prvide infrmatin abut the electrnic band structure, the band tail, and lcalized states [3]. This practical and fundamental significance has led t a number f studies [4] cncerned with the ptical prperties f a-si:h and related allys. 1 assem_sedfy@asunet.shams.edu.eg.

2 Assem Bakry 19 The apprach f allying a-si:h with materials f lwer crdinatin number was previusly attempted. The di-valent O-atms was used [5] and fund t decrease the average crdinatin number in a prnunced matter. Allying a-si:h with the tri-valent Al was als perfrmed [6], and fund t reduce the netwrk strain due t lwering f the average crdinatin number. In this wrk, a cmprehensive study fr the ptical prperties f a- Si:Al:H is carried ut. The dispersin behavir f this structure allws the real and imaginary parts f the refractive index t be btained. The real part f the refractive index prvides values fr the scillatin energy, dispersin energy and lattice energy t be quantified. The imaginary part f the refractive index yields the variatin f the absrptin cefficient due t the increase in Al cncentratin. The disrder in the material is traced thrugh the evaluatin f the change in the Urbach energy. The indirect transitins in the ptical gap have been studied as well.. Experimental Prcedures The preparatin f the films was carried ut in Klaushal Ziellerfield Technical University in Germany. The investigated films were prepared n Crning 759 glass substrates at a temperature 3 C as fllws. First, silicn was evaprated frm an electrn beam heated vitreus Carbn crucible at a rate f apprximately 3 A per secnd t a thickness f abut 5 A. Then the dpant material (Al) was intrduced int the material thrugh thermally evaprating different rates. The thickness f evaprated films was determined interfermetrically [7]. The base pressure f vacuum was 1-7 mbar. During the entire evapratin prcess, atmic hydrgen was blwn at the grwing film frm a radi frequency dissciatin system. The resulting hydrgen pressure in the vacuum vessel was mbar and the hydrgen flux thrugh the dissciatr was abut 16 ml N/min. In this envirnment mst dangling bnds in Si were saturated by hydrgen and the prperties f amrphus films f pure Si are similar t thse f a-si:h prepared by Silane decmpsitin [8]. Al cncentratins were estimated using Secndary In Mass Spectrmetry (SIMS). It is an analytical technique that detects very lw cncentratins f dpants and impurities. It can prvide elemental depth prfiles ver a depth range frm a few angstrms t tens f micrns. SIMS wrks by sputtering the sample surface with a beam f primary ins. Secndary ins frmed during the sputtering are extracted and analyzed using a mass spectrmeter. These secndary ins can range frm matrix levels dwn t sub-parts-per-millin trace levels. The cncentratin f dpants was fund t range frm at.%. The hydrgen cntent in all the used films was kept fixed at C H =1 at.%. The transmissin, T, and reflectin, R, spectra were carried ut between 4 and 5 nm in steps f

3 Egypt. J. Slids, Vl. (31), N. (), (8) 193 nm using a cmputer-aided duble-beam spectrphtmeter (Shimadzu 311 PC UV-VIS-NIR). The relative uncertainty in the transmittance and reflectance given by manufacturer is.%. Transmittance scans were perfrmed using a glass substrate in the reference cmpartment f the same kind as the ne used fr the film depsitin. The transmittance and reflectance were measured at the same incidence angle f 5º. 3. Results and Discussin 3.1 Evaluatin f ptical cnstants Fr the calculatin f the ptical cnstants, the refractive index n and extinctin cefficient k were calculated using the envelpe methd suggested by Manifacier et al. [9] and mdified by Swanepel [1, 11]. The spectral envelpes f the transmittance, T max (λ) and T min (λ),.which are assumed t be cntinuus functins f the wavelength, were cmputed using a plynmial interplatin between extremes. The transmittance spectra near the absrptin edge and in the transparent regin fr the a-si:h films is shwn in Fig. (1). The cmputed envelpe fr the interference maxima is shwn in the same figure as well. It can be bserved that the thickness f films is almst unifrm because the shrinking f the interference fringes is nt remarkable. Cnsidering the cherent interference f light inside the studied films, the ptical cnstants, refractive index (n) and extinctin cefficient (k), can by deduced frm the transmittance (T) spectrgram using the Swanepel prcedure [1, 11]. 1.8 Transmissin T Wavelength λ (nm) Figure (1): The transmissin spectrum fr a-si:h film alng with the calculated envelpe spectrum

