Gray scale lithography consists of numerous sophisticated fabrication steps making it necessary to characterize the process of substrate structuring. We expose the photoresist with random intensity, i.e. speckle fields instead of conventional specific test patterns and observe their behavior in Fourier plane caused by coherent illumination of this processed substrate

Kelly, Damien P.

Meinecke, Thomas

Sinzinger, Stefan

Digitale Bibliothek Thüringen

  Thomas Meinecke, Damien P. Kelly, Stefan Sinzinger: Characterization of photoresost using speckle fields - a theoretical investigation   Zuerst erschienen in: DGaO-Proceedings. - Erlangen-Nürnberg: Dt. Gesellschaft für angewandte Optik, ISSN 1614-8436. - Bd. 114.2013, P57,  insg. 2 S.  URN: urn:nbn:de:0287-2013-P057-6      DGaO Proceedings 2013 – http://www.dgao-proceedings.de – ISSN: 1614-8436 – urn:nbn:de:0287-2013-P057-6  Characterization of Photoresist Using Speckle Fields - A Theoretical Investigation - Thomas Meinecke*, Damien P. Kelly**, Stefan Sinzinger* * Fachgebiet Technische Optik, Technische Universität Ilmenau ** Fachgebiet Optik-Design, Technische Universität Ilmenau mailto:thomas.meinecke@tu-ilmenau.de Gray scale lithography consists of numerous sophisticated fabrication steps making it necessary to characterize the process of substrate structuring. We expose the photoresist with random intensity, i.e. speckle fields instead of conventional specific test patterns and observe their behavior in Fourier plane caused by coherent illumination of this processed substrate. 1 Introduction In order to reliably fabricate structures using a lithographic process, it is essential to properly characterize the photoresist material that is used. Generally this is done by carefully fabricating test structures and using these to illuminate the photo-resist with a specific pattern.  Here we wish to use a different type of patterned illumination - a speckle field. There appear to be several advantages to this approach, (i) a speckle field is easy to gener-ate using a coherent light source and a diffuser, (ii) the complex amplitude of the resulting light field obeys well known statistical distributions. The scat-tered light representing a speckle field distribution with intensity ISp impinges on the substrate coated by photoresist. This photoresist is sensitive to the exposure ESp:  ExpSpSp TIE  , (1)   (1) where TExp is the exposure time. For initial obser-vations we assume linear photoresist with a thick-ness of some wavelengths, see Eq. 1. In the fol-lowing numerical analysis, we have carefully cho-sen our sampling rate such that the spatial varia-tions in the output speckle field are adequately sampled, i.e. the average speckle size is chosen to 8/π of pixel size [1].  Fig. 1 Experimental setup and process steps. 2 Modeling of the Lithographic Process Material changes in the photoresist structure at a specific location are assumed to depend on the amount of light energy incident on the photoresist at that point, i.e. the height distribution of the sub-strate is determined by the exposure. The amount of energy deposited is assumed to be linearly re-lated to the intensity of the incident illumination. The intensity distribution of the illumination follows a negative exponential probability density function PDF(ISp) (with the mean value of ‹ISp› [2])    SpSpSpSp IIIIPDF exp1 , (2) whose statistics are transferred into the exposure ESp and ultimately in the height distribution d. When this substrate is then illuminated with a prob-ing coherent plane wave, see wavelength λ2 in Fig. 1, the phase distribution is given by the following expression:    ,mod2; dEd Sp  . (3) We note that the phase φ is wrapped. We examine the statistical properties of the scattered wave field by recording its Fourier plane distribution with a CCD array, see Fig. 1. In order to compare the effects of different exposure times on the statistical properties of the scattered field, the intensities from different exposure times are normalized to their total power. 3 Results First we consider the influence of exposure to phase of complex structure function in object, i.e. substrate plane (see Fig. 2). Low exposures imply that only parts of the photo-resist microstructure are significantly changed due to the statistical nature of the illuminating intensity. This produces a high DC (unscattered) part and minor scattered part. For long exposures there are two dominant effects: (i) Uniformly random distributed phase is imparted   DGaO Proceedings 2013 – http://www.dgao-proceedings.de – ISSN: 1614-8436 – urn:nbn:de:0287-2013-P057-6  to a probing plane wave, (ii) the auto-correlation of the phase function was found to narrow as the exposure time increases. This is attributed to the phase wrapping effect described by Eq. 3. This effect can be seen in Fig. 2.   Fig. 2 Histograms of phase distribution of complex struc-ture function at various exposures (left) and examples of 100x100 pixel central subsections of corresponding distributions (top right: low exposure of 0.5 – bottom right: high exposure of 2000) in the object plane. The phase function in object (structure) plane in-fluences the scattered field in Fourier plane as follows: Generally the intensity statistics obey a negative exponential distribution defined by a mean param-eter (see Eq. 2) remaining constant due to the normalization of the total power (see Fig. 3 left). The phase statistics of the structure function influ-ence the corresponding characteristics of intensity statistics: A smaller decay of the phase PDF in object plane leads a broader spread of actual in-tensity fluctuations tending to uniform intensity distribution (see Fig. 3 right).  Fig. 3 Intensity histograms (left) driven by various expo-sures and examples of 50x50 pixel central subsection (top right: low exposure of 0.5 – bottom right: high expo-sure of 2000) in Fourier plane. The DC bias is effected by the phase distribution in object plane: A more uniform phase PDF lowers the DC intensity, scattering the light more effective-ly. After an exposure time of 5, the DC content in the scattered signal is approximately 2.63%, see diagram in Fig. 4. This confirms the common habit of using diffuser plates with a roughness of some wavelengths for the generation of fully developed speckle fields in lab setups.   Fig. 4 The relationship of DC intensity to total power in Fourier plane. This DC bias can be modified effectively within a small range of substrate depth height up to closely 5 wavelengths. 4 Conclusions In summary by varying the speckle exposure on photoresist either a high power concentration or nearly a uniform lower distribution can be adjusted [3]. Conversely the exposure can be retrieved by observing the DC/Total Power ratio.  References [1] D. Li, D. P. Kelly, J. T. Sheridan Experimental explo-ration of the correlation coefficient of static speckles in Fresnel configuration, (Proc. SPIE 2011), 813310 [2] J. Goodman, Speckle phenomena in Optics: Theory and Applications, (Roberts  and Company Publish-ers 2007) [3] R. W. Cohn, A. A. Vasilev, W. Liu, D. L. Hill, Fully complex diffractive optics by means of patterned dif-fuser arrays: encoding concept and implications for fabrication, (J. Opt. Soc. Am. A 1997), S. 1110-1123  

Characterization of photoresist using speckle fields - a theoretical investigation

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Characterization of photoresist using speckle fields - a theoretical investigation

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