JPH0462915A - Resist coating process - Google Patents

Abstract

PURPOSE:To make the highly precise resist film thickness control feasible by a method wherein the formulas quantitatively interpreting the dependence of a resist film thickness (h) upon the relative humidity H are followed. CONSTITUTION:When the humidity dependence of film thickness in the coating process is represented by the formula [1], the relative humidity is highly set up within the range of 35-60% to perform the spin coating process with a resist solution. Furthermore, when the humidity dependence of the resist film thickness is represented by the formula [2], the relative humidity H is set up within the range of 35-60% to perform the spin coating process with the resist solution.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a resist coating method, and particularly to a method for suppressing variations in resist film thickness.

[Invention (already required)]

The present invention derives a method for quantitatively interpreting the dependence of resist film thickness on relative humidity H based on classical statistical mechanics or empirical statistical mechanics, and calculates lnh and e n (100-
H) or j! n h and 12 n ((100-H
)/H) is in a linear relationship, making it possible to control the resist film thickness with high precision.

[21 [Prior Art] As a method for applying a resist solution onto a substrate such as a semiconductor wafer, a spin coating method has been widely applied.

It is phenomenologically known that the thickness of the coating film obtained in this manner (hereinafter referred to as resist film thickness) varies depending on temperature and humidity. Regarding temperature dependence, the present inventor previously provided a quantitative interpretation in Japanese Patent Application No. 2-67276, and based on this interpretation, disclosed a resist coating method that can minimize the influence of temperature. As I said. On the other hand, with regard to humidity, it is empirically known that a 1% change can cause a change in resist film thickness of 10 to 20 people. If the thickness of the resist film (especially photoresist) is non-uniform within the wafer surface, uneven sensitivity to exposure light will occur and line width controllability will deteriorate. This process is carried out in a resist coating device called a temperature control coater, which can control the temperature of the rotating means and the humidity of the atmosphere.

[Problem to be solved by the invention]

By the way, the design rules for semiconductor devices are becoming finer year by year, and in recent years, processing from the submicron level to the quarter micron level has been discussed. As the exposure wavelength for resist films becomes shorter as design rules become finer, the influence of variations in resist film thickness on line width becomes more and more significant.

For this reason, there is a need for a method of controlling resist film thickness with higher precision than ever before. For example, 0.35μm
The permissible range of variation in resist film thickness according to the rules is only ±25 people. However, the accuracy of humidity control using a conventional temperature control coater is about ±2%, and with such accuracy it is difficult to keep the resist film thickness within the above-mentioned variation tolerance range. Therefore, in order to respond to future miniaturization of design rules, the influence of humidity on resist film thickness must first be interpreted quantitatively, and any control method can be used to minimize variations in resist film thickness. It is necessary to understand.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to quantitatively interpret the humidity dependence of resist film thickness and provide a resist coating method that allows highly accurate control of resist film thickness based on this interpretation.

[Means to solve the problem]

In order to achieve the above-mentioned object, the present inventor conducted intensive studies, and based on a certain assumption, treats water molecules in the coating atmosphere and solvent molecules contained in the resist solution as the same molecule. In fact, when the interaction with solvent molecules is relatively weak, the entropy change due to solvent evaporation is analyzed according to classical statistical mechanics, and when the interaction is relatively strong, it is analyzed according to empirical statistical mechanics. We found that a theoretical formula that can explain well can be derived.

The present invention was completed based on the above-mentioned findings.

That is, in the resist coating method according to the first aspect of the present invention, the humidity dependence of the resist film thickness in spin coating is expressed by the following formula [11% formula %] [1] [However, in the formula, the resist film thickness, T is temperature (K), H
is relative humidity (%), to 33. 16. 1. is a constant. ], the resist solution is spin-coated with the relative humidity H set to less than 35% or higher than 60%.

Furthermore, in the resist coating method according to the second aspect of the present invention, the humidity dependence of the resist film thickness in spin coating is expressed by the following formula [21% formula %)] [21 is temperature (K), H
is relative humidity (%), 5. 18. 2° is a constant. ] When expressed as follows, it is characterized in that the relative humidity H is set in the range of 35 to 60% and the resis-me solution is spin-coated.

[Effect]

Formula [1] expressing the dependence of resist film thickness on relative humidity H
was derived from an analysis of entropy changes due to evaporation of solvent molecules using classical statistical mechanics for a system in which the interaction between water molecules in the coating atmosphere and solvent molecules in the resist solution is relatively small. Such a system is
This is achieved when the relative humidity H is less than 35% or higher than 60%. As is clear from this 2[11, there is a linear relationship between in h on the left side and ln (100-H) on the third term on the right side.