4 Assem Bakry 194 The change f the refractive index n as a functin f wavelength fr different dping cncentratins is shwn in Fig. (). It has been fund that, the incrpratin f Al 3+ ntably decreases the refractive index f the films. The same behavir was previusly reprted using brn as a dpant [1]. The estimated errr fr the refractive index, δn, is Si Al1 Al Al3 Refractive Index n Wavelength λ (nm) Figure (): The change f the refractive index n versus wavelength λ fr different dping cncentratins 3. Calculatin f the Crdinatin Numbers T calculate the crdinatin number, the cmplete netwrk apprach was used accrding t the fllwing equatin [13]: 1 r = rn r (1) N where N = r 1 N r r 1 and N r is the ttal number f atms with r bnds. The values f the calculated crdinatin numbers are given in Table (1). Frm the table, the decrease f the crdinatin number with dping culd be seen. The reductin f the crdinatin number causes reductin f the mechanical hardness f the material as predicted by the rigidity perclatin thery [13]. The expected perclatin threshld fr ideal glass <r> =.4. Similar behavir was fund in a- SiO:H films dped with brn [13]. The decrease in the crdinatin number with dping culd attribute t the decrease in the refractive index [14].

5 Egypt. J. Slids, Vl. (31), N. (), (8) 195 Table (1): The dping cncentratin, crdinatin number, scillatin energy E, dispersin energy E d, lattice energy E l, static refractive index n, the average interband scillatr wavelength λ and the average scillatr strength S fr different evaluated films. Sample Dping Cnc. (at. %) Crdinatin number E (ev) E d (ev) E l (ev) n λ (nm) S 1-5 (nm - ) Si Al Al Al Analysis f energy gap and absrptin cefficient The methd develped by Swanepel [1, 11] was used t calculate the absrptin cefficient α. Fig. (3) shws the change f α as a functin f energy fr different dping cncentratins, where three characteristic regins are indicated. Regin I crrespnds t band-t-band absrptin, regin II riginates frm absrptin prcesses invlving band tail states, and regin III arises frm absrptin via Si dangling bnd defect states in the middle f the band-gap. It culd be seen frm Fig. (4) that the absrptin edge shifts twards lwer phtn energies as the Al cntent increases. A prnunced bradening f the absrptin edge is als bserved. Similar behavir was reprted when dping with Al [6] and dibrane [15]. 1E+5 Si Al1 Al Al3 III II I 1E+4 α (cm -1 ) 1E+3 1E hν (ev) Figure (3): The absrptin cefficient α (cm -1 ) as a functin f the dping cncentratin.

6 Assem Bakry Optical Gap Static Refractive Index Plasma Frequency Average Gap Dispersin Energy Arb. Units X Al cnc. (at %) Figure (4): The change f average gap E (ev), dispersin energy E d (ev), static pt refractive index n, indirect energy gaps E g (ev) and the plasma frequency ω p (s -1 ) with dping cncentratin fr different evaluated films An expressin fr the absrptin cefficient, α (ν), as a functin f phtn energy (hν) fr direct and indirect ptical transitins is given by the fllwing expressin [16] pt m A( hν Eg ) α( ν ) = () hν where the expnent m =1/ fr allwed direct transitin, while m = fr allwed indirect transitin. E pt g is ptical band gap energy and A is a cnstant related t the extent f the band tailing. Pltting (αhv) 1/ against phtn energy (hv) gives a straight line with intercept equal t the ptical energy band gap fr indirect ( E ) transitins as shwn in Fig. (5). Table lists the different pt g determined energies, where the errr fr bandgap energies is ±.3. The value f the ptical gap fr the undped sample agrees with previusly reprted values [6, 15, 17-19]. Frm Table (), it culd be seen that the ptical band gap energy decrease with increasing the Al cntent. Similar results were previusly reprted [6, 15, 18-4]. This behavir was attributed t that the energy gap is

