Electrical Conduction and Dielectric Relaxation in Selenium Films Doped with Dysprosium Rare Earth

Transcription

1 American Jurnal f Cndensed Matter Physics 2017, 7(2): DOI: /j.ajcmp Electrical Cnductin and Dielectric Relaxatin in Selenium Films Dped with Dysprsium Rare Earth Fathy A. Abdel-Wahab *, Heba Abdel Maksud Physics Department, Faculty f Science, Ain Shams University, Abbassia, Cair, Egypt Abstract Selenium (Se) films implanted with Dysprsium (Dy) atms are prepared using thermal evapratin technique. The temperature dependence f ac cnductivity measured in frequency range 50 Hz-80 KHz is fund t be prprtinal t ω s (s 1). This prprtinality is reasnably well interpreted, in the lw temperature regin, by crrelated barrier hpping (CBH), f bi-plarn between bth randm and paired defect states. In the same time the high temperature part the ac cnductivity is well fitted using Mayer-Neldel rule. Furthermre, the dielectric relaxatin times f the dped a-se films are determined frm the dependence f the lss factr (ε") n the applied frequency relatins. The Cle-Cle diagrams have been presented and are used t determine the values f the static (ε s ) and ptical (ε ) dielectric cnstants f a-se dped with Dy atms. Keywrds Amrphus Selenium, Dped chalcgenides, Rare earths, ac cnductivity, Dielectric relaxatin and lss, Cle-Cle diagram 1. Intrductin Rare-earth (RE)-dped glass fiber amplifiers perating at a 1.3 μm wavelength band have received extensive attentin due t the zer dispersin f the silica fiber glass in the 1.3 μm-wavelength regin, and mst installed fibers wrldwide are ptimized at this wavelength. [1-4]. In cntrast, Dysprsium rare earth atms, Dy which have an active unfilled f shells in its electrnic cnfiguratin ([Xe] 4f 10 4s 2 ), can prvide 1.3 μm emissin due t the 6 F 11/2, 6 H 9/2 6 H 15/2 transitin [5]. In additin, Dy has a gd absrptin band at apprximately 800 nm, at which level a cheap cmmercial laser dide culd be used fr excitatin. On the ther hand, amrphus Selenium (a-se) is characterized by existence f lcalized states in its mbility gap. These states are created due t presence f defects and absence f lng range rder [6-8]. The structural disrder made a-se and its allys t have a high ptical transparency in the infra-red (IR) spectral regins up t 10 μm. Besides, it has large refractive index, thermal stability and high degree f cvalent bnding. Furthermre, due t high rare earth slubility, high emissin quantum efficiency [9] and the lw phnn energy (~ 250 cm -1 ) f amrphus selenides cmpared with flurides (~ 550 cm -1 ), r xide glasses (~ 1100 cm -1 ) [10] it culd be used as a hst medium fr Dy t enhance its mid-ir laser emissin. It shuld be nted that the * Crrespnding authr: fabdelwahab2003@yah.cm (Fathy A. Abdel-Wahab) Published nline at Cpyright 2017 Scientific & Academic Publishing. All Rights Reserved lw phnn energy f a-se decreases the multi phnn relaxatin which enables an active transitins between rare earth atm levels in the middle IR spectral regin. The ptical excitatin and emissin f Dy is very sensitive t the surrunding media cnsideratins such as dielectric parameters which plays an imprtant rle t cntrl the relaxatin prcesses and cnsequently the perfrmance f the laser emissin f Dy [11]. In the present wrk, the dependence f ac cnductivity n the applied frequency and temperature are analyzed with reference t the current cnductin mdels. The analysis shwed that the crrelated barrier hpping ver barriers (CBH) is the mst prbable mdel t describe the a.c. cnductin mechanism in the lw temperature range. Furthermre, the mdified CBH with Mayer-Neldel rule is well fitted with the ac cnductin in the high temperature range. The dependence f the lss factr (ε") n the applied frequency and Cle-Cle diagrams shwed that the dielectric relaxatin times fr Se-Se and Se-Dy diples are 2.46x10-5 and 1.27x10-4 s in sequence. 2. Experimental Bulk Selenium sample f weight 3g and dped with (at. %) f dysprsium (Dy) is prepared by mixing apprpriate quantities f Se and Dy, f purity 5N, in evacuated pre-cleaned silica tube sealed at 10-5 Trr. The synthesis f the mixture was carried ut by heating the ampule in an electric furnace t 400 C and keeping it at this temperature fr 3 hrs. Then, the temperature (T) was

