JPS58102534A - Non destructive diagnostic system - Google Patents

Abstract

PURPOSE:To effectively estimate internal conditions of a diagnostic object F even in case it is impossible to destroy such object F and a longer time is taken for such estimation, by making use of a model (f) of a diagnostic object F, giving a relation between parameter P indicating the internal condition of F and an output Q of F and by calculating P which satisfies an output Q* when an input i* is given to F. CONSTITUTION:100 indicates a diagnostic object F, 110 is a signal generator which applies an input signal to F, 120 is a receiver which receives an output signal from F, 130, 140 are output, input interfaces of a computer 150. 160 is a non-destructive diagnostic program stored in a memory 165 which diagnoses F using a model (f) 170 of F. 180 is a data storage table. 185 is a calculation program which calculates deviation between actual output value and calculated value. 190 is an input/output interface between user and this system and is usually a graphic display unit.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for non-destructively diagnosing the properties of an object.

For example, non-destructive diagnosis is used to diagnose failures in combinational logic circuits. In this case, various failure locations and failure modes (1 fixed failure, 0 fixed failure, etc.) are assumed, and what kind of output is obtained under each test input signal is maintained as a failure dictionary. Then, a test input signal is given to the sound test target, the output is observed, and the fault word 1i1 is
1) A method is often used in which a cause of failure is found that matches the input/output signal by performing a k search. This method requires the creation of a very troublesome fault dictionary prior to diagnosis. As another example, measuring the carrier concentration distribution in the depth direction at a specific location on a wafer in a semiconductor manufacturing process is an extremely important task for controlling the actual semiconductor process. Patent No. 56-1 filed earlier by Honde
As mentioned in No. 7012, in the past, a time-consuming procedure was used in which the steps of etching a certain amount from the surface of a silicon wafer and quantifying the amount of carrier by electrical measurement were repeated. For this example as well, it is important to develop a non-destructive method, and the above-mentioned previous study proposed a carrier distribution measurement method using infrared light. The proposed method utilizes the fact that the electric field of reflected light when an infrared element is irradiated onto the inspection site on a silicon wafer at an angle of incidence that reflects the shape of the carrier distribution at the inspection site.
The aim is to estimate the shape of the unknown carrier distribution from the observation results of the reflected light electric field. In the above invention, a method is shown in which the distribution of carriers in the depth direction is rectangular, but the actual distribution shape is not necessarily rectangular. One possible method is to smoothen and assume various distribution shapes, create a table that combines this with data representing the reflected optical electric field observed when an incident optical electric field is applied, and A possible method is to use a table to estimate the carrier distribution from the observed reflected light electric field data. However, this method has the disadvantage that the table must be created in advance.

Furthermore, it is difficult to accurately estimate the shape of a distribution other than the smoothed carrier distribution.

The purpose of the present invention is to diagnose the properties of the target F.
The present invention aims to provide a non-destructive diagnostic method that is effective in cases where it is impossible to use methods such as destruction, or even if it is possible, it takes a long time.

In the present invention, a model f of the object F is used in order to avoid using direct means such as destroying the object F'. f gives the relationship between the input 11 to F, the parameter P representing the internal state of the diagnostic target F, and the output Q from F. Let us temporarily write this as Q = ru, p). Now, suppose that when input if is given to F, an output Q is obtained. At this time, by calculating P that satisfies Q rice = f (i rice, P), F
Estimate the internal state of. , In the following, examples of the present invention are shown.

FIG. 1 shows a non-destructive diagnostic system using the present invention. In the figure, 100 is a diagnostic target (denoted as F), 110 is an input signal generator to F, 120 is an output signal receiver from F, 1
30 and 140 are the output of the computer 150 and the input interface 7A, respectively. 160 is a non-destructive diagnostic program stored in the memory 165;
70) Diagnose Fk using t-. (The processing procedure of 160 is shown in FIG. 2). 180 is a data storage table, 18
5/I′i output actual measured value and calculated value deviation calculation program,
190 is the input/output interface 7 between this system and the user.
In this figure, a graphic display device is used.

FIG. 2 Fi to a processing flowchart of the program 160 in FIG. 1 are shown. 200 in the figure is an initial setting process 61, which receives an instruction from the user whether or not to continue the analysis process via the graphic display device 190 shown in FIG. interface 130 of
At a certain time, the input signal generating device 110 to the target F is set to the initial state (the signal line is omitted, but the initial setting of tj: 100°120 is also performed depending on the case). Subsequently, the data storage table 180t is cleared to zero. In addition, the parameter values (
initial value, constant, etc.) t set.

In FIG. 2 210, 220, the input signal generator 110 is driven through the first mV interface 13 (l), and an input signal (indicated by 115) i(θk) is provided to F.