7 Egypt. J. Slids, Vl. (31), N. (), (8) 197 determined by the weakest bnd present in the ally system (Si-Al r Si-B) which cntributes t states near the band edges, lwering the Fermi level and cnsequently affecting the energy gap. Anther reasn was the increase f disrder in the netwrk and bradening in the band tails prduced by the intrductin f large amunt f threefld crdinated dpant atms. (αhν) 1/ (cm -1 ev) 1/ Si Al1 Al Al hν (ev) Figure (5): Tauc plt t btain the indirect energy gap fr different dping cncentratins. Table (): Indirect energy gaps E pt g, the Urbach energy E U, the rati f free carrier cncentratin t the free carrier effective mass N/m *, the plasma frequency ω p and the ptical relaxatin time τ fr the used films. Sample pt E g E U (mev) N/m* (cm -3 ) ω p (s -1 ) τ 1-8 (s) (ev) Si Al Al Al Urbach energy and the tail f absrptin edge It is well knwn that the shape f the fundamental absrptin edge in the expnential (Urbach) regin can yield infrmatin n the disrder effects [5]. With energy fr the incident phtn less than the band gap, the increase in

8 Assem Bakry 198 absrptin cefficient is fllwed with an expnential decay f density f states f the lcalized int the gap [6] and the absrptin edge is knwn as Urbach edge. The lack f crystalline lng-range rder in amrphus/glassy materials is assciated with a tailing f density f states [6]. At lwer values f the absrptin cefficient (1 cm -1 < α < 1 4 cm -1 ), the extent f the expnential tail f the absrptin edge characterized by the Urbach energy is given by [7]. ( hν ) β ( hv ) α = exp E U (3) where β is a cnstant, E U is the Urbach energy which indicates the width f the band tails f the lcalized states. The ptical absrptin cefficient just belw the absrptin edge shws expnential variatin with phtn energy indicating the presence f Urbach s tail. Pltting ln(α) vs. hα and taking the reciprcals f the slpes f the linear prtin in the lwer phtn energy f these curves, E U culd be btained where the errr in cmputing E U is ±.1. The values f E U fr different cmpsitins are listed in Table () and demnstrated in Fig. (6). As it can be seen, the additin f Al 3+ ins is remarkably increasing the Urbach energy values, in agreement with thers using different material fr dping [1, 3]. Such increase culd be related t the increase in the defect density due t the incrpratin f threefld crdinated atms and the spntaneus cnversin f weak Si-Si bnds int dangling bnds [3]. The decrease in the ptical gap, shwn frm Table (), culd be crrelated t increase f disrder in the netwrk, indicated by Urbach s energy E U. 7 6 Urbach Energy Free Carrier Cnc./ Effective mass 5 X 1 1 Arb. Units 4 3 X 1-3 ev Al cnc. (at. %) Fig. (6): The change f the Urbach energy E U (mev) and the rati f free carrier cncentratin t the free carrier effective mass N/m * (cm -3 ) with dping cncentratin fr different evaluated films

