Investigation of Anisotropic Cylindrical Semiconductor-Dielectric Waveguides

Transcription

1 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN , VOL. 21, NO. 5, 2015 Invetigation of Aniotropic Cylindrical Semiconductor-Dielectric Waveguide Dariu Ploni 1, Vaciu Maliauka 1, Andriu Katkeviciu 1 1 Department of Electronic Sytem, Vilniu Gedimina Technical Univerity, Naugarduko St , LT Vilniu, Lithuania dariu.ploni@vgtu.lt 1 Abtract The ue of emiconductor-dielectric waveguide i low at the moment due to diadvantage of high attenuation of electromagnetic microwave. The attenuation depend on tructure and material of emiconductor-dielectric waveguide. Dependence of tranmiion coefficient on the frequency of emiconductor-dielectric waveguide and on different denitie of electron in emiconductor are tudied in thi paper. A well a the influence of periodicity on tranmiion of electromagnetic microwave in emiconductordielectric waveguide i dicued. It i hown that frequency dependence of tranmiion coefficient of periodical emiconductor-dielectric waveguide obtain the propertie of the band pa filter. Alo it i hown that the choice of emiconductor and dielectric material have a ignificant impact on the nature of the tranmiion and attenuation of electromagnetic microwave. Index Term Electromagnetic propagation, electron, charge carrier denity and mobility, periodic tructure. I. INTRODUCTION Variou waveguide ytem are widely applied for travelling-wave tube, delay line, phae modulator or converter and other microwave device [1] [5]. On the other hand the ue of emiconductor waveguide i low at the moment. Other author have hown what attenuation of electromagnetic (EM) microwave in emiconductor waveguide i high [6]. High attenuation of EM microwave reduce poibilitie to ue emiconductor waveguide in microwave ytem. For intance SiC emiconductor waveguide could be ued a microwave phae hifter due to high phae converion range of EM microwave. The temperature controllable waveguide without external dielectric could be manufactured from dipolar gla but the ue of thee material doe not reduce the high attenuation of EM microwave [7]. The Gau pule ditortion in layered cylindrical dielectric waveguide i invetigated by I. O. Vardiambai [8]. The analyi of waveguide i performed when dielectric are ideal without loe. Structure of EM field in dielectric waveguide with aniotropic wall are invetigated in paper [9]. The tranmiion and reflection coefficient of periodic ferrite emiconductor waveguide are dicued in paper [10] [12]. Application of the trong loy-dielectric loaded periodic Manucript received March 24, 2015; accepted June 27, waveguide in millimeter-wave gyro travelling microwave tube i decribed in paper [13]. Dielectric-loaded metal cylindrical waveguide for application of gyrotron-travelingwave amplifier i dicued in paper [14]. The relevant cientific problem of development and application of electrodynamical model (further model) of gyrotropic device i partially addreed in thi paper. The problem i olved by uing model of open cylindrical, generalized circular cro ection, layered emiconductordielectric (gyroelectric) waveguide. Characteritic of microwave which propagate in thee waveguide are obtained by applying the method of numerical experiment (modelling). Analogical model of ferrite-dielectric (gyromagnetic) waveguide are ued occaionally. Thee model are invetigated uing the method of numerical and phyical experiment. Thi paper i part and continuation of our other cientific work on thi topic [15], [16]. Gyrotropy i a type of aniotropy and i characterized by iotropic material which experience artificial aniotropy by operating under contant magnetic field [15]. Gyrotropic device are often ued in microwave range: phae hifter and modulator, polarizer and circulator, element of antenna and o on. Aniotropic ferrite-dielectric device are well invetigated, but their control i limited to a magnetic field. Aniotropic emiconductor-dielectric waveguide are le invetigated, but their control capabilitie are ignificantly higher. Semiconductordielectric waveguide can be controlled by the magnetic field, temperature, infrared ray, viible light, γ-ray. Therefore it now important to invetigate emiconductordielectric waveguide by comparing their reearch method and electrodynamical propertie with ferrite-dielectric waveguide. There are problem encountered in aniotropic waveguide modelling and material election by invetigating and applying aniotropic device. Ferrite and emiconductor core are hard and brittle therefore core uually have the hape of cylindrical circular cro ection rod. Model with external emiconductor or dielectric layer can be applied in order to modify the electrodynamical propertie and increae reitance of emiconductor core. The choice of ferrite i mall but they are ditinguihed by low attenuation of propagating wave in microwave device. A large choice of emiconductor i determined by the ued material, the conductivity type of material and denitie of free carrier 48

