JPH0346968B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a method for determining an exposure dose in a photoresist process, and particularly to a method for determining an exposure dose suitable for a miniaturized photoresist process.

[Prior Art] FIG. 1 shows a schematic diagram of an exposure apparatus used in a photoresist process.

Light emitted from a light source 1 is condensed by a condenser lens 2, passes through a mask 4, is further condensed by a projection lens 5, and is projected onto a resist film 6 for exposure.

The silicon wafer has a structure in which a first base film 8 , a second base film 7 , and a resist film 6 are stacked on a silicon substrate 9 .

The exposure time is determined by opening and closing the shutter 3 using the exposure time adjustment device 10.

[Problems to be Solved by the Invention] Conventionally, the exposure time has been manually set by humans through trial and error based on experience. For this reason, there were drawbacks such as large errors, large variations in resist line width after wafer development, and low product yield.

An object of the present invention is to enable a computer to determine the exposure amount in a photoresist process, thereby reducing deviations from optimal exposure conditions and enabling photoresist process control with a high product yield. The purpose is to provide a method.

[Means for Solving the Problems] In order to achieve the above object, according to the present invention, the exposure energy (Dose) required for exposing a mask pattern to a resist is calculated for a specific resist and development conditions, and A method for determining an exposure dose in a photoresist process is provided, which determines at least one of an exposure intensity and an exposure time necessary for exposing a mask pattern based on energy (Dose).

Here, the exposure energy (Dose) is determined as follows.

In other words, uniform irradiation critical exposure energy E _TU represents the minimum exposure energy required to completely remove the resist when uniform light is irradiated onto the resist surface, and η representing the relative light intensity at the line edge part of the resist located in the area, the exposure energy (Dose) when the above relative light intensity η is assumed to be 1.0, and the above uniform irradiation critical exposure energy E _TU
and the logarithm of the above relative light intensity _η .
n, which represents the rate of change in the logarithm log(Dose・η) of the product of exposure energy (Dose) and relative light intensity η with respect to a change in logη, is determined in advance for a specific resist and development conditions, and based on this, Exposure energy (Dose) for that particular resist is calculated using the relationship Dose=E _TU ·C ₁ ·η ^n-1 .

[Function] The line width of the resist line formed in the photoresist process varies depending on various factors, but among various parameters, the relative light intensity of the resist line edge and the amount of light irradiated to the resist line edge are determined. It has become clear that there is a strong correlation between exposure energy and exposure energy. The present invention determines the exposure amount for the resist line edge portion based on this characteristic. This controls the exposure energy applied to the photoresist,
The resist line width can be formed with high precision relative to the design value.

When a photoresist is uniformly applied to a silicon wafer, irradiated with uniform light, and then developed, the relationship between the irradiated exposure energy and the residual thickness of the resist is as follows.
It will look like Figure 2. That is, the relationship is such that the greater the irradiation exposure energy, the smaller the residual thickness of the resist. From this characteristic, the exposure energy E _TU at which the resist residual thickness becomes zero can be obtained.
This exposure energy E _TU represents the minimum exposure energy required to completely remove the resist when the resist surface is irradiated with uniform light. This is referred to herein as the uniform exposure critical exposure energy _ETU .

On the other hand, when resist lines are formed by projecting a mask pattern onto the photoresist surface,
A resist shape shown as 301 in FIG. 3 is obtained.
In this case, the edge portions A and B of the resist line 301 are the boundaries between the remaining resist and the area from which the resist has been completely removed. It can be considered that the minimum energy necessary for irradiation, that is, the edge portion irradiation critical exposure energy E _t ' is irradiated.

Here, the edge portion irradiation critical exposure energy E _t ′ is
This is the critical exposure energy at the resist line edge portion during mask pattern exposure, and is different from the uniform irradiation critical exposure energy E _TU when the resist surface is irradiated with uniform light.

FIG. 4 shows the exposure time dependence of the edge irradiation critical exposure energy when a mask pattern is exposed on the photoresist surface. The graph shown in the figure was obtained by experimentally determining the change in edge portion irradiation critical exposure energy E _t ' with respect to the exposure time to the resist, using the intensity of the irradiation light to the resist as a parameter.