9 Egypt. J. Slids, Vl. (31), N. (), (8) Evaluatin f material characteristic energies An interesting mdel (single scillatr mdel) describing the index dispersin behavir was prpsed by Wemple and Di Dmenic [8, 9]. This mdel is given t btain a prper evaluatin f the real part f the dielectric cnstant ε r (ω). Hyptheses given t satisfy the mdel; (1) the imprtant interband transitins can be apprximated by individual scillatrs ω n, () the summatin ver scillatrs can be apprximated, fr ω < ω n, by a summatin f the first strng scillatr and a prper cmbinatin f the higher rder cntributins in which nly the terms t rder ω are retained prviding a single effective scillatr mdel f ε r (ω). It accunts fr the dispersin curve accrding t the relatin: Ed E n ( hω) = 1+ (4) E ( hω) where hω is the phtn energy, E and E d are tw parameters cnnected t the ptical prperties f the material and they are knwn as the single scillatr energy and the scillatr strength (r dispersin energy) respectively. E defines the average energy gap usually cnsidered as the energy separatin between the centers f bth the cnductin and the valence bands. E d is a measure f the average strength f the interband ptical transitins and is related t the crdinatin number f the atms. Pltting (n -1) -1 against ( h ω), and fitting it t the straight part f the curve in the high-energy regin allws btaining frm the slpe and the intercept values f the single scillatr parameters (E and E d ). Table 1 lists the btained values f E and E d fr the film cmpsitins. The decrease in E values btained fr the films are in accrdance with the red shift in the edge f the recrded absrptin spectra and the decrease in the ptical band gap. As shwn frm table and demnstrated in Fig. (4), the average gap decreased with increase in dping cncentratin, same as previusly reprted cnclusin using dibrane fr dping [15]. The decrease in values f E d culd be attributed t the decrease in the average crdinatin number f the atms. In case f wavelengths much shrter than the phnn resnance, the lattice cntributin is given frm [3]. n 1 = Ed E /( E E ) El / E (5) where E l is the lattice energy. A plt f (n 1) versus 1/E appraches a straight line. At lng wavelengths where E << E Eq. (5) can take the frm [31] The intercept is the rati / E f E l are listed in Table (1). n 1 = Ed E El E (6) E l. Thus the btained values E d, and the slpe is

10 Assem Bakry 3.6. Determinatin f inherent absrptin wavelength and scillatr strength Many semicnductrs materials have generally an inherent absrptin in the ultravilet range. The inherent wavelength f the ultravilet absrptin r the average interband scillatr wavelength, λ, and the average scillatr strength, S, is determined using Drude-Vigt dispersin frmula as [3]. n 1= ( e / π m c ) N S /(1/ λ 1/ λ ) (7) 1 where N 1 is the number f mlecules per unit vlume f the film. Eq. (7) culd be expressed in a single term Sellmeier scillatr with the refractive index as [33]. ( λ where n is the static refractive index, which prvides a gd indicatin n the structure and density f the material, and it equals t ε st (static dielectric cnstant). n and λ can be evaluated frm the plts f (n -1) -1 versus λ -. Table (1) lists the btained values f n and λ. As shwn frm table, values f n increased with increase in dping. The same behavir was previusly reprted when dping with brn [15,, 1]. Furthermre, Eq. (8) can als take the frm n 1)/( n 1) = 1 ( λ / ) (8) n 1 = ( S λ ) /(1 λ / λ ) (9) where the average scillatr strength S is defined as S ( λ (1) = n 1) / The cmputed values f S are given in Table 1. The decrease in the average gap E can be crrelated with the increase in n accrding t the frmula [34]: ( hω ) p n = 1+ A (11) E where ω p h is the plasma energy fr valence electrns and A is a parameter depending n the matrix elements. As culd be seen frm Eqn. (11), there exist an inversely prprtinal relatinship between the average gap and the static refractive index, which is applied t the btained data shwn in Table (1).

