ࡱ> pH#`:bjbjmm 8@ p 2228L205d Ղ599L99:::8::::::$_hdž^1T;::T;T;^99iiiT;%998iT;8iip{|95 0\l2 a|~0Ղ|f(||::i: :Y:::^^i:::ՂT;T;T;T;          VODLJIVOST KOMPOZITNIH TANKIH FILMOVA OD SILICIJA Silicon Composite Thin Film Conductivity mr.sc. Vladimir Tudi Tomislav Luke, student Sa~etak: Poluvodi ka svojstva kompozitnih tankih filmova od silicija dobivenih jednom od poznatih tehnologija nanoaenja (CVD) presudne su za realiziranje u inkovitih solarnih elija. Velika slo~enost mikrostrukture tankog filma od nekoliko stotina nanometara i postojanje mnoatva kristala utvrena su prethodnim istra~ivanjem nekoliko grupa autora koriatenjem odgovarajuih metoda i postupaka, mikroskopske topografije atomske strukture i mjerenjem lokalne struje. Za utvrivanje karakteristika vodljivosti tankih filmova koriatene su razne metode koje su imale cilj usporediti aktivacijsku energiju Eact i konstantu najjednostavnijeg transportnog svojstva sD tamne vodljivost strukture bez prisutnosti svjetla. Specifi na vodljivost mjerena je paralelno sa supstratom na velikom broju uzoraka razli itih kristalini nih omjera razli itih debljina na relativno visokim temperaturama 200K-400K i u airokom frekvencijskom opsegu. Rezultati istra~ivanja DC vodljivosti kompozitnih slojeva ukazuju na mogue modele transporta veinskih nosilaca naboja koji ukazuju na injenicu da formacije zrna i njihovih skupina zna ajno mijenja mehanizam transporta energetskim pojasom. Klju ne rije i: kompozitni, lokalna struja, mikroskopska topografija, model transporta, vodljivost Abstract: Silicon composite thin films properties produced by traditional deposition technique (CVD) play crucial role as candidate in next generation of solar cells. Complex microstructural properties of few hundred nanometers thickness thin films were revealed by measuring techniques investigated in many scientific groups and institutes in the world. Many techniques and methods were used to establish correlation of activation energy and prefactor of the simplest transport property dark conductivity  EMBED Equation.3  measured parallel to the substrate with local current map technique. Specific conductivity of composite nanocrystalline silicon samples in various thickness and cristalline fraction were investigate in temperature range of 200-400K and wide frequency range. Eksperimental results suggests possible model of transport of the majority carriers based on the formation and crystalline fraction of their aggregates. Keywords: composite, dark conductivity, local current, microstructural properties, transport model UVOD Ispitivanja DC vodljivosti amorfno-nanokristalini nih tankih filmova od silicija (a-nc-Si:H) provode se u nekoliko istra~iva kih centara i instituta airom svijeta, jer sustavna definicija ovisnosti vodljivosti takvih kompozitnih slojeva o ostalim strukturnim parametrima materijala joa nije postignuta. Amorfna podloga kao i oblici i koncentracija nano-kristala razlikuje se od uzorka do uzorka zahvaljujui mikroskopskoj strukturnoj nehomogenosti. Postupak formiranja kristala zapo inje rastom stup aste strukture iz baznog temeljnog sjemena koje je usko na podlozi opisano u radu autora Fejfar. Stupii su jednake debljine a promjer se razmjerno poveava tijekom rasta. U amorfnoj podlozi odreene gustoe volumnog udjela kristala, pojedina ni kristali mogu biti raznih veli ina, ovisno o odnosu izmeu nukleacije i individualnog kristalnog izrasta. Ukoliko nukleacija prevlada, struktura sadr~i viae manjih kristala i obrnuto. Nadalje, amorfna matrica mo~e imati razli ite stupnjeve strukturnog ureenja i doprinos elektri nom transportnom svojstvu mo~e se razlikovati uz isti volumni odnos amorfnog i kristalnog udjela ato je opisano u radu autora Finger. Pregled znanstvenih istra~ivanja Velika slo~enost mikrostrukture vodikom generiranog a-nc-Si:H i postojanje mnoatva kristala autor Ko ka a prije njega Meier objasnili su pomou mikroskopske topografije atomske strukture i mjerenjem lokalne struje (engl. local current map). Usporeena je aktivacijska energija i konstanta najjednostavnijeg transportnog svojstva DC vodljivost  EMBED Equation.3  ili vodljivost bez prisutnosti svjetlosti (tamna vodljivost  EMBED Equation.3 ), mjerena paralelno sa supstratom na velikom broju uzoraka razli itih kristalini nih omjera. To je omoguilo izradu jednostavnog modela transporta koji je zasnovan na ideji da, suprotno malim zrnima, formacija njihovih skupina zna ajno mijenja mehanizam transporta energetskim pojasom kao da je rije  o sekvencijalnom preskakivanju nosilaca naboja. Vrijednost AC vodljivosti kompozitnih tankih filmova silicija do 2003. godine je vrlo rijetko istra~ena. Autor Wang u radu iz 2003. godine opisuje mjerenja temperaturno ovisnih parametara a-nc-Si:H filmova uzgojenih PECVD tehnikom. Rije  je o vodljivosti i kapacitivnosti filmova ovisnih o frekvenciji te strujno naponskoj karakteristici. Autor je predlo~io poboljaani model