JPH0346969B2 - - Google Patents

Description

[Detailed description of the invention]

[Industrial Application Field] The present invention relates to a method for determining the optimum exposure energy when exposing a photoresist coated on an object to a target pattern using a photomask. [Prior Art] FIG. 1 shows a schematic diagram of a pattern exposure apparatus used in a photoresist process. The light emitted from the light source 1 is condensed by a condenser lens 2, passes through a mask 4, and then passes through a projection lens 5.
As a result, the resist film 6 is exposed by projection. The wafer 9 has a first base film 8 and a second base film 7.
A photoresist film 6 is formed in a laminated structure. The length of the exposure time is determined by adjusting the opening/closing time of the shutter 3 by the exposure time control device 10. [Problems to be Solved by the Invention] Conventionally, the exposure time has been manually set by an operator. Therefore, the error is large,
There was a problem in that the deviation of the exposure amount from the optimum value became large, and the variation in line width of the resist pattern on the wafer after development became large. this is,
Since this degrades the product yield during the manufacture of semiconductor devices, a solution to this problem has been desired in the photoresist process. The reason for this is that the exposure energy, which is the basis for determining the optimal exposure amount, for example, the exposure time, cannot be determined depending on the thickness of the photoresist film applied to the object. SUMMARY OF THE INVENTION Therefore, an object of the present invention is to be able to optimally control exposure in a photoresist process, thereby improving the yield of semiconductor devices. An object of the present invention is to provide a method for determining exposure energy. [Means for Solving the Problems] In order to achieve the above object, the present invention provides an optimum exposure energy when exposing a photoresist coated on an object to a desired pattern using a photomask. This is a determination method for a specific photoresist film coated on an object with a standard film thickness t ₀ , when the photoresist film is uniformly irradiated with light and processed, The uniform irradiation critical exposure energy _ETU , which represents the minimum critical exposure energy required to dissolve the photoresist film, and the relative value at a point corresponding to the line edge produced in the photoresist film by exposing the photoresist film through a photomask. Relative light intensity η〓 represents the exposure intensity, and represents the ratio between the minimum critical exposure energy required to completely dissolve the photoresist at the line edge portion during photomask exposure and the above uniform irradiation critical exposure energy _ETU . The relative critical exposure energy E _T is determined in advance by experiment or calculation, and when determining the exposure energy in the photoresist process, the actual film thickness d ₀ of the photoresist film applied to the object is measured, These uniform irradiation critical exposure energy E _TU , relative light intensity η〓 and relative critical exposure energy E _T
and the film thickness d ₀ actually measured for the photoresist film, and the correction coefficient for the deviation between the measured value d ₀ and the reference value t ₀ for the photoresist film is set as K ₁ , and the photomask pattern is A photoresist process characterized in that the exposure energy dose for forming a faithful photoresist pattern is determined using the relationship: Dose=E _TU [E _t +K ₁ (d ₀ − t ₀ )]η〓 ^-1 A method for determining exposure energy is provided. [Effect] The uniform irradiation critical exposure energy E _TU of the photoresist film applied to the object is determined by the thickness of the photoresist film and the optical properties and development characteristics specific to the resist, so it is determined by determining these. be able to. Also, the relative light intensity η〓,
The relative critical exposure energy E _T and the correction factor k ₁ are:
It can be determined by optical theory and/or experiment. Therefore, by measuring the thickness of the photoresist film to be actually exposed and using the above relational expression, the exposure energy Dose can be determined. Once this exposure energy Dose is determined, the exposure time can be determined from the relationship with the irradiation intensity of the exposure device. [Example] Examples of the present invention will be described with reference to the drawings. Generally, in the photoresist process, as shown in FIG.
A pattern exposure device 22 that exposes a semiconductor element pattern onto the photoresist coated on the wafer 20, and a development device 23 that develops the pattern. The present invention provides a method for determining exposure energy for optimal exposure of a photoresist film in such a process. below,
A plurality of embodiments suitable for controlling such a process will be described. (First Embodiment) FIG. 2 shows a process to which the exposure energy determining method of the first embodiment of the present invention is applied and the configuration of its control system. The photoresist process control system shown in FIG.
, a film thickness measuring device 16 that measures the applied photoresist film thickness d ₀ , and a control computer 20 that takes in the outputs of these devices and executes various calculations.
