US007241542B2
`
`(12) United States Patent
`Hudek et a].
`
`(10) Patent N0.:
`(45) Date of Patent:
`
`US 7,241,542 B2
`Jul. 10, 2007
`
`(54) PROCESS FOR CONTROLLING THE
`PROXIMITY EFFECT CORRECTION
`
`(75) Inventors: Peter Hudek, Jena (DE); Dirk Beyer,
`Weimar (DE)
`
`(73) Assignee: Leica Microsystems Lithography
`GmbH (DE)
`
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`patent is extended or adjusted under 35
`U.S.C. 154(b) by 112 days.
`
`(21) Appl. No.: 11/165,312
`
`(22) Filed:
`
`Jun. 23, 2005
`
`(65)
`
`Prior Publication Data
`
`US 2005/0287450 A1
`
`Dec. 29, 2005
`
`(30)
`
`Foreign Application Priority Data
`
`Jun. 29, 2004
`
`(EP) ................................ .. 04103020
`
`(51) Int. Cl.
`(2006.01)
`G03F 9/00
`(52) US. Cl. ...................... .. 430/30; 430/296; 430/942;
`716/19
`(58) Field of Classi?cation Search ................ .. 430/30,
`430/296, 942; 716/19
`See application ?le for complete search history.
`
`(56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`
`5,432,714 A
`
`7/1995 Chung et al.
`
`FOREIGN PATENT DOCUMENTS
`
`EP
`
`0 813 231 A1 12/1997
`
`OTHER PUBLICATIONS
`
`Cui, Zheng, et al., “Proximity Correction of Chemically Ampli?ed
`Resists for Electron Beam Lithography,” Microelectronic Engineer
`ing 41/42 (1998) pp. 183-186.
`Simecek, Michal, et al., “A New Approach of E-beam Proximity
`Effect Correction for High-Resolution Applications,” JPN. J. Appl.
`Phys., vol. 37 (1998) pp. 6774-6778.
`
`Yang, Seung-Hune, et. al., “Fogging Effect Consideration in Mask
`Process at SOKeV E-Beam Systems,” Proc. of SPIE, vol. 4889
`(2002), pp. 786-791.
`Stevens, L., et al., “Determination of the Proximity Parameters in
`Electron Beam Lithography Using Doughnut-Structures,” Micro
`electronic Engineering 5 (1986) pp. 141-150.
`Park, Eui Sang, et al., “Optimum PEC Conditions Under Resist
`Heating Effect Reduction for 90nm Node Mask Writing,” Proc.
`SPIE, vol. 4889, Part Two, pp. 792-799.
`Rishton, S.A., et al., “Point exposure distribution measurements for
`proximity correction in electron beam lithography on a sub-100nm
`scale,” Journal of Vacuum Science & Technology B (Microelec
`tronics Processing and Phenomena) USA, vol. 5, No. 1, pp. 135
`141.
`Misaka, Akio, et al., “Determination of Proximity Effect Parameters
`in Electron-Beam Lithography,” J. Appl. Physics, vol. 68, No. 12,
`Dec. 15, 1990, pp. 6472-6479.
`Vermeulen, P., et al., “Proximity-Effect Correction in Electron
`Beam Lithography,” Journal of Vacuum Science & Technology B
`(1989) Nov./Dec., No. 6, NY, PP. 1556-1560.
`Harafuji, Kenji, et al., “Proximity Effect Correction Data Processing
`System for Electron Beam Lithography,” Journal of Vacuum Sci
`ence & Technology B, vol. 10, No. 1, 1992, pp. 133-142.
`
`Primary Examiner4Christopher G. Young
`(74) Attorney, Agent, or F irmiHouston Eliseeva LLP
`
`(57)
`
`ABSTRACT
`
`A process for controlling the proximity effect correction in
`an electron beam lithography system. The exposure is con
`trolled in order to obtain resulting pattern after processing
`Which is conform to design data. In a ?rst step an arbitrary
`set patterns is exposed Without applying the process for
`controlling the proximity correction. The geometry of the
`resulting test structures is measured and a set of measure
`ment data is obtained. Within a numerical range basic input
`parameters for the parameters (X, [3 and 11, are derived from
`the set of measurement data. A model is ?tted by individu
`ally changing at least the basic input parameters (X, [3 and 11
`of a control function to measurement data set and thereby
`obtaining an optimised set of parameters. The correction
`function is applied to an exposure control of the electron
`beam lithography system during the exposure of a pattern
`according to the design data.