Here, θ is a parameter for changing the input signal, LllOFiθk is received from the computer side, a predetermined signal i(θk)t- is generated, and it is input to F. Under this input signal, the diagnostic target F generates the full output O(θk) (
1 118). This output is detected by receiving device 120. Processing 230 in FIG. 2 reads the output 0 (θk) detected at 120 into the computer. Subsequently, in process 240, information θh,j(θk
), 0(θk) are stored in the table 180. After this,
It is determined whether or not to repeat the processes of 210 to 240 above (245), and if necessary, repeat the process to obtain a total of M pieces of θ.
k.

A set of i(θk) and 0(θk) is stored in 180.

The subsequent process is a parameter estimation process using the model fy shown at 170 in FIG. Here, the input i to F
(θk), the output (0(θk)), and the model 0(#h)=f(i(θk) , P
) e is used to estimate the parameter P't- of the model. First, in 250, the parameter P is generated in excess. As a generation method, there is a method of generating a random number vector to obtain P, or a method of generating P11i stored in the computer memory as used last time.
kKi minute ΔPt - method of addition. In the latter case, calculate the sensitivity '7i-Pt- of the function δ shown in FIG.
A method or the like is used in which ΔP is taken in the direction of P where ΔP becomes smaller.

In process 255, each input value i(θk) stored in the table 180 in FIG. 1 in the previous process 240 is calculated.

k=1 to M1 and the parameter value P generated in step 250 above
and the model f of FIG. 1 170, the output value 0 (θk) corresponding to each input value is calculated as =1-Mt-.

In process 260, a deviation value δ between the output value calculated in 255 and the actual output value stored in 240 is calculated. For example, the following equation may be used as δ.

δ = 10 towns θ, ) - f (i rice (0M), P month + I O'
(θ leak) - f (i (0 m), P) 1+...
...+10(θ--f(i-town θ-9P)1 This is the total sum of the absolute values of the differences between the calculated output value and the actual output value for all input values.

In process 265, it is determined whether the error δ of the model determined above is small by comparing it with the convergence determination parameter 6 given in initial establishment process 200. δ is ε
If it is larger, the process returns to step 250. If not, the process moves to step 270, and the determined parameter Pt is displayed on the display device 190 in FIG. At this time, if it is possible to clearly visualize the state of the diagnosis target F, which is the source of the parameter P, this visualized image (ψ(P)
) are also displayed at 190.

After the above processing, return to the first processing 200,
Replace with another one and repeat the same procedure as many times as necessary.

Next, a failure diagnosis system for a combinational logic circuit using the present invention will be described.

The M3 diagram 300 is a combination circuit consisting of a two-man power OR (310) and a two-man power AND go (320). This corresponds to diagnosis target F in FIG. The normal operation of this circuit is given by the following equation.

Ot=("IV"*)'s Now, let us assume that there is a possibility that only the part 330 in the figure is stuck at 0 and 1 and a failure occurs. At this time, the operation of this circuit F including failures can be expressed by the following equation.

0*-((P+ (1+ V Is )V (P warehouse(1
+V 1m,))) ImHere, P is a parameter that takes 0 or 1. P*=P*=1 (0 o'clock 1/Cn
, Or= (i+V is ) is and represents a normal circuit. P*=1. FiOIm 1 when Ps=0
m, and P represents the 1-fixed fault in part 330 of Fig. 3.
1=0. When P*=1, 0=0, indicating a 0-stick failure. 1 or more, the above equation may be used as the model f in FIG. 1 170.

Next, the output 0.0 is calculated using the model f shown in FIG. 1 170. The deviation δ between the output 0 and the output 0− that was observed in the past can be calculated using the following two formulas.

δ=Up (0-■01) Here, ■ is the EOR symbol, and when 0- and 01 are different, 1
, takes 0 at the same time. Σ means the sum of all observed 0-. Other than this, δ=ΣI O+'
Otl may also be used.

Next, an explanation of the main parts of the diagnostic procedure processing (160 in FIG. 1) in this example? Perform according to Figure 2. In the process 220, three random numbers having a value of 0 or 1 are generated, a three-dimensional vector consisting of these three elements is generated, and the vector shown in FIG.
Input to terminals 0, 350, 360. In process 230, the output signal from terminal 370 is read and compiled. In process 240, the above output signals are stored in the table 180 in FIG. Repeat the above operation kM times. FIG. 4 shows an example of the contents of the table obtained as described above. In this example, the case where M=3 is shown.

As described in the introduction to this example, the failure states include fixed 0 failure and fixed 1 failure. As mentioned earlier, these are (P+, Pg)-(0,1).

(Pr, Pg)=(1,0), respectively. Further, in a normal case, it corresponds to (P+, Ps) = (1, 1). Therefore, in the process 250 of FIG. 2, (Pr
, Pg )=(1,1), (0,1), (1,0
) It is better to generate the map in t-order (In addition, in this example, we are using a simple example with only one failure location, so the above simple method is fine, but when considering one failure location, is, 2
It is sufficient to generate a one-dimensional parameter vector. If the failure location is θ, one location, two locations, etc. may occur, but since the probability of multiple locations failing at the same time is low, the 21-dimensional parameter vector Pt- Just generate it.