Moreover, as can be seen from the fact that the temperature T is included in the second term on the right side, the relative humidity I4 and the temperature T can be treated as independent variables.

Furthermore, equation [21] was derived as a result of analyzing the entropy change due to evaporation of solvent molecules using empirical statistical mechanics for a system in which the interaction between water molecules in the coating atmosphere and solvent molecules in the resist solution is relatively large. It is something that

Such a system is realized when the relative humidity H is between 35 and 60%. As is clear from this equation [21, 1 on the left side
．． n h and the third term on the right side, 42 n ((100-H)/
There is a linear relationship with Hl. Also, as in the case of equation [11], relative humidity H and temperature T are independent variables.

In either equation, the resist film thickness and relative humidity H are quantitatively expressed by a relatively simple relationship. Therefore, if control is performed based on equation 11) or equation 121 depending on the relative humidity H in the coating atmosphere, the resist film thickness can be precisely and easily controlled.

(Example) Equation [11 and equation [11] expressing the humidity dependence of resist film thickness
21 is the following formula [201% formula % [20] which expresses the temperature dependence of the resist film thickness that was previously clarified by the present inventor [wherein is the resist film thickness and Δeh is the latent heat of the resist solution] , R is a gas constant, A is a state function representing affinity,
τ is the number of time points, t is the application time, Ev is the flow activation energy, and T is the temperature. 2. to 13 to 3. is a constant. ] It was derived by adding further consideration to.

Therefore, in this specification, the derivation of the above formula [201] will be first described, and then the derivation of the formula [11] and the derivation of the formula [2] based on this will be explained in order.

A-1 ■ Karitatsu λ1 edition This induction is performed according to the following procedure.

(A-1) Derivation of the relational expression between resist film thickness and viscosity (A-2
) Derivation of the relational expression between temperature and viscosity (A-3) Derivation of the relational expression between resist film thickness and temperature Note that in the process of deriving equation [20], constant terms that are not directly related to the discussion are used to simplify the mathematical expression. from time to time.

I organized it using 14 symbols for , h, 2, and so on.

8-1) Resist The resist solution of and is a polymer solution and is a non-Newtonian fluid that does not follow Newton's law of viscosity.

Non-Newtonian fluids have a property called pseudoplasticity, in which the viscosity η decreases as the shear stress τ increases, and the shear stress τ
, and the deviation speed (θV/θ2 described later) do not have a linear relationship. Furthermore, resist solutions also have a property called thixotropy, in which the viscosity changes over time under stress. As described above, the behavior of the resist solution is extremely complex.

However, when the shear stress τ5 is very large or very small, the non-Newtonian fluid begins to exhibit behavior similar to a Newtonian fluid. In particular, when applying the resist solution by spin coating, high speed rotation of about 4000 rpm is performed, so the shear stress τ is considered to be very large. Further, the viscosity of the resist solution is originally about several tens of cps, and the spin coating time is usually about 20 seconds, which is long, so the apparent viscosity is considered to be sufficiently low. Therefore, even if the resist solution is treated as a Newtonian fluid, a large error will not occur.

Newtonian fluid is a liquid that follows Newton's law of viscosity, and the shear stress τ3 and velocity gradient or shear velocity are proportional. Resist on the board now? '8? Considering the situation in which the resist solution is applied to a film thickness of m and the resist solution is pulled outward at a speed of {circle around (1)} by rotation around the l axis, the above relationship is expressed by the following equation.

τ3-η(θV/θZ)-η(θγ/θt)...[3
1 Here, γ is the amount of deviation, t is time, and therefore θ
V/θ2 is the velocity gradient in the film thickness direction, and θγ/θL is the deviation velocity. The proportionality constant η is called viscosity.

Also, consider a minute volume at a point where the distance from the center (l axis) is r and the height from the substrate is h. When the substrate is rotated about the l-axis at an angular velocity ω, the gradient in the film thickness direction of the shear stress τ applied to the microvolume due to the rotation is expressed by the following equation.

θτS/θ2−−ρω2r ・・・141 Formula 1
31 and equation [4], θrs/θZ=77(θ2v/θz2)=-pω2r
It can be written as Solving this differential equation results in v−-(ρω2rz”/2η)+Az×B. The above A and B are integral constants.