As can be seen from the figure, as the exposure time increases, the critical exposure energy for irradiating the edge portion decreases. Furthermore, if the light intensity of the light source is changed to change the intensity of the irradiation light on the resist, the critical exposure energy for irradiating the edge portion will change even for the same exposure time, as shown in characteristic curves 41, 42, and 43. Become. Note that the intensity of the irradiated light increases in the order of the characteristic curves 41, 42, and 43.

Next, if we calculate the critical exposure energy for edge irradiation with respect to the relative light intensity η of the edge of the resist line formed after resist development, it will be as shown in FIG. 5A, which is independent of the irradiation light intensity and exposure time,
It can be represented by two curves.

The graph of FIG. 5A is obtained as follows.

First, for example, a photoresist is applied to each of a plurality of silicon substrates to a thickness of, for example, 1 μm. After each of these photoresists is uniformly irradiated with exposure energies of different magnitudes, they are developed. Here, a photoresist with a film thickness of zero after development is selected, and among the exposure energies irradiated thereon, the smallest energy is determined as the uniform irradiation critical exposure energy E _TU .

Next, exposure is performed at various exposure energies Dos using a mask pattern consisting of line portions and space portions. After developing them, the dimensions of the resulting resist lines are measured for each exposure energy Dos.

Also, the light intensity distribution of the mask projection image at this time is determined. This light intensity distribution can be determined by measurement or calculation. Here, we will show an example of finding it by calculation. As a calculation formula, for example, the following formula is used. Here, the light intensity distribution η(Xi) at the position Xi is determined with the width direction of the mask as the X axis and the origin as 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 ₁ ) A ^* (X ₂ ) dX ₁ dX ₂ ...(1) 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
...(1b) 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 (1b) when the focus at the time of exposure is correct. . 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(−0.5ivρ2)ρdρ……(1c) u=(2π/λ)NA {(X ₁ −Xi) ² } ^1/2 v=(2π/λ)(NA) ² Z Here, J ₀ : Bessel function of the first kind and zero order ρ : Bessel function parameter Z : Defocus (Defocus) For these calculation formulas, refer to 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.

From these η and the exposure energy Dos corresponding to the resist line dimension for each η, the edge portion irradiation critical exposure energy E _t ′ is determined, and the dependence of this E _t ′ on η is determined. FIG. 5A is obtained by plotting the edge irradiation critical exposure energy E _t ' against this η.

By taking the ratio of the edge portion irradiation critical exposure energy E _t ′ and the uniform irradiation critical exposure energy E _TU , the relative critical exposure energy E _t ^* is obtained as shown in equation (2).

E _t ^* =E _t '/E _TU (2) Next, the data of E _t ^* with respect to the above-mentioned relative light intensity η is logarithmized and plotted as shown in FIG. 5B.

A straight line is fitted to this plotted point, and its slope n and the intercept logC ₁ of the vertical axis at the point where the relative light intensity η is 1.0 are determined. The following equation is obtained from this n and logC ₁ .

logE _t ^* =logC ₁ +nlogη (3) Therefore, the relative critical exposure energy E _t ^* can be experimentally obtained from the following equation using the line edge relative light intensity η as a parameter.

E _t ^* =C ₁ ·η _o (4) Here, C ₁ and n are constants determined by the type of resist and the characteristics of the developer.

Next, a formula for calculating the exposure energy dose for forming the line width after development as the designed value is derived.

Equation (5) holds from equations (2) and (4).

E _t ′=E _TU・C ₁・η ⁿ ……(5) Figure 6 shows the exposure energy dose irradiated to the photomask when exposing the photomask pattern to the resist surface, the relative light intensity distribution on the resist surface,
The exposure energy distribution to the resist is shown.

If the relative light intensity on the photoresist at a point corresponding to the line edge of the photomask is η, the exposure energy E _Tl at that point is the product of the exposure energy Dose applied to the photomask shown in FIG. 6 and the relative light intensity η. and is expressed by equation (6).

E _Tl = Dose·η (6) If the exposure energy is adjusted so that E _Tl is equal to E _t ', the line width can be formed as designed. (5)
Substituting into equation (6), equation (7) is obtained.

E _TU・C ₁・η ⁿ ＝Dose・η ...(7) From equation (7), the required exposure energy Dose is:
It is expressed as equation (8).

Dose=E _TU・C ₁・η _o-1 ...(8) By irradiating the resist with the exposure energy Dose calculated from equation (8) and developing it, it is possible to form resist lines according to the designed value. can.
That is, based on this exposure energy Dose,
By setting the exposure time or exposure intensity,
A desired resist line can be formed.