2 (i, n, n, n +, p, p, p + ), mobility of carrier and effective ma, contant of crytal lattice, the relative permittivity and other. The aim of thi paper i to invetigate dependence of tranmiion coefficient on the frequency of non-periodical and periodical model of emiconductor-dielectric waveguide (SDW) on different temperature and denitie of electron in emiconductor a well a to invetigate poibilitie of application of uch model. Non-periodical layered ferrite and emiconductordielectric waveguide are naturally aniotropic in croection. The ame type periodical waveguide are naturally aniotropic in cro-ection and longitudinal-view. Thee waveguide are compoed of everal different material and waveguide propertie are different in different direction. Tak which are addreed in thi paper: the improvement of electrodynamical model of emiconductor-dielectric waveguide; development and invetigation of computer model of layered SDW uing a commercial oftware CST Microwave Studio [17]; the invetigation of poibilitie of SDW application in microwave device. Method ued at work: commercial oftware CST Microwave Studio i dedicated to the development of computer model of SDW, calculation of parameter of SDW and comparion of their parameter; hybrid numerical method which are ued in CST Microwave Studio oftware divide the analyed area into the element; teting, phyical and numerical experiment (modelling) are dedicated to the invetigation and verification of parameter and characteritic of model of SDW. There were created new computer model of nonperiodical and periodical SDW and obtained reult of their numerical experiment uing modern commercial oftware. II. THE ELECTRODYNAMICAL MODEL In thi chapter i preented electrodynamical model of periodical emiconductor-dielectric waveguide which i ued for analyi of non-periodical and periodical SDW. For verification of modelling reult are ued electrodynamical model which are preented in our previou work [15], [16], [18]. Dependence of tranmiion coefficient of propagating microwave in SDW veru frequency are calculated in 8 GHz 80 GHz frequency range in thi paper. Thi frequency range correpond to the 37.5 mm 3.75 mm length microwave range in the air. The length of propagating microwave in SDW i from 9.7 mm to 0.1 mm taking into account the relative permittivity which i approximately equal to 15 and permeability which i approximately equal to 1 of emiconductor and dielectric which have been ued. Tranveral and longitudinal dimenion of the invetigated SDW are in the row of length of microwave. Therefore SDW are electrodynamical ytem with ditributed parameter. The dielectric and magnetic permeabilitie, diameter and length are not only tructural SDW parameter, but, mot importantly, electrodynamical parameter a well. It i difficult to perform the phyical experiment due to the relatively mall diameter of SDW, long length, hardne and fragility of material, cylindrical circular cro ection hape, complex contruction, monocrytal emiconductor tructure and the low denity of free carrier m m 3 which i influenced by microwave attenuation. Semiconductor monocrytal are produced by the zone melting or pulling from the melt method. Quite large 150 mm 300 mm in diameter and 1.5 m 2 m long rod are anded mooth and liced into 0.4 mm 0.8 mm thick plate. Thee dimenion and cro-ectional hape are not compatible with the SDW tructure and deign. Diffuion of impuritie, implantation of ion i carried out to a depth of a few micrometer. The thickne of epitaxial layer, dielectric layer i alo up to everal micrometer. Denity of impuritie in typical emiconductor device i about cm cm 3, o 10 6 time higher than permiible in SDW. Therefore we were unable to obtain adequate ample and had to be confined to