0 and the irradiation intensity I ₀ provided outside the computer 200
Measuring device 17 and exposure time Texp control device 18
It is composed of: Further, the photoresist process control device has a development time control device 19 and a development device 23 added to the structure, and is configured to execute processes from photoresist coating to development on the wafer. The control computer 200 functions at least as a means for executing calculations for determining the exposure time for performing mask pattern exposure on the photoresist film, and determines the critical E _TU calculation routine 11 for calculating exposure energy E _Tu
and the exposure energy required for mask pattern exposure using the critical exposure energy E _Tu .
It has an exposure amount calculation routine 12 that calculates Dose, and an exposure time calculation routine 13 that calculates exposure time based on the exposure energy Dose and the irradiation intensity at the time of exposure. Corresponding programs for these routines are executed within the computer 200 to achieve their respective functions. That is, the E _Tu calculation routine 11 functions as an E _Tu calculation means, the exposure amount calculation routine 12 functions as an exposure amount calculation means, and the exposure time calculation routine 13 functions as an exposure time calculation means. The program can be stored within computer 200. In the present embodiment, the computer 200 also functions as a development time setting unit for executing control calculations for controlling the development time of the exposed photoresist film, so that the development time is set at the time of E _Tu calculation. A development time setting routine 14 is provided which sets the development time of the photoresist in accordance with the above and outputs it to the development time control device 19. Furthermore, each parameter is input to the computer 200 by the input device 100, the temperature drying time measuring device 15, the film thickness measuring device 16, and the irradiation intensity measuring device 17. Next, a method for determining the exposure energy Dose for forming a photoresist pattern faithful to a photomask pattern in such an apparatus will be described. First, a process for determining the uniform irradiation critical exposure energy E _Tu will be explained. The uniform irradiation critical exposure energy E _TU is determined from the optical properties and development characteristics of the photoresist and the measured value of the photoresist film thickness. Optical properties of photoresists The method for determining the optical properties of photoresists described below is as follows:
ELECTRON DEVICES, Vol.ED−22, No.7,
JULY 1975, pages 445-451. First, determine the absorption coefficient and photosensitivity, which are the optical properties of the photoresist. The absorption coefficient is the concentration of the photosensitizer contained in the resist, which acts as a development inhibitor. Coefficient A related to M
and the absorption coefficient B of the base resist, which is unrelated to the photosensitizer concentration M. The photosensitive agent serves to prevent the photoresist from dissolving in the developer. That is, parts of the photoresist film with a high concentration of photosensitizer are difficult to dissolve in the developer, but parts with a low concentration of photosensitizer quickly dissolve in the developer. Photosensitivity C is a coefficient representing the ease with which a photosensitizer is destroyed by light. Generally, it is known that these coefficients A, B, and C can be determined if the type of photoresist, drying temperature, drying time, and wavelength of the exposing light are known. For example, as shown in Table 1, coefficients A, B,
C can be found. In Table 1,
(A), (B), and (C) indicate the type of photoresist, and indicate the values of coefficients A, B, and C when the drying time is 1 hour and the exposure wavelength is 404.7 nm. This optical characteristic is stored in the computer.

[Table] Development characteristics of photoresist As shown in Figure 3, the development characteristics are as shown in Figure 3, where M is the photosensitive agent concentration and development speed is Ra, Ra=exp(E ₁ + E ₂・M + E ₃・M ² )... This is the curve shown in (1). Here, the coefficients E ₁ , E ₂ , and E ₃ are coefficients determined by the types of photoresist and developer. Note that this development characteristic is described in the above-mentioned literature. This development characteristic is stored in the computer. Actual Measurement of Photoresist Film Thickness The film thickness of the photoresist coated on the wafer to a predetermined thickness is measured by the photoresist film thickness measuring device 16, and the measured value d ₀ is determined. Using this measured value d ₀ , the absorption coefficients A, B and photosensitivity C of the photoresist determined by , and the development coefficients E ₁ , E ₂ , E ₃ determined by , uniform irradiation critical exposure energy E _{TU is} calculated. is calculated by the uniform irradiation critical exposure energy calculation routine 11. E _TU calculation flow Next, uniform irradiation critical exposure energy E _TU is calculated. The methods for calculating the photoresist's sensitivity and calculating the film thickness after development are as follows:
“IEEE TRANS-ACTIONS ON
ELECTRON DEVICES, Vol.ED−22, No.7,
JULY 1975, pages 456-464.The program flowchart of the uniform irradiation critical exposure energy _ETU calculation routine 11 is shown in the fourth page.