[Examples] Hereinafter, the present invention will be explained in more detail with reference to specific examples.

FIG. 7 shows the configuration of photoresist process control to which the first embodiment of the exposure amount determining method of the present invention is applied.

The photoresist process to which this embodiment is applied includes a resist coating process 14 in which a photoresist is spin-coated onto a semiconductor wafer using, for example, a spinner, and a photomask pattern is projected and exposed onto the resist-coated wafer using, for example, a mask aligner. Mask pattern exposure process 18
, an exposure control process 15 that controls the light source of the mask aligner to control the irradiation light intensity or exposure time to the photomask, and a control calculation process 20 that implements the exposure amount determination method of this embodiment.

As the mask aligner used in the mask pattern exposure process 18, for example, an exposure apparatus as shown in FIG. 1 can be used.

The control calculation process 20 calculates the exposure energy (Dose) necessary for exposing the mask pattern to the resist for a specific resist and development conditions, and calculates the exposure energy (Dose) necessary for exposing the mask pattern based on this exposure energy (Dose). determining at least one of intensity and exposure time;

In addition, in this embodiment, this control calculation process 2
0, the uniform irradiation critical exposure energy is used to measure the minimum exposure energy required for the resist to be completely developed and removed when the resist surface is irradiated with uniform light, that is, the uniform irradiation critical exposure energy E _TU . Measurement process (hereinafter also referred to as E _TU measurement process) 16 and the coefficient in the general formula for relative critical exposure energy E _t ^* shown in equation (4)
Coefficient measurement process to measure C ₁ , n (hereinafter referred to as C ₁ ,
It is also called n measurement process. ) 17 and a defocus amount measurement process 19 for measuring the defocus amount of the mask pattern image projected onto the resist surface are executed.

In the above-mentioned differential focus amount measurement process 19, for example, the distance between the projection lens (not shown) of the mask aligner and the resist surface is measured by the differential pressure of the fluid, etc., and the deviation from the focus position of the mask aligner is determined. , the amount of defocus is measured.

The control calculation process 20 calculates the exposure energy (Dose) necessary for exposing the mask pattern to the resist based on the relative light intensity η at the line edge portion of the resist and the measured values E _TU , C ₁ and n using the following equation. Calculate by

Dose=E _TU・C ₁・η ^n-1 ...(8) The control calculation process 20 calculates the exposure energy Dose
Based on this, at least one of the exposure intensity and the exposure time, which determine the amount of exposure necessary for exposing the mask pattern, is determined.

Further, the control calculation process 20 is performed using a computer. This computer includes, for example, a central processing unit (CPU) that executes various calculations, etc., as well as a memory, an interface, etc. that stores its operating programs, various data, and the results of the calculations.

The exposure control process 15 controls at least one of the exposure intensity and the exposure time necessary for exposing the mask pattern, based on at least one of the exposure intensity and the exposure time determined by the control calculation process 20.

Next, the operation of this embodiment will be explained.

The E _TU measurement process 16 is a process of measuring uniform irradiation critical exposure energy E _TU obtained by irradiating a resist surface with uniform light and developing it. The obtained measured values are stored in the memory of the computer that executes the control calculation process 20, or the like.

In the C ₁ , n measurement process 17, a plurality of resist films are developed by changing the exposure energy, and the resist line width after development is measured.

Next, the relative light intensity η at the resist line edge portion is calculated using the above equation (1), and
The dependence of the critical exposure energy shown in the figure on the relative light intensity of the line edge portion is determined. Furthermore, the coefficient C ₁ in the general formula for relative critical exposure energy shown in formula (4),
Find n using the least squares method. Here, the relative critical exposure energy E _t ^* is calculated by dividing the critical exposure energy E _t ′ as shown in equation (2) by the uniform irradiation critical exposure energy E _TU measured by the uniform irradiation critical exposure energy measurement process 16. It can be obtained as something.

The above operations are performed while changing the amount of defocus, and the coefficient C ₁ for each amount of defocus is determined.
Find n.

Next, a mask pattern is irradiated onto the resist surface. In this case, a defocus amount measurement process 19 measures the defocus amount of the mask pattern image on the resist film. In the control calculation process 20, the required exposure energy Dose is calculated by substituting C ₁ , n, η, and E _TU corresponding to the values into equation (8). Furthermore, in the control calculation process 20, the calculated exposure energy
From the Dose, the exposure amount, for example, the exposure time is determined.