the numerical experiment (modelling). A. The Electrodynamical Model of Periodical Semiconductor-dielectric Waveguide The cro-ection of electrodynamical model of open cylindrical emiconductor-dielectric waveguide with periodical layer i preented in (Fig. 1(a)). The model conit of everal layer: 1 emiconductor core (parameter upper index i ), 2 emiconductor or emiconductor-air layer, 3 external dielectric layer, 4 air. d 1 d 2 L 1 L 2 r (a) R 1 R 2 ε r1 ε r2 d ε r3 a εr4 1 d 2 d 1 (b) Fig. 1. The electrodynamical model of open cylindrical emiconductordielectric waveguide with periodical emiconductor layer: (a) cro-ection; (b) longitudinal-view. The complex permittivity of emiconductor core and external emiconductor layer (ring) could be calculated by uing cold-plama expreion r 49

3 2 n ωp ε r ε k, ω(ω i ζ) n where ε k i the n-type emiconductor dielectric contant; ω p i the angular plama frequency; ω = 2πf i the angular frequency; f i the frequency of EM microwave; ζ i the electron total colliion frequency with emiconductor lattice contant. The emiconductor core radiu i r = 1 mm. External layer are characterized by complex permittivitie r2 and d r3 repectively, which width are d 1 and d 2. Radii of external layer are R 1 and R 2. The longitudinal-view of electrodynamical model of open cylindrical SDW with periodical emiconductor-dielectric layer i preented in (Fig. 1(b)). The analyi of the model of periodical SDW wa performed by taking into account that waveguide conit of ix emiconductor ring, which length are equal to L 1 = 5 mm, and length of air ring are equal to L 2 = 5 mm. The overall length of the model i L = 55 mm. Thicknee of external layer were increaed in order to obtain propertie of microwave filter in model of periodical SDW. Relative thicknee are elected d 1 / r 0.3 and d 2 / r 0.2. The periodical waveguide could be tranformed in to non-periodical waveguide, when econd layer of the waveguide i continuou and it i made from emiconductor or air, and the boundary between ring diappear, when permittivitie of ring will be the ame. B. Verification of Modelling Reult of Waveguide For verification of phyical and numerical experiment reult wa elected model of open waveguide of 1SCh11 ferrite. Experimental invetigation of ferrite waveguide were carried out in company JSC Elmika. The permittivity of 1SCh11 ferrite wa equal to f r 14.6 and the tangent of the lo angle wa tan δ = , and complex relative f 3 permeability of waveguide i equal to μ 1 i5 10. r Meaurement were performed with a R2400 calar analyer which wa produced in the company JSC Elmika. Limit of meaurement of R2400 calar analyer are equal to 25 GHz 40 GHz frequency range, tanding microwave ratio and tranmiion coefficient 0 db 35 db range. Reult of phyical experiment were compared with the reult of numerical experiment which were obtained uing the CST Microwave Studio oftware package. The reearch tructure of model ferrite waveguide i preented in Fig. 2. EM microwave generator generate the main type H 10 microwave in the rectangular waveguide. Ferrite iolator pread the wave only in one direction. The firt coupler direct the main type microwave to the analyer and to the econd coupler. The econd coupler direct the microwave into invetigated waveguide. The reflected microwave from the invetigated waveguide i directed to the R2400 calar analyer through the econd coupler. The third coupler i ued to tranfer microwave to the R2400 calar analyer and to the load. Microwave are reinforced in amplifier before reaching the calar analyer. (1) Scalar analyer and EM microwave generator are managed by peronal computer (PC). Reearch reult are viualized uing the PC. The longitudinal-view and cro-ection of 1SCh11 ferrite waveguide model i preented in Fig. 3. The length of the invetigated waveguide rejecting the conical end i equal to L 1 = 40.2 mm, the length of conical end L 0 = 22.5 mm, the overall length of the waveguide i equal to L = L L 0 = 85.2 mm, the radiu of the waveguide f r = 1.1 mm. Fig. 2. Reearch tructure of ferrite waveguide model. Fig. 3. The longitudinal-view and cro-ection of 1SCh11 ferrite waveguide model. Dependence of tranmiion coefficient on the frequency of propagating microwave in ferrite waveguide obtained uing phyical and numerical experiment are preented in Fig. 4. It can be een that dependence of tranmiion coefficient on the frequency of