11 Egypt. J. Slids, Vl. (31), N. (), (8) Cmplex dielectric cnstant and related characteristic parameters The cmplex dielectric functin describes the interactin f electrmagnetic waves with matter. The cmplex dielectric cnstant ε f the material in terms f the ptical cnstants n and k is given as: ε ( ε1 + iε ) ( n + ik) = = (1) ε ε where ε is the dielectric cnstant f free space. Separatin f the real part and the imaginary ne leads t the real part, [35]. e N ε1 = n k = ε λ, (13) * 4π c ε m and t the imaginary part, ε ω p 3 ε = nk = λ, (14) 3 3 8π c τ where determinatin f the imaginary part f dielectric cnstant culd be emplyed in determinatin f the ptical relaxatin time, τ, f films. Here ε is the free space dielectric cnstant, N/m * the rati f free carrier cncentratin, N, t the free carrier effective mass, m * and ε is the high frequency dielectric cnstant. ω p is the plasma frequency fr the valence electrns and is given by: * ( e N ε ε m ) 1 ω (15) p = Using Eqs. (14)-(15) the parameters N/m *, ω p, τ culd be determined. Table lists the evaluated values f the previus parameters. It is clear that bth ε and N/m * (Fig. (6)) change in the same manner with the average crdinatin number. Such unusual similarity in ε and N/m * behavirs has been bserved fr p-type Pb-Sn-Te chalcgenide system [36] and t Ge-Sb-Se system [37]. It may be attributed t the relatively higher carrier cncentratin that is cnsistent (assuming that m * is cnstant in the first apprximatin) with ur case. The ε spectra pltted in Fig. (7) characterize the effect f dping a-si:h films. As seen in figure, the entire curve is redshifted with increase in dping level. The same behavir was previusly reprted when using B with high dping levels [1].

12 Assem Bakry 3 'Si' 'Al1' 'Al' 'Al3' ε hν (ev) Figure (7): The change f the imaginary part f the dielectric functin ε with dping. Within the framewrk f the single scillatr mdel, the psitin f the maximum f ε crrespnds t the resnance energy h ω f the scillatr. The ο resnance frequency ω is sensitive t the lcal chemical envirnment. The mdificatin f this parameter is linked t the changes f the average separatin between the valence band and the cnductin band [8]. The static refractive index can be linked t the resnance frequency and the vlume plasma frequency [8, 9]: ω p n = n( ω ) = 1 (16) ω The abve equatin suggests that n is imaginary fr ω < ω p, i.e., the reflectivity f the material is 1%. The plasma frequency depends n the density f the material. The redshift f ε and the decrease f the ptical gap with dping are cmpatible with a decrease f the resnance frequency f the scillatr. As a cnsequence, the increase f n with dping is supprted by an increase f ω p, as shwn in Tables (1) and (), and a decrease f ω in agreement with Eq. (16). The same behavir was previusly reprted [3].

13 Egypt. J. Slids, Vl. (31), N. (), (8) 3 4. Cnclusins: The inclusin f Al 3+ in a-si:h thin films caused a decrease in the refractive index values due t a decrease in the average crdinatin number f the system. A Decrease in dispersin energy values was als bserved, indicating a strng inic envirnment, which increases with increasing the aluminum cncentratin causing a decrease in the verall crdinatin number. The average gap decreases as well as the Tauc ptical band gaps due t a decrease in the average bnd energy f the system. An increase in Urbach energy indicating that mre static disrder has taken place. An increase in free carrier cncentratin and a remarkable decrease in the relaxatin time are btained. An increase in the plasma energy and static refractive index is bserved. References: 1. D. E. Carlsn, C. R. Wrnski,. Appl. Phys. Lett., 8, 671 (1976).. J. Yang, A. Banerjee, K. Lrd, S. Guha, Prceedings f the nd Wrld Cnference n Phtvltaic Slar Energy Cnversin, Vienna, Austria, p. 387 (1998).. 3. J. I Pankve,.Slar Cells, 4, 99 (1988). 4. J. I Pankve, Semicnductrs and semimetals, vl. 1B, Orland Academic Press, A. Jantta, R. Janssen, M. Schmidt, T. Graf, L. Görgens, C. Hammerl, S. Schreiber, G. Dllinger, A. Bergmaier, B. Stritzker, and M. Stutzmann, J. Nn-Cryst. Slids, 99-3, 579 (). 6. G. H. Lin, M. Kapur, J. O M. Bckris, Sl. Energy Mater. Sl. Cell., 8, 9 (199). 7. S. Tlansky, in: Multiple-Beam Interference.Micrscpy f Metals, Academic, Lndn, p.55 (197 ). 8. A. K. Gsh, T. Mc Mahn, E. Rck, H. Wiesmann, J. Appl. Phys., 5, 347 (1979). 9. J. C. Manifacier, J. Gasit and J. P. Fillard, J. Phys. E:Sci. Instrum., 9, 1 (1976). 1. R..Swanepel, J. Phys. E : Sci. Instrum., 16, 114 (1983). 11. R. Swanepel, J. Phys. E:Sci. Instrum., 17, 896 (1984). 1. M. H. Brdsky and P. A. Leary, J. Nn-Cryst. Slids, 35&36, 487 (198). 13. A. Jantta, R. Janssen, M. Schmidt, R. Graf, M. Stutzmann, L. Görgens, A. Bergmaier, G. Dllinger, C. Hammerl, S. Schreiber and B. Stritzker, Phys. Rev. B69, 1156 (4). 14. M. Abdel-Baki, F. A. Abdel-Wahab, A. Radi and F. El-Diasty, J. Phys. Chem. Slids, 68, 1457 (7). 15. A. Llret, Z. Y. Wu, M. L. Theye, I. El Zawawi, J. M. Siefert and B. Equer, Appl. Phys., A55, 573(199).