As shown in the figure. First, in step 35, select the photoresist type,
Using the exposure wavelength, drying temperature, and drying time, resist parameters of optical properties and development properties stored in the computer are determined and set as program variables. In addition, photoresist film thickness measurements
d ₀ , irradiation intensity I ₀ and development time t _dev are also set as program variables. Next, in step 36, the photoresist film is divided into 100 sublayers as shown in FIG.
This is because the light intensity distribution in the depth direction of the photoresist film is calculated using the multilayer thin film theory. In step 37, the exposure energy applied to the photoresist film is slightly increased. In step 38, the photosensitizer concentration within the sublayer is calculated. The calculation formula for this step is shown below. The reflectance r _n of the mth (m≦100) interface is (2)
The transmittance t _n is expressed by the equation (3). r _n =n ₀ −m _n+1 /n ₀ +n _n+1 ……(2) t _n =2(n ₀ Real [n _n+1 ]) ^1/2 /n ₀ +n _n+1 ……( 3) Furthermore, regarding the reflectance and transmittance of the (j-1)th layer, equations (4) and (5) hold true. r _j-1 = [exp (−2iφ _j )] (F _j − r _j )−F _j (1−F _j r _j )
/F _j [exp(−2iφ _j )](F _j −r _j )−(1−F _j r _j )……
(4) t _j-1 = (F〓-1) t _j [exp(-iφ _j )]/F _j [exp(-
2iφ _j )] (F _j −r _j )−(1−F _j r _j )……(5) Here, F _j =n ₀ −n _j /n ₀ +n _j ……(6) φ _j =2π /λn _j δz _j ...(7) The ratio of the Poynting vectors of the j-th and (j-1)th layers is shown by equation (8), and using it, the absorbance A _j is ( 9) can be shown by the equation. P _j /P _j-1 = |t _j-1 | ² (1-|r _j | ² )/|t _j | ² (1-
｜r _j-1 ｜ ² )……(8) A _j = (1-R) [1-P _j /P _j-1 ]〓〓〓〓〓〓〓
[P _q /P _q-1 ] ...(9) Here, R is the reflectance of the photoresist as seen from the outside and is expressed as |r ₀ | ² . Using A _j , the light intensity of the j-th layer is expressed as in equation (10). I _j = I ₀ A _j / (AM _j + B) δz _j ...(10) The rate of change in the photosensitizer concentration M _j in the j-th layer is
As shown in equation (11), light intensity I _j and photosensitizer concentration
M is proportional to the product of _j . ∂M _j /∂t=−I _j M _j C ...(11) Using equation (11), the minute time Δt〓 is calculated from the exposure time t〓
The photosensitizer concentration after the elapse of time is expressed by equation (12). M _j ｜t〓+Δt〓=M _j ｜t〓exp(−1 _j CΔt〓) ……(12) When the exposure time t〓 is zero, the photosensitizer concentration is 1 and is shown in equation (13). . M _j |t〓 ₌₀ =1 (13) The photosensitizer concentration M _j inside the photoresist film can be determined using equations (9), (10), and (12). Here, Δt in the equation is expressed by equation (14), where I ₀ is the intensity of light irradiated to the photoresist, and ΔDose is the slight increase in exposure energy. Δt = ΔDose/I ₀ (14) This calculation is performed for all sublayers. In step 39, the development rate R _j of the sub-layer is determined using equation (1), and the time t _dj for dissolving the j-th sub-layer is determined using equation (15). t _dj = δd/R _j ... (15) If the dissolution time t _dj is added and the set time is reached when the nth sub-layer is added, then equation (16) holds true. . t _dev = t _d1 + t _d2 +...t _dj +...+t _do ... (16) Therefore, the number n of sublayers dissolved within the t _dev time
can also be determined, and the thickness d _r of the remaining photoresist layer can be determined using the following equation. d _r =δd·(100−n) (17) In step 40, it is determined whether the photoresist film residual thickness d _r is zero, and if it is not zero, the process returns to step 37 and the calculation is repeated. Also,
If it is zero, the exposure energy at that time is the uniform irradiation critical exposure energy _ETU . In this way, the uniform irradiation critical exposure energy can be determined. Find the exposure energy Dose. The exposure energy Dose for exposing the photoresist film 6 with the photomask pattern is calculated in the exposure amount calculation routine 12 (FIG. 2). A conceptual diagram of photomask pattern exposure to a photoresist film is shown in FIG. A photoresist film 6 is coated on a silicon substrate 9, and exposure energy is applied from above a photomask 4 consisting of line portions 45 and space portions 44.