This exposure amount is given to the exposure control process 15, and the exposure in the mask pattern exposure process is controlled.

FIG. 8 shows a flowchart showing the exposure amount determination method of this embodiment.

First, in step 21, the uniform irradiation critical exposure energy E _TU is measured, and then in step 22, the coefficients C ₁ and n in the general equation shown in equation (2) are measured. Next, in step 23, the amount of defocus is measured. Subsequently, in step 24, the relative light intensity η at the line edge portion is determined. These are performed prior to determining the exposure energy.

In step 25, using these values, the exposure energy Dose required to form the resist line width as the designed value is calculated using equation (8).

Next, in step 26, the exposure energy Dose is divided by the exposure irradiation intensity I to calculate the exposure time.
Set the exposure time. This setting allows
Actual exposure is performed. (Step 27). That is, in the mask pattern exposure process 18,
The light source of the mask aligner used in this process is set to the exposure irradiation intensity I, and the photoresist is exposed to light under the control of the exposure control process 15 so that irradiation is performed for the exposure time set above (step 27). .

Thereafter, the exposed photoresist is developed (step 28).

According to this embodiment, since the amount of defocus can be measured, C ₁ , η, and n can be set precisely in correspondence with the amount of defocus. As a result, the exposure energy
This has the effect of increasing the accuracy of dose calculation and allowing precise control of resist line width.

Next, a second embodiment of the exposure amount determining method of the present invention will be described.

FIG. 9 shows a flowchart for determining the exposure amount in the second embodiment.

In this embodiment, the exposure time setting in step 26 is
This embodiment differs from the embodiment shown in FIG. 8 in that the setting of the irradiation intensity is changed over, as indicated by step 26'.

In this example, by dividing the required exposure energy Dose obtained in step 25 by the exposure time,
After calculating the necessary exposure intensity and setting the irradiation intensity to a necessary value in the exposure control process 15 shown in FIG. 7, the photoresist is exposed in the mask pattern exposure process 18, and then development is performed. .

According to this embodiment, since there is no need to precisely change the exposure time, there is an effect that the exposure control process 15 can be simplified.

Next, a third embodiment of the exposure amount determining method of the present invention will be described.

FIG. 10 shows the configuration of photo process control to which the exposure amount determining method of this embodiment is applied.

In this embodiment, the defocus amount measurement process 19
This embodiment differs from the embodiment shown in FIG. 7 in that the process is switched to a relative light intensity measurement process 30 at the line edge.

In this embodiment, the uniform irradiation critical exposure energy E _TU is determined in the uniform irradiation critical exposure energy measurement process 16, similar to the embodiment shown in FIG. Next, in the coefficient measurement process 17, the coefficient C ₁ ,
Find n.

Next, in the relative light intensity measurement process 30,
The relative light intensity η of a point on the resist surface corresponding to the line edge portion of the photomask is measured. The above is
This is performed prior to execution of the control calculation process 20.

By substituting the above measurement results into equation (8), the exposure energy Dose required to form the resist line width as the designed value is calculated. C ₁ used in this calculation,
For n, the average value of the values measured while changing the amount of defocus is used.

Exposure control process 15 is performed by dividing the exposure energy Dose by the exposure irradiation intensity I to find the exposure time texp.
is set to this exposure time, exposed, and the resist is developed.

FIG. 11 shows a flowchart of resist line width control according to this embodiment.

The uniform irradiation critical exposure energy E _TU is measured (step 21), and the parameters C ₁ and n are measured (step 22). Next, in the relative light intensity measurement process 30, the relative light intensity η at the line edge portion is
(Step 31).

By substituting the above measurement results into equation (8), the required exposure energy amount Dose is calculated (step 25). Further, the exposure time is obtained by dividing the exposure energy Dose by the exposure irradiation intensity I (step 26).

Next, using this exposure time, the exposure time of the mask pattern exposure process 18 is controlled in the same manner as the procedure shown in FIG. 8 described above, and the photoresist is exposed.

In this example, the defocus amount measurement process 1
Since the relative light intensity measurement process 30 is used instead of step 9, the measurement becomes simpler and the measurement time becomes shorter.

Next, a fourth embodiment of the exposure amount determining method of the present invention will be described.

