JPS63140940A - Measuring method for refractive index and film thickness - Google Patents

Abstract

PURPOSE:To know a refractive index and film thickness automatically by measuring the reflection factor of energy by using homogeneous light beams which are equal in angle of incidence and different in wavelength. CONSTITUTION:S-Polarized and P-polarized homogeneous light beams of wavelength lambda1 are made incident on a thin film 10 on a substrate 12 at a specific angle of incidence and energy reflection factors RS(lambda1) and RP(lambda1) to the incident light beams are measured. Further, S-polarized and P-polarized homogeneous light beams of wavelength lambda2 are made incident at the same angle of incidence and energy reflection factors RS(lambda2) and RP(lambda2) to the incident light beams are measured. The refractive indexes N1(lambda1) and N1(lambda2) of the thin film are calculated automatically by specific arithmetic by using the measured energy reflection factors RS(lambda1) and RP(lambda1), and RS(lambda2) and RP(lambda2). Then the film thickness of the thin film is calculated automatically by specific arithmetic by using the energy reflection factors RS(lambda2) and RP(lambda1), and RS(lambda2) and RP(lambda2), and refractive indexes N1(lambda1) and N1(lambda2).

Description

[Detailed description of the invention] (Technical field) The present invention relates to a method for measuring refractive index and film thickness.

(Prior Art) It is often necessary to measure the refractive index and film thickness of thin films in the optical technical field, and ellipsometry is known as a non-contact, non-destructive measuring method. However, ellipsometry requires complex and large-scale equipment for its implementation.

(Objective) The present invention aims to provide a novel method for measuring refractive index and film thickness that is simple and easy to implement and has high accuracy.

(Structure) The present invention is a method of measuring the refractive index and film thickness of a thin film formed on a substrate having a known refractive index. Two methods are proposed herein.

The first type of method is to make monochromatic light of wavelength λ1 of S-polarized light and P-polarized light incident on a thin film on a substrate at a predetermined incident angle, and measure the energy reflectance Rs (λ1) and Rp (λ1) for each incident light. Furthermore, at the above incident angle, the wavelengths λ2 of S-polarized light and P-polarized light are
input monochromatic light, and measure the energy reflectance Rs(λ2), Rp(λ2) for each incident light, and calculate the refractive index of the substrate and the energy reflectance R3(λ1), Rp(
λl), Rs(λ2), Rp(λ2), the refractive index N1(λ1) and N1(λ2) of the thin film are automatically calculated according to a predetermined calculation, and the energy reflectance Rs(λ1 ), Rp(λ1), Rs(λ2),
Rp (λ2), and refractive index N1 (λ1), N1 (λ2
), the thickness of the thin film is automatically calculated according to a predetermined calculation.

In the second type of method, monochromatic light of S-polarized light and P-polarized light is incident on a thin film on a substrate at a predetermined incident angle θl, and the energy reflectances Rs(01) and Rp(01) for each incident light are measured. , Furthermore, the monochromatic light of S polarization or P polarization is made incident at an incident angle of 02, and the energy reflectance Rs for the incident light is
(02) or Rp(02), and automatically calculate the refractive index N1 of the thin film according to a predetermined calculation based on the refractive index of the substrate and the energy reflectance Rs (θ1), RpH). And the above energy reflectance Rs(θ1)
, Rp(θ1) and Rs(02) or Rp(θ2)
, and the refractive index N1, the thickness of the thin film is automatically calculated according to a predetermined calculation.

Next, the present invention will be described in detail with reference to FIG. In the figure, reference numeral 12 is a substrate, reference numeral 10 is a thin film, and reference numeral 20 is a thin film.
Reference numeral 30 indicates a light source, and reference numeral 30 indicates reflected light. Further, the interface between air and the thin film 10 is S1, and the interface between the thin film 10 and the substrate 12 is indicated as 32. The known refractive index of the substrate 12 is N
2, and the unknown refractive index of the thin film 10 is assumed to be N1.

As shown in the figure, when monochromatic light is incident on the thin film 10 from the light source 20, the reflectance, which is the sum of all the light waves 30 that are multiple-reflected in the thin film 10 and reflected outside the film, is calculated using Snell's law and Fresnel's law. can be expressed as follows.

However, the subscripts 1 and 2 represent reflections at the interfaces Sl and S2, and Pus represents whether the incident light is P-polarized light or S-polarized light.

If the angle of incidence and angle of refraction are α, β, and γ as shown in the figure,
The above n P i r, 5. The plane Gβ can be expressed by Fresnel's equation as follows.

