Calculation of etching profile in the photolithographic process on As2S3 thin films S. Mamedova) Chemical Department, St. Petersburg University, Universitetski pr.2, Staryi Petergof, 198904, Russia CIS
A. Kisliuka) Institut fu¨r Experimentalphysik, Freie Universita¨t Berlin, Arnimallee 14, 14195 Berlin, Germany
~Received 14 July 1995; accepted 15 March 1996! The model of the formation etching profile in the photolithographic process on the As2S3 thin films has been proposed. Using experimental dependence of dissolution rate versus exposure the evolution of the etching profile was calculated. The model allows one to predict the etching profile and simulates the process. © 1996 American Vacuum Society.
I. INTRODUCTION Thin films of amorphous semiconductors have many features which make them suitable for the microelectronics photoresists and as media for high-resolution diffraction grating.1–3 After the illumination of the as-deposited amorphous As2S3 films the rate of dissolution decreases by a factor up to 100 times.4,5 This effect of photoinduced change of dissolution rate give a possibility to form the relief in those films. It is known that arsenic trisulfide films are being used as photoresist in photolithographic processes on PbSe~Te!, CdSe~Te!,6 and as media for holographic gratings.7–9 The resulting form and height of the relief depend on many factors. Among such factors the most important are: ~1! light-absorption coefficient; ~2! the rate of dissolution as function of exposure; ~3! distribution function of exposure.
II. METHOD Lets us consider a simple model for the calculation of relief which forms during the dissolution process of the film. The rate of dissolution in every point for a given etchant is determined by the exposure. The exposure in each point of the surface F(X) is determined by ~1!
where I(X) is the distribution function of the intensity incident beam on the film’s surface along X direction and t is the time of irradiation. To calculate the exposure inside of the a!
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J. Vac. Sci. Technol. B 14(3), May/Jun 1996
I ~ X,Y ! 5I ~ X ! exp~ 2 a Y ! ,
~2!
where a is the absorption coefficient of material and Y is the distance from surface. Therefore, it is possible to calculate exposure in every point E(X,Y ), E ~ X,Y ! 5F ~ X ! exp~ 2 a Y ! .
~3!
The rate of dissolution W(X,Y ) in the point with coordinates X,Y are determinated by exposure in this point. The dependence the rate of dissolution as function of exposure for given etchant is determined by the equation W ~ X,Y ! 5V ~ E ! ,
The light-absorption coefficient is determined by the properties of material and the wavelength incident light. The factor 2 is determined not only by the material properties but by the etchant as well. The distribution function of exposure is determined by the desired relief. In Ref. 6 a simple method was proposed for the calculation of the relief but this method had a few limitations. The aim of the present work is to develop a common algorithm for calculation of the relief using experimental parameters.
F ~ X ! 5I ~ X ! t,
film ~Y direction! one must take in account the light absorption in the film. The absorption of the light in the film is described by the Beer–Lambert law,
~4!
where E is the photon energy. The function V(E) is found from experiment. Expression for calculation of the rate of dissolution of the film for linear function V(E) in any point with the coordinates X,Y is given by W ~ X,Y ! 5V ~ E ! F ~ X ! exp~ 2 a Y ! .
~5!
We assume that the direction of dissolution in every point with the coordinates X,Y for a given time t is normal to the film surface. This normal direction D (D x ,D y ) is a unit vector. The evolution of relief after short time Dt for every point of the relief with coordinates X(t). Y (t) is determined ~in the case Dt→0! by a system of of two differential equations,
]X 5D x W ~ X,Y ! , ]t ~6!
]Y 5D y W ~ X,Y ! . ]t
This is a local equation for evolution of the relief in the time. The components of the unit vector D (D x ,D y ) are determinated by a curvature of the relief in a given point. Because the profile is going to change due to dissolution, the direction cosines (D x ,D y ) also change and they are calculated for every point of profile and for every moment of time. The
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©1996 American Vacuum Society
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S. Mamedov and A. Kisliuk: Calculation of etching profile
FIG. 1. Dependence of the dissolution rate As2S3 films in diethylamine ~10 vol %!–benzonitryl ~90 vol %! solution vs exposure.
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FIG. 2. The profiles calculated at different exposures.
The parameter K is defined by normal direction to the relief is determined by the perpendicular to the tangent in every point with the coordinates X,Y . III. CALCULATION The Euler method with time step Dt51024 s was used to solve the differential equation ~6!. The dissolution of the film begins from some starting profile. The flat surface film with linear dimension along X axis equals 1 mm and the thickness h ~Y axis! of 1 mm was considered. The sinus profile of exposure was used, I ~ X ! 5A sin~ KX ! .
H
ln~ 2 ! at 0,E,0.3 J/cm2 ln@ V ~ E !# 5 ln~ 2 ! 2E @ ln 22ln~ 0.1!# / ~ 0.8– 0.3! ln~ 0.1! at E.0.8 J/cm2
~7!
~8!
where n the number of self-waves per unit of the length; n52 was used in these calculations. Under the above conditions a diffraction grating having 2000 lines/mm was modeled. Let us devide the surface of the film into N equidistant points. In the calculation procedure N51024 was used. The starting condition at t50 was defined as X n (0)5n and Y n (0)5h, where n runs from n51 to N. The experimental dependence @function V(E) in Eq. ~3!# of the rate of dissolution As2S3 thin film on exposure in the organic mixture ~propylamine-valeronitryl! is shown in Fig. 1. The following linear approximation function was used in the calculation:
at 0.3