ekvivalentnog serijskog otpora za bolji opis elektri kih parametara nano-kristalini nih uzoraka od silicija. Frekvencijska ovisnost AC vodljivosti na niskim temperaturama sli na je amorfnim materijalima, ukazujui pri tom da slo~ena i promjenjiva vodljivost igra vrlo va~nu ulogu u a-nc-Si:H filmovima na niskim temperaturama. Temperaturna ovisnost AC vodljivosti otkriva postojanje mehanizma djelomi no skokovitog tuneliranja nosilaca u nc-Si:H filmovima. Autor je otkrio da je temperaturna ovisnost kapacitivnosti odreena meusobnim izmjenjivanjem procesa punjenja/pra~njenja izmeu energetskih nivoa postojeih kvantnih to aka i lokaliziranih stanja amorfnih grani nih podru ja. Stoga je i vrijednost kapacitivnosti slojeva ovisna o frekvenciji. Autor Gracin u radu opisuje mjerenje DC vodljivosti tankog filma koja su provedena na a-nc-Si:H uzorcima pripremljenim kemijskom depozicijom potpomognutom plazmom (PECVD). Direktna vodljivost struje (engl. Direct Current) krae oznake DC vodljivost prou ena je kao funkcija strukturnih svojstava provedena s pomou Raman spektroskopije i metode GISAXS (engl. Grazing Incidence Small Angle X-ray Scattering). Mjerenja su provedena na uzorcima pripremljenim kemijskom depozicijom potpomognutom plazmom (PECVD). Volumni udio kristala ili tzv. kristalna frakcija XC utvrena pomou Raman spektra u podru ju je od 0% do 60%, dok je prosje na veli ina kristala varirala od 2nm do 7nm. Ta metoda upuuje na injenicu da je vrijednost DC vodljivosti filma kao elektri nog svojstva materijala direktno povezano sa slo~enom strukturom filma. U radu je dokazana konstantna DC vodljivost strukture gotovo kroz cijelu strukturu, vrlo niske vrijednosti sve do 30% vrijednosti kristalne frakcije. Daljnje poveanje postotka volumnog udjela kristala u amorfnoj matrici rezultira skokovitom promjenom vodljivosti u uskom podru ju. Iznad tog podru ja vrijednost DC vodljivosti je puno vea i prevladava konstantna. Ovaj rezultat je u skladu s vrijednoau perkolacije sadr~ane u prora unskom modelu aesterostrane kristalne reaetke koja se pojavljuje u slu aju 32% volumnog udjela kristala u strukturi. Pojava odreenog odstupanja eksperimentalnih podataka od pretpostavljenih vrijednosti objaanjena je kao posljedica mogueg odstupanja veli ina pojedina nih kristala i njihovog oblika u odreenoj koncentraciji i njihovoj dubinskoj nejednolikoj rasprostranjenosti. Metoda impedancijske spektroskopije Izravna mjerenja elektri ne vodljivosti predstavljaju jednu od najkorisnijih tehnika karakterizacije amorfnih i kompozitnih struktura poluvodi a i zbog toga se intenzivno provode u znanstvenim istra~ivanjima. Takva je mjerenja mogue izvesti pomou istosmjernog DC i izmjeni nog AC napona i struje malih amplituda. Meutim DC-mjerenja povezana su s viae poteakoa prakti ne prirode, a osim toga iz rezultata AC-mjerenja mo~e se dobiti viae podataka o ispitnom uzorku. Zato su AC-mjerenja u ispitivanjima u posljednje vrijeme izbila u prvi plan. Problemi koji se javljaju kod materijala visoke vodljivosti, kad se u mjerenju mora ii do vrlo visokih frekvencija (fis e"1 MHz) pri emu razni efekti maskiraju pravi otpor ispitnog uzorka, nadilaze se mjerenjem AC-odziva preko velikog raspona frekvencija. Takva mjerenja nazivaju se impedancijskom spektroskopijom, a analiza dobivenih podataka provodi se metodom kompleksne ravnine. Bilo koji ispitni sustav mo~e se prikazati u obliku ekvivalentnog RC, RCPE kruga serijskog ili paralelnog spoja usporeujui eksperimentalno dobivene krivulje u kompleksnoj ravnini sa standardnim elementima u strujnim krugovima. Provedena mjerenja AC-vodljivosti na ispitnim a-nc-Si:H uzorcima ija su strukturna svojstava poznata i opisana u radu autora Gracina, omoguila su analizu rezultata pomou poboljaanog modela ekvivalentnog strujnog kruga opisanog u radu autora. Dobiveni rezultati analizirani su u kompleksnoj ravnini a prora unate i procijenjene vrijednosti u velikoj mjeri se poklapaju s rezultatima ostalih grupa znanstvenika u drugim istra~iva kim centrima ukoliko se uzmu u obzir istovjetne debljine ispitnih a-nc-Si:H uzoraka, temperaturni uvjeti ispitivanja, specifi ni otpor  EMBED Equation.3  i naravno, konstante vodljivosti  EMBED Equation.3 . U daljnjem tekstu rada biti e analizirani rezultati istra~ivanja vodljivosti tankih filmova od silicija od navedena tri tima autora i posljednje izvorno istra~ivanje autora ovoga teksta. REZULTATI ISTRA}IVANJA DRUGIH AUTORA Vodljivost mikro-kristalini nog silicija Najjednostavniji na in opisa transportnih svojstava svakog kompozitnog sloja mikro-kristalini nog silicija (mc-Si) je mjerenje tamne vodljivosti  EMBED Equation.3  kod protoka istosmjerne struje pomou paralelno postavljenih kontakata na obje strane sloja uzorka. Za potpuno razumijevanje mehanizma DC transporta, naglaaava autor Ko ka, vrlo je va~no poznavati vrijednost aktivacijske energije EMBED Equation.3  i konstante vodljivosti  EMBED Equation.3 , koji