Here, since , the above integral constants are A=ρω2r, respectively.
h/η, B=0. Therefore, v= ((-pω”r z2/2)+pω2r h z
lc...[5l The flow rate q of the resist solution can be determined by integrating equation [51].

q−脣vdz=pω2rh3/3η···−[6] On the other hand, the following formula is known as a continuity formula in cylindrical coordinates.

ocIDt +ty f(1/r)θ(rL)/θ,
+(1/r)θ11. /θψ1θU, /θzl=o
' -・- [7] Where, σ represents the specific gravity of the resist solution, ψ represents the rotation angle, Ur represents the velocity component in the radial direction, Uψ represents the velocity component in the rotational direction, and Uz represents the velocity component in the film thickness direction, respectively. . Further, D/D t is called a real derivative and is expressed as follows.

D/Dt=U, (θ/ar)+U; (θ/θψ)
10 U2 (θ/θ2) + (θ/θt) Here, since the specific gravity of the polymer compound that is the resist material and the solvent are almost equal, even if the solvent evaporates over time, the specific gravity σ of the resist solution as a whole is almost the same. It is assumed that it will not change. In addition, the resist solution is 0 after the start of spin coating.
．． Since it is considered that the body becomes a substantially rigid body of rotation in 1 second, the velocity gradient in the rotational direction ψ can also be ignored. In other words, it can be set as Dσ/Dt=OD ψ /Dψ −〇. Furthermore, U, l−θh/θt, U, −θ
Since q/θ2, continuity equation 17] is sequentially transformed as follows.

(1/r)θ(rU,)/θr＋θU,/θz=0(θ
/θr)(r・θq/θz)+r(θ/θz)(θh/
θt)=0(θ/θz)(θrq10r)+r(θ/θ
zNθh/θt)−〇 Therefore, θrq/θr +r−θh/θ1=0. Substitute equation [6] into this.

(θ/θr) (p ω”rb3/377) +r-
θh/θ1=0 here. -ρω2/3η, θh/θL-1' o(1/r) (θ/θr) (r
"h3)--2K. h3. Solving this differential equation yields θL--θh/2. h3 L = 174 K oh2+C However, C is an integral constant. Here, when t=0, h
=ho (initial film thickness), C=-1/4 aha'', t=1/4 oh''-1/4 oho'' Therefore, h=ho/(]+4 1. o21) I/2 where,
In an actual rotary coating system. Since several mmh is several μm and we can set h,>h, he/h-(1±4 Ko
ho't) "" = (4 to oha"t)"2 Therefore, h = ho/(4 to h07t) 172 - h0pa4ρω2ha"t/3η)+7= C+/2ω
)(3η/ρo)1″... [81 In other words, from equation [81], it can be seen that the resist film thickness is proportional to the viscosity η to the 172nd power.

A-2) Among the parameters in the equation [81], the one that can change depending on the temperature is the viscosity η. Therefore, the relationship between temperature and viscosity will be considered below.

There are two possible types of changes in viscosity η due to temperature: (1) essential viscosity changes derived on the assumption that momentum is transported by vibrations of liquid molecules; and (2) viscosity changes due to solvent evaporation.

The above (■) is expressed by the following formula % formula % [9], which is famous as Andrade's viscosity formula, and generally indicates that the viscosity decreases as the temperature of the liquid increases. However, in the above, 1 is a constant, Ev is the flow activation energy R is a gas constant, and T is the absolute temperature.

In the present invention, consideration will be given to the above (2).

In order to quantify the change in viscosity due to solvent evaporation, we first determined the change in evaporation amount due to temperature change.

Since the actual application of the resist solution is not performed in a closed system, the resist solution and the surrounding air are non-equilibrium with respect to the solvent concentration. However, it is thought that the solvent concentration is high in the air very close to the wafer surface, and an approximately equilibrium state is established.

A state function A representing affinity is defined by the following equation.

a s = d Q/T-(A/T)・dξ...
- [10] However, the above S represents entropy, Q represents the heat generated inside the system, ξ represents the degree of progress of change, and T represents the absolute temperature. Equilibrium occurs when the state function A=0.