Dose2 is irradiated. The relative light intensity distribution η on the photoresist film is as shown by the dotted line 46,
Points 49 and 5 corresponding to the edge part of the line part 45
The relative light intensity above 0 is η〓. This η can be calculated using optical theory. Next, this relative light intensity η〓 is calculated. As a calculation formula, for example, the following formula is used. Here, the width direction of the mask is taken as the X axis,
The light intensity distribution η(Xi) at the position of Xi is determined by setting the origin at the center of the width of the mask. η (Xi) = ∫∫ ^∞ _-∞ B ₀ (X ₁ , X ₂ ) K (X ₁ , Xi) K ^* (X ₂
,
Xi) A (X ₂ ) A ^* (A ₂ ) dX ₁ dX ₂ ... (18) Here, B ₀ (X ₁ , X ₂ ) is the light source intensity,
It is given by the following formula. _{B 0 ( X 1 , _ _ _} ^{_ _} ₁ : First-order Bessel function of the first kind λ: Light source wavelength σ: Light source coherency NA: Numerical aperture of the projection lens * represents a complex conjugate function. K(X ₁ −Xi) represents the projection lens coherent transfer function and is given by the following equation. K(X ₁ −Xi) = (NA) ² (2π/λ ² )∫ ₀ ¹ J ₀ (uρ)ρd
ρ
...(18b) u = (2π/λ) NA {(X ₁ − Xi) ² } ^1/2 where, J ₀ : Zero-order Bessel function of the first kind ρ : Parameter of the Bessel function Also, A(X ₁ ) is the transmittance function of the photomask and is given as follows. A(X ₁ ) = 1 (space part) = 0 (line part, light shielding part) The above projection lens coherent transfer function is given as the above equation (18b) when the focus is correct during exposure. . On the other hand, if the focus is not correct, it is necessary to consider the amount of defocus. In this case, the following equation is used as the projection lens coherent transfer function. K(X ₁ −Xi) = (NA) ² (2π/λ ² )exp(iv/
(NA) ² )∫ ₀ ¹ J ₀ (uρ)exp(−0.5ivρ ² )ρdρ
...(18c) Here, u = (2π/λ) NA {(X ₁ − Xi) ² } ^1/2 v = (2π/λ) (NA) ² Z Z: Defocus For these calculation formulas, please refer to the general 2
Regarding the dimensional light intensity distribution, see BJLin, “Partially
Coherent Imaging in Two Dimensions and
the theoretical limits of projection printing
in Microfabrication”IEEE Transactions on
Electron Devices, Vol.ED−27, No.5, pp.931
-938, 1980. From the relative light intensity distribution obtained by such calculation, the relative light intensity η〓 at the edge of the resist line is determined. For example, by substituting the value of 1/2 of the resist line dimension measured above into the above Xi, η〓
seek. Next, the exposure energy for forming a photoresist pattern faithful to photomask pattern 4 is determined.
Dose is determined in exposure amount calculation routine 12 (19)
It is determined by the formula. Dose=E _TU [E _t + K ₁ (d ₀ − t ₀ )] η〓 ^-1 ...(19) Here, E _TU is the uniform irradiation exposure energy, d ₀ is the photoresist film thickness, and η〓 is the photoresist film thickness. This is the relative light intensity of points 49 and 50 corresponding to the line edges shown in FIG. In addition, E _t is a relative critical exposure energy that represents the ratio of the minimum critical exposure energy required to completely dissolve the photoresist at the line edge portion and the uniform irradiation critical exposure energy E _TU during photomask exposure. , can be determined in advance by experiment.