2 42 Fathy A. Abdel-Wahab et al.: Electrical Cnductin and Dielectric Relaxatin in Selenium Films Dped with Dysprsium Rare Earth gradually raised by a rate f ~ 200 C/h t 900 C and kept again at that temperature fr anther 9 hrs. Finally, the ampule is left t cl dwn t rm temperature (RT=25 C). The btained bulk ingts were used as surce materials t prepare thin film samples by the thermal evapratin technique using vacuum cating unit type Edwards E306 A. The base pressure f the vacuum system was 1.5x10-6 Trr. After evapratin, the thickness f the fresh films was accurately determined by an ptical interference methd and is fund t be 750 nm. The structure f the btained films are studied using x-ray diffractin cmputerized system (mdel: Philips EXPERT-MPDUG PW-3040 diffractmeter with Cu Kα radiatin surce) in the 2θ range Fr electrical characterizatin, sandwich structure devices cnsisting f Au/Se:Dy/Au were prepared in situ by thermal sublimatin under high vacuum (~10-5 Trr). A prgrammable vltage current surce (type Keithley 228 A) was used as a surce f applied vltage and a Keithley-616 digital electrmeter was used t measure the utput current. The electrical cnductivity measurements were dne under vacuum and steady state cnditins, using lck-in amplifier mdel Oxfrd-DN 1714 in the temperature range K and frequency range 50 Hz 80 khz in the dark cnditins. 3. Results and Discussin The recrded XRD patterns fr the studied as-prepared a-se, previus wrk f SeSm films [12] and Dy dped Se (present wrk) samples are shwn in figure (1). In this figure, the XRD pattern f the fresh Se films reflects its amrphus nature. Furthermre, the dped Se film with at.% Sm [12] reflects an amrphus matrix embedded with sme crystalline znes. These znes appear thrughut tw characteristic selenium lines lying in the regin f the main diffractin hump cvering rughly the range f in 2θ angular units. Disappearance f such diffractin hump in case f Se dped with at. % Dy (present wrk) mean the grwth f crystalline phase n the expense f amrphus state. This crystalline phase cnsists f mixed phases f elemental Se (100), (101), (012), (110), (111), (022) elemental Dy (102), (110) and SeDy with tetragnal (002), (003), (112) and rthrhmbic (603), (116), (117) structures as shwn in Fig. (1) Electrical Cnductin ac Cnductin The temperature dependence f ac cnductivity (σ ac ) f the investigated samples at different values f frequency is shwn in Fig. (2). Fr clarificatin purpse, nt all the recrded frequency data pints are represented in the figure. In this figure, the ac cnductivity shws a frequency dependence which becmes mre prnunced at higher frequencies. On the ther hand, and in lw temperature range ( K) the cnductivity increase slightly less than linear against temperature and tends t becme a temperature dependent at higher temperatures ( K) in the studied frequency range. The graphical relatin between the applied frequency and ac cnductivity (σ ac ) at different temperatures is shwn in Fig. (3). This figure illustrates that σ ac depends n temperature nearly in the whle studied frequency range. The enhance f ac cnductivity at any frequency and temperature may be explained as fllws: the Dy atms enters the structural netwrk f a-se with crdinatin number f 7-8 bnds t Se with bnd length frm 2.92 t 2.97 A [13]. This means that a redistributin f electrnic charges takes place which built up a space charge regin arund Dy atm and the surrunding Se atms resulting an increase in σ ac. It is knwn that dc and ac cnductivities are related t each ther by an empirical relatin f the frm [14]: σ(ω,t) = σ dc +σ ac, where ω is the angular frequency f the applied alternating electric field. The a.c. cnductivity is generally analyzed by cnsidering a pwer law: σ ac (ω)=aω s where A is a temperature dependent pre-expnential factr, d ln σω ( ) s is the pwer expnent, s = which is used t d ln ω determine the a.c. cnductin mechanism [15]. The temperature dependence f the expnent s calculated using Fig. (3) is shwn in Fig. (4). This figure illustrates that the highest value f s is btained at a lwer measured temperature and decreases gradually with increasing temperature t reach a minimum value at T = 312 K. In the literature, varius mdels have been prpsed t explain the behavir f s which represents the expnent f Jnscher universal lw fr ac cnductivity fr semicnductrs [6, 16]. These mdels differentiate between tunneling and hpping mechanisms. The tunneling which describes the verlap f the expnentially decaying wave functin f the electrns due t its transitin between tw neighbring sites at a separatin R are explained by simple quantum mechanical tunneling (QMT) [14], nn-verlapping small plarns (NSPT) [14] and verlapping large plarn tunneling (OLPT) [17] mdels. On the ther hand, "hpping" which is represented by crrelated barrier (CBH) mdel, Ellitt [18, 19] stated that fr neighbring sites at a separatin R, the Culmb wells verlap, resulting in a lwering f the effective barrier height frm W M t a value W. Here the index s is evaluated as [18]: s = 1 6KT [ W + KTln( ωτ )] M Thus, in the CBH mdel a temperature dependent expnent s is predicted, with s increasing twards unity as T 0.0 K. Mre details abut these cnductin mdels are given elsewhere [14, 20]. Taking int cnsideratin the studied temperature range and at typical values f the parameters τ 0 =10-12 s, ω =10 4 s -1, the theretical trend f the functin s = f(t) fr the QMT [14], NSPT [14], OLPT [17] and CBH mdels (Eq. (1)) is shwn in Fig. (4) tgether with the experimental data f the present B B 0 (1)

3 American Jurnal f Cndensed Matter Physics 2017, 7(2): wrk [P. W.]. The similarity between the experimental s and CBH mdel reveal that CBH is fairly gd t describe the ac cnductin mechanism fr the studied samples in the lw temperature range ( K) and deviate frm experimental data trends in the higher temperature regin. The cincidence in s in the lw temperature range is als bserved fr ther cmpsitins such as Bismuth-Vanadate glassy semicnductr [14] as shwn in Fig. (4). The frequency dependent cnductivity in the CBH mdel [18] is given by the fllwing equatin: 3 π 2 6 σ ( ω) = N εεωr ω (2) 12 where εε is the dielectric permittivity f the material, N is the cncentratin f pair sites and R ω 2 2e 1 = πεε [ W + KTln( ωτ )] M B (3) Se (101) SeDy [P. W.] Se (101) Intensity, a.u. Se (111) Se (100) SeSm (111) C Sm (221) SeDy (002)T Se (100) SeDy (003) T SeDy (112) T Dy (102) Se (110) Se (012) Se (111) Dy (110) SeDy (603) O SeDy (116) O Se (013) SeDy (117) Se (022) SeSm (105) T Sm (015) Sm (043) Se (430) SeSm (103) T Sm (103) SeSm [12] a-se Diffractin angle, 2θ, degree Figure (1). XRD pattern fr a-se, previus wrk f SeSm [12] and the present wrk [P. W.] f SeDy thin films. It shuld be nted that the diffractin pattern f SeSm [12] is added t the figure fr the sake f cmparisn

4 44 Fathy A. Abdel-Wahab et al.: Electrical Cnductin and Dielectric Relaxatin in Selenium Films Dped with Dysprsium Rare Earth Figure (2). Temperature dependence f ac cnductivity fr SeDy thin films measured at different frequencies Figure (3). ac cnductivity dependence n frequency fr the studied SeDy thin films measured at different temperatures 0.9 Expnent s CBH mdel MN rule [P. W.] [14] T, K OLPT NSPT QMT Figure (4). Temperature dependence f the frequency expnent s (pen circles) fr the studied thin film samples [P. W.] btained frm slpes f Fig. (3). The dash-dtted curves represent the values calculated using the mdels: QMT [14], NSPT [14], OLPT [17] while the slid line represents the MN rule (Eq. (6)). The dashed curve represents the CBH mdel (Eq. (1)). The values f s calculated fr Bismuth-Vanadate glassy semicnductr [14] are inserted in the figure fr the sake f cmparisn