Now, if we consider the state function A as a function of (T, p, ξ), the total differential of A/T can be expressed as follows.

d(A/T)-θ/θT (A/T) ,,,, d
T ten θ/θ11 (A/T)? , ゎdp ten θ/θξ(A/
T) T,, dξ = (1/T2) (θH/θξ)t, pdT (
1/T) (θV#ξ).

dp + (1/T) (θA/θξ)t, , dξHowever,
The above p represents pressure, H represents enthalpy, and ■ represents volume, respectively. Since we are considering evaporation of the solvent here, θ11/
θξ is equal to the latent heat Δeh. Furthermore, (θV/θξ)T+ p ””T+ D(θA/θξ
)T, t+ = aT, p, the above equation can be rewritten as follows.

dA-(Δeh/T)dT VT, pdll +
at, pdξ , , [111 Next, the time change of equation [111] is investigated.

dA/dt-(Δeh/T) (dT/dt) VT
, p(dp/dt)+a,, p(dξ/d t) Here, dξ/dt is the rate of change, so dξ/
It can be set as dL=V. Furthermore, when considering the resist solution coating system to be approximately in equilibrium, V=kA (k is a constant)
, dT/at=0, and dp/dt=0. Therefore, dA/dt=a7. , kA Solving this differential equation, aT + pkdt - dA/A A = exp (at, pkt + D) (D is the constant of integration) Here, if A is defined as 80 when 1 = 0, then An
-exp(D), so A -Aoexp(at, pkt) Furthermore, since the time constant τ-17at, J, A =
It can be written as A oeXp(t/r). Therefore, 2[111 can be transformed as follows.

dA/dt A/r=(Δeh/T) (dT/dt)
VT, p (dp/dt)... [121 Next, the temperature change in equation [121] will be investigated.

dA/dT+(A/r)(dt/dT) −(Δeh
/T) VT, p(dp/dT)...[13] Here, d A/d T is negligibly small compared to the second term on the left side of equation [13], so it is set to 0. moreover,
It has been experimentally confirmed that the temperature T of the resist solution changes during coating according to the following equation.

T- to 2-t to 3 eXp ((t+ to m
) to sl where dt/dT=-1/ and T, so equation [131 can be written as follows.

(A/p: 5 T T)-Δeh/T-V7+p(
dp/dT)... [141 Here, when the volume of vapor is Vv and the volume of liquid is VL (where vv>v), VT, p = VV VL 'i Vv. Furthermore, when considering the neighborly equilibrium state, since Vv=RT/p (R is a gas constant), equation [141] can be written as follows.

dp/dT −(Δeh/T 10A/ K s r T
) (p/RT) Solving this differential equation, Inn p − (Δeh/R0A/ x s r R)
(-1/T). Therefore, the relationship between the temperature T and the evaporation amount Δ■ of the solvent is expressed as follows, where V is the evaporation rate.

ΔV = 6pt to vt-6texp((Δeh/R+ A/ x s r
R) (1/T) ] [151 As above, the relational expression of V to temperature T and the amount of evaporation of solvent [
Now that 151 has been found, let's consider expressing it in relation to concentration viscosity.

First, since the viscosity η is proportional to the concentration C of the resist solution,
The following formula holds.

η-7C (where 7 is a proportionality constant) Also, the initial volume ■ containing N resist molecules per unit volume. The concentration C when the solvent evaporates by Δ■ from the resist solution is expressed as follows.

c = N/(Vo-ΔV) The following equation is derived from these relationships and equation [151].

7N η 0 (Vo <,, t eXIl+ ((Δeh/R+A
/5rR)(-1/T)1... [161 This is the formula representing the change in viscosity due to evaporation of the solvent.

(8-3) In the process of coating resist and resist, the untraded viscosity equation (
The woody viscosity change represented by 2 [91] and the 2 [161
It is thought that the viscosity change due to the evaporation of the solvent is occurring at the same time.

First, take the natural logarithm of both sides of equation [16].

En 1=lnx7N-j2n[Vo-to 6t exp
((Δeh/R0A/, rR) (-1/T)l] Here, in the second term on the right side, if we look at the antilog part of the natural logarithm, that is, within [1, the antilog part is (- Since it can be seen that there is a linear relationship with 1/T), the following transformation can be performed.

In　η=fin to J-I! , n to 8. V.

+ (6t to ln) (5rR to (Δeh/R0A/) (
-1/T)1-42 n(J/Vo) + ±((Δeh/R+A/5rR)(1/T)l (n
bt to n)... [17] Also, if we take the natural logarithm of both sides of the above equation [91, j2
n η−KIEv/I? T, -
[1B]. Adding both sides of equation [17] and equation [18], we get 2j! n y7-EncgqN/Vo)"-((Δeh
/R+A/, rR) ffin 6t ＜+Ev/R
1(1/T)... [191 On the other hand, in the relational expression (formula [81)] between resist film thickness and viscosity η, if the natural logarithm of both sides is taken, I2. n h −(1/2)ffin 77 +x+.