se mo~e izvesti iz temperaturne ovisnosti vodljivosti iz izraza  EMBED Equation.3 . Na slici 1 prikazane su obje vrijednosti kao funkcije debljine sloja za slu aj 3% i 4,5% otopine silana i kao funkcije kristalini nog udjela u a-Si/nc-Si podlozi. Za slu aj debljine sloja d d" 0,6mm ili postotka volumnog udjela kristala manjeg od 80% konstante vodljivosti  EMBED Equation.3  prakti ki se ne mijenja, a  EMBED Equation.3  se polako smanjuje. Nakon toga  EMBED Equation.3  naglo pada za sve uzorke slojeva silicija. Kako se takvo ponaaanje mo~e objasniti? Najprije treba naglasiti da se transport nosilaca naboja dogaa na svim nivoima raspolo~ivih energija. Obi no postoji poneki dominantni smjer ili put na energiji na kojoj je umno~ak mobilnosti elektrona mt, vidljiv kroz vrijednost  EMBED Equation.3  i koncentracije nosilaca (odreeno s  EMBED Equation.3 ) najvei, kao ato je navedeno u istra~ivanju autora Shimakawa. Promjena vrijednosti aktivacijske energije mo~e nastati uslijed pomaka transportnog smjera (koji je u slu aju tipi nog kompozitnog sloja na vrijednosti sobne temperature iznad rubne vrijednosti mobilnosti elektrona  EMBED Equation.3 ) ili/i zbog pomaka Fermijeve energije  EMBED Equation.3  jer je aktivacijska energija definirana kao  EMBED Equation.3 . Ukoliko se vrijednost Fermijeve energije pomakne navie prema rubu vodljivog pojasa EMBED Equation.3 ,  EMBED Equation.3  bi se morala smanjiti a  EMBED Equation.3  ostati nepromijenjen. To se upravo i dogaa na vrijednostima debljine sloja dd"0,6 mm ili postotka volumnog udjela kristala manjeg od 80 %. Meutim, postavlja se pitanje koja sila tjera slobodne naboje na gibanje? Imajui na umu bezna ajni pomak vodljivog pojasa izmeu a-Si:H i c-Si:H dijelova, kako je navedeno u radovima autora Hamma i Xu prirodno objaanjenje za pomak  EMBED Equation.3  je poveanje postotka kristalizacije, uz vrstu potporu rezultata Raman spektroskopije koju je u svom radu dokazao autor Ko ka. Slika 1. Procjena vrijednosti konstante vodljivosti  EMBED Equation.3  i aktivacijske energije  EMBED Equation.3  izraenih kompozitnih uzoraka za slu aj 3 % (kvadratii) i 4,5 % (kru~ii) otopine silana dane i kao funkcija debljine sloja (donja vodoravna linija).  Izvor: Ko ka, J.: "Model od transport in microcrystalline silicon", Journal of Non-Crystalline Solids, Vol. 299-302, 2002., str. 355-359. Koji je mogui razlog za naglo smanjenje vrijednosti konstante vodljivosti  EMBED Equation.3 ? Prijelom krivulje kristalini nosti na vrijednosti  EMBED Equation.3  nastala slijedom poveanja strukturne hrapavosti i zasienja kristalizacije, prikazuje formaciju nakupina u usko pakiranim malim strukturama. Zahvaljujui provedenim istra~ivanjima i navedenim rezultatima kao i mnogim AFM topografskim slikama model transporta izgleda kao ato je predo eno na slici 2. Na po etku rasta prevladavaju male nakupine veli ine do 20nm. Udio kristalini nosti se poveava porastom broja nakupina. Transport veinskih nosilaca (elektrona) je unutar vodljivog pojasa  EMBED Equation.3  uz vrijednost konstante vodljivosti  EMBED Equation.3  oko 100 EMBED Equation.3  koja se ne mijenja. Sa poveanjem vrijednosti volumnog udjela kristala  EMBED Equation.3  se smanjuje u skladu s poveanjem vrijednosti  EMBED Equation.3 . Slika 2. Shematski prikaz strukture nc/mc-Si:H filma i DOS raspodjelu u razli itim dijelovima uzorka, gdje je  EMBED Equation.3  Fermijeva energija a  EMBED Equation.3  je energija ruba vodljivog pojasa.  Izvor: Ko ka, J.: "Model od transport in microcrystalline silicon", Journal of Non-Crystalline Solids, Vol. 299-302, 2002., str. 355-359. Obzirom da je koncentracija malih nakupina oko 1018 cm-3 i koncentracija ne istoa oko 1016 cm-3 male nakupine i njihove granice skoro su bez ne istoa, kako naglaaavaju autori Finger i Kondo u svojim radovima. Kakva god da je njihova priroda te granice ne predstavljaju prepreku za transport nosioca u pojasu ( EMBED Equation.3  je konstantan). Premda je tetraedarski raspored granica atoma relativno sa uvan ipak ima odstupanja u duljini veza i kutovima, tako da se DOS slika velikih nakupina mora ura unati u sliku stanja repova energetskih krivulja. Rezultati i rasprava Autora Ko ke Zamijeeno poveanje hrapavosti povraine sloja i veliki pad vrijednosti  EMBED Equation.3  nastalo je formiranjem veih nakupina kristala svih formi istih nano/mikrokristala ili izotropskih agregata tzv. super kristala ato je opisao autor Kudrna. Postavlja se pitanje koji je mikroskopski razlog tome? Naravno pretpostavka da se u skladu s prirodom manjih skupina veina ne istoa (kao ato su O, N, C kao i H) formira na granicama tvorei a-Si:H tkivo s poveanim vrijednostima mobilnog pojasa. Tako da je nagli pad vrijednosti  EMBED Equation.3  formirana potencijalna barijera nastala postojanjem granica velikih skupina (vidljivo i iz slike 2 pomak krivulje  EMBED Equation.3 ). Dodatna potpora ovoj pretpostavki je poveana osjetljivost  EMBED