In addition, δ is the phase delay that occurs while the light passes between the interfaces Sl and 32, and if the wavelength is λ, then δ = 4x (Nl) (di) (cos β)/λ
It is given by (3).

Calculating the energy reflectance Rp,s using equation (1) results in the following equation.

Here, if the incident angle α is 45 degrees, equations (2) and (3) can be simplified as follows.

y'7P=((T1-1)/(T1+1))y';
= (1-TI,)/(1+T1)6F = (TI
T2-1) (TIT2-Tl)/(TIT2+1)(T2+
T1) Stomach'z= (TI-T2)/(T1+T2)δ
=2f2π(di)TI/λ However, here n-, , rTr, Takumi, T 2 = ,
r7177].

Also, equation (4) expresses this for each of S and P polarized light,
Solving for COS δ is as follows.

When formulas (5) and (6) are used, the following formula (7) is obtained.

In this equation (7), if the energy reflectances Rp and Rs are known, since the refractive index N2 is known, (7)
The unknown quantity in the equation is only N1. Therefore, Rp and Rs are determined by measurement, and N2. By putting Rp and Rs into equation (7) and solving equation (7) for N1, it is possible to know the refractive index N1 as the measurement target.

-++- Incidentally, since equation (7) holds true regardless of the value of the incident angle α, it can be determined appropriately during measurement, but if α is set to 45 degrees, the capacitance in equation (7) Since N1 is expressed by a simple formula as described above, the calculation for calculating N1 becomes simple.

Once the refractive index N1 is calculated in this way, the thickness di of the thin film can be calculated as follows by modifying the formula (3): dl=λδ/ (47C(Nl) (CO3β) )
It can be expressed as (3a).

Here, CO3β is determined by Snell's law, cosβ=!
It is 〒y revised edition/Nl.

In addition, if the refractive index N1 is known, δ can be calculated using the above (5) and (6).
Since it is determined by the formula, if the value of CO3δ at this time is C, then δ is given by δ=27Cm + ARCCO3C (8) where m is an integer.

Since the wavelength λ, refractive index N1, and angle of incidence α are already known,
When m (hereinafter referred to as the order) in the above equation (8) is known, δ is determined, and the film thickness d1 can be determined according to the above equation (3a).

There are two ways to determine the order m: (a) measuring the energy reflectance by changing the wavelength of the incident light; and (b) measuring the energy reflectance by changing the angle of incidence.
The first type of method of the present invention employs the method (a) above, and the second type of method employs the method (b).

First, to explain the theory of the first type of method, in this method, the energy reflectances Rs and Rp are measured using monochromatic light with the same incident angle and different wavelengths as in the previous explanation, and Calculate the refractive index of the thin film based on this and convert it to (3a)
Put it in the formula.

The wavelengths of the two types of monochromatic light used in the measurement were λ1. When λ2 is assumed, dl for these lights becomes. m and m' are orders.

The above d1(λ1) and d1(λ2) are originally the same amount.

Therefore, by changing rn and m' to various values, dim(λ1)
, dim' (λ2) is calculated, and S (m, m') = (dlIT1 (input 1) - dim'
(λ2))2 and dim(A() when S(m, m'') is the minimum.

Find the film thickness d1 by dim (dim).
Cλ1) +d1m' (λ1))/2.

FIG. 1A shows the first type of method described above as a flow diagram.

FIG. 1(B) shows the second type of method as a flow diagram. This second type of method will be explained below.

In this method, first, the energy reflectance Rs(θ/) and Rp(θI) are measured at the first incident angle θ/, and the refractive index N1 is calculated. Further, one of the energy reflectances Rs (θ2) and Rp<θ2) is measured at the second incident angle θ2. For the sake of concreteness, a case will be described below in which Rs (θ2) is measured.

When the refractive index N1 is known, as mentioned above, the order sequence d of the film thickness d1
i(m) is obtained from the two equations (3a) and (8).

Therefore, by substituting these dHm) into equations (2) and (3), and further using equation (4), calculate and determine the order sequence Rsm (02) of the energy reflectance for the order m at the incident angle θ2. The power order - should theoretically satisfy the equation (2). Therefore, in the present invention, S (m)
= (calculate Rs(θ2)-Rsm(θ2))2 and S axis)
The film thickness d1 is determined according to equation (9) based on the order m when the value is the minimum.

FIG. 3 shows only the essential parts of an example of an apparatus for carrying out the first type of method of the present invention. A thin film 10 whose refractive index is to be measured is formed on a substrate 12 .

