JPH021904A - Exposure of mask - Google Patents

Abstract

PURPOSE:To restrain the temperature rise of a mask or a pattern, etc., from occurring for reducing the high load due to thermal stress and the slip in a pattern by a method wherein the pattern is intermittently exposed to an irradiated element through the intermediary of the mask. CONSTITUTION:When the transient deformation process due to the thermal damage resultant from the exposure of a mask and an irradiated element is mathematically analyzed to divide the exposure time taug (t) e.g., into ten each of rectangular pulse rows and further to be intermittently exposed in the period taup longer than the pulse width DELTAtaug, the temperature rise per pulse is reduced to restrain the thermal stress and expansion resultant from the temperature rise from occurring. Through these procedures, the irregular deformation of a pattern on the mask e.g., in case of exposing to a wafer can be restrained from occurring to enhance the patterning precision.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a method for suppressing thermal damage to a mask and an irradiated object in order to form a highly accurate pattern.
In particular, the present invention relates to a method of suppressing thermal damage to a mask and an object to be irradiated by exposure using a pulse that can be approximated to a periodic rectangular wave in exposure technology.

[Conventional technology]

FIG. 6 shows the exposure time τ and the light power density F of the conventional mask exposure method using continuous irradiation. This is a graph showing which relationship. tl is the irradiation start time, and t2 is the irradiation end time. Light power density F.

and irradiation time τ. The exposure amount determined by is highly dependent on the sensitivity characteristics of the resist used. For example, when trying to obtain a predetermined pattern using a resist with low sensitivity, when the power density F0 is constant, the exposure time τ. need to be made longer. In this way, the exposure method for obtaining the appropriate exposure amount for the resist is a constant power density F as shown in FIG. There are many examples of continuous irradiation, such as those disclosed in Japanese Patent Laid-Open No. 60-207339.60-224226. Such an exposure method is commonly used in a photolithography process (lithography) of a semiconductor manufacturing method.

Pattern materials attached to masks, such as chromium and molybdenum silicide for photomasks, and gold, tungsten, or tungsten-titanium alloys for X-ray masks, have two effects on incident light: reflection and absorption. Show characteristics. However, with an X-ray mask, the reflected light is extremely small, and most of it does not transmit or absorb. Most of the absorbed light is converted into thermal energy. Also,
Resist pattern materials made of organic polymers also absorb light efficiently and easily generate heat.

Although it is desirable that the thermal conductivity of each mask pattern material and resist pattern material be as large as possible, there is no material that has completely infinite thermal conductivity. Therefore, the pattern material of a mask and the exposed portion of a resist become a heat source, inducing expansion due to temperature rise and affecting the dimensional accuracy of the pattern.

Next, a mathematical analysis of the influence of heat on pattern dimensional accuracy is performed on an unsteady-dimensional semi-infinite body, and a relational expression between the temperature field and thermal stress is derived. Although the actual phenomenon is unsteady and three-dimensional, the above model is sufficient for explanation using mathematical analysis in the sense that it facilitates understanding of the phenomenon.

FIG. 7 is a diagram showing a model of a one-dimensional semi-infinite body whose surface is heated. Here, the semi-infinite body is assumed to be the bulk of the pattern material of the mask, the resist, etc., and the surface has a uniform power density F. Assume that a heat flux of (W/li) is absorbed. Since this heat flux means surface heating, any heat source that can be approximated to such a heat source may be used, such as a high-pressure mercury lamp, laser beam, electron beam, ion beam, plasma, or X-ray. The equations governing the temperature field, the initial conditions, and the boundary conditions are expressed by the following equations (1), (2), and (3).
) is given by

...(1) T(z, o)=0 (t=o) ...(
2) T (2=0) ... (3) Here,
K, ρ, C and k are thermal conductivity, density, specific heat and thermal diffusivity, respectively. Furthermore, in the surface heating boundary condition equation (3), H(t) represents a Heaviside unit step function with respect to time. However, equation (3) is the uniform power density F at the continuous exposure time i1<'j<1:2. The heating process due to the heat flux of and F at t2<t. = 0. In addition, it is 12-11+. It is.

Since the heat conduction equation (1) is a linear partial differential equation and relates to a -dimensional semi-infinite field, an exact solution can be easily obtained using the Fourier transform method or the Laplace transform method.

First, we seek understanding using the Laplace transform method. Temperature T(z,
The Laplace transform of t) is defined by the following equation.