It can be written as Substituting the formula [191 into this equation, we get nn h−x z + [f(Δeh/R) 10(+zRr to A/)l +3t(to 14Ev)/R1(
-1/T) ... [201 is obtained. This is the relational expression between the resist film thickness and the temperature T. From this equation, it is clear that the natural logarithm of the resist film thickness and the reciprocal of the temperature T are in a proportional relationship. In addition, the above formula [2
01, the coefficient part of the time term (-1/T) is a function of time. In addition, in the above constant, 1 is the initial concentration ■. is a constant containing

B, x'l f7)'1 In the derivation, the resist film thickness and relative humidity H
We will consider the relationship with To do so, the square formula [
20], the term that is the humidity state function must be specified.

What is affected by changes in relative humidity are the amount of evaporation of the solvent in the resist solution, the number of states corresponding to the number of existing patterns in the phase space of water molecules or solvent molecules, and the entropy determined by these.

The entropy change is d5-(A/T), dξ-.-[101, as expressed by the above equation [101]. ξ
is the degree of progress of change, which can be thought of as a change in the number of solvent molecules as they evaporate.

On the other hand, the entropy S is determined by Boltzmann's relational expression as follows: S −kBln W ...[2
1]. However, km is Boltzmann's constant, W
is the number of states.

The number of states W increases as the relative humidity increases, that is, as the number of water molecules present in the system increases.

However, as the number of states W increases, the entro and -S become more difficult to increase. This is clear from equation [211] which shows that the entropy S is proportional to the natural logarithm of the number of states W. On the other hand, the entropy change is proportional to A/T from equation [10]. Therefore, it can be seen that A/T is a state function related to humidity.

Alternatively, considering that A is a function describing a non-equilibrium state, it can be intuitively predicted that A/T is a state function related to humidity. In other words, when the relative humidity is other than 100%, everything is in a non-equilibrium state.

This A/T can be easily separated as an independent term by transforming equation [201 as follows.

ff1nh=z+(Δehffin 13t/R-zEv/R) (1/T)+(ffin 13t/+
zRr) (A/T) - to 11+ +s (1/T) 1 to 10
6 (A/T)... [211 Here, we will consider a method of expressing relative humidity statistically mechanically.

The state of motion of one molecule moving in one-dimensional space is determined by the position (x, y, z) and motion M Cp at a given time.
x, py, pz), and a six-dimensional phase space is required to describe this motion. Similarly, a gas containing N molecules has a phase space of 6N dimensions.

Now, when a space having a certain volume is saturated, that is, the relative humidity is 100%, let N be the number of water molecules that can exist in the phase space at a certain moment. This number N is considered to be the maximum number of seats in which water molecules can exist, and the relative humidity H is a numerical value representing the proportion of seats occupied by water molecules.

Here, if we apply the idea of classical statistical mechanics, when the number of actually existing water molecules is n, the number of states W at a certain moment is the seat occupied by n molecules from N seats. Represented in permutations. That is, w= Npl1 =N! /(N-n)! It is.

Furthermore, if the arrangement of N seats changes in U ways after a certain period of time has passed, the number of states W is expressed as the following equation [221].

W=uw-uN! /(N-n)! ---[
22] Next, we will consider the entropy change due to solvent evaporation, and here we will make one important assumption. That is, it is an assumption that water molecules and solvent molecules are treated as the same molecule. This is based on the fact that both water and the solvent of the resist solution are liquids at room temperature, have low vapor pressures, have strong polarity, and therefore mix well with each other.

Based on this assumption, if we consider the case where ξ solvent molecules are added by evaporation into a space where n water molecules exist, the number of states Wζ can be calculated as follows by replacing n in equation 1221 with (n+ξ). is expressed in

J-uw=uN! /(N-(n0ξ)) Therefore, the entropy Sζ is expressed by the following equation [231].

Sξ=kIIIV, nWξ=kJn[u N! / (N-(n0ξ))! ]...
・123) If we differentiate Equation [23] by ξ, then from the definition of 2[101, A
/T is required.

Here, since N is a sufficiently large number, prior to differentiation, the right side of equation [23] is subjected to Starling approximation [N! =(N/e
)N) and transform it as follows.

