Natarajan R, Dube D C

Tripathi, V K

IACS Institutional Repository

Microwave measurement of complex permittivity of thin metal hlmsD. C. D ube. K. N a t a k a j a n  and V K. T k ip a t iitDepartineni of Phi/fsiM, Indian InMitntv oj TccJrnologjf,New DelJii-lUnm){Pecawad 4 Januauf 1977, rwispAl 7 Jinip 1977)Tn rvcent years tUore has been jiu iiirivasiiifr mteiost in tbo study of iniero'wave proijnitios of iUm seiui-iuntal and metal films ((hmn 1907, D ’Aiello  ^ Kieedman 1969, Raln(^y ci al 1970). The dieJeetiie proiiei t ies ol these films are utilist'd in material eharactGi'izatioii toi tlu'f purpost  ^ of deviee fnbrieation and are helpful in the evaluation of useful liee earner ]>aramoters viz mobility jind relaxation time Bismuth is a jjojmlai semi-metal, well known ior ds typieal band stine- ture and has evoked gieat mterest iii the past l(‘v 3'^ ()ars (Smith vt al 1963, Williams •fc Smith 1964, Tiijiathi 1970) The nneiowavi  ^ applieations ol thin metallic- films have also gained iiuportanee lecently as exoinplifieil by the use of liJins as microwave mirrors and as large size tilm iefl<‘otois (Koiolev & Gridnev 1963). However, the iniemwave iuvestipations ol hismnfh and metal films liave received v(U‘y little attention Since the properties of thin films are ipiitn diffeienl from those of the bulk, it is of mterest to liave measurements on films It may be added li^io that the skin de[)th of those films is of the order of iew microns for inierowavoH and hence microwaves AvonkI In* best' suii.ed foi the investigation (*f thill films.Wo eousider the jiitipagatiou ol eleetronuignel le waves u a reelaiigidar wave­guide in TEj„ mode. Tlim metal film is mounted along iJie axis ol tlic Ava,\eguido and the length o f the film is around 2 ein The surface o f the film is parallel to the naiTow'  ^ wall ol the wav^eguidi  ^ in much the siini(‘ Avay as in an ordinaiy vane type atteiiuatoiFor the portion of thii w^ aA^ egiiide loaded with the tliin film, we (^ aii di^ fino a x)ro])agatioii constant, an expi'cssion lor wdiich may be obtained from oui earlier }>aper (Dube Ik, Natarajaii 1973). Tlic semi-inntal film may be emisidercd as a lossy dielectric AAotli an effective dieloetne constant defined asrndum J .  Phys. 52A. 405-410 (1978)4:7TI(T(1).whore hi, is the lattice dieleetric constant, a is tlie complex conductivity and w IS the frequoiiey of the AA'^ ave It may be mentioned lierc that ecj (1) is justified406406 D . C . D u b e  R .  N a ta ra ja n  a n d  V .  K .  T r ip a t h ionly whon thfi dimonsion of mtereal (e.g. tho thickness of the film) is greater than the Dobye length  ^ i.o. tho screening length Ad =  the Boltzmannconstant, —e, iVand T are the charge, concentration and temperature of electrons).In a typical bismuth sample with electronic concentration N  ~  6xl0^’ /cc. the Debye length at room temperature is of the order of lOoA Tho films consi­dered in the present investigation are thicker than tho Debye length and hence can bo treated as blocks ot lossy dielectric. The boundary conditions of the continuity of tangential component of electric vector and its space derivative at the two faces of tho sample arc then justified and tho propagation constant is governed by the same dispersion relation (Dube & Natarajan 1973)It may bo added hero that tho complex conductivitj of Ihe film may be ox- pT Ossed aswhere t is the momentum relaxation time of carriers. For films under discussion]  ^the film thickness is smaller than the bulk mean free path and hence the surface '^ scattering of electrons is important. So far no analytical expression for r due to surface scattering is available.Thin bismuth, gold and aluminium films were prepared by tho thermal eva­poration of 99.99% pure material m a vacuum of about 10 ®mm Hg The films worn dopo.sitod on to freshly cleaved mica substrates approximakdy 0,006 cm thick. Film thicknesses were measured utilising tho frequency shifts c^ ;l a cr5' s^tal. coutrollod oscillator (Chopra 1969).The phase shift and attenuation for the samples wei e measured using the standard two channel bridge technique described earlier (Dube ^ Natarajan 1973). One arm of the microwave bridge contains the calibrated vaiiablo phase shifter and attenuator and the othei contains tho sample holder which is nearly 5 cm long waveguide having a sharply cut longitudinal slot at the cenlei in