5 American Jurnal f Cndensed Matter Physics 2017, 7(2): KHz -ln σ ac, (Ω.cm) /T, K KHz 20 KHz 15 KHz 10 KHz 6.0 KHz 2.0 KHz 0.6 KHz 0.1 KHz Figure (5). Temperature dependence f ac cnductivities measured at different frequencies fr the studied thin films. The pen circle symbls crrespnd t experimental data. The dashed curves represent the fitting f ac cnductivity using the CBH mdel (Eq. (2)) while the slid curves are the fitting using the MN rule (Eq. (5)) T facilitate the btained data shwn in Fig. (4) the experimental σ ac data in Fig. (2) are fitted using equatins (2) and (3) as shwn in Fig. (5). Values f the parameters W M, τ, ε, and N used in the fitting prcedure are 2.1 ev, 4x10-13 s, 3.5 and 1.4x10 21 cm -3 in sequence fr the investigated films. It shuld be nted that values f the dielectric cnstant, ε, f the studied thin films are btained frm the Cle Cle diagram given in Sectin (3.2). In Fig. (5), it is bserved that in the studied frequency range the fitting using CBH mdel (dashed lines) appears t be reasnable in the lw temperature range and deviates frm the experimental σ ac trend in the high temperature regin as deduced frm Fig. (4) f the present wrk. On the ther hand, fitting using MN rule fits well in the high temperature regin and deviates frm this trend as the temperature decreases with respect t the fitting by the CBH mdel (Eq. (2)) Mdificatin f CBH Mdel using MN Rule It is knwn that the CBH mdel explains the variatin f σ ac (ω) with temperature at relatively lw temperature and des nt predict the strng temperature dependence at high temperatures [21, 22]. Mayer-Neldel (MN) [23] has imprved the CBH mdel in rder t accunt fr the ac cnductivity, σ ac, and fr the frequency expnent s in the high temperature range. In the case f thermally activated prcesses, the MN rule states that the electric cnductivity can be expressed by Arrhenius relatin E σ = σ exp (- ), KBT the dependence f the pre-expnential factr, σ, and activatin energy, E, in its lgarithmic frm is given by: E ln σ ( ω) = σ + (4) K T B where σ and are cnstants and refer t the nrmal and inverted MN rule in sequence. T apply MN rule n the studied samples, btain the slpes and pre-expnential factrs f the curves in Fig. (2) in the high temperature regin. Plt the graphical representatin f the pre-expnential factr, σ and activatin energy, E, is shwn in Fig. (6). The data pints shwn in Fig. (6) bey Eq. (4). Als, in this figure, it is bserved that the experimental data at lw frequencies bey the nrmal MN rule, while the high frequency data are fund t bey the inverted MN rule. + Obtained values f σ, σ, T + and T fr the studied samples are 5.7x10-8 (Ω.cm) -1, 6x10-6 (Ω.cm) -1, 845 K and 580 K respectively. The expressin f ac cnductivity f the CBH mdel based n the MN rule can be given as [24]: where ζ T MN σ ac ( ω) = π N εεωr ω (5) 12ζ T T T =. While the pwer expnent s beys the fllwing relatin: 6 KT B / ζ s = 1 [ W + ( KT / ζ )ln( ωτ )] M B It shuld be nted that Eqs. (5) and (6) differ frm Eqs. (1) and (2) by the presence f MN rule factr (ζ) in the frmer equatins. It is instructive t see the effect f the ζ factr (i.e., T ) n the ac cnductivity and the frequency expnent s. These have been calculated numerically using values f the parameters characterizing samples under study. The variatin f expnent s with temperature as calculated (6)

6 46 Fathy A. Abdel-Wahab et al.: Electrical Cnductin and Dielectric Relaxatin in Selenium Films Dped with Dysprsium Rare Earth using the MN rule (Eq. (6)) is represented in Fig. (4). Hwever, it can be clearly seen frm this figure that the trend f s is t decrease frm nearly unity with increasing temperature and des nt fit with the experimental data f s. This trend culd be explained as fllws: When an atm is dped in a hst material such as the present case f dping selenium with Dy atm an electrn phnn cupling takes place between an electrn f Dy atm and phnn which results frm the scillatins f hst lattice. These cupling has a quantized energy in a quantized states. These states will lie at the bttm f cnductin band and tp f valence bands and are used fr relaxatin f the excited electrn in cnductin band and its crrespnding hle in the valence band [25, 26]. At high temperatures, the lattice scillatins increase which affect tw main factrs 1) increase the density f the electrn-phnn cupling which in turn speeds up the relaxatin prcess. 