Further, k ₁ is a correction coefficient for the deviation between the measured value d ₀ and the reference value t ₀ for the photoresist film. The relative critical exposure energy E _t and the correction coefficient k ₁ are constants determined by the exposure apparatus. The above equation (19) is derived as follows. First, as shown in FIG. 6, a photoresist film 6 having a standard film thickness t ₀ is irradiated with various exposure energies Dose 2 from above the photomask 4 and developed. Thereby, the line width of the obtained residual photoresist film is measured. Using each of these line widths, each η〓 is determined as described above. Then, the edge critical exposure energy Et' is determined from these η〓 and the exposure energy Dose2 corresponding to each η〓. At this time, as shown in FIG. 17, if the width Wl of the edge of the residual photoresist 51 is equal to the width of the line portion 45 of the photomask 4, the exposure energy Dose2 applied at that time is the optimum exposure energy Dose. I can think about it. The edge critical exposure energy Et′ at this time is Et′=Dose′η〓 (19a) where the relative light intensity of this portion is η〓. On the other hand, this edge critical exposure energy Et′ is
This quantity depends on the optical properties and development properties of the photoresist, and can be expressed as the product of the uniform irradiation critical exposure energy E _TU and the relative critical exposure energy E _t as shown in the following equation. Et'=E _TU・E _t (19b) From the above equations (19a) and (19b), the following equation is obtained. Dose・η〓＝E _TU・E _t ……(19c) Equation (19c) is the standard film thickness of the photoresist film.
Applicable only if t ₀ . However, in an actual process, the film thickness of the photoresist is not necessarily a standard value, but may take various values. Therefore, assuming that this film thickness is d ₀ , let us consider its correction. In this case, the above (19c) is expressed by the following equation, where f(Δd) is the correction function. Here, Δd is the amount of deviation of the photoresist film from the reference value. Dose・η〓=F _Tu・E _t +f(Δd) ...(19d) Here, f(Δd)=a ₀₊ a ₁ (Δd) ₊ a ₂ (Δd) ² ₊ ... ... ₊ a _o (Δd) ⁿ , and by setting a ₀ = 0 and eliminating quadratic terms and above, it can be approximated as f(Δd)≒a ₁ (Δd) ... (19e), so this can be approximated as , (19d)
Substituting into , we get the following equation. Dose・η〓=E _TU・E _t +a ₁ (Δd) =E _TU {E _t +a ₁ /E _TU・(Δd)} ...(19f) Therefore, a ₁ /E _TU =K ₁ Δd=d ₀ −t ₀ , the relationship Dose=E _TU [E _t +k ₁ (d ₀ −t ₀ )]η〓 ⁻¹ is obtained. Find the exposure time. Exposure energy Dose obtained in this way
Exposure time calculation routine 1 from exposure time texp
3 (Figure 2). Then, the exposure time control device 18 controls the pattern exposure device 22 to operate at the exposure time texp. Exposure time texp is exposure time calculation routine 1
In step 3, the irradiation intensity is determined from the measured value Iexp of the irradiation intensity by the irradiation intensity measuring device 17 using equation (20). texp=Dose/Iexp (20) Development The development device 23 is controlled by the development time control device 19. The development time is the development time tdev used to calculate the uniform irradiation critical exposure energy E _TU .
is set and used in the development time setting routine 14. In order to control the development time so that the resist line dimensions match the design values, it is sufficient to measure the error of the resist line dimensions from the design values, and correct the development time based on the measured value. Effects of this Example According to this example, even if the photoresist coating thickness on the wafer deviates significantly from the specified value, the uniform irradiation critical exposure energy can be determined from the measured value of the photoresist coating thickness. , a resist pattern with few errors can be formed on a wafer. (Second Embodiment) Next, a second embodiment of the present invention will be described. In the first embodiment above, an example was shown in which the optical properties were stored in the computer, but the optical properties include the transmittance of the photoresist film before exposure, the transmittance after sufficient exposure, and the transmittance at the start of exposure. It can be determined by the calculation method described later by measuring the rate of change in transmittance. FIG. 7 shows a configuration diagram of a photoresist process control system used in this example.
Components having the same functions as those in FIG. 2 are given the same reference numerals. Note that the measuring device 15 is replaced by a resist transmittance measuring device 60, and the step 35 in FIG. 4, which is a flowchart of the uniform irradiation critical exposure energy calculation routine 11, is replaced with the optical property calculation step shown in FIG. . The coefficients A, B, and C of the optical characteristics are determined as follows, assuming that the transmittance T(t) is the exposure time t. A=(1/d)ln[T(∞)/T(0)]...(33) B=-(1/d)lnT(∞)...(34) C=A+B/AI ₀ T(0 ) {1-T(0)}・dT(0)/
dt (35) T(0) is the transmittance before exposure, T(∞) is the transmittance after sufficient exposure, and I ₀ is the irradiation intensity on the photoresist film surface. FIG. 8 shows the flow of the optical property calculation step for calculating the optical properties using equations (33), (34), and (35). In step 71, the development characteristics of the photoresist film, the photoresist film thickness d ₀ , and the irradiation intensity on the film surface are determined.