〒(z, s) = ta(T (z, t)) f'' -5t -.e T(z, t) dt ... (4) Also, using the differential of the Laplace transform, equation (1) can be When converted, an ordinary differential equation 2 as shown in equation (5) below is obtained.

Note that equation (6) is a defining equation for q.

From equations (5) and (6), the general solution is T(z, 5) −qz qz =C(s)e +02 (s)e (7). Here, if we use the natural boundary condition of 2→ω, then T(
Since Z, S) must converge, 02 (s)=C in equation (7).

The integral constant C1CS> can be obtained by Laplace transforming the boundary condition of equation (3) and substituting it into equation (7). Here, the Laplace transform of equation (3) becomes 9Z S .

Substituting equation (8) into equation (7) to find C1(s), we get:
...(5) becomes.

The special solution is (1) In the formula (9) Substituting the expression becomes.

-H(t-τ9 G here (Z.

G(z, -τg))...(14) is a Laplace transformation table, q...(10). Next, the shift law ξ”1(e
-chi8〒(Z, 5)) -H(t -τc+) T (z -t rg)
...Using (11), equation (10) is inversely transformed back to the original function. Here, if we set -qz G(Z, 5)-- q...(12), then. 7G(z, s>=G(z, t) ・ (13
), so the original function of equation (10) is as follows. J3 Equations (16) and (17) are the defining equations of the error function.

Next, the formulas for displacement and stress caused by thermal expansion derived from the theory of elastic bodies are shown. The stress generated within an object must satisfy a differential equation of balance. When rectangular coordinates x, y, and z are defined inside an object and a microhexahedron is imagined with surfaces parallel to each coordinate plane, the balance of stress and force occurring on the surface of the hexahedron is given by the following differential equation. Note that σ
,σ,.

σ , τ τ τ , τ τ , τ are
xy'xz' yx yz
'zx zy force component.

ε , ε , ε and shear strain γ γ , γ and x
y z xy' xz yz
There is a relationship between the displacement and the following equations (19) and (20).

u 8w ax ay az ax az ax ay az When an object is deformed, each point within the object moves. X.

Displacements in the y and z directions are represented by U, V, and W. Vertical strain γxy
= , 9u av □+□ ay ax aLI aw γyz""-;-F"+F1;- Also, since thermal expansion is uniform in all directions in an isotropic object, the resulting strain If α is the coefficient of linear expansion, then ε8=ε, = ε2−αT.When this thermal expansion is restricted, thermal stress is generated, so the strain of the object is the sum of the strain due to stress and the strain due to thermal expansion. The following equation (21) is obtained.

ε = - (σ8 - ν (ay to σ2)) + αTE ε so - (σy - ν (σ8 + σ, )) + αTε = - (
σ2−ν(σ8+σy))+αTE (21). Here, F and ν are Young's modulus and Poisson's ratio, respectively. Since shear strain is unrelated to normal stress, the following equation (22) is obtained, where G is the transverse elastic modulus.

τ8. =Gγxy τxz”'γxz −(22)
τy7=Gγy2. Here, using the relationship 2G(1+ν)=E,
When stress is expressed in terms of strain, it becomes as shown in equation (23) below. In addition, the following formula (24) is e. This is the definition formula.

ν 1 +ν 1-2ν ax The second and third equations are also expressed in a similar form...(23) eo−ε8+εy+ε2 (24) where e. Since it is equal to the volume change of a cube, it is called the volumetric expansion coefficient. By substituting the relationships between stress and strain and strain and displacement into the stress balance equation, an equation regarding displacement can be obtained. That is,
Differentiating the first equation of equation (23) with respect to X, the first equation of equation (18)
By substituting into the equation and using equations (19), (20), and (21), the following equation (25) is obtained.

Shishishi -- ax ay az 1-2ν,
If 9x is true, the following equation (27) is obtained. U, V, W
is given by the following equation (28), and Ω is the thermoelastic potential.

1-2ν ax 1 +ν aΩ U ; α □ 1-ν ax 2 (1+ν) 2ν T α□ , 9x 2ν ay 1-2ν ay 1-2ν 2 (1+ν) az 1-2ν T α□ θ2 1-ν ay 1tν aΩ W(α□ 1−ν az Equation (27) is a displacement equation, and the displacement in an elastic body must satisfy this equation. The solution to the displacement equation is the normal equation with the right-hand side set to zero. It is the sum of the solution and the special solution of the displacement equation.The relationship shown in the following equation (29) holds between the thermoelastic potential Ω and the temperature T.