Equation.3  do nivoa ne istoa kada dolazi do stvaranja velikih nakupina. Poveana veli ina stupaca kristala dokumentirana pomou AFM za slu aj slojeva izraenih uz 4,5% otopinu silana kako je opisao autor Ko ka kao i smanjenje broja velikih nakupina je prirodno objaanjenja tzv. oporavka vrijednosti  EMBED Equation.3  za debljine sloja d e"1mm (v. sliku 1). ini se da formiranje nakupina zrna u strukturi kvari transportna svojstva mc/nc-Si:H slojeva u oba slu aja formiranja izotropskih velikih zrna i anizotropnih stupi astih struktura. Jednostavan na in otkrivanja njihove prisutnosti je mjerenje temperaturne ovisnosti tamne vodljivosti  EMBED Equation.3  kod protoka istosmjerne struje pomou paralelnih kontakata na obje strane sloja. Kada je vrijednost konstante vodljivosti  EMBED Equation.3  i  EMBED Equation.3  nepo~eljni sadr~aj u strukturi je isklju en. To pravilo je ispunjeno u slu aju uzorka s 76 % volumnim udjelom kristala, gdje su detektirana mala zrna prema opisu autor Ko ke uz takoer relativno veliku vrijednost izotropske difuzijske duljine  EMBED Equation.3 . Drugi primjer dao ja autor Nasuno. Uzorak mc-Si:H izraen je na niskoj temperaturi supstrata  EMBED Equation.3  a taj uzorak daje izvrsnu efikasnost solarne elije  EMBED Equation.3 . Ovaj materijal i prema istra~ivanju autora `vr eka ima vrijednost izotropne difuzijske duljine  EMBED Equation.3  i vodljivost izmjeni ne i istosmjerne struje na sobnoj temperaturi  EMBED Equation.3  uz naravno izmjerene vrijednosti konstante vodljivosti  EMBED Equation.3  i aktivacijske energije  EMBED Equation.3 . Vodljivost nano-kristalini nog silicija 2.2.1. Iskustva svjetskih istra~iva a Dobro je poznato da je ispitivanje vodljivosti i kapacitivnost vrlo u inkovita spektroskopska metoda za nerazorna ispitivanja poluvodi kih slojeva i procjenu njihovih strukturnih i fizikalnih parametara za jednostavne hetero-spojeve, viaestruke kvantne bunare, super kristale i strukture kvantnih to aka, omoguujui ispravnu interpretaciju eksperimentalnih podataka. Vrijednost AC vodljivosti do istra~ivanja autora Wanga i objave njegova rada 2003. godine nije bila kvalitetno i sveobuhvatno ispitana, tako da je zbog toga svojim istra~ivanjem obuhvatio frekvencijsku i temperaturnu ovisnost AC vodljivosti i kapacitivnosti nanokristalini nih filmova. Uobi ajeno je da se koristi jedan od ekvivalentnih modela za razumijevanje AC svojstava materijala kako u svom radu navodi profesor West. Nema sumnje da je odabir ekvivalentnog modela najkriti niji korak za interpretaciju elektri nih fenomena struktura ispitnih materijala. Ipak, nije uobi ajeno da se eksperimentalni podaci tuma e isklju ivo na temelju rezultata pretpostavljenog modela ekvivalentnog kruga. Autor Wang predla~e doraeni model zasnovan na serijskim otporima, iz kojeg se mo~e direktno izvui korisna informacija vezana za odreeni nc-Si:H uzorak. Ovisnost vrijednosti vodljivosti i kapacitivnosti o temperaturi i frekvenciji potvrda je intrinzi ne prirode nc-Si:H filmova. Autor je otkrio da je frekvencijski ovisna AC vodljivost nc-Si:H uzorka na relativno visokim temperaturama sli na kao kod amorfnih materijala, naglaaavajui dominantni doprinos promjenjive vodljivosti na tim temperaturama. Temperaturna ovisnost AC vodljivosti otkriva mehanizam tuneliranja prekrivanjem velikog polarona, kratice OLPT (engl. Overlapping Large Polaron Tunneling), u a-nc-Si:H materijalu. Razli ite temperaturno ovisne karakteristike kapacitivnosti uglavnom nastaju uslijed naizmjeni nog procesa punjenja/pra~njenja izmeu energetskih nivoa postojeih kvantnih to aka i lokaliziranih stanja amorfnih grani nih podru ja. Karakteristika eksperimentalne ovisnosti AC vodljivosti Gp u odnosu na recipro nu vrijednost temperature na razli itim frekvencijama prikazana je na slici 3. To kasta crta slu~i za jasniji prikaz rezultata AC vodljivosti na frekvenciji od 1MHz. Postignuto je dobro poklapanje eksperimentalnih podataka i rezultata prora una na svim izmjerenim temperaturama i frekvencijama. U prora unu vodljivosti uzoraka, vrijednost serijske vodljivosti oznake G1 pokazala se vea od konstante vodljivosti G0, uz pretpostavku njene vrijednosti od pribli~no  EMBED Equation.3 . Slika 3. Karakteristika eksperimentalne ovisnosti AC vodljivosti Gp u odnosu na recipro nu vrijednost temperature na razli itim frekvencijama.  Izvor: Wang, K., Chen, H., Shen, W.Z.:  AC electrical properties of nanocrystalline silicon thin films , Physica B, Vol. 336, 2003., str. 369-378. Ranije navedeni autor Wang poboljaao je tradicionalni model  ekvivalentni serijski otporni ki strujni krug za dobivanje valjanog opisa skupa elektri kih svojstava i karakteristika nc-Si:H filmova iz eksperimentalnih podataka kvantitativnim izra unom vrijednosti AC vodljivosti i kapacitivnosti. Slo~eni eksperimentalni podaci otkrili su karakteristi nu prirodu nc-Si:H uzoraka. Vrijednosti AC vodljivosti i trendovi krivulja otkriveni na relativno visokim temperaturama vrlo su sli ni amorfnim strukturama otkrivajui pri tome dominantni doprinos skokovite vodljivosti. Odnos parametra i temperature otkriva OLPT-ov mehanizam u nc-Si:H. Jasnija je i temperaturno ovisna karakteristika kapacitivnosti koju odreuju naizmjeni ni procesi punjenja/pra~njenja izmeu energetskih nivoa prirodnih kvantnih to aka i lokaliziranih stanja amorfnih grani nih podru ja koja je takoer i frekvencijski ovisna. 