propagating microwave in 1SCh11 ferrite waveguide obtained uing phyical experiment are imilar to dependence obtained uing commercial oftware. Reult of phyical and numerical experiment are imilar. Reonance i in the frequency range from 32 GHz to 38.8 GHz due to coupler and incompatibility of characteritic impedance in the invetigated waveguide Fig. 4. Fig. 4. Phyical and numerical experiment dependence of tranmiion coefficient on the frequency of propagating microwave in ferrite waveguide model. Part of the EM microwave are reflected from the end of invetigated waveguide therefore the attenuation uddenly increae in the reonance frequency range. The reonance appear in the ame frequency range and in computer imulation, but in thi cae the ditortion of characteritic i lower. The tranmiion coefficient in the reonance frequency range at 34.1 GHz frequency i about 2 time larger during the phyical experiment then in modelling. Dependence of attenuation coefficient on the frequency of propagating HE 11 microwave in ferrite 1SCh11 waveguide model are preented in Fig

4 Since it i impoible to meaure attenuation coefficient of propagating microwave phyical experiment and comparion of reult i carried out in order to find difference between the numerical experiment. Therefore the comparion i carried out of reult which were obtained uing the author' algorithm [18] and commercial oftware With algorithm preented in [18] CST Microwave Studio Frequency (GHz) Fig. 5. Dependence of attenuation coefficient on the frequency of propagated HE11 microwave in ferrite waveguide model. The major difference between reult are in the lower frequency ide Fig. 5. Difference eek up to 9 % and decreae until it reach the 0.1 % level becaue of increaing frequency of EM microwave. The reult of phyical and numerical experiment varie no more than two time. However the accuracy of comparable characteritic remained unknown in both cae. III. THE ANALYSIS OF MODELS OF NON-PERIODICAL SEMICONDUCTOR-DIELECTRIC WAVEGUIDES Several model of non-periodical SDW are dicued in thi chapter. The tructure of the electrodynamical model are: n-insb core and n-sige, TM-15 layer; n-sige core and n-insb, TM-15 layer; n-gaa core and n-ina 1-xSb x, TM-15 layer. The TM-15 dielectric i ued for the external d 4 layer. It complex permittivity i r3 15(1 i 10 ). The analyi of model of SDW i performed by taking in account denity of electron N, emiconductor electron mobility µ, effective ma m* and temperature T. Value of following parameter are elected baed on the literature [19], [20]. The model of non-periodical waveguide which tructure conit of n-insb core and n-sige, TM-15 layer i invetigated, when external temperature i T = 300 K and denitie of electron are N = ; ; m 3. The length of waveguide i L = 55 mm and normalized width of external layer are d1 / r d2 / r Frequency dependence of tranmiion coefficient of propagated HE 11 mode of above dicued waveguide model are preented in Fig. 6. The SDW ha a lower attenuation of EM microwave when the denity of electron i N = m 3. Tranmiion characteritic of EM microwave of the waveguide are imilar to characteritic of the high pa filter. The highet attenuation of EM microwave could be received when denitie of electron are equal to N = ; m 3. The highet attenuation of EM microwave i at 45 GHz. Since the energy of EM microwave i aborbed and above dicued feature are maintained the SDW could be ued for manufacture of attenuator and aborber of EM microwave when denitie of electron are equal to N = ; m 3. The attenuation of EM microwave could be decreaed by changing the type of emiconductor. Frequency dependence of tranmiion coefficient of propagated mode of SDW which core i from n-sige emiconductor, firt external layer i from n-insb emiconductor and econd external layer i from TM-15 dielectric are preented in Fig. 7. The electron mobility i 17.5 time lower in n-sige than in n-insb. The dielectric contant are almot the ame for both emiconductor. The effective ma i ~114 time higher in n-sige than in n-insb. The electron mobility ha the greatet influence on variation of attenuation of EM microwave comparing with other parameter. From analyi of dependence of tranmiion coefficient on the frequency (Fig. 6 and Fig. 7) it een, that attenuation of EM microwave i lower in model of nonperiodical SDW which tructure conit of n-sige core and n-insb, TM-15 