FIG. 12 shows the configuration of photoresist process control to which the fourth embodiment is applied.

This embodiment differs from the embodiment shown in FIG. 10 in that the relative light intensity measurement process 30 is omitted.

The operation of this embodiment will be explained below with reference to the flowchart shown in FIG.

First, the uniform irradiation critical exposure energy E _TU is measured by the uniform irradiation critical exposure energy measurement process 16 (step 21). Thereafter, the coefficients C ₁ and n in general formula 8 are measured by the coefficient measurement process 17 (step 22). _C1 and n are constants determined only by the resist, and do not change even if the amount of defocus changes.

The relative light intensity η at the line edge portion may not be directly measurable due to the lack of a measuring instrument with high resolution. In this case, .eta. in the case of 1 .mu.m, which is the average value of the actual defocus amount variation range of 0 to 2 .mu.m in the photoresist process, is calculated and used according to the above equation (1).

By substituting E _TU , C ₁ , η, and n obtained in this way into equation (8), the exposure energy dose required to form the resist line width according to the designed value is calculated (step 25).

Next, the exposure control process 1 obtains the exposure time by dividing the exposure energy Dose by the exposure irradiation intensity I.
5, and under the control of the exposure control process 15, the photoresist is exposed in the mask pattern exposure process 18 and then developed (steps 27 and 28).

In this embodiment, the relative light intensity measurement process can be omitted, which has the effect of simplifying the apparatus.

[Effects of the Invention] As explained above, according to the present invention, the exposure amount can be determined by a computer, thereby reducing the deviation from the optimum exposure conditions and realizing a photoresist process with a high product yield. There is an effect that can be done.

[Brief explanation of drawings]

Figure 1 is a schematic diagram of the exposure equipment used in the photoresist process, Figure 2 is a graph showing the relationship between exposure energy and resist residual thickness, Figure 3 is an explanatory diagram showing the resist line shape, and Figure 4 is the critical Graph showing exposure time dependence of exposure energy, 5th
Figure A is a graph showing the dependence of the critical exposure energy on the relative light intensity of the line edge portion, Figure 5B is a graph showing them in logarithm form, and Figure 6 is a graph showing the relative light intensity distribution and resist when exposing a photomask pattern to the resist surface. FIG. 7 is a block diagram showing the configuration of photoresist process control to which the first embodiment of the present invention is applied, and FIG. 8 is a diagram showing the exposure energy distribution on the surface. FIG. 9 is a flowchart for determining the exposure amount according to the second embodiment of the present invention. FIG. 10 is a block diagram showing the configuration of photoresist process control to which the third embodiment of the present invention is applied. FIG. 11 is a flowchart of resist line width control according to the third embodiment;
FIG. 12 is a block diagram showing the configuration of photoresist process control to which the fourth embodiment is applied;
The figure is a flowchart of resist line width control according to the fourth embodiment. 15...Exposure control process, 16...Uniform irradiation critical exposure energy measurement process, 17...Coefficient measurement process, 18...Mask pattern exposure process, 19...Defocus amount measurement process, 20
. . . Control calculation process, 30 . . . Relative light intensity measurement process.

Claims (1)

[Claims] 1. The exposure energy (Dose) required for exposing the mask pattern to the resist is calculated for a specific resist and specific development conditions, and based on this exposure energy (Dose), the exposure energy (Dose) required for exposing the mask pattern to the resist is calculated. An exposure amount determination method in a photoresist process that determines at least one of the required exposure intensity and exposure time, the minimum amount of exposure required to completely remove the resist when the resist surface is irradiated with uniform light. Uniform irradiation critical exposure energy E _TU representing the energy,
When exposing through a mask pattern, η represents the relative light intensity at the line edge part of the resist located at the edge part of the mask pattern, the exposure energy (Dose) when the above-mentioned relative light intensity η is assumed to be 1, and the above-mentioned uniformity. C ₁ representing the ratio to the irradiation critical exposure energy E _TU and the logarithm of the above relative light intensity η
n, which represents the rate of change in the logarithm log(Dose・η) of the product of exposure energy (Dose) and relative light intensity η, with respect to a change in logη is determined in advance for a specific resist and specific development conditions, and based on this, A method for determining an exposure amount in a photoresist process, characterized in that the exposure energy (Dose) for a particular resist is calculated using the relationship: Dose=E _TU・C ₁・η ^n-1 .