2.2.1 Iskustva hrvatskih istra~iva a Kako je navedeno u poglavlju 1.1. ovog rada opisana su mjerenja DC vodljivosti tankih filmova koja su provedena na a-nc-Si:H uzorcima u Institutu Ruer Boakovi. Vrijednosti specifi ne otpornosti uzoraka prikazane su na slici 4 kao funkcija vrijednosti kristalne frakcije XC. 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Na toj vrijednosti vrijednost otpornosti se smanjuje za nekoliko redova veli ine u uskom intervalu vrijednosti kristalne frakcije i smanjuje se nadalje na veim vrijednostima XC. Ovakvo ponaaanje mo~e se objasniti pomou teorije perkolacije, ranije opisano u radu autora Essam. Model podrazumijeva estice velikih vrijednosti vodljivosti uronjene u slabo vodljivu matricu. U slu aju male koncentracije vodljivih estica prakti ki nema utjecaja estica velike vodljivosti na ukupnu vodljivost. Kada se broj estica velike vodljivosti povea na odreenu vrijednost, vjerojatnost meusobnog doticanja estica se poveava i tada dolazi do bitnog poveanja ukupne vodljivosti. Takva grani na vrijednost naziva se  perkolacijska vrijednost (engl.  percolation treshold ) i pojavljuje se u 2D modelima izmeu 40% i 45% volumnog udjela vodljivih estica kako je opisano u radu autora Shimakawa. Nedavna istra~ivanja istog autora za slu aj 3D struktura od silicija odreuju perkolacijsku vrijednost u uskoj domeni volumnog udjela od 32% do 33%, ato se savraeno poklapa s obavljenim rezultatima vrhunskog hrvatskog istra~iva a dr. Gracina s IRB-a. Ovakvo preklapanje rezultata sa Raman spektroskopijom koja se koristi za utvrivanje vrijednosti kristalne frakcije XC potvruje ispravnost metode, gdje je presudna pretpostavka da su vrijednosti presjeka kroz materijal istovjetne za nano-kristale od 2nm do 7nm (stvarna veli ina) i za amorfnu matricu. Takoer, mogunost objaanjenja ispravnosti koriatene mjerne metode DC vodljivosti sa perkolacijskim modelom sna~no podupire pretpostavku da su  estice detektirane pomou GISAXS metode stvarne i pojedina ne nano-kristalne strukture. U hrvatskoj je nastavljeno istra~ivanje svojstava vodljivosti i kapacitivnosti a-nc-Si:H uzoraka pomou IS metode pod vodstvom dr. Gracina na Institutu Ruer Boakovi, a rezultati kapacitivnosti i vodljivosti uzoraka uskoro e biti objavljeni u znanstvenom asopisu Scientifis Research - Engineering i drugim Peer Review asopisima. Provedena su mjerenja admitancije Y, impedancije Z, dielektri ne permitivnosti e i elektri nog modula M na nekolicini a-nc-Si:H uzoraka pomou metode impedancijske spektroskopije (IS). Pretpostavljen je model ekvivalentnog strujnog kruga s dva paralelna R-C elementa spojena u seriju i poboljaani model s dva paralelna R-CPE elementa spojena u seriju. U fazi prilagodbe eksperimentalnih rezultata s prora unom u skladu s predlo~enim modelima otkriveno je da posljednji model bolje odgovara. Uzorci su ispitani u temperaturnom opsegu od 170-400K u frekvencijskom opsegu od 10mHZ do 10MHz. Slika 4. Predod~ba vrijednosti specifi ne otpornosti (u W cm) u odnosu prema volumnoj kristalnoj frakciji (u %). Puni krugovi predstavljaju RF PECVD uzorke dok otvoreni krugovi predstavljaju uzorke dobivene MW PECVD postupkom.  Izvor: Gracin, D., Etlinger, B., Juraji, K., Gajovi, A., Dub ek, P., Bernstorff, S.:  DC conductivity of amorphous-nanocrystalline silicon thin films , Journal Vacuum, Vol. 84, No. 1, 2010., str. 243-246. Rezultati vodljivosti i elektri nog modula uzoraka mogu se prezentirati u kompleksnom dijagramu, izra~avajui realnu i imaginarnu komponentu vrijednosti, kao i obzirom na frekvenciju ili logaritamsku vrijednost frekvencije. Iz dobivenih krivulja na temperaturi 400K gdje su najbolje formirane tzv. Deby polukru~nice iz vrijednosti eksperimentalne impedancije Z prora unate su vrijednosti specifi ne otpornosti  EMBED Equation.3 , te posljedi no obzirom na volumen ispitnog uzorka izra~ene su i vrijednosti specifi ne vodljivosti  EMBED Equation.3 . Analizom eksperimentalne impedancije Z temeljene na usvojenom modelu i poznatih tjemenih vrijednosti krivulje u skladu s jednad~bom  EMBED Equation.3  kao i krivulje logaritamske ovisnosti mogu se prora unati vrijednosti otpornosti i kapacitivnosti uzorka. Iz konstante strujnog kruga RC=t kao i iz modela prilagodbe krivulja odreene su vrijednosti specifi nog otpora i specifi ne vodljivosti amorfne faze i vrijednosti specifi nog otpora i specifi ne vodljivosti nanokristalini ne faze. Vrijednosti specifi ne vodljivosti nanokristalini ne faze s01 (304kS/cm) viae su od reda veli ine vee u odnosu na specifi nu vodljivost amorfne faze s02 (12,2kS/cm), dok su prora unske vrijednosti kapacitivnosti nanokristalini ne faze tankog kompozitnog filma A2 =16,1nF vee nekoliko puta od vrijednosti kapacitivnosti amorfne faze A1 = 3,1nF kako je objavljeno u radu autora. Slika 5. Eksperimentalna impedancija prikazana Cole-Cole polukru~nicom u tri slu aja (manja slika u desnom kutu): pri temperaturi 360oC (plava krivulja), 380oC (zelena krivulja) i 400 K oC (mala crvena krivulja).  