layer than in model of waveguide which tructure conit of n-insb core and n-sige, TM-15 layer. EM microwave are more concentrated in emiconductor core in model of multilayer emiconductor waveguide. Frequency dependence of tranmiion coefficient of model of non-periodical waveguide, which tructure conit of n-gaa core and n-ina 1-xSb x, TM-15 layer are preented in Fig. 8. The denity of electron i N = m 3 and external temperature i varied from 125 K to 200 K. N 5 10 m 20 3 Fig. 6. Propagated HE11 mode' tranmiion coefficient' frequency dependence of non-periodical emiconductor-dielectric waveguide model which conit of n-insb core and n-sige, TM-15 layer. ; N 5 10 m 20 3 Fig. 7. Propagated HE11 mode' tranmiion coefficient' frequency dependence of non-periodical emiconductor-dielectric waveguide model which conit of n-sige core and n-insb, TM-15 layer. Fig. 8. Propagated HE11 mode' tranmiion coefficient' frequency dependence of non-periodical emiconductor-dielectric waveguide model which conit of n-gaa core and n-ina1 xsbx, TM-15 layer. 51

5 The attenuation of EM microwave i table in frequency range from 30 GHz to 80 GHz (Fig. 8). The attenuation of EM microwave i lower, when external temperature i T = 200 K. After the analyi of electrodynamical model of non-periodical SDW it can be concluded, that lower attenuation of EM microwave could be received in model of waveguide which tructure conit of n-sige core and n-insb, TM-15 layer. However the attenuation of EM microwave could be controlled only in model of waveguide which tructure conit of n-gaa core and n-ina 1-xSb x, TM-15 layer. IV. THE ANALYSIS OF MODELS OF PERIODICAL SEMICONDUCTOR-DIELECTRIC WAVEGUIDES The analyi of electrodynamical model of periodical SDW which tructure conit of n-sige core and n-insbair, TM-15 layer i performed, when denitie of electron are N = ; m 3. Thee denitie are elected in order to reveal the influence of propagating HE 11 mode. Dependence of tranmiion coefficient on the frequency of HE 11 mode propagating in model of periodical SDW are imilar to characteritic of the band pa filter (Fig. 9). The bet characteritic of band pa filter are achieved, when denity of electron i N = m 3. The attenuation of EM microwave in waveguide increae and propertie of band pa filter decreae when denity of electron increae. ; 20 3 Fig. 9. Propagated HE11 mode' tranmiion coefficient' frequency dependence of periodical emiconductor-dielectric waveguide model which conit of n-sige core and n-insb-air, TM-15 layer. Ten time higher denity of electron N = m 3 increae attenuation of EM microwave approximately 20 db and decreae reonance in all analyed frequency range. Reonance appear when EM microwave reflect from the edge of emiconductor ring (Fig. 9). Frequency dependence of tranmiion coefficient of propagated HE 11 mode in model of periodical SDW which tructure conit of n-gaa core and n-ina 1 xsb x -air, TM-15 layer are preented in Fig. 10. The analyi of thi model i performed by taking in to account the denity of electron N = m 3 and temperature T = 125; 200 K. The attenuation of EM microwave decreae, when temperature increae till 200 K. The top band i viible and the width of the top band i from 43 GHz to 52 GHz. The highet attenuation of EM microwave i in the middle of the top band and it i equal to 45 db. The attenuation of the HE 11 mode could be adjuted by changing temperature T. Therefore thee model of waveguide are more uitable than waveguide which tructure conit of n-sige core and n-insb-air, TM-15 layer. Comparing (Fig. 9) and (Fig. 10) it een, that the attenuation of HE 11 mode i 4 db in frequency range from 24 GHz to 47 GHz, when denity of electron i N = m 3. The attenuation of EM microwave i obtained in model of SDW which tructure conit of n-sige core and n-insb, TM-15 layer. Fig. 10. Propagated HE11 mode' tranmiion coefficient' frequency dependence of periodical emiconductor-dielectric waveguide model which conit of n-gaa core and n-ina1 xsbx -air, TM-15 layer. The attenuation of EM microwave in model of SDW which tructure conit of n-gaa core and n-ina 1 xsb x, TM-15 layer i 5 db at frequency range from 25 GHz to 43 GHz and temperature T = 200 K. But the width of the top band i moother in thi type of waveguide in comparion with other waveguide. From analyi of dependence of tranmiion coefficient on the frequency it een, that characteritic are