Page - 70 - in Photovoltaic Materials and Electronic Devices

roughness thickness (ě1 Å between successive time points) and by increases inσas spectra in ε for a-Si:H are no longer adequate to fit ellipsometric spectra collected as nanocrystallitesevolve. Theunweightederror function,σ, isdefinedby[40]: σ“ gfffffffe 13N´M Nÿ j“1 »————– ´ cos2ψmodj ´cos2ψexpj ¯2 ` ´ sin2ψmodj cos∆ mod j ´sin2ψexpj cos∆expj ¯2 ` ´ sin2ψmodj sin∆ mod j ´sin2ψexpj sin∆expj ¯2 fiffiffiffiffifl (1) whereN is thenumberofmeasuredvalues;andM thenumberoffitparameters;“exp” denotes experimental spectra; and “mod” denotes that generated from the model. Anadvantageofconducting in situRTSEmeasurementsduringgrowthofSi:Hby PECVD is that spectra in ε can be obtained prior to the exposure of the sample to ambientandpotentialoxidation. Near IRtonearUVroomtemperatureellipsometric spectraoverarangefrom 0.734 to 5.88 eV were collected at a single spot ex situ prior to the collection of the ex situ IR-SE data as those measurements were not able to be collected in situ during film growth. IR-SE data was collected at a single spot using a similar single rotating compensator instrument (J. A. Woollam Company, Lincoln, NE, USA, model FTIR-VASE) from 0.04 to 0.75 eV at 1 cm´1 resolution [41]. The angle of incidence for all ex situ measurements was nominally 70˝. Ellipsometric spectraover themid-IRtonearUVrangecollectedfromthetwoinstrumentswere analyzed simultaneously using a common parameterization for εbased on structural models initially developed from RTSE and near IR to near UV measurements and J. A. Woollam Co. WVASE software (Lincoln, NE, USA). The error function in Equation1 isalsousedforanalysisandfittingof exsitu IR-SEdata. For in situ RTSE, ex situ near IR to UV SE, and ex situ IR-extended SE data analysis, theoptical responseof thesurfaceroughness layerof thickness ds forSi:H andZnOisrepresentedusingBruggemaneffective [42,43]mediumapproximation mathematicallyrepresentedas: ÿ n fn εn´ε εn`2ε“0. (2) in thisexpression,material fractions (fn)andcomponentmaterialoptical response (εn) are used to generate a composite ε for the mixture. For surface roughness in thiswork, spectra in ε fromBruggemaneffectivemedium approximationconsistof 0.5voidand0.5underlyingmaterialvolumefractions, regardlessofcompositionof theunderlying layer. 70