Set I ₀ etc. to the program variables. In step 72, the photoresist film transmittance T(t) at the exposure time t is input from the transmittance measuring device and plotted on the coordinates as shown in FIG. In step 73, from the graph plotted on the coordinates, the transmittance T (0) when unexposed, the value T (∞) when the exposure time t is sufficiently long and the transmittance reaches its maximum,
Rate of change in transmittance at the start of exposure of photoresist film
Find dT(0)/dt. In step 74, optical characteristics A, B, and C are determined using equations (33), (34), and (35). Optical properties are calculated for each lot when processing wafers in the photoresist process, and the measured values are used to control the photoresist process. The calculation method for calculating equations (33), (34), and (35) is, for example, “IEEE TRANSACTIONS ON
ELECTRON DEVICES, Vol.ED−22, No.7,
JULY 1975, pp. 445-451, but a brief explanation will be given below. Rate of change in photosensitizer concentration with respect to exposure time t
∂t is photosensitivity C, photosensitizer concentration M(x, t) at position x in the photoresist film, light intensity I(x, t)
It can be obtained as in equation (21a). ∂M/∂t=-CM(x,t)I(x,t)
...(21a) Equation (21a) shows that the rate of decrease in photosensitizer concentration is proportional to the product of photosensitizer concentration and photosensitivity. The internal transmittance T(t)25 of the photoresist film 24 having the thickness d as shown in FIG. 10 is expressed by equation (21b). T(t)=exp[−∫ ₀ ^d ₀ {AM(x, t)+B}dx]
...(21b) Here, M(x, t) is the photosensitizer concentration at time t and depth x from the surface. Since the photosensitizer concentration is 1, the transmittance before the photoresist film is irradiated with light can be expressed by equation (22). T(0)=exp[-(A+B)d]...(22) Next, the transmittance when the exposure time is made infinitely long and the photoresist film is irradiated with enough light to completely destroy the photosensitizer. In equation (21b), T(∞) is
It is expressed as equation (23) with M(x, t) set to zero. T (∞) = exp [−Bd] ... (23) Differentiate equation (21d). dT(t)/dt=-T(t)d/dt[∫ ^d ₀ {AM(x, t) +B}dx] ...(24) =-T(t)A∫ ^d ₀ ∂M(x, t)/∂tdx ...(25) The light intensity I(x, t) at time zero at a point at depth x from the surface of the photoresist film is M(x, 0)
= 1, it is expressed as equation (26). I(x,0)= _I0exp [-(A+B)x]...(26) Here, _I0 is the light intensity at the surface within the photoresist film. The photosensitizer concentration at time t at the point of depth x is M
When (x, t), equation (27) holds true from equation (21a). ∂M (x, t) / ∂t = -CM (x, t) I (x, t) ... (27) Here, I (x, t) is the light intensity at time t at the point of depth x It is. Therefore, the rate of change in the photosensitizer concentration M(x, 0) at time zero at the point of depth x is expressed by equation (28). ∂M(x, 0)/∂t=−CM(x, 0) I(x, 0) (28) Substitute equation (26) into equation (28) to obtain equation (29). ∂M(x, 0)/∂t=-C・I ₀ exp [-(A+B)x] ...(29) From equation (25), the transmittance at time zero is as shown in equation (30). . dT(0)/dt=-T(0)A∫ ^d ₀ ∂M(x, 0)/∂tdx...(30) =T(0)A∫ ^d ₀ CI ₀ exp [-(A+B)x] dx
...(31) =T(0){-T(0)}A/A+BI ₀ C ...(32) From (22), (23), and (32), the optical properties of the photoresist film are as follows. It can be calculated as follows. A=(1/d)ln[T(∞)/T(0)]...(33) B=-(1/d)lnT(∞)...(34) C=A+B/AI ₀ T(0 ) {1-T(0)}・dT(0)/
dt (35) (Third Embodiment) Next, a third embodiment of the present invention will be described. In the above embodiment, an example was shown in which the development characteristics were stored in the computer, but they may also be obtained by calculation as follows. FIG. 11A shows a configuration diagram of a photoresist process control system used in this example. Components having the same functions as those in FIG. 2 are given the same reference numerals. Note that in place of the measuring device 15, a second photoresist film thickness measuring device 16' is provided, and the developing device 23 is provided with a second photoresist film thickness measuring device 16'.