The light source 20A is an output stabilized He-Ne laser that emits laser light with a wavelength λt of 6328 mm, and the light source 21 is a He-Ne laser with a wavelength λ2 of 5941 A. Reference numerals 23, 25, and 27 indicate a shutter, a shutter, and a filter, respectively. Filter 27 is a dichroic filter. When only the shutter 23 is opened, the monochromatic light emitted from the light source 20A enters the thin film 10 via a Plant-Thompson prism (not shown). The angle of incidence is fixed at 45 degrees. Adjust the Glan-Thompson prism to S-polarized light or P-polarized light, and use photodetector 2.
If the reflected light intensity is measured by 4, the energy reflectance R
s(λ1) or Rp(λ1) can be known. Similar measurements were made with only the shutter 25 open, and Rs(λ
2) , Rp (λ2) can be known.

Therefore, Rs(λ(), Rp(
Based on the substrate refractive index N2 known in advance as λ)), Rs (input 2), Rp (λλ), the data processing system 26 calculates the values of the refractive index N1 (λI) and N1 (λ″l). It is calculated and displayed on the display 28.

The calculation is basically to solve Equation (7) for N1, and various methods are possible, but here, calculation using the well-known bisection method will be explained as an example.

FIG. 2 is a flow diagram for explaining this calculation example.

A specific program example (based on BASIC) is shown below.

10 REM＊＊＊ri・nosetsuritsunoenrin＊
**50 DIM N(5), A(5), B(5)
,C(5)70 INPIJT "Ns=",
N580 INPtJT “Rsm”, R39
0INPtJT ”)lp= −, Rploo
T2=SQR(2*NS*NS-1)120 E1=
0.000001 130 N(1)=1.4 140 N(2)=1.9 150 IF NS<=Death+(2) THEN
N(2)=MS-0.00001160 )+(3
)=(N(1)+N(2))/2170 FORI=
I TO3 180T1=SQR(2*N(I)*N(1)-1)2
00 RIP=(Tl-1)*(Tl-1)/(T1
+1)/(T1+1)210 R2P=(T2-TI
)*(T1*T2-1)/(T1*T2+1)/(
T2÷TI) 220 RIS=(1-TI)/(1+T1)230
R25=(TI-T2)/(T1+T2)240
RIP2=RIP*RIP 250 R2P2=R2P*R2P 260 RIS2=RIS*I? l5270 R2
52=R2S*I? 2S280 A(I)=(RIP
2+R2P2-Rp*(1+RIP2*R2P2))
/<2*RIP*R2P*(Rp-1)) 290 B(I)=(RIS2+R2S2-R3*(
1+RIS2*R252))/(2*RIS*R2S*
(RS-1)) 300 C(1)=A(I)-B(I)310 N
EχTl 315 IF C(I)*C(2)>OGo T
O390320IF ABS (N(1)-N(2))
<EI Go To 360330 IF
C(1)*C(3)<OTHEN N(2)=N
(3) ELSEN(1)=N(3) 340 Go TO160 360PRINT "tH=", N(3) 380
END 390 N(1)=NS+O,OO001400
N(2)=1.9 410 Go To 160 The calculation procedure will be briefly explained below. See Figure 2. First, input Ns, Rs, and Rp. These are treated as variables NS, R3, and Rp in the calculation process (line numbers 70 to 90 of the above program).

Ns is the refractive index of the substrate and has been explained as N2 in the above explanation, but if it is fixed, it can be entered as a constant in the program, or if it is likely to change each time a measurement is made. is entered from the keyboard. Rs.
, Rp inputs the digitally converted output of the photodetector 24. Therefore, input of Rs and Rp is performed via the interface of the data processing system 26.

Now, in the program, the rough range of the refractive index of the thin film 10 is set as a lower limit of 1.4 and an upper limit of 1.9. These upper and lower limit values may be revised depending on the object to be measured.

First, the magnitude relationship between the input Ns and the upper limit value is compared, and when Ns<1.9, N(2)=NS-0, OOO'
01. N(1)=1.4. N(3)=(N(1)+N(
2))/2, A(I)=F for these three variables
p(N(f)), B(I)=Fs(N(I)), C(1
)=A(I)-B(I), (■=1-3) are calculated (row numbers 150-310). Fp and Fs are each (5
), which is a function given by the right side of equation (6).

Next, the sign of the product of C(1) and C<2) is determined.

Since N(1)〈N(3)〈N(2), C(1)*
If C(2)>O, then the root of equation (7) is the above N(1
), N(2), so in this case, the area in which the root should be searched is newly set to N(1)=NS+0.00001.
Set between N(2) = 1.9 and repeat the above calculation (
line number 390 and below).