S=to++fn[uN! / (N-(n+ξ))!
1-kBNin (N/e) +++ln uk++
(N(n0ξ)l in, [(N −(n+ξ)l/
el... [241 A/T is obtained by differentiating equation [24] with respect to ξ.

dS/dξ= k++ [j! n[(N-(n+ξ)
)/el(N-(n0ξ))・e/(N-(n+ξ)
)] = k B (e-1) 10k B ff1n (N
-(n+ξ))-A/T...[
25j Substituting this relationship into the above equation [211 and rearranging the constant terms appropriately, we get /, n h = x 1+ + +5 (1/T) + +6 [kn (e-1) + knjl! n (N-(n0ξ
))] - to 17+ +s(1/T) + x Hj2n
(N (n0ξ))... [26].

Here, when applying the resist solution, exhaust is generally performed and solvent molecules are always removed, so approximately ξ−0
You can think about it. Also, the relative humidity H (%) is H=
Since it is defined as 100n/N, n = N H/
It is 100. By substituting these relationships into equation [261, the relationship between resist film thickness and relative humidity H is expressed as equation [11
is obtained.

ln h- to +7+ to +s (1/T) ten to +effi
n (N (Nll/100))- to +q+- to +s
(1/T) +512n (100H)...[1
1 From the above considerations, En h and ff1n (100-H)
It is expected that there is a linear relationship between Furthermore, the slope of the graph representing this linear relationship is expected to be unaffected by temperature.

In the previous section B, we investigated the relationship between resist film thickness and relative humidity H when classical statistical mechanics was applied. Let the number of states W be n from the N locations where a water molecule can exist in the phase space.
It was expressed as a permutation that selected the locations occupied by each molecule.

In other words, the states obtained by exchanging two equivalent molecules are considered to be two different states.

However, in systems where some degree of intermolecular interaction is expected, it is empirically known that interpreting these states as the same state better matches experimental results.

In other words, even if two equivalent molecules are exchanged in the phase space, it is considered that no change in state occurs macroscopically. This way of thinking will be referred to here as empirical statistical mechanics.

According to the treatment of empirical statistical mechanics, the relative humidity H can be calculated from the actually existing n seats of the molecule in the saturated state.
It is expressed as a combination that selects seats occupied by molecules.

That is, w-NC1l-N! /n! (N-n) It is.

Furthermore, if the arrangement of the N seats changes in U ways after a certain period of time has passed, the number of states W is expressed as the following equation [271].

W=uw=uN! /n! (N-n)! ...-[2
7] Here, considering the case where ξ solvent molecules are added due to evaporation into a space where n water molecules exist due to evaporation of the solvent, the number of states Wξ is calculated by subtracting n in equation [271 from (n+ξ
) is expressed as follows.

W4=uw=uN! /[(n+ξ)! (N-(n+ξ)
)! ) Therefore, the entropy S is expressed by the following equation [28].

S@ = kBln J = k n l n [uN! / [(n+ξ)! (N
−(n+ξ)l! ]]... [28] Here, similarly to the above, Starling approximation is applied to the right side of equation [28].

S=to++nn[uN! / [N (n+ξ))
! 1((N+ξ)/e) ”ξ[(N-(n-+-ξ)
] /el'-width゛P-keNj2n(N/e) +
kml! , n ukB (n + ξ) ffn ((n + ξ)/
e) to 8(N(n+ξN j!n [(N-(n+
ξ))/el... [29] When formula [29] is differentiated by ξ, A/T is obtained.

d S/dξ−k++[Nn((n+ξ)/e)+(n
1ξ)・e/(n+ξ)] ke [-I! , n[(N-(n+ξ)]/el(N
-(n0ξ))・e/ (N=(n+ξ))]=kBj
! n(N (n+ξ)) −kBI! , n(n+ξ)
=kgfn[(N-(n0ξ))/(n+ξ)-A/T
... [301 Substituting this relationship into the above equation [211 and rearranging the constant terms appropriately, we get En h=++ 10+s(1/T)−+−x+b
[kBj2n[(N-(n0ξ))/(n0ξ)]-go + K +s(1/T) +e to 10[ff1n[(N-(n+ξ)l/(n+ξ)
)】... [311.

Here, by substituting the relationship ξ′:0 and n=NH/100 into equation [311], equation [2] expressing the relationship between resist film thickness and relative humidity H is obtained.

ff1n h = K zo 1K +, (1/T) +
+l1fn [(N (NH/100)) /(N
il/100)] - to 2o+ to +s(1/T) 10K +
aj2n ((100H)/llll... [21 From the above consideration, ln h and ln ((100-H)/
It is expected that there is a linear relationship with H). Furthermore, the slope of the graph representing this linear relationship is expected to be unaffected by temperature.

Since the equations [11 and 21] describing the humidity dependence of resist film thickness were theoretically derived as described above,
Next, we examined how well these formulas explained the experimental facts.