Izvor: Tudi, V.:  AC Impedance Spectroscopy of a-nc-Si:H Thin Films , Scientific Research - Engineering, Vol. 6, No. 8, 2014., str. 449-461., preuzeto sa  HYPERLINK "http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766" http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766, (01.05.2014.) Vrijednosti DC vodljivosti i trendovi krivulja eksperimentalne impedancije otkriveni na relativno visokim temperaturama od 360K, 380K i 400K vrlo su sli ni amorfnim strukturama otkrivajui pri tome dominantni doprinos vodljivosti slo~ene nano-kristalini ne faze. Prora unata vrijednost specifi ne vodljivosti od 13,85mS/cm za red veli ine vea je u odnosu na rezultat koji je objavio autor Ko ka (1mS/cm). Meutim, rezultati oba istra~ivanja ipak se ne razlikuju toliko zna ajno ako se uzme u obzir da je autor Ko ka radio istra~ivanja s 6 puta debljim slojem silicija a koji je upravo zbog svoje debljine prelazio iz nano-kristalini ne u mikro-kristalini nu strukturu te time zna ajno izgubio na vodljivosti kompozitne strukture. Analiza vodljivosti u nazna enom radu ukazuje na vrijednost konstante vodljivosti uzoraka  EMBED Equation.3  od oko 300kS/cm koja se bitno ne mijenja u ispitanom temperaturnom opsegu. Iz eksperimentalnih podataka DC vodljivosti (linearnog dijela nagiba krivulje u ovisnosti o temperaturi) prora unate su vrijednosti aktivacijske energije u skladu s Arrhenius-ovim zakonom. Sa poveanjem temperature aktivacijska energija  EMBED Equation.3  a-nc-Si:H uzorka se poveava. Sa vrijednosti 0,51eV koja je identi na za isti kristalini ni uzorak tankog filma od silicija pri temperaturi od 200K na vrijednost od 0,71eV pri temperaturi od pribli~no 400K, ato je naravno viae karakteristi no za kompozitnu strukturu kao ato je a-nc-Si:H. 5. ZAKLJU AK Specifi na svojstva vodljivosti tankih filmova od mikro-kristalini nog i nano-kristalini nog silicija ispitane su u nekoliko znanstveno-istra~iva kih centara airom svijeta i opisane u znanstvenim publikacijama. Primjenom poznatih metoda i modela ispitana AC i DC vodljivost pokazala je usku povezanost s prethodno utvrenom strukturnim svojstvima materijala omoguujui ispravnu interpretaciju eksperimentalnih podataka. Utvrene su karakteristi ne konstante vodljivosti kompozitne strukture silicija naglaaavajui naglu promjenu vodljivosti strukture u slu aju poveanja udjela kristala i njihovih nakupina. Takoer su utvrene vrijednosti kapacitivnosti ispitnih tankih filmova od silicija u temperaturnoj i frekvencijskoj domeni. Razli ite primijenjene tehnike kao rezultat komparacije vodljivosti i kapacitivnosti uzoraka dale su rezultat u vrlo uskoj domeni vrijednosti potvrujui time usporedivost eksperimenta i ispravno tuma enje rezultata ispitivanja hrvatskih znanstvenika. Literatura 1. Essam, J.W.:  Percolation theory , Reports on Progress in Physics, Vol. 43, No. 7, 1980., str. 833. 2. Fejfar, A., Mates, T., ertik, O., Rezek, B., Stuchlik, J., Pelant, I., Ko ka, J.:  Model of electronic transport in microcrystalline silicon and its use for prediction of device performance , Journal Non-Crystalline Solids, Volums 338-340, 2004., str. 303-309. 3. Finger, F., Muller, J., Malten, C., Carius, R., Wagner, H.:  Electronic properties of microcrystalline silicon investigated by electron spin resonance and transport measurements , Journal of Non-Crystalline Solids, Vol. 266-269, 2000., str. 511. 4. Gracin, D., Etlinger, B., Juraji, K., Gajovi, A., Dub ek, P., Bernstorff, S.:  The DC conductivity and structural ordering of thin silicon films at the amorphous to nano-crystalline phase transition , Journal Vacuum, Vol. 82, No. 1, 2008., str. 205-208. 5. Gracin, D., Etlinger, B., Juraji, K., Gajovi, A., Dub ek, P., Bernstorff, S.:  DC conductivity of amorphous-nanocrystalline silicon thin films , Journal Vacuum, Vol. 84, No. 1, 2010., str. 243-246. 6. Hamma, S., Roca i Cabarrocas, P.:  Determination of the mobility gap of microcrystalline silicon and of the band discontinuities at the amorphous/microcrystalline silicon interface using in situ Kelvin probe technique , Applied Physics Letters, Vol. 74, 1999., str. 3218-3320. 7. Ko ka, J., Stuchlkova, H., Stuchlk, J., Rezek, B., Mates, T., `vr ek, V., Fojtk, P., Pelant, I., Fejfar, A.:  Model od transport in microcrystalline silicon , Journal of Non-Crystalline Solids, Vol. 299-302, 2002., str. 355-359. 