2Ω −T (29) Using the relationship between displacement and strain, and strain and stress, (23) (28)
From the equation, the following equation (30) is obtained.

Eα a2Ω (-T) 0゛=1-ν ax2 σ2= (-T) 1-ν az2 To calculate the thermal stress, first find the temperature distribution, and then calculate (2
If Ω is determined from equation (9), the displacement and stress caused by thermal expansion can be derived from equation (28) and (30).

The temperature field model assumes a one-dimensional semi-infinite body, so the temperature T
is a function of depth direction 2 and time t. The thermoelastic potential Ω generated by this temperature field is calculated from equation (29) as follows (
31).

It can be seen that compressive stress proportional to temperature always acts in the direction horizontal to the heated surface. Thermal expansion fiW in two directions (
Z, t> becomes the following equation (33) from equation (28).

...(33) Based on the above calculation results, the temperature of Cr (chromium) material -
Simulate the climb. Table 1 below shows the physical property values of the Cr material in this simulator.

The generated thermal stress is expressed by the following equation (32) from equation (30).

Table 1 FIG. 8 is a graph showing the relationship between the temperature increase of the Cr material and the exposure time, in which the horizontal axis represents the exposure time and the vertical axis represents the temperature rise of the Cr material.

FIG. 9 is a diagram showing the temperature rise distribution in the depth direction when the exposure time is 3 Q Q 1llsec, where the horizontal axis represents the distance from the surface to the inside of the material, and the vertical axis represents the temperature rise.

FIG. 10 is a diagram showing the relationship between the amount of expansion on the surface of the Cr material and the exposure time, with the horizontal axis representing the exposure time and the vertical axis representing the amount of expansion on the surface of the Cr material.

FIG. 11 is a diagram showing the distribution of the expansion amount in the depth direction during an exposure time of 300 m5ec, where the horizontal axis represents the depth from the surface to the inside of the material, and the vertical axis represents the expansion amount.

In the following simulations, no measures were taken to cool the mask or the irradiated object, and an adiabatic system was used that completely relied on the heat conduction of the material. From this result, for example, when a heat flux with a power density of 170 W/ri is absorbed, the exposure time on the surface of the Or material is 3Q Q ll5eC, and the temperature rises by 30°C, and the amount of expansion at the surface increases to 700r+n+. , and calculated that the compressive stress at the surface is approximately 64
It turns out that it reaches as much as 0 K9/ci. In addition,
When the exposure time is 3001 seconds or more, the supply of heat flux stops, so FIG.

FIG. 10 also shows the temperature change and the expansion amount change during the cooling process.

(Problem to be Solved by the Invention) Since the conventional mask exposure method is configured as described above, the irradiated object with finite thermal conductivity, such as a photomask or pattern, is exposed as shown in the above simulation.・Sea urchin exposure tends to cause the temperature to rise.As a result, the irradiated object is subjected to a high load due to its thermal stress, and furthermore, the thermal expansion causes local pattern misalignment, resulting in problems such as the inability to perform accurate patterning. was there.

This invention was made in order to solve the above-mentioned problems.It suppresses the temperature rise of the irradiated object due to exposure, and reduces, for example, high loads due to thermal stress and pattern deviation due to thermal expansion. The purpose is to obtain a method.

(Means for Solving the Problems) The mask exposure method according to the present invention is characterized by intermittent exposure.

[Effect]

The intermittent exposure in this invention suppresses the temperature rise of the irradiated object, such as a mask or a pattern.

〔Example〕

An embodiment of the present invention will be described below with reference to the drawings. 1st
The figure shows the power density F of the mask exposure method according to an embodiment of the present invention. It is a graph showing the relationship between the exposure time τ, (pulse width Δτ,), and the exposure time τ.

Power density F. The pulse width Δτ of the illumination pulse has the total exposure time τ and the number of rectangular pulses (l
If there are QN pieces, then C (3
4) Given by Eq.

Moreover, the period τ of the pulse train is τ > 2Δτ. degree p
Let it be the value of ρ.

The boundary condition for surface heating by irradiation with such a pulse train is given by the following equation (35).

-H(t-Δτ -nτpN a (z-0)...(35) As mentioned above (1
) is solved using the boundary condition of equation (35), the temperature change due to the periodic rectangular pulse train becomes as shown in equation (36) below.

xG(z, t-nτp) -H(-Δτ-nτp) Given. The amount of thermal stress expansion generated by this exposure method was described above (3
2) is obtained by substituting equation (36) into equation (33).