2) the value f the dielectric cnstant (ε, (equatins (2 and 5)) which is directly prprtinal t the scillatins f the hst lattice. These tw factrs increase the cnductivity f the system. By lwering the temperature the lattice scillatin decreases which slw dwn the relaxatin prcess and in the same time it decrease the dielectric electric cnstant (ε) and led t a decrease in the cnductivity f the system T T The ζ term ( ζ = ) which differentiate between the T cnductivity f CBH mdel (eq. (2)) and MN rule (eq. (5)) has a big rle in the cnductivity f the system. As temperature increase, ζ decrease which increase the cnductivity term in MN rule ver the CBH mdel. On the ther hand, at lw temperature the value f ζ increase leading t a decrease f the cnductivity value f CBH mdel ver the MN rule Dielectric Prperties Figure (7) shws the dependence f bth real, ε', and imaginary, ε" parts f the cmplex dielectric cnstant n the applied angular frequency fr the investigated samples in the studied temperature range. In this figure the real part f the dielectric cnstant, ε', changes nly slwly with frequency in the lw frequency range (400 Hz khz) and decreases mre rapidly at higher frequencies ( khz). Furthermre, in this figure it is bserved that lss factr ε" exhibits tw relaxatin peaks in the lw and high frequency regins. Appearance f these tw peaks culd be explained as fllws: Accrding t scillatr mdel f Lrentz [26] the natural resnant frequency f diple is determined by ω = k / µ where μ is the reduced mass f the tw s scillatrs f the diple and k s is the restring frce f the spring that cnnects them. It is knwn that dping f Selenium with Dy ins creates a Se-Dy bnds besides the Se-Se bnds f a-se. Taking int cnsideratin the atmic masses f Se (78.96) and Dy (162.5) we can cnclude that fr Se-Dy bnds, ω will shift twards lwer frequencies with respect t the Se-Se bnds and causes the frmatin f the peak at lwer frequency as shwn in Fig. (7). Accrding t this mdel, the transitin time τ f the tw peaks (τ 1 and τ 2 ) culd be calculated as the reciprcal f the angular frequency at the tp f the lss peak. The calculated average values f τ 1 and τ 2 fr the investigated samples calculated frm ε"=f(ω) are 1.72x10-4 s and 2.31x10-5 s respectively. As is well knwn, the dependence f dielectric cnstants f a slid n the applied frequency decrease frm a static value ε s at lw frequency t a smaller value ε at higher frequencies. The difference between values f ε s and ε is attributed t the plarizatin f the scillating diple [27]. In this case, the relatin between ε s, ε and ε* is given by Cle and Cle [28] as: and * ε ε ε = + 1 iωτ ε ' ε ε = ( ωτ ) 2 (7) ' ε ( ωτ ) ε = (8) 1 + ( ωτ ) where ε = εs ε. The dependence f ε" n ε' is btained by applying the Cle Cle mdel fr the investigated samples in the studied temperature range and is shwn in Fig. (8). In this figure, the symbls represents calculated data with the slid line shwing the best fit t the calculated data using Eq. (7). After extraplating the fitted values t the real axis (ε'-axis), the plt shws that, fr lwer frequency the experimental pints deviate frm the dashed semicircles giving different values f the dielectric cnstant ε s in the studied temperature range as shwn in the inset f Fig. (8). In this inset f the figure it is clear that, in the lw temperature regin up t 200 K static dielectric cnstant, ε s, changes by rati ~ 26% against temperature while at higher temperatures (T > 200 K) the dependence becmes mre prnunced and ε s increase by 58 %. The direct prprtin between ε s and temperature is due t the dependence f the static dielectric cnstant n the lattice scillatins f the hst material [25]. On the ther hand in Fig. (8), at higher frequencies, all the data at different temperatures cnverge in ne pint that represents a unique value f ptical dielectric cnstant, ε. The calculated values f ε fr samples under study are It shuld be nted that presence f tw dielectric cnstants ε s and ε suggest the presence f tw relaxatin prcesses with time cnstants whse values are rather clse t each ther.