`
`17 Claims, 24 Drawing Sheets
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`US 7,241,542 B2
`
`1
`PROCESS FOR CONTROLLING THE
`PROXIMITY EFFECT CORRECTION
`
`RELATED APPLICATIONS
`
`This application claims priority of the European patent
`application EP 04 103 020.6 which is incorporated by
`reference herein.
`
`FIELD OF THE INVENTION
`
`The invention refers to process for controlling the prox-
`imity effect correction in an electron beam lithography
`system. The process is suitable for precise numerical deter-
`mination of the proximity parameters of the Point Spread
`Function (PSF) for optimised controlling the proximity
`correction in the high-resolution electron beam lithography
`(EBL).
`
`BACKGROUND OF THE INVENTION
`
`The proximity effect parameters are specific numerical
`inputs to control an arbitrary Proximity-Elfect correction
`software. This satisfies high Critical Dimension control
`“CD-control” requirements (depending on actual Interna-
`tional Technology Roadmap for Semiconductors ITRS from
`International SEMATECH) as well as to compensate pattern
`bias in the Mask and/or Direct-Write working with Gaussian
`and/or Shaped beam in connection with the subsequent
`technology steps (development, etching, etc.).
`Many methods have been proposed for the determination
`of the proximity parameters reflecting various effectiveness.
`In addition to the proximity effect a fogging effect occurs
`simultaneously in a electron beam lithographic system.
`There are several publications, which deal with the proxim-
`ity effect correction.
`The article “Optimum PEC Conditions Under Resist
`Heating Effect Reduction for 90 nm Node Mask Writing”;
`disclosed in Proc. SPIE, Vol. 4889, Part Two, pp 792-799
`(paper No. 86), show the problem of 50 k V e-beam writing
`causing critical dimension (CD) change, resist heating and
`proximity effect. This experimental method is used for
`determination of the proximity input-parameters in the mask
`making process using large area matrices of proximity-
`corrected test patterns written under various conditions with
`discrete step-by-step individually changed proximity param-
`eters. The optimal parameter set is then determined from
`direct measurements on these test patterns where the pattern
`deformation effects are minimal. The experiment and also
`the pattern evaluation is highly time consuming. Because of
`the large number of possible combinations of the input
`parameters,
`the method is
`limited to only 2 Gaussian
`approximation of the resulting PSF. This method is mas-
`sively used in the mask production.
`The article in Microelectronic Engineering 5 (1986) 141-
`159; North Holland with the title “Determination of the
`Proximity Parameters in Electron Beam Lithography Using
`Douglmut-Structures”. The test structures, used to determine
`the parameters for a correction function, are doughnuts. This
`method offers a straightforward technique for determining
`the proximity parameters from an array of exposed donuts
`by means of optical microscopy. This method is not sensitive
`enough to achieve CD control with a e-beam and not suitable
`for high-resolution patterning EBL methods.
`In the article “Point Exposure Distribution Measurements
`for Proximity Correction Electron Beam Lithography on a
`sub-100 nm Scale”; in J. Vac. Sci. Technol. B 5(1), January/
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`2
`
`February 1987 a single point/pixel is exposed in a wide
`range of doses and the diameters of the patterns measured
`and the results directly approximated by Gaussian functions.
`The method is applicable for special high-contrast resist
`only (i.e. insensitive to changes in development rate effects),
`needs high-resolution measurement technique (SEM) and
`also additional processes (“lift-ofl” or deposition coatings of
`patterns). This method may not be applicable to the com-
`mercially used Chemically Amplified Resists (CAR). With
`the point exposure method using extremely high doses, acid
`dilfusion effect may outweigh the true nature of the prox-
`imity effect [Z. Cui, Ph.D. Prewett, “Proximity Correction of
`Chemically Amplified Resists for Electron Beam Lithogra-
`phy”, Microelectronic Engineering 41/42 (1998) 183-186].
`The article “Determination of Proximity Effect Param-
`eters in Electron-Beam Lithography” in J. Appl. Phys. 68
`(12), 15 Dec. 1990, discloses a empirical method for deter-
`mining the proximity parameters in electron-beam lithogra-
`phy from rectangular array of mesh patterns from which,
`after
`the processing proximity parameters
`should be
`retrieved by means of light-optical inspection. A test pattern
`to be measured is used to determine the proximity effect.