A simulation is performed using equations (36) and equations derived using equations (36) below.

Figure 2 shows the total exposure time τ. is 300 m5ec,
This is divided into 10 equal parts, and the period of the pulse train is τ, -1QsOc.

Pulse width Δτg-30m5ec, power density Fo-17
It is a graph showing the relationship between the temperature increase on the surface of a Cr material and the exposure time at 0 W/m.

FIG. 3 is a graph showing the temperature distribution in the depth direction inside the material under the same conditions as above.

FIG. 4 is a graph showing changes in the amount of expansion of the material surface due to a rectangular pulse train, where the horizontal axis is the exposure time and the vertical axis is the amount of expansion.

FIG. 5 is a graph showing the distribution of the expansion amount in the depth direction inside the material due to the rectangular pulse train, where the horizontal axis is the depth from the material surface to the inside, and the vertical axis is the expansion amount.

From the above simulation results, the exposure time r =
When 30011 sec is divided into pulse widths Δrg-aomsec and 10 pulses are exposed, the temperature rise per pulse is 10°C. Even with 10 pulses, the maximum temperature is 10
The cumulative temperature increase on the surface is only a few degrees Celsius.
5 It's stuck. Further, the amount of surface expansion is suppressed to 1100n or less. Therefore, according to the exposure method of the present invention, the temperature rise is suppressed to 1/3 and the amount of expansion is suppressed to 1/7 compared to the conventional method.

As mentioned above, we mathematically analyzed the transient deformation process due to thermal damage caused by exposure of the mask and the irradiated object, for example, based on the exposure time. is divided into 10 rectangular pulse trains, and the pulse width Δ
Period τ longer than τ. When exposed intermittently, the temperature rise per pulse is reduced, and the thermal stress and expansion amount accompanying the temperature rise are suppressed. In this way, unsteady deformation of the pattern on the mask and the resist pattern during, for example, exposure of the wafer can be suppressed, and patterning accuracy is improved.

In addition, in this actual droplet example, one-dimensional heat conduction in a semi-infinite body was explained, but thermal stress occurs along with the temperature field and a similar phenomenon occurs in three-dimensional heat conduction, so the mask exposure method of the present invention A similar effect can be achieved by applying. Further, in the above embodiment, a Cr material has been described, but molybdenum silinide or an organic polymer film may also be used, and the same effects as in the above embodiment can be obtained.

〔Effect of the invention〕

As described above, according to the present invention, intermittent exposure suppresses the upper temperature limit of the irradiated object, such as a mask or pattern, so that, for example, a mask that reduces high loads due to thermal stress and pattern displacement due to thermal expansion, etc. exposure method can be obtained.

[Brief explanation of the drawing]

FIG. 1 is a graph showing the relationship between the exposure time and power density of the mask exposure method according to an embodiment of the present invention, and FIG. 2 is a graph showing the relationship between the exposure time and power density of the mask exposure method shown in FIG.
Figure 3 is a graph showing the relationship between depth and temperature rise using the mask exposure method shown in Figures 2 and 4. Figure 4 is a graph showing the relationship between depth and temperature rise using the mask exposure method shown in Figure 2. A graph showing the relationship between time and expansion amount, Figure 5 is the second
Figure 6 is a graph showing the relationship between depth and expansion amount according to the mask exposure method shown in Figure 6. Figure 6 is a graph showing the relationship between exposure time and power density for the conventional mask exposure method. Figure 7 is a model of surface heating. Figure 8 is a graph showing the relationship between exposure time and temperature rise due to the mask exposure method shown in Figure 6, and Figure 9 is a graph showing the relationship between depth and temperature rise due to the mask exposure method shown in Figure 6. FIG. 10 is a graph showing the relationship between the exposure time and the expansion amount according to the mask exposure method shown in FIG. 6, and FIG. 11 is a graph showing the relationship between the depth and expansion amount according to the mask exposure method shown in FIG. 6. This is a graph showing the relationship between. In the figure, Fo is the power density, Δτ. is the pulse width. Note that the same reference numerals in each figure indicate the same or corresponding parts.

Claims (1)

[Claims] (1) A method for exposing a pattern onto an object to be irradiated through a mask, the method comprising: performing the exposure intermittently.