7 American Jurnal f Cndensed Matter Physics 2017, 7(2): ln σ, (Ω.cm) Inverted MN Nrmal MN E, ev Figure (6). Nrmal and inverted Meyer Neldel plts fr the studied samples. The symbls represent the experimental data and the straight lines are the best fit t the experimental data using least squares fits Figure (7). Dependence f the real, ε', and imaginary, ε" parts f the cmplex dielectric cnstant n the applied angular frequency fr the investigated samples in the studied temperature range

8 48 Fathy A. Abdel-Wahab et al.: Electrical Cnductin and Dielectric Relaxatin in Selenium Films Dped with Dysprsium Rare Earth Figure (8). Cle Cle diagram fr the investigated thin film samples at different temperatures. The slid curves drawn are the fitting f Cle Cle equatins t the calculated values f ε' and ε". The dependence f the calculated ε s n the applied temperature are represented in the inset 4. Cnclusins A cmprehensive electric and dielectric study n the effect f dping f a-se thin films with at. wt.% f Dy in the temperature range K and frequency range 50 Hz 80 khz allws us t draw the fllwing cnclusins: (1) A graphical relatin between ac cnductivity and temperature illustrated a strng temperature dependence and small frequency dependence (f 40 khz) fr σ ac in the regin f high temperature (312 K T >152 K). While fr f > 40 khz, σ ac depends mainly n the applied frequency and this dependence decreases as frequency increases. (2) The calculated values f the pwer expnent s shwed decreases frm high t lw values with increasing temperature. (3) Amng the different calculated ac cnductin mdels, the CBH mdel is fitted fairly well with the experimental data f the functin σ ac = f(t) in the lw temperature range ( K) with a deviatin in the high temperature range. (4) The calculated values f nrmal and inverted MN parameters ( σ and T ) are used t fit the measured electrical cnductivities f investigated film samples. A reasnable fitting appears in the high temperature regin ( K) with a deviatin in the lw temperature range. (5) The arc shape f the Cle Cle diagram leads t ne value fr the ptical dielectric cnstant, ε, and different values fr the static dielectric cnstant ε s, thrughut the temperature range, K. REFERENCES [1] Z. Yang, W. Chen and L. Lu, Dy 3+ -dped Ge-Ga-Sb-Se glasses fr 1.3 μm ptical fiber amplifiers, J. Nn-Cryst. Slids 351 (2005) [2] J. He, 1.3 μm-emissin prperties and lcal structure f Dy 3+ in chalchalide glasses, C. R. Chimie. 5 (2002) [3] D.W. Hewak, B.N. Samsn, J.A. Medeirs Net, R.I. Laming and D.N. Payne, Emissin at 1.3 μm frm dysprsium-dped Ga:La:S glass, Electrn Lett. 30 (1994) [4] K. Wei, D.P. Machewirth, J. Wenzel, E. Snitzer and G.H. Sigel, Jr, Spectrscpy f Dy 3+ in Ge-Ga-S glass and its suitability fr 1.3 μm fiber-ptical amplifier applicatins, Opt. Lett. 19 (1994) [5] G. Tang, Z. Yang, L. Lu and W. Chen, Dy 3+- dped chalchalide glass fr 1.3-µm ptical fiber amplifiers, J. Mater. Res. 23 (2008) [6] N.F. Mtt and E.A. Davis, Electrnic Prcesses in Nn-Crystalline Materials, 2 nd edn Clarendn Press, Oxfrd, [7] S.R. Ellitt, Physics f Amrphus Materials, 2 nd edn Lngmann Scientific & Technical, New Yrk, [8] A. Zakery and S. R. Ellitt, Optical Nnlinearities in chalcgenide glasses and their applicatins, Springer Berlin Heidelberg, 2007.

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