8. Ko ka, J., Fejfar, A., Vorl ek, V., Stuchlkova, H., Stuchlk, J.:  Microcrystalline Silicon - Relation of Transport Properties and Microstructure , MRS Symposium Procedings 557, 1999., str. 483. 9. Ko ka, J., Stuchlkova, H., Stuchlk, J., Rezek, B., Mates, T., `vr ek, V., Fojtk, P., Pelant, I., Fejfar, A.:  Microcrystalline Silicon - Relation between Transport and Microstructure , Solid State Phenomena, Vol. 80-81, 2001., str. 213-224. 10. Ko ka, J., Stuchlkova, H., Stuchlk, J., Rezek, B., Mates, T., `vr ek, V., Fojtk, P., Pelant, I., Fejfar, A.:  Technical Digest of PVTEC-NEDO , Review Meeting, 2001., str. 27. 11. Kondo, M., Yamasaki, S., Matsuda, A.:  Microscopic structure of defects in microcrystalline silicon , Journal of Non-Crystalline Solids, Vol. 266-269, 2000., str. 544. 12. Kudrna, J., Trojanek, F., Maly, P., Pelant, I.:  Carrier diffusion in microcrystalline silicon studied by the picosecond laser induced grating technique , Applied Physical Letters 79, 2001., str. 626. 13. Mates, T., Fejfar, A., Drbohlav, I., Rezek, B., Fojtk, P., Luterova, K., Ko ka, J., Koch, C., Shubert, M., Ito, M., Ro, K.H.: Uyama, these Preceedings, 2000., str. 767. 14. Meier, J., Fluckiger, R., Keppner, H., Shah, A.:  Complete microcrystalline p-i-n solar cell - Crystalline or amorphous cell behavior , Applied Physical Letters 65, 1994., str. 860-862. 15. Nasuno, Y., Kondo, H., Matsuda, A.:  Amorphous/microcrystalline silicon superlattices the chance to control isotropy and other transport properties , Preceedings of the 3th World Conference on Photovoltaic Energy Conversion, 2000. 16. Overhof, H., Otte, M., Schmidtke, M., Backhausen, U.:  The transport mechanism in micro-crystalline silicon , Journal Non-Crystalline Solids, Vol. 227-230, Part 2, 1998., str. 992-995. 17. Shimakawa, K.:  Percolation-controlled electronic properties in microcrystalline silicon: effective medium approach , Journal Non-Crystalline Solids, Vol. 266-269, Part 1, 2000., str. 223-226. 18. Shimakawa, K.:  Photo-carrier transport in nanocrystalline silicon films , Journal of Non-Crystalline Solids, Vol. 352, 2006., str. 1180-1183. 19. `vr ek, V., Fejfar, A., Fojtik, P.,. Mates, T, Poruba, A., Stuchlkova, H., Pelant, I., Ko ka, J., Nasuno, Y., Kondo, H., Matsuda, A.:  Importance of the transport isotropy in c-Si:H thin films for solar cells deposited at low substrate temperaturesv, Journal of Non-Crystalline Solids, Vol. 299-302, Part 2, 2002., str. 395-399. 20. Tudi, V.:  AC Impedance Spectroscopy of a-nc-Si:H Thin Films , Scientific Research - Engineering, DOI:  HYPERLINK "http://dx.doi.org/10.4236/eng.2014.68047" \t "_blank" 10.4236/eng.2014.68047, , Vol. 6, No. 8, 2014. str. 449-461., preuzeto sa  HYPERLINK "http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766" http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766, (01.05.2014.). 21. Xu, X., Yang, J., Banerjee, A., Guha, S., Vasanth, K., Wagner, S.:  Band edge discontinuities between microcrystalline and amorphous hydrogenated silicon alloys and their effect on solar cell performance , Applied Physics Letters 67, 1995., str. 2323-2325. 22. Wang, K., Chen, H., Shen, W.Z.:  AC electrical properties of nanocrystalline silicon thin films , Physica B 336, 2003., str. 369-378. 23. West, A.R., Sinclair, D.C., Hirose, N.:  Characterization of Electrical Materials, Especially Ferroelectrics, by Impedance Spectroscopy , Electroceramics, Vol. 1, No. 1, 1997., str. 65-71.  Veleu iliate u Karlovcu, I. Meatrovia 10, Karlovac, e-mail: vladimir.tudic@vuka.hr  Veleu iliate u Karlovcu, I. Meatrovia 10, Karlovac, e-mail: tomislav.luke@gmail.com  Fejfar, A., Mates, T., ertik, O., Rezek, B., Stuchlik, J., Pelant, I., Ko ka, J.:  Model of electronic transport in microcrystalline silicon and its use for prediction of device performance , Journal Non-Crystalline Solids, Volums 338-340, 2004., str. 303-309.  Finger, F., Muller, J., Malten, C., Carius, R., Wagner, H.:  Electronic properties of microcrystalline silicon investigated by electron spin resonance and transport measurements , Journal of Non-Crystalline Solids, Vol. 266-269, 2000., str. 511.  Ko ka, J., Stuchlkova, H., Stuchlk, J., Rezek, B., Mates, T., `vr ek, V., Fojtk, P., Pelant, I., Fejfar, A.:  Model od transport in microcrystalline silicon , Journal of Non-Crystalline Solids, Vol. 299-302, 2002., str. 355-359.  Meier, J., Fluckiger, R., Keppner, H., Shah, A.:  Complete microcrystalline p-i-n solar cell - Crystalline or amorphous cell behavior , Applied Physical Letters 65, 1994., str. 860-862.  Wang, K., Chen, H., Shen, W.Z.:  AC electrical properties of nanocrystalline silicon thin films , Physica B 336, 2003., str. 369-378.  Gracin, D., Etlinger, B., Juraji, K., Gajovi, A., Dub ek, P., Bernstorff, S.:  The DC conductivity and structural ordering of thin silicon films at the amorphous to nano-crystalline phase transition , Journal Vacuum, Vol. 82, No. 1, 2008., str. 205-208.  