That is, we conducted an experiment in which a resist solution was actually spin-coated under certain conditions using a temperature-controlled coater under various relative humidity conditions, and the thickness of the resulting resist film was measured. value to ln h, and relative humidity ■] to f
fn (100-H) or in((100-H)/
H] and printed on the graph.

In this experiment, the temperature control coater was a Clean Track Mark If-V type manufactured by Tokyo Electron, the substrate was a 5-inch wafer, and the resist was a novolak-based positive photoresist (manufactured by Tokyo Ohka Kogyo Co., Ltd.).
Product name TSMR-V3. (viscosity: 20 cps), and ethyl cellosolve acetate (ECA) was used as the solvent.

Here, the rotation speed during constant speed rotation was set to 4ooorpm, the constant speed rotation time was set to 20 seconds, and changes in the resist film thickness were investigated when the relative humidity was changed.

Figure 1 shows Nn h, p, n(1
Figure 2 shows a graph plotting the relationship between in h and 4211 [(100
Graphs plotting the relationship of H)/H1 are shown. In addition, the horizontal axis of each figure is j2n (100-H) and E
n I (100-H)/Hl, but a scale of relative humidity (%) is also shown for convenience of explanation.

First, looking at Figure 1, a generally good linear relationship is obtained, but the graph is slightly curved when the relative humidity approaches 50%. This means that in equation [11] the coefficient is 18
This means that the relative humidity changes around 50% relative humidity. A very good linear relationship was shown in the regions where the relative humidity was higher and lower than 50%, respectively.

Further, when looking at FIG. 2, a generally good linear relationship is obtained, but the graph becomes slightly curved in both the region where the relative humidity is less than 35% and the region where it is higher than 60%. A very good linear relationship was shown in the relative humidity range of 35-60%.

Considering the results of the above two types of plots together, in the region where the relative humidity is less than 35% and the region higher than 60%, the formula derived based on classical statistical mechanics [1]
However, in the region of relative humidity of 35 to 60%, it can be seen that Equation [21] derived based on empirical statistical mechanics explains the experimental facts well.

The reason why the applicable ranges of the formulas differ in this way is considered to be as follows.

Classical statistical mechanics is originally applied to systems with few intermolecular interactions. When the relative humidity is high, the evaporation rate of the solvent is low and the number of solvent molecules present in the coating atmosphere is also small, so it is thought that the interaction between water molecules and solvent molecules is reduced. On the other hand, when the relative humidity is low, the evaporation rate of the solvent is high and the number of solvent molecules present in the coating atmosphere increases, while the number of water molecules decreases.
It is considered that there is little interaction between water molecules and solvent molecules. According to the above experimental results, it can be said that high relative humidity substantially corresponds to higher than 60%, and low relative humidity substantially corresponds to lower than 35%. Therefore, in these regions, equation [11 is considered to explain the experimental facts well.

On the other hand, when the relative humidity is an intermediate value, ie, 35 to 60%, relatively strong intermolecular interactions between water molecules and solvent molecules are considered.

In general, the effectiveness of empirical statistical mechanics is known in systems where interactions exist, and in this area, equation [21] is considered to explain the experimental facts well.

From the above considerations, the effectiveness of formula [11] and formula [2] was demonstrated.

In order to actually control the resist film thickness with high precision based on the relationships expressed by these equations, the following device may be used.

That is, a humidity sensor is installed in the resist coating chamber, a calculation means is provided for converting the measurement result by the humidity sensor into a resist film thickness based on the relationship of formula [11] or formula [21], and furthermore, the calculation of this calculation means is It is sufficient to provide means for controlling the rotation speed or rotation time of the wafer based on the results.

An example of the configuration of such a device is shown in FIG. This apparatus includes an ordinary temperature control coater including an enclosing means for isolating the resist coating environment from the external environment, a rotary coating means housed within the enclosing means, an air suction/exhaust means, a temperature/humidity control means, a resist solution supply means, etc. In addition to the above components, a calculation means for calculating the resist film thickness based on the humidity measurement result, and a rotation control means for controlling the rotation of the spin coating means based on the calculated resist film thickness are provided. It is.

