JPS62165103A - Method for measuring film thickness - Google Patents

Abstract

PURPOSE:To detect an exact film thickness even if there is variance in measured values by making use of the theoretical max. value and min. value of spectral reflectivity to detect only the desired extreme value. CONSTITUTION:The max. value Rmax and min. value Rmin of the spectral reflectivity from a thin film are obtd. regardless of the film thickness. Only the desired extreme value can be detected by regarding the maximal value and minimal value obtd. from the measured values as the maximal value or minimal value only when said values are above or below the certain specified value with respect to the values Rmax, Rmin. For example lambda1, lambdaX, lambda2 are detected as the maximal value and lambda3, lambdaY are detected as the minimal value when the measured values have an error in the central part thereof. However, the specified value l, for example, l=RmaxX0.9 is provided with respect to the value Rmax and the value l or above is determined as the maximal value, then only the lambda1, lambda2 can be detected. With respect to the minimal value, only the lambda3 can be detected when the specified value m=RminX1.1 is provided. The correct extreme value is thereby detected even if there is variance in the measured values in the above-mentioned manner. The film thickness is thus detected by using the extreme value.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field) The present invention relates to a method for detecting and measuring thin films, particularly film thicknesses of micrometers or less, such as oxide films on silicon in semiconductor processes.

(Principle) The basic measurement principle of film thickness detection used in the present invention will be explained below using FIGS. 1(a) and 1(b).

The refractive index of the medium is 1. from the incident side. 2. kA, and the film thickness to be measured now is d. The incident angle of each wavelength used (wavelength λ in vacuum) is 01°θ2. Let it be θ3. At this time, the amplitude reflectance Y is as follows.

[Reference: M. Born and Ei, Wolf,
@Pr1ncip'1esof 0ptics' 3r
dedition, PERGAMON PRESB.

Page 62] Here, Y12 is the Fresnel reflection coefficient at the boundary between the media ■ and ■, and Y2S is the Fresnel reflection coefficient at the boundary between the media ■ and ■. The quantity that can actually be measured is the reflection intensity, that is, R=lY12 (usually called reflectance), which is as follows.

Here, by differentiating equation (2) with respect to λ and finding β such that R′=mouth, 111n2β=0 and 2β=N・2
π...(3) searches for a trench.

Here, N is an integer.

By the way, when the wavelengths are λ1 and λ2, β1. β2 is 2π β1=2. as shown in the previous table. nla CO2O3 where nl and n2 are wavelengths λ1. It is the refractive index at λ2.

Therefore, from equation (3), 2π 2β1 = 2 ・, B, nl d CO[ilθ2=
N-2π, 2(β2-β,)=2・2π・acosθ2(T2-“
)=2π Here, if 02=0, d can be found by the following formula.

Regarding the local minimum value, λ3. λ4 and the 71 refractive index n3, n4 at each wavelength. Also, the maximum value and minimum value λ1. Even if λ3 is used, the film thickness can be obtained.

(Prior art) However, if an error occurs in the measured value as shown in Figure 3, λX is determined to be the maximum value and λY is determined to be the minimum value, making it difficult to accurately detect and measure the film thickness. I couldn't do it.

(Objective) An object of the present invention is to detect only the correct extreme value and accurately detect the film thickness even when errors in measurement values as described above occur.

(Example) The spectral reflectance from the film thickness is generally given by the following formula (5).

here: ρo1 is the amplitude coefficient between the air layer and the first layer φo1 is the phase coefficient between the air layer and the first layer ρ12 is the amplitude coefficient between the first layer and the second layer φ12 is the phase coefficient between the first layer and the second layer δ is a phase term, and δ=2πna/λ.

(5) In the hole, the CO8 term falls between -1 and 1, so the spectral reflectance has a maximum value and a minimum value. Both can be obtained regardless of the film thickness d. The maximum and minimum values obtained from the measured values are Rmaw −” mi
Only desired extreme values can be detected by regarding n as a maximum value only when it is greater than a certain value, and as a minimum value only when it is less than a certain value. That is, as shown in FIG. 4, when there is an error in the center of the measured value, if the extreme value is detected directly from the measured value, it will be determined as the local maximum value λ1. fart,
λ2 is detected, and λ5. λY is detected. However, if RmaX has a certain constant value t, for example, t=
If RmaxX is set at 0.9, etc., and only the values above are considered as local maximum values, only λ1 and λ2 can be detected. Similarly, regarding the local minimum value, for RInln, a certain constant value m,
For example, if m = Rmin x Ll, etc., only λ5 is detected as the minimum value. This constant value t or m is determined by the measurement pitch or possible error of the device.

Additionally, in the case shown in Figure 5, the detected extreme value is λY
is excluded by the method described above, so the maximum value λ1. Eight dechiru. However, in a function with periodicity such as the spectral reflectance of film thickness, the maximum value, the maximum value, and the I value should exist alternately, so the Hitsugi Daishins exist side by side as in this case. That can't happen. Therefore, the larger one of A1 and λX is considered to be the maximum value.