Also, when C(1)*C(2)<O, the root to be sought is between N(1) and N(2), so in this case, the area where the root is to be found is C(1)* Depending on the sign of C(3), N(
1) to N(3) or N(3) to N(2) and repeat the above calculation (line numbers 330 to 340).

As the calculation is performed, the area in which roots should be found is sequentially reduced to 1/2.
The longer it gets, the smaller the absolute value of N(1)-N(2) becomes. Therefore, the above absolute value is 0.0
If it becomes smaller than 00001, N(3) is assumed to be sufficiently close to the desired refractive index, and N(3) is output as the desired refractive index Nf (line number 320.3).
60). Note that Nf was written as N1 in the above explanation. Thus, the refractive index of the thin film also stops. If the value of El in the program is set smaller, the accuracy of measurement can be further improved.

In this way, wavelength input 1. Obtain the refractive index N1 () and N1 (N2) for λ2, and display these on the display 28.
, then use these refractive indices to calculate the film thickness order series dimCin(), dim'(N2) for each order m,
d, which is calculated for m' and gives the minimum value of S(m, m')
The film thickness d is the average value of lm (λi) and dim' (N1).
1 is determined and the result is displayed on the display 28.

To give a specific example, using a sample of SiO sputtered on a Si substrate with a refractive index of 3.42, using the apparatus shown in FIG. 3, and performing calculations according to the program shown above, The refractive index of the SiO thin film was found to be Rs(χ1)=0.417574. RpOi)=0.
177269, Rs (λZ) =0.07082
53. Rp (N1) = 0.0852274, the refractive index of the thin film N1 (λ (), N1 (N2) are both m 1.4
I was able to find 571.

Table 1 shows an example of the order sequence of film thickness for light with a wavelength of 6328 people.

Table 1 m dim(λj) −m
dlm(N1)5 12547.04
-5 12286.076 15030.3
5 -6 14769.387 17
513.66 -7 17252.708
19996.97 -8 1973
6.019 22480.28 -9
Table 2 shows an example of the order sequence of film thickness for 22219.30 wavelengths of 5941 human light.

Table 2 m'd1m' (SZ) -m'
dim' (λλ)5 12645.10
-5 10672.856 14
976.90 -6 13004.65
7 17308.69 -7 15
336.408 19640.49 -8
17668.249 21972.29
-9 20000.04S (m, m')
The value of m takes the minimum value for light with a wavelength of 6328
= 8, 19996.97, and m''=-9, 20000.04 for the wavelength of 5941 people's light.

Therefore, the desired film thickness d1 is dl=(19996,97+20000.04)/2=
19998.5 people.

FIG. 4 shows an embodiment of the second type of method. code 2
2 shows a Plant-Thompson prism. In this device, each energy reflectance is calculated for incident angles of 45 degrees and 60 degrees.
It can be measured. FIG. 5 shows another embodiment of the second type of method. The difference from the example in FIG. 4 is that the light source 20B is a randomly polarized He-Ne laser;
The point is that a polarizer 22A is used. If you measure the reflected light intensity while rotating the polarizer 22Δ, the maximum value is S-polarized light, and the minimum value is P-polarized light (
or vice versa), the ratio of Rs and Rp can be determined with extremely high accuracy.

Further, a linearly polarized He-Ne laser may be used instead of the randomly polarized He-Ne laser, and a rotational rotator may be used instead of the polarizer.

A specific measurement example according to the embodiment shown in FIG. 4 will be given below.

Using a sample made by sputtering SiO on a Si substrate with a refractive index of 3.42, the Glan-Thompson prism 22 is set to S-polarized light or P-polarized light, and the energy reflectances Rs (Ak@) and Rp (at an incident angle of 45 degrees) are obtained. 4t'
) and the incident angle of 60 degrees were measured. Rs (4F') = 0.417574. Rp
<lr') =0.177269. Rs (1; )
=0.0976178. Rs (*f')
, Rp (4t') according to the above program, the refractive index is N1=1.457. Using this refractive index, the film thickness can be changed in order. Also, depending on each order m, the energy reflectance Rs for an incident angle of 60 degrees
m(At) is calculated.

Film thickness dim and energy reflectance Rsm for each order m
(, to') is shown in Table 3.