`This method is not suitable for the contemporary conven-
`tional high-resolution production e-beam lithography sys-
`tems.
`
`In some publications the fogging effect is considered as
`well. The article “Fogging Effect Consideration in Mask
`Process at 50 KeV E-Bearn Systems” shows a suggestion to
`reduce the fogging effect in high voltage electron e-beam
`systems. The fogging effect
`influences for example the
`difference between a calculated/theoretical feature width
`
`and the experimental feature with generated by the litho-
`graphic process.
`The article in Microelectronic Engineering 5 (1986) 141-
`159; North Holland with the title “Determination of the
`Proximity Parameters in Electron Beam Lithography Using
`Doughnut-Structures”.
`The article “Determination of Proximity Effect Param-
`eters in Electron-Beam Lithography” in J. Appl. Phys. 68
`(12), 15 Dec. 1990, discloses as well
`influence of the
`fogging effect on the resulting features of a lithographic
`process.
`
`SUMMARY OF THE INVENTION
`
`It is the object of the present invention to create a method
`which allows a reliable correction of the illumination param-
`eters of a e-beam lithographic system by considering the
`influence of the fogging effect.
`The above object is achieved by a process as claimed in
`claim 1
`
`The above object is achieved by a process for controlling
`the proximity effect correction in an electron beam lithog-
`raphy system wherein the exposure is controlled in order to
`obtain resulting pattern after processing which are conform
`to design data comprising the steps of:
`exposing an arbitrary set patterns without applying the
`process for controlling the proximity correction;
`measuring the geometry of the resulting test structures
`and thereby obtaining a set of measurement data;
`determining a numerical range of proximity of basic input
`parameters (X,
`[3 and 11, from the set of measurement data;
`fitting a model by individually changing at least the basic
`input parameters (X,
`[3 and 11 of a control function to
`measurement data set and thereby obtaining an optimised set
`of parameters,
`
`DSS-2003 /Page 26 of 34
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`applying the correction function to an exposure control of
`the electron beam lithography system during the exposure of
`a pattern according to the design data.
`Additionally, it is useful to apply the determined proxim-
`ity parameter set to a calculation and comparison of the
`results with the measured data set with nominal doses
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`exposed isolated clear and opaque lines, “ON THE TAR-
`GET”. Another possibility is to apply the fitted proximity
`parameter set to a calculation and a comparison of the results
`with the measured data set from other arbitrary pattern,
`which is a pyramid like pattern and comparing the results
`with the measured data set from measurements in represen-
`tative points on the test patterns. A further possibility is to
`apply the fitted proximity parameter set to a calculation and
`a comparison of the results with the measured data set from
`other arbitrary pattern, which is a plurality of lines in
`Duty-Ratio and comparing the results with the measured
`data set from measurements in representative points on the
`test patterns.
`The method is based on the analysis of the pattern
`geometry variation as a direct process response (electron
`energy, resist material, substrate material, pre- and post-
`exposure processes, pattern transfer, etc.) to non-interacting
`and/or interacting non-corrected patterns in the EBL. The
`measured pattem-variation behaviour is reconstructed using
`a back-simulation by inserting the specified proximity
`parameters into the model. From the model calculated data
`represent the lateral contour localizations of the simulated
`pattern at the same points where they were measured on the
`real pattern. A comparison of measured data with the cal-
`culated results at the same points on a representative test
`pattern (single clear/opaque lines, pyramid like patterns,
`array of lines in duty-ratio, etc.) visualise the quality of the
`determined proximity parameter set.
`In the case,
`that the requested requirement,—that the
`correction algorithms are working under the same model
`conception as used in the model—is fulfilled, the method all
`at once also predicts the possible pattern uniformity devia-
`tions (pattern conformity) and the resolution limits after
`using the actually determined proximity parameter set in the
`proximity correction.