The residual thickness d(t) of the photoresist film to be developed is measured. Furthermore, step 35 in FIG. 4, which is the flowchart of the uniform irradiation critical exposure energy calculation routine 11, is replaced by a development characteristic calculation step shown in FIG. 11B. In step 81, the optical characteristics of the photoresist film, the photoresist film thickness d ₀ before development, the irradiation intensity I ₀ on the film surface, etc. are set as program variables. In step 82, after the exposure time texp has elapsed, the photosensitizer concentration distribution inside the photoresist film (14th
Figure). The flow is shown in FIG. 13, and details will be described later. In step 83, the development of the photoresist film is started, and the residual thickness d(t) of the photoresist film is measured as the development time t elapses. As time passes, the photoresist film dissolves in the developer and becomes thinner, exhibiting changes as shown in FIG. 15. In step 84, the slope of the development dependence curve of photoresist film thickness is determined from the measured values shown in FIG. This slope becomes the reduction rate of the photoresist film thickness, that is, the development speed. In this way, the development rate with respect to the depth x from the surface of the photoresist film is determined as shown in FIG. Here, the depth x from the surface of the photoresist film in FIG. 16 is the value obtained by subtracting the residual thickness of the photoresist film d(t) in FIG. 15 from the photoresist film coating thickness d ₀ before development. (36)
It is determined by the formula. X=d ₀ −d(t) ... (36) In step 85, the characteristics of the photosensitizer concentration versus the depth from the surface of the photoresist film (Fig. 14) and the development speed versus the characteristic from the surface of the photoresist film ( 1st
6), the development speed with respect to the photosensitizer concentration M is determined. That is, in FIGS. 14 and 16, the depth x from the surface of the photoresist film is sequentially selected, the photosensitizer concentration and development speed Ra in each case are read, and the dependence of the development speed Ra on the photosensitizer concentration M is calculated. When drawn, it will look like Figure 3, and the curve will be
It is shown by equation (37). Ra = exp (E ₁ + E ₂ M + E ₃ M ² ) ... (37) The development coefficients E ₁ , E ₂ , and E ₃ are coefficients determined by the type of photoresist and developer, and these coefficients are calculated as shown above. The development speed characteristics can be determined by following the following steps. The development speed Ra is calculated for each lot when processing wafers in a photoresist process, and the calculated value is used to control the process. The method for determining the photosensitizer concentration is, for example, “IEEE
TRANSACTIONS ON ELECTRON
DEVICES, Vol.ED−22, No.7, JULY 1975,
Details are provided on pages 456-464.
I will briefly explain. As shown in FIG. 12, consider the case where a photoresist film 28 is formed on a substrate 29 and light 27 is irradiated from above. In this case, the photosensitive agent near the surface of the photoresist film is rapidly destroyed and disappears, while the photosensitive agent concentration remains high in the portion near the substrate because the light intensity is low. Using equations (9), (10), and (12), the photosensitizer concentration distribution inside the photoresist film after the exposure time texp has elapsed can be determined. The calculation flowchart is the first
Shown in Figure 3. In step 30, the photoresist film is divided into 100 sublayers. In step 31, the internal light intensity I _j is calculated for each of the sublayers using equation (10). In step 32, the concentration of the photosensitizer after the elapse of a minute time Δt is calculated using equation (12). In step 33, a minute time Δt is added to the exposure time. In step 34, it is determined whether the exposure time has reached the preset maximum exposure time, and if it has not, the process returns to step 31 and repeats the calculation. When calculated in this way, the distribution of the photosensitizer concentration inside the photoresist film is as shown in FIG. 14. Since the light intensity is strong near the surface of the photoresist film, the photosensitizer is rapidly destroyed and its concentration becomes low. On the other hand, in a portion near the bottom of the photoresist film, the light intensity is low, so the photosensitizer concentration is high. Furthermore, the pulsations in the photosensitizer concentration distribution curve that appear in FIG. 14 are caused by the pulsations in the light intensity caused by interference between the light reflected from the substrate below the photoresist film and the incident light from the top of the photoresist film. It is something to do. FIG. 17 shows the shape of the photoresist line when the photoresist process is controlled, exposed, and developed by determining the optical properties and development characteristics using the calculation methods of the second and third embodiments described above. Shown below. A resist line 51 is formed in a portion of the photomask 4 corresponding to the mask line portion 45 . The error with the set value of the line width Wl52 is shown in FIG. If the horizontal axis is the number N of the processed wafer and the vertical axis is the average value of the error in the resist line width formed on the wafer, then in the case of the photoresist process control according to this embodiment, it is 53.