14 Assem Bakry E. A. Davis, N. F. Mtt, Phil Mag., 93 (197) 17. P. Hess, Thin Slid Films, 41, 318 (1994). 18. D. Jusse, J. Said and J. C. Bruyere, Thin Slid Films, 14, 49 (1985). 19. S. Ray, P. Chaudhuri, A. K. Batabyal and A. K. Barua, Sl. Energy Mat. Sl. Cells, 1, 335 (1984).. V. Bursikva, P. Sladek, P. St ahel, and J. Pursik, J. Nn-Cryst. Slids, 35, 138 (6). 1. A. Hadjadi, P. St ahel, P. Rca i Cabarrcas, V. Paret, Y. Bunuh, and J. C. Martin, J. Appl. Phys., 83, 83 (1998).. A. M. Perez, F. J. Rener, C. Zuniga, A. Trres and C. Santiag, J. Phys.: Cndens. Matter, 17, 3975 (5). 3. M. M. de Lima and F. C. Marques, J. Nn-cryst. Sl, 99-3, 65 (). 4. G. Talukder, J. A. Cwan, D. E. Brdie and J. D. Leslie, Can. J. Phys., 6, 848 (1984) 5. G.D. Cdy, T. Tiedje, B. Abeles, B. Brks and Y. Gldstein, Phys. Rev. Lett., 47, 148 (1981). 6. B. Abay, H. S. Guder and Y. K. Ygurtchu, Slid State. Cmmun., 11, 489 (1999). 7. M. A. Hassan and C. A. Hgarth, J. Mater. Sci., 3, 5 (1988). 8. S. H. Wemple, M. Di Dmenic, Phys. Rev., B3, 1338 (1971). 9. S. H. Wemple, Phys. Rev., B7, 3767 (1973). 3. S. H. Wemple, Appl. Opt., 18, 31 (1979). 31. H. Pignant, Electrn. Lett., 17, 973 (1981). 3. S. Hirta, T. Izumitani, J. Nn-Cryst. Slids, 9, 19 (1978). 33. M. Abdel-Baki, F. A. Abdel Wahab and F. El-Diasty, Mater. Chem. Phys., 96, 1 (6). 34. D. R. Penn, Phys. Rev., B18, 93 (196). 35. T. S. Mss, G. J. Burrell and E. Ellis, Semicnductr Opt-Electrnics, Butterwrths, Lndn, (1973) 36. V. Gpal, Infrared Phys., 161 (198) 37. M. M. Wakked, E. Kh. Shker and S. H. Mhamed, J. Nn-Cryst. Slids, 65, 157 ()