`The present
`invention has the advantage that uses a
`model-based analyses and interpretations of native geo-
`metrical distortions of exposed non-corrected representative
`patterns (analysing the direct process response as a typical
`pattem-geometry variation) which are measured in specified
`points (using commercial measuring tools, e.g. CD-SEM)
`and the data are recorded for the subsequent processing. A
`successive “back-simulation” procedure is used for the best
`possible reconstruction of these effects. “Back-Simulation”
`means a computational method how to find the optimum
`numerical input parameter set for the best approximation of
`the measured geometry variation of a concrete pattern detail
`in dependence on pre- and post exposure condition and/or
`proximity (pattern-size and neighbourhood) effects (:pat-
`tern and process reconstruction). Once such a pattern detail
`can be the dimensional variation of a pattern in a specified
`point as a function of the exposure intensity (e.g. in the
`simplest case line width and/or contact dimensional varia-
`tion vs. exposure dose in both tonalities). Another variable
`can be for example the location of a neighbourhood pattern
`(e.g. line width measurements vs. gap width variation of
`large pads—pyramid-like patterns, and/or lines in grat-
`ings—lines in duty-ratio). In consequence, after inserting the
`obtained parameters into the model, the appropriate simu-
`lations should show the same tendency of pattern geometry
`variations dependency as obtained from measurements.
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`Accordingly, if the correction algorithms are working under
`the same model conception as used in the model, it results
`in a good recovery of the parasitic distortion effects using
`these input parameter sets in the proximity correction.
`Measurements and simulations can be performed down to
`the smallest resolvable pattern dimension, which allows also
`a precise determination of parameters describing the so
`known “short-range” effects arising from the forward scat-
`tering of electrons, secondary electron distribution, beam
`blur, resist effects (development, acid diffusion, quenching)
`and pattern transfer (microloading). Consequently, the prox-
`imity corrector with working with this parameter set will be
`able to work correctly also in the deep sub-100 nm lithog-
`raphy node.
`Experimental measurements on a couple of exposed pat-
`terns (described in Appendix “Test patterns”) are the pre-
`condition to provide all necessary numerical inserts into the
`PROX-In (PROX-In is a user-friendly WindowsTM based
`software tool serving as a help for lithographers to determine
`the proximity effect parameters) active-free edit dialog
`boxes and to create simple ASCII-files containing the mea-
`sured data. Subsequently these data serve as the basis for the
`selected particular built-in algorithms required for the prox-
`imity parameter determination in this program. To maxi-
`mally avoid pattern degradations/distortions with submicron
`features it is unavoidable to apply a correction method for
`handling this effect. Existing techniques rely on: a) shot-by-
`shot modulation of the exposure dose, b) a modification of
`the pattern geometry, or c) combining of both methods
`mentioned before.
`
`The main advantages of this process is, that it does not
`employ large matrices of exposed proximity-corrected pat-
`terns with various input parameters. The parameters will be
`here determined from measurements on non-corrected
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`simple test patterns. The amount of data and/or parameters
`to be analysed are reduced enormously. The advantage of the
`present invention is as follows. The present invention uses
`only a small amount of a relatively simple set of test patterns
`exposed. The substrate (5-inch and larger) area covered by
`the test pattern which is limited to under 1%. Furthermore
`the test patterns are exposed without any proximity correc-
`tion. Additionally there is the possibility to vary the global
`pattern loading by help of substrate “dummy” exposures of
`additional assistant patterns around the test patterns. This
`allows to determine the changes of pattern load depending
`on bias in the development and/or etching process. There is
`the additional possibility to directly observe the tendency of
`pattern degradation by individual varying the value of one of
`the input parameters. Then there is an interactive fine-tuning
`of the input parameters to achieve the best possible CD-
`requirements (CD-Linearity). The use of two or more Gaus-
`sian input parameter sets (Gaussian functions) with a direct
`check possibility, where and why the additional Gaussian
`functions with the various parameters are needed, enable the
`to achievement of better results. The back-simulation and
`
`reconstruction of specific pattern details for arbitrary prox-
`imity parameter sets allows a prediction of possible changes
`in the CD for the given parameter set for various geometry
`combinations of patterns.
`A computer program “PROX-In” was developed and
`realized for optimisation and testing purposes of the method
`described in this application under real conditions in the
`production.