The enclosing means is composed of a downflow type chamber (1) in which air whose temperature and humidity are controlled flows from above to below, and the upper part of which is supplied with temperature and humidity controlled air (2). air into the chamber (1)
An air supply duct (3) is opened for introducing the air into the interior. The temperature and humidity controlled air sent from the air supply duct (3) is further removed from dust by an air filter (4) and then supplied into the chamber (1). The rotary coating means is coaxially attached to a rotating shaft (7) of a rotating means (not shown) such as a motor, and rotatably holds a substrate (5) such as a semiconductor wafer by fixing it. Chuck(
8), and a resist solution (11) disposed so as to surround the outer periphery of the chuck (8) as the substrate (5) rotates.
It consists of a cup (6) etc. to prevent the scattering of the water. At the bottom of the cup (6) is a resist solution (11).
An exhaust duct (9) is provided for suctioning and removing droplets, solvent vapor, etc. together with the air in the chamber (1).

Above the center of the substrate (5) is a resist solution supply pipe (1) for discharging a temperature-controlled resist solution (11).
0) is open.

Furthermore, a humidity sensor (13) for measuring the humidity in the coating atmosphere is provided inside the chamber (1), and a humidity/film thickness conversion circuit (14) and a rotation control circuit (15) are provided outside. There is. The humidity/film thickness conversion circuit (14) takes in the humidity measured by the humidity sensor (13) as a humidity information signal, and calculates the humidity based on the relationship theoretically predicted by equation [11 or equation [21]. A film thickness information signal is generated from the information signal, and this is further compared with a preset target film thickness to generate a film thickness difference signal indicating the difference between the two. Here, which of equation [1] and equation [2] to select is automatically determined according to the content of the humidity information signal. The rotation control circuit (15) takes in the film thickness difference signal and controls the motor ( A rotation control signal that increases or decreases the rotation speed or rotation time of the motor (12) is generated, and this signal is sent to the motor (12).
).

In such a configuration, if the relative humidity in the chamber (1) is continuously monitored by the humidity sensor (13),
Even if the relative humidity fluctuates during spin coating, rotation control that follows the fluctuations becomes possible. In this case, since changes in the rotation of the motor (12) are immediately reflected in changes in the resist film thickness, sensitive film thickness control is possible.

Control of resist film thickness according to the present invention has the advantage of not being affected by temperature. As understood from Equation [11] and Equation [21], relative humidity H and temperature T are treated as independent variables, and the slope of the straight line does not change depending on temperature T. Therefore, if the relationship between the relative humidity H and the resist film thickness is determined once at a certain constant temperature, this relationship can be applied as is even if the temperature T changes. Furthermore, this relationship holds true regardless of the type of resist solution.

It becomes possible to interpret it. Based on this interpretation, the resist film thickness can be controlled extremely accurately and quickly. Therefore, if the present invention is applied to, for example, the manufacturing of semiconductor devices, it will be possible to achieve excellent line width controllability, excellent yield, reliability,
A semiconductor device having a high degree of integration can be easily manufactured with high reproducibility.

[Brief explanation of drawings]

Figure 1 is based on formula [1]! nh and in (100
It is a graph showing the relationship of H). Figure 2 is a graph showing the relationship between in h and ffn ((100-H)/1 month based on formula [21]. Figure 3 is a graph showing the relationship between in h and ffn ((100-H)/1 month) based on formula [1] or formula [2]. 1 is a block diagram schematically showing an example of the configuration of a resist coating device in which the thickness is controlled. [Effects of the Invention] As is clear from the above description, if the present invention is applied, Quantitatively solved the relationship between relative humidity and resist film thickness, which had only been understood qualitatively 1... Chamber 5... Substrate 11... Resistant liquid 12... Motor 13... Humidity Sensor 14 ... Humidity/film thickness conversion circuit 15 ... Rotation control circuit

Claims (2)

[Claims] (1) The humidity dependence of resist film thickness in spin coating is expressed by the following formula [1] lnh=κ_1_9+κ_1_5(-1/T)+κ_1
_8ln(100-H)...[1] [In the formula, h is the resist film thickness, T is the temperature (K), and H
is relative humidity (%), κ_1_5, κ_1_8, κ_1_
9 is a constant. ] When the relative humidity H is less than 35% or 60%
A resist coating method characterized by performing spin coating of a resist solution at a setting higher than %. (2) The humidity dependence of resist film thickness in spin coating is expressed by the following formula [2] lnh=κ_2_0+κ_1_5(-1/T)+κ_1
_8ln{(100-H)/H}...[2] [In the formula, h is the resist film thickness, T is the temperature (K), and H
is relative humidity (%), κ_1_5, κ_1_8, κ_2_
0 is a constant. ] A resist coating method characterized by performing spin coating of a resist solution with relative humidity H set in a range of 35 to 60%.