the broad side dimonsion. The sample is introduced tlirough this slot Proper care is taken for the films to have good contacts with the top and bottom sides of the waveguide walls. Adjustment of variable impedance to bring about null conditions at tho detector end with and without the specimen measures the phase and attenuation introduced by the film. The components of permittivity are obtained using the values of phase constant and attenuation constant (Dube &r Natarajan 1973)In terms of an appropriate effective mass m* and a relaxation time t, the dielectric constant and conductivity of a metal film may bo written as€r^  Cl ____eom*fl+(«oT)2] ... (3)Microwave measurement of complex permittivity 407N e h -W*[l + ( o)T)*] ui€„et (4)The lattice tJioloctrio constant ei, in the present (?asc can bo neglected as the electron contribution is highly df)minant. Thus measured values of cr and tf can be used to evaluate the relaxation time from (3) and (4).The experimental data for phase and attenuation constants for thin films of bismuth, gold and aluminium are showm m tables 1 to 3 The variations of phase and attenuation for bismuth films with thickness from 240 to 720A have been shown in figure 1Table 1. Complex permittivity for thin bismuth films of various thic'hness. The measurements w'ore taken at room temperature (312“K) and at a frequency of 9.410 GHz.Thickness(Angstroms)Phoso shift/ Length (Degrees)Attenuation/Length(Decibels)Cr ei240 2 6 T-.T V 0-30 X lO'i 3 12X 10“300 12-0 10-8 0-91x10“ 2 01X 10“480 15-r) 12-2 0-89x10“ 2-38 X 10“600 200 1.37 0-83x10“ 1-88x10“720 30-4 16-3 1-05x10“ 1-86X 10“Table 2. Complex permittivity for thin gold films of various thicknesses. The meaaui'ements were taken at room temperature (310“K) and at a frequency of 9 410 GHz.Thickness(Angstroms)Phase shift/ Length (Dogreos)Attenuation/Length(Decibles)e, ei80 20-5 15-1 7-74x10“ 1-67 X 10“105 28-6 17 7 7-65x10“ 1-36x10“120 42-5 19-8 8-16x10“ 1-17x10“140 55-8 23-4 7-86x10“ 1-15x10“408 D. C. D u b e , R .  N a ta ra ja n  aa d  V .  K .  T r ip a t h iFiii 1. VariationH of phase Hhifl, and atiommtioii with film thicknPHs,riio high vftliiGs of 6V ftiul Cf as sliowii in tho t-afilos are duo to free carrier effects in bismuth and in metal films Tho same order of magnitude of those paiameteis is obtained by subsiitulmg appropriate values for the. quantities in­volved in eqs. 3 and 4 Variation of relaxation time t with thickness for bismuth films is plotted in figure 2 The decrease in t with tho decrease in thickness may bo attributed f><j surface scattorinfj! Hfiwover. a quantitative treatment ol‘ this scattering-is not-availitble in litoraturo- - - . _Microwave measurement of complex permittivity 409Table 3. Complex peiinitt ivity for thin nlluminmin films oi Yarions thiek- nossos. The measutemeiits Avere taken at room temeprature (310^ ’K) and at a frequency of 9.410 CHzThickneas(.A.ngstroma)120i:io160200Phuao shift/ kwigth519 5 I8-7 13-0At (I'liuation/ Longih10-6 15 2 20-7 24-S2 58 10''4 01 V 10'55 57 ' 10''5 11 1 O'"’7 7(Y\ or- 12 0x10'^ ' 10 (ix 10" H 12.. 10"AoknowlistagementsThe authors are thankful to Professor K. L. Chopra and Professoi M. S. Sodha for valuable discussions. Thanks are also duo to Dr. D. K Pandya lorhis help in the preparation of thin films. The finanial support of CSIR (India) is also acknowledged.410 D. C. Dube, R. Natarajan and V* K. TripathiR eferencicsChopra K L. 1909 Thin Film Phenomena, McGraw-Hill, New York D’Aiollo K. V. & Ji’rcedman S. J. 1969 J. Aj>pl Phye. 40. 2156,Dubo D. C. & Nalarajun K. 1973 J. Appl, Phya, 44 4927.Gunn M. W. 1907 lEE Proceedinya 114- 207.Koi’olov F. A &  Gnrinev V, 1. 1963 BadioteMmika i EkMronilca 8. 1480,ICorolrv F. A. & Gridnev V, I. 1963 VeMnik Moak, TJniv,. Ser, Fiz,, Aatron, 14.Ramey R, L , Landes H. S. & Manus E. A. 1970 IEEE Trans, Microwave Theory and Tech,MTT-18. 196,Smith G, E,. Hebei L. C. & Buchsbauin S. J. 1903 Phya., Bev. 129,  164,Tnpathi V. K. 1970 Interaction of ElcHromaynetic Waves with Oaaeous and Solid State Plaamai^ .J>h,D, Thesis. I.l.T , DeDiilWdlimas G. A. & Smith G, E. 1964 IBM J. Besearch and Development 8. 276, ^

Microwave Measurement of Complex Permittivity of Thin Metal Films

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Microwave Measurement of Complex Permittivity of Thin Metal Films

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