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`BRIEF DESCRIPTION OF THE DRAWINGS
`
`The nature and mode of operation of the present invention
`will now be more fully described in the following detailed
`description of the invention taken with the accompanying
`drawing figures, in which:
`FIG. 1 is a block diagram of an e-beam lithographic
`system;
`FIG. 2a is an example for a pattern written with a
`Gaussian beam;
`FIG. 2b is the shape of the cross section of the Gaussian
`beam, which has a constant diameter;
`FIG. 3a is an example for a pattern written with a shaped
`beam;
`FIG. 3b is the shape of the cross section of the shaped
`beam, wherein the shape can be adjusted according to the
`pattern which needs to be written;
`FIG. 4a shows simulated trajectories for 100 electrons
`scattered in a Poly-(Methyl-MethAcrylate) (PMMA) coated
`on a GaAs substrate;
`FIG. 4b shows simulated trajectories for 100 electrons
`scattered in a Poly-(Methyl-MethAcrylate) (PMMA) coated
`on a GaAs substrate, wherein the primary energy of the
`electrons is higher as in the calculation shown in FIG. 4a;
`FIG. 5a shows a schematic View of the form of a pattern
`which needs to written in a resist on a substrate;
`FIG. 5b shows the result of the pattern which was written
`in the resist and no correction according to the invention is
`was applied;
`FIG. 6 shows a first test pattern which is written into the
`resist;
`FIG. 7 shows a second test pattern which is written into
`the resist;
`FIG. 8 shows an input window for the user to initiate the
`exposure of the first test pattern as shown in FIG. 6;
`FIG. 9 shows a table of measurement result gained from
`the exposed first test pattern;
`FIG. 9a shows the result in a graph form from PROX-In,
`where the goal is to find a parameter set;
`FIG. 10 shows an input window for the user to initiate the
`exposure of the second test pattern as shown in FIG. 7;
`FIG. 11 shows a table of measurement result gained from
`the exposed second test pattern;
`FIG. 11a shows the result in a graph form from PROX-In,
`where the goal is to find such a parameter set;
`FIG. 12 shows the main window of the program PROX-In
`provided on the display associated with the computer;
`FIG. 13 shows a sub-window of the first part of the main
`window on the display or user interface used for the calcu-
`lation of (X;
`FIG. 14 shows a sub-window of the first part of the main
`window on the display or user interface used for the calcu-
`lation of [3 and 11;
`FIG. 15 shows a table of a exposed line width as a
`function of the applied dose;
`FIG. 16 shows a change in line width as a function of the
`dose exposed;
`FIG. 17 shows a sub-window of the first part of the main
`window on the display or user interface used for the calcu-
`lation of 11;
`FIG. 18 shows a second portion of the main window (see
`FIG. 12) which serves for the “fine-tuning” of the numerical
`input parameters
`FIG. 19 shows a simulation of a 15 um line width
`variation using “2G” approximation;
`FIG. 20 shows a simulation of a 15 um line width
`variation using “3G” approximation;
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`FIG. 21 shows a selection box;
`FIG. 22 shows a comprehensive table with calculated
`results from the model;
`FIG. 23 shows a selection box;
`FIG. 24 shows the comparison of the optimal doses for a
`measured line width of a single clear line and the simulated
`one; using “2G” approximations;
`FIG. 25 shows the comparison of the optimal doses for a
`measured line width of a single clear line and the simulated
`one, using “3G” approximations;
`FIG. 26 shows a graph representation of the resulting
`control function;
`FIG. 27 shows a schematic representation pattern which
`is to be written by a lithographic process and the break-down
`of the pattern into subelements; and
`FIG. 28 shows a schematic representation of a pattern
`written with and without the applied control function.
`
`DETAILED DESCRIPTION OF THE
`INVENTION
`
`FIG. 1 shows a block diagram of an e-beam lithographic
`system 1. The e-beam lithographic system 1 has an e-beam
`source 2 which emits an e-beam 3. The specification men-
`tions the use of an e-beam 3 only. Nevertheless, it has to be
`understood that the invention is not limited to e-beams only.
`The invention can be used with particle beams in general,
`which are applicable to write a pattern 5 on substrate 4. The
`substrate 4 itself is placed in stage 6 which can be moved by
`electric motors 7 and 8 in a plane which is sparmed by the
`X-coordinate X and the Y-coordinate Y. The e-beam 3 passes
`beam alignment coil 9 after the emerge from the e-beam
`source 2. After the beam alignment coil 9, in the direction of
`e-beam 3 propagation, a beam blanking unit 10 is provided.