In the example shown in FIG. 6, when f is a small value, it is possible to determine that A3 is a local minimum value in the same way as in the case of a local maximum value. In such cases, the measurement pitch is small relative to the position of the extreme value, so
The error in film thickness calculation is not large.

When the film thickness to be measured becomes very thin, theoretically no extreme values can be seen in the wavelength scanning range, as shown in FIG. Even in such a case, if a measurement error occurs, an extreme value will be detected. In the case of Fig. 7, by using the method described above,
Although X1 +λY1 can be removed, λxo remains as a minimum value.

In such a case, if λXO, which is determined by the slopes of the measured values before and after λXO, is truly an extreme value, the signs of the slopes before and after the λXO should be different, but in the example shown in FIG.
Since the sign of the average slope at λ which is smaller than λXO is the same as that of the average slope at λ which is smaller than λXO, λxo is the same as in the book regarding the six maximum values excluded from the extreme values.

By the above method, it is possible to detect the correct extreme value even if there are variations in the measured values.

FIG. 8 is a system block diagram for implementing the present invention. The fiber probe 3 illuminates the light separated by the spectrometer 1 onto the sample surface placed on the sample stage 2, and the light reflected from the sample surface is received again by the fiber probe 3 and is converted into a photoelectric converter installed in the spectrometer 1. The controller 4 controls the wavelength setting of the spectrometer 1 and the movement of the sample stage 2, and also converts the electric signal of the photoelectric conversion element of the spectrometer 1 into a digital signal.
Then, confirm the position of the sample stage 2. The computer 5 controls the controller 4, receives the digital signal obtained from the controller 4, determines the reflectance R, and calculates the film thickness d from the equation (3).

The results are output to a CRT 8, floppy disk drive 9, or printer 10. Using the operation panel 6 and full keyboard 7, conditions such as the refractive index are specified to the computer 5, the wavelength of the spectrometer 1 and the amount of movement of the sample stage 2 are specified, and commands such as the start of measurement are issued. The operation panel 6 is provided with the minimum number of keys needed to prevent the operator from operating the device erroneously, when measurements are to be made under commonly used conditions.

The operation of FIG. 8 will be explained along the flow chart of FIG. 9A. First, in step S1, the measurement data of the spectral reflectance is taken in, and in step S2, the measurement points before and after are compared to obtain the maximum value m.
ax(k) and the minimum value m1n(k) are determined. On the other hand, since the theoretical maximum reflectance Rmax and minimum reflectance Rmin can be obtained from the refractive index of the film and the substrate, they are determined in step S6.

Based on the obtained theoretical value, for example, Rma:t
'= 1.

Rmin x 1.1=m A4, and the reference values m and t used for determining the extreme value are calculated in step S4. In steps S5 and S7, the maximum value ma:c(k) and the minimum value m1n(k) are determined, and those that deviate from the reference are excluded in steps B6 and 8B. Further step S
In steps P and S11, it is determined whether or not local maximum values or local minimum values exist side by side. If they exist side by side, the optimal one is selected in steps 810 and 812. max(k) finally obtained.

Using mtn(k), the film thickness may be determined in step 813 by formula (4-5) to (a-1).

If there is only one extreme value, the flowchart shown in FIG. 9B may be added before executing step S13 in FIG. 9A.

At this time, the film thickness is determined by: Equation (4-4) is used when A1 is the maximum value, and Equation (4-5) is used when A1 is the minimum value. When the number of extreme values is 0, the film thickness cannot be calculated using the methods of equations (4-1) to (4-3) or equations (4-4) to (4-5). Therefore, when formula (5) is solved with respect to d, it is found that the inside is 0.1.2·,·, and d can be found by setting K=Q.

Even if there is an extreme value of Sen, the order K = 2nd/λ
(7'I), so the formula (4
-1) to (4-3), (4-4).

K is obtained using d obtained in (4-5), and d can be calculated from the reflectance R of each wavelength.

(Effects) As seen above, the present invention detects only the desired extreme value by using the theoretical maximum and minimum values of spectral reflectance even when there are variations in the measured values, allowing accurate film formation. Thickness can be detected.

[Brief explanation of drawings]

Figures 1 (a) and (b) are diagrams explaining the principles of the present invention;
The figure is a graph showing reasonable spectral reflectance, and Figures 3 to 7 are flowcharts for explaining the operation of spectroscopic diagrams with measurement variations. 1... Spectrometer 2... Sample stage 4 mark controller 5... Computer

Claims (1)

[Claims] A method for measuring film thickness from the interval between extreme values of spectral reflectance of a sample, comprising: calculating the theoretical maximum and minimum values of spectral reflectance of the sample;
A reference value l that is more constant than the maximum value, a reference value m that is more constant than the minimum value
is determined, and the reference value l is determined for the extreme value obtained from the measured value of spectral reflectance.
A film thickness measuring method characterized in that the film thickness is accurately detected by determining the true maximum value in the above cases and determining the true minimum value in the case below the reference value m.