not mother. It could be explained by the fact that emiconductor ring change impedance of the waveguide. Impedance of waveguide could be combined with air pace by changing the edge of emiconductor ring. The edge of emiconductor ring hould be conical. Thee change of tructure of model of periodical SDW are preented in Fig. 11. The length of conical edge of periodical ring are ΔL = 0.5 mm and the emiconductor layer thickne i d 1 = 0.3 mm. Frequency dependence of tranmiion coefficient of propagated HE 11 mode in model of periodical SDW with conical edge of emiconductor ring are preented in Fig. 12. Comparion of (Fig. 10) and (Fig. 12) how that in thee model of waveguide expoe more propertie of band pa filter. The top band move to the higher frequencie approximately 10 GHz, when the tructure of waveguide conit of n-gaa emiconductor core and n-ina 1 xsb x -air, TM-15 external layer. d 1 L1 L2 L d ε r3 a ε 1 r4 ε r2 ε r1 Fig. 11. The longitudinal-view of model of periodical emiconductor-dielectric waveguide, when edge of emiconductor ring are conical. The attenuation of EM microwave i lower than 10 db in frequency range from 23.5 GHz to 55 GHz, when tructure of waveguide conit of n-sige core and n-insbair, TM-15 layer. However the lowet attenuation in thi frequency range could be received till 3 db, when the tructure of periodical waveguide conit of n-sige core and n-insb -air, TM-15 layer. The frequency range in which the attenuation of EM 52

6 microwave i lower than 10 db i from 25 GHz to 54 GHz. The lowet attenuation of EM microwave could be 5 db in thi frequency range, when the tructure of periodical waveguide conit of n-gaa core and n-ina 1 xsb x -air, TM-15 layer. n-sige; n-insb-air; TM-15 N = 10 m ; T = 300 K n-gaa; n-ina1 x Sbx -air; TM-15 N = 10 m ; T = 200 K Fig. 12. Propagated HE11 mode' tranmiion coefficient' frequency dependence of periodical emiconductor-dielectric waveguide model, when edge of emiconductor ring are conical. The lower attenuation of EM microwave i received in model of waveguide which tructure conit of n-sige core and n-insb -air, TM-15 layer. On the other hand the control poibilitie of thee model by changing external temperature T i lower comparing with model of waveguide which tructure conit of n-gaa core and n-ina 1 xsb x -air, TM-15 layer. The eential principle of the functioning of relevant model and application' poibilitie expected to be clarified in thi paper. The improvement and optimal deign of elected perpective device will be addreed in the future. V. CONCLUSIONS Comparion reult of ferrite waveguide phyical experiment and numerical experiment uing commercial CST Microwave Studio oftware howed that ratio of tranmiion coefficient i about two time larger in phyical experiment due to reflection from the end of waveguide at 34.1 GHz frequency. In both tudie, the attenuation coefficient in lower frequencie varie no more then 9 % and in higher frequencie 0.1 %. The lower attenuation of EM microwave could be received in electrodynamical model of waveguide which conit of n-sige core and n-insb, TM-15 layer, when denity of electron i N = m 3. Frequency dependence of tranmiion coefficient of propagated HE 11 mode in electrodynamical model of periodical emiconductor-dielectric waveguide which conit of n-sige core and n-insb -air, TM-15 layer or n-gaa core and n-ina 1 xsb x -air, TM-15 layer obtain propertie of the band pa filter. Dependence of tranmiion coefficient on the frequency become more mother and top band expand in to both ide, when the edge of emiconductor ring are conical. It ha been found, that the periodical SDW could be ued in the microwave filter. The EM microwave attenuation i lower ~2.2 time in model periodical waveguide which conit of n-sige core and n-insb-air, TM-15 layer, than in periodical waveguide which conit of n-gaa core and 53 n-ina 1 xsb x -air, TM-15 layer, when denity of electron i N = m 3. REFERENCES [1] K. Itenikova, D. Faktorova, Invetigation of metamaterial tructure influence on elective propertie of microwave waveguide enor, Electrical Review Przeg1ąd Elektrotechniczny, vol. 88, no. 7b, pp , [2] B. Hrycak, D. D. Czylkowki, M. Jainki, J. Mizeraczyk, Novel low power microwave plama ource at atmopheric preure, Electrical Review Przeg1ąd Elektrotechniczny, vol. 88, no. 8, pp , [3] M. D. Rotaru, J. K. 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