`After that the e-beam 3 reaches a magnetic deflection unit
`11, which comprises in general four magnetic coils 12. After
`that the e-beam 3 is directed to the substrate 4. As already
`mentioned the substrate 4 is positioned on the stage 6. The
`actual position of the stage is controlled by a position
`feedback device 13. Additionally, an electron detector 14 is
`positioned in close proximity of the stage 6. A computer 15
`is provided for controlling the whole e-beam lithographic
`system 1. Especially, to control, measure and adjust the
`beam parameters in order to produce pattern with a constant
`dimension. The computer 15 is linked to the e-beam litho-
`graphic system 1 by an interface 16, which carries out the
`analog to digital and/or the digital to analog conversion. The
`interface 16 is connected to the beam blanking unit 10, the
`magnetic deflection unit 11, position feedback device 13, the
`electron detector 14 and the electric motors 7 and 8 for
`
`moving the stage 6. The user is informed via a display 17
`about the settings and/or the adjustment parameters of the
`e-beam lithographic system 1.
`FIG. 2a is an example for a pattern 20 which covers a
`certain area 21 and the area 21 is filled with a plurality of
`Gaussian beams 22. Each of the Gaussian beams 22 has the
`
`same diameter. In FIG. 2b the shape of the cross section 23
`of the Gaussian beam 22 is shown. The plurality of beams
`cover the area 21, which the pattern 20 requires.
`FIG. 3a shows an example for a pattern 30 which is
`written with a shaped beam 32. The total area 31 of the
`pattern 30 is cover by a plurality of variable shaped figures.
`The variable shaped figures fill the area of the pattern 31 to
`be written. In the present case the area 31 is covered by three
`different shapes 321, 322 and 323 of the electron beam. FIG.
`3b shows the shape of the cross section 33 of the shaped
`beam 32, wherein the shape of the individual beams can be
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`adjusted according to the pattern which needs to be written.
`As shown in FIG. 3b, the shape of the beam can be changed.
`This is indicated by the arrows 34.
`In both cases (Gaussian beam or Shaped beam) the
`submicron features or pattern became the crucial factor for
`mask writing. With this pattern size, e-beam lithographic
`systems are confronted with common parasite electron scat-
`tering effects, which cause unwanted exposure depositions
`in the area surrounding the pattern to be written. This
`parasite electron scattering effects are known as proximity
`effects (see for example: T. H. P. Chang, “Proximity effect in
`electron beam lithography,” J. Vac. Sci. Technol. 12 (1975)
`p. 1271). In case the minimum feature size becomes less
`than the backscattered range of electrons, pattern coverage
`affects the dimensional control of the pattern to be written.
`On the other hand, forward scattering limits the maximum
`resolution. The difference between back-ward and forward
`
`scattering increases as the energy of the electrons increases.
`Any pattern detail, which falls within a specific area, suffers
`significant distortions from his originally designed size and
`shape in the realized resulting lithographic pattern image. To
`maximally avoid pattern degradations/distortions with sub-
`micron features it
`is unavoidable to apply a correction
`method for handling this effect.
`FIG. 4a shows simulated trajectories 42 for one hundred
`electrons scattered in a Poly-(Methyl-MethAcrylate) layer
`40 (PMMA), which defines a resist, coated on a GaAs
`substrate 41. The primary energy of the electrons is set to 15
`keV. As the e-beam 43 impinges on the PMMA-layer the
`electrons are scattered and move according to the calculated
`trajectories. FIG. 4b shows simulated trajectories for 100
`electrons scattered in the PMMA-layer 40 coated on a GaAs
`substrate 41, wherein the primary energy of the electrons is
`higher as in the calculation shown in FIG. 4a. In electron
`beam lithography the dominant distortion originates from
`the interaction of electrons with the resist/substrate system
`convoluted with additional effects, which are not exactly
`detachable and separately treatable. Here the major role
`plays the absorbed energy density distribution (AEDD)
`spread in the resist with the corresponding radiation-chemi-
`cal event distribution in the resist volume creating the latent
`image (resist differentiation) in the resist. A modeling of the
`AEDD in the resist layer is possible by using statistical
`(Monte Carlo) or analytical (Transport Equation) calcula-
`tions of electron-scattering processes. The real latent image
`is then created by local chemical modifications of the
`irradiated resist volume after absorbing a necessary radiation
`quantum from the exposure.
`FIG. 5a shows a schematic view of the form of a pattern
`50 which needs to written in a resi