Table 3 m dml Rs
m<j;)÷1 2613.79
0.541302-1 2352.80
0.50221+2 5097
．． 11 0.512296-2
4836.14 0.428837+3
7580.42 0.44702
-3 7319.14 0
．． 312593+4 10063.70
0.3:39668-4
9802.76 0.163712+5
12547 0.19477
8-5 12286.1
0.0360576+6 15030.
3 0.0556253-6
14769.4 0.0192554
+7 17513.7 0
．． 110021-7 17252.7
0.128063+8 1
9997 0.0994979-8
19736 0.27
9207÷9 22480.3
0.249358-9 22219.
3 0.40514Rsm<lj) is Rs
(to) is closest to the actual measured value of 0.0976178,
It can be seen that the value of (Rs(lO')-Rsm(&o)) takes the minimum value when m=8. Therefore, the desired film thickness dl=19997 is determined by calculation in the data processing system 26 and displayed on the display 28.

(Effects) As described above, the present invention can provide a novel method for measuring the refractive index and thickness of a thin film.

Since this method is configured as described above, it is possible to automatically determine the refractive index and film thickness by simply measuring the energy reflectances Rs and Rp. Furthermore, it can be performed with a simple device and has high measurement accuracy. The method of the present invention consists of a measurement part and a calculation part, and the measurement part may be performed first and then the calculation part; however, as shown in the flow diagram of FIG. It is also possible to perform part of the calculation after performing the first part, then perform the remaining measurement part, and then perform the remaining calculation part.

In addition, in the first type of method, the order sequence of the film thickness has a period that differs depending on the wavelength, such as 2 + - 6 (λ), so the order sequence of the period f (input 1) is The film thickness is determined by the value that minimizes the difference from the order sequence of the period f(λ2).

In the second type of method, the order sequence Rsm(θ2) or l'? pm(θ2) and actual value Rs(θ2) or Rp
The film thickness is determined by comparison with (θ2).

Therefore, in the case of the first type of method, when comparing order sequences with different periods, since there is a beat in both periods, the point of agreement between the two appears at the beat period, and although it is not possible to specify the film thickness mathematically, The size of the film thickness that is actually measured is not unknown at all, and the approximate order is known, so there is no practical problem in determining the film thickness. The beat period can be increased by reducing the difference between the two measurement wavelengths, so if this period is set sufficiently large, it is easy to narrow down the value that gives the actual film thickness to only one value.

In the case of the second type of method, the order sequence Rsm (+5'2) or Rpm (θ2) is periodic, so the same problem as above exists mathematically, but for the same reason as above, the film thickness There are no particular practical problems. Further, the above mathematical problem can be solved by using three or more types of measurement wavelengths and measurement angles of incidence.

[Brief explanation of the drawing]

FIG. 1 is a flowchart for explaining the present invention, and FIG. 2 is a diagram for explaining the principle of an example of a calculation method for calculating a refractive index.

Claims (1)

[Claims] 1. A method for measuring the refractive index and film thickness of a thin film formed on a substrate having a known refractive index, the method comprising: Monochromatic light with a polarized wavelength λ1 is incident, and the energy reflectance Rs(λ
1), Rp(λ1) is measured, and at the above incident angle, S
Inject monochromatic light of wavelength λ2 of polarized light and P-polarized light, and calculate the energy reflectance Rs(λ2) and Rp(λ2) for each incident light.
is measured, and the refractive index of the substrate and the energy reflectance Rs
(λ1), Rp (λ1), Rs (λ2), Rp (λ2)
Based on the refractive index N1(λ1), N1(
λ2) is automatically calculated according to a predetermined calculation, and the energy reflectances Rs(λ1), Rp(λ1), R
s(λ2), Rp(λ2), and refractive index N1(λ1),
The refractive index and
Film thickness measurement method. 2 A method for measuring the refractive index and film thickness of a thin film formed on a substrate having a known refractive index, in which monochromatic light of S-polarized light and P-polarized light is applied to the thin film on the substrate at a predetermined incident angle θ1. energy reflectance Rs (θ1) for each incident light,
Measure Rp(θ1), and then inject the monochromatic light of S polarization or P polarization at an incident angle θ2, and measure the energy reflectance Rs(θ2) or Rp(θ2) for the incident light.
The refractive index of the substrate and the energy reflectance Rs (
θ1), Rp(θ1), the refractive index N1 of the thin film is automatically calculated according to a predetermined calculation, and the energy reflectance Rs(θ1), Rp(θ1),
A refractive index/film thickness measuring method, characterized in that the thickness of the thin film is automatically calculated according to a predetermined calculation based on Rs (θ2) or Rp (θ2) and the refractive index N1.