In the case of conventional control, it becomes 52. It can be seen that the variation in line width is reduced compared to the conventional one. [Effects of the Invention] According to the present invention, since the exposure time is determined by measuring the thickness of the photoresist film, the process can be controlled in accordance with the thickness of the photoresist film, and the manufacturing yield of semiconductor devices can be improved.

[Brief explanation of drawings]

FIG. 1 is a block diagram of a pattern exposure apparatus, FIG. 2 is a block diagram of a photoresist process control system in which the first embodiment of the present invention is used, FIG. 3 is a graph showing the dependence of development speed on the photosensitive agent, and FIG. The figure is a flowchart of a calculation program for uniform irradiation critical exposure energy, and Figure 5 is an explanatory diagram showing the parameters of each sublayer when a photoresist film is divided into sublayers.
FIG. 6 is a conceptual diagram of photomask pattern exposure, FIG. 7 is a configuration diagram of a photoresist process control system in which the second embodiment of the present invention is used, FIG. 8 is a flowchart of optical property calculation steps, and FIG. 9 10 is a graph showing the measured value of the exposure time dependence of the transmittance of the photoresist film, FIG. 10 is an explanatory diagram showing the internal transmittance of the photoresist film, and FIG. 11A is a graph in which the third embodiment of the present invention is used. A configuration diagram of the photoresist process control system, FIG. 11B is a flowchart of the development characteristic calculation step, FIG. 12 is a conceptual diagram of light irradiation to a photoresist film coated on a substrate, and FIG. 13 is a diagram of the photoresist process control system. A flowchart of a program for calculating the photosensitizer concentration distribution inside the film, FIG. 14 is a graph showing the photosensitizer concentration distribution inside the photoresist film, and FIG. 15 is a diagram showing the development time dependence of the photoresist film thickness. Fig. 16 is a graph showing the dependence of the development speed on the depth from the photoresist film, Fig. 17 is a cross-sectional view of the resist line formed after development, and Fig. 18 is a graph showing the control of the photoresist process using the present invention. 3 is a graph showing the error of the width of a resist line formed in the case of the present invention from a reference dimension. 1... light source, 3... shutter, 4... mask,
5... Projection lens, 6... Photoresist film, 9... Wafer, 10... Exposure time control device, 11... Uniform irradiation critical exposure energy calculation routine, 12... Exposure amount calculation routine, 13...
...Exposure time calculation routine, 15... Temperature/drying time measuring device, 16... Photoresist film thickness measuring device, 17... Irradiation intensity measuring device, 18... Exposure time control device, 22... Pattern exposure device, 23 …
...Developing device, 46...Relative light intensity, 49,50...
... Relative light intensity of line edge portion, 51 ... Registration line, 52, 53 ... Registration line width error.

Claims (1)

[Claims] 1. A method for determining the optimal exposure energy when exposing a photoresist coated on an object to a desired pattern using a photomask, the method _comprising : For a specific photoresist film when coated, the minimum criticality required to completely dissolve the photoresist film when the photoresist film is uniformly irradiated with light and developed under specific development conditions. Uniform irradiation critical exposure energy E _TU representing exposure energy and relative light intensity η representing relative exposure intensity at a point corresponding to a line edge generated on the photoresist film by exposing the photoresist film through a photomask. 〓
and the relative critical exposure energy E _T which represents the ratio of the minimum critical exposure energy required to completely dissolve the photoresist at the line edge portion during photomask exposure and the uniform irradiation critical exposure energy E _T , experimentally or The uniform irradiation critical exposure energy E _TU is determined in advance by calculation, and when determining the exposure energy in the photoresist process, the actual film thickness d ₀ of the photoresist film applied to the object is measured. and relative light intensity η〓 and relative critical exposure energy E _T
and the film thickness d ₀ actually measured for the photoresist film, and the correction coefficient for the deviation between the measured value d ₀ and the reference value t ₀ for the photoresist film is set as k ₁ to form the photomask pattern. A photoresist process characterized in that the exposure energy dose for forming a faithful photoresist pattern is determined using the relationship: Dose=T _TU [E _t +K ₁ (d ₀ − t ₀ )]η〓 ^-1 Exposure energy determination method.