Gracin, D., Etlinger, B., Juraji, K., Gajovi, A., Dub ek, P., Bernstorff, S.:  DC conductivity of amorphous-nanocrystalline silicon thin films , Journal Vacuum, Vol. 84, No. 1, 2010., str. 243-246.  Tudi, V.:  AC Impedance Spectroscopy of a-nc-Si:H Thin Films , Scientific Research - Engineering, 2014., ISSN Online: 1947-394, preuzeto sa  HYPERLINK "http://www.scirp.org/journal/Home.aspx?JournalID=64" http://www.scirp.org/journal/eng.  Shimakawa, K.:  Percolation-controlled electronic properties in microcrystalline silicon: effective medium approach , Journal Non-Crystalline Solids, Vol. 266-269, Part 1, 2000., str. 223-226.  Hamma, S., Roca i Cabarrocas, P.:  Determination of the mobility gap of microcrystalline silicon and of the band discontinuities at the amorphous/microcrystalline silicon interface using in situ Kelvin probe technique , Applied Physics Letters, Vol. 74, 1999., str. 3218-3320.  Xu, X., Yang, J., Banerjee, A., Guha, S., Vasanth, K., Wagner, S.:  Band edge discontinuities between microcrystalline and amorphous hydrogenated silicon alloys and their effect on solar cell performance , Applied Physics Letters 67, 1995., str. 2323-2325.  Ko ka, J., Fejfar, A., Vorl ek, V., Stuchlkova, H., Stuchlk, J.:  Microcrystalline Silicon - Relation of Transport Properties and Microstructure , MRS Symposium Procedings 557, 1999., str. 483.  Mates, T., Fejfar, A., Drbohlav, I., Rezek, B., Fojtk, P., Luterova, K., Ko ka, J., Koch, C., Shubert, M., Ito, M., Ro, K.H.: Uyama, these Preceedings, 2000., str. 767.  Finger, F., Muller, J., Malten, C., Carius, R., Wagner, H.:  Electronic properties of microcrystalline silicon investigated by electron spin resonance and transport measurements , Journal of Non-Crystalline Solids, Vol. 266-269, 2000., str. 511.  Kondo, M., Yamasaki, S., Matsuda, A.:  Microscopic structure of defects in microcrystalline silicon , Journal of Non-Crystalline Solids, Vol. 266-269, 2000., str. 544.  DOS  engl. Density of States je gustoa stanja nosilaca naboja u energetskim pojasevima poluvodi a.  Kudrna, J., Trojanek, F., Maly, P., Pelant, I.:  Carrier diffusion in microcrystalline silicon studied by the picosecond laser induced grating technique , Applied Physical Letters 79, 2001., str. 626.  Ko ka, J., Stuchlkova, H., Stuchlk, J., Rezek, B., Mates, T., `vr ek, V., Fojtk, P., Pelant, I., Fejfar, A.:  Microcrystalline Silicon - Relation between Transport and Microstructure , Solid State Phenomena, Vol. 80-81, 2001., str. 213-224.  Ko ka, J., Stuchlkova, H., Stuchlk, J., Rezek, B., Mates, T., `vr ek, V., Fojtk, P., Pelant, I., Fejfar, A.  Model od transport in microcrystalline silicon , Journal of Non-Crystalline Solids, Vol. 299-302, 2002., str. 355-359.  Nasuno, Y., Kondo, H., Matsuda, A.:  Amorphous/microcrystalline silicon superlattices the chance to control isotropy and other transport properties , Preceedings of the 3th World Conference on Photovoltaic Energy Conversion, 2000.  `vr ek, V., Fejfar, A., Fojtik, P.,. Mates, T, Poruba, A., Stuchlkova, H., Pelant, I., Ko ka, J., Nasuno, Y., Kondo, H., Matsuda, A.:  Importance of the transport isotropy in c-Si:H thin films for solar cells deposited at low substrate temperaturesv, Journal of Non-Crystalline Solids, Vol. 299-302, Part 2, 2002., str. 395-399.  West, A.R., Sinclair, D.C., Hirose, N.:  Characterization of Electrical Materials, Especially Ferroelectrics, by Impedance Spectroscopy , Electroceramics, Vol. 1, No. 1, 1997., str. 65-71.  Essam, J.W.:  Percolation theory , Reports on Progress in Physics, Vol. 43, No. 7, 1980., str. 833.  Shimakawa, K.:  Percolation-controlled electronic properties in microcrystalline silicon: effective medium approach , Journal Non-Crystalline Solids, Vol. 266-269, Part 1, 2000., str. 223-226.  Shimakawa, K.:  Photo-carrier transport in nanocrystalline silicon films , Journal of Non-Crystalline Solids, Vol. 352, 2006., str. 1180-1183.  Gracin, D., Etlinger, B., Juraji, K., Gajovi, A., Dub ek, P., Bernstorff, S.:  DC conductivity of amorphous-nanocrystalline silicon thin films , Journal Vacuum, Vol. 84, No. 1, 2010., str. 243-246.  Scientific Research - Engineering, Peer Review, Online znanstveni asopis s meunarodnom recenzijom, preuzeto sa  HYPERLINK "http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766" http://www.scirp.org/journal/ , (11.03.2014.)  Deby tip polukru~nice je prikaz impedancije strujnog kruga koja se sastoji od otpora, induktivnih i kapacitivnih elemenata u ovisnosti o frekvenciji u polarnom dijagramu.  Tudi, V.:  AC Impedance Spectroscopy of a-nc-Si:H Thin Films , Scientific Research - Engineering, Vol. 6, No. 8, 2014., str. 449-461., DOI:  HYPERLINK "http://dx.doi.org/10.4236/eng.2014.68047" \t "_blank" 10.4236/eng.2014.68047, preuzeto sa  HYPERLINK "http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766" http://www.scirp.org/journal/PaperInformation.aspx?PaperID=47766, (01.05.2014.)  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