(Ps, Pa, Pg, Pa,...
Pa-t+Ps*)口(1,1,1,・・・・・・・・・
・・・・・・・・・・・・1.1)(:) (0,1,1,
...Song...River...1.1) Mouth (1,0,1,
・・・・・・・・・・・・・・・・・・1. ．． 1)φ(
1,1,0,1,・・・・・・・・・・・・1.1)φ
(1, 1, 1, 0, 1, 1)
Time (1, 1, ・・・・・・・・・・・・・・・・・・
...0.1)φ(1,1,...song number/song...1
．． 0) Next, in the process of FIG. 2 255, the parameter vectors sequentially assumed in the above method and the input signal values i, i, elE, in the cheetah table shown in FIG.
Using i- and the above-mentioned model f, the estimated output value corresponding to each row in FIG. 4 based on the assumed parameters is determined. In FIG. 5, P=(1,1), (0,1).

The estimated output values in the case of (1, 0) are shown in correspondence with FIG.

Next, in the process of FIG. 2 260, the previously defined deviation function δ
is calculated from the estimated output value and the actual measured output value calculated above. This result is also shown in FIG. In the process of 265, if the determination condition parameter ζ is set to 1, for example, 0.5, case 3 in FIG. 5 satisfies δ≦C. Therefore, processing 2
In 70, #! 1 figure 190KP” (Pl, Pg)
= (1,0), and if we display, for example, Fig. 3 at 190 in Fig. 1 as the function ψ(P), and then display that the point 330 in Fig. 3 has a 1 fixed failure. good. Figure 6 shows an example of this. During the program of FIG. 1 160,
It is assumed that the table shown in FIG. 6(a) is prepared.

In the first, second, and third rows of the table, the parameter P is (1
, 1) is marked with a Qreen color, a part where (Oll) is found is marked with l(, ed, and a part where (1, 0) is found is marked with Yellow-. 6(b) shows a display example.

In the case of the above example, the diagram of FIG. 6(b) is displayed on the ag1 diagram 190, and the system user is informed that the 600th copy has a YellowK color In% 1 failure.

In the above embodiments, the case where there is only one failure part was shown, but it is easy to extend the system to failures in multiple places. In this case, it is sufficient to change the model to the ft-multiple parts failure model shown in FIG. 1 170. Furthermore, although the circuit in Figure 3 rarely has one output, if multiple outputs can be observed, the circuit in Figure 1
00f, prepare as many actual output storage columns as the number of output signals in the data table of FIG. 4, and use the following equation as the deviation δ of FIG. 1 185.

δ=ΣΣ(01−■01k) First, Osb is determined by the output signal value of the i-th output terminal under the input signal. ΣΣ means creating a harmony for all output terminals and all input signals.

In some cases, there may be a plurality of parameter vectors P that satisfy the judgment sound 265 in FIG. In this case, it is a good idea to examine all the parameter vectors that satisfy the conditions, list the failure parts corresponding to each parameter vector, and use the same as the diagnosis result. At this time, although it is not possible to find a single faulty part through diagnosis,
Parts that are considered to be malfunctioning will be restored.

As can be seen from the above description, when this method is adopted, the task of creating a fault dictionary in advance can be omitted, and non-destructive diagnosis of the combinational circuit can be performed.

Next, an example will be shown in which the present invention is applied to non-contact measurement of carrier distribution within a silicon wafer in a semiconductor manufacturing process. As mentioned above, in Japanese Patent No. 56-17012, linearly polarized infrared light is incident on the wafer surface and the change in polarization of the reflected light is measured to determine the distribution of carrier concentration in the depth direction within the wafer. A method for measuring carrier concentration distribution was demonstrated.

As shown in Fig. 7, when monochromatic linearly polarized light is incident on the wafer surface at an incident angle θ, the incident light electric field and the reflected light 1 [fields are Es, Ep, EI', EP' ( The subscripts S and P indicate the S-polarized light component and the P-polarized light component, respectively), which utilizes the existence of the following relational expression between incident light and reflected light.

Here, jK, r@e'φl, r, and elφPa are the reflection widths of S-polarized light and P-polarized light, respectively.

When monochromatic linearly polarized light is incident on the surface of a desired substance and the state of change in polarization of the resulting reflected light is measured, the quantities Δ and ψ defined by the following equations can be actually measured.

ψ=tu−’ (rJ r@) Δ=φ? −φ1 This measurement method is called ellipsometry.

Now, the above 'l+'P*φ-1φpFi is summed up by the dielectric constant 1(ω) of the material into which the polarized light is incident (ω is the angular frequency of the incident light) and the incident angle θ. Therefore, the data ψ and Δ obtained by ellipsometry are based on the dielectric constant 8 (ω) of the material.
and becomes a function of θ.

Here, the dielectric constant g(ω) can be approximately calculated using the following formula when infrared light is used as the incident light beam.

here, ε--material constant 9m7=effective mass of carrier.

τ = carrier relaxation time, ω = incident light angular frequency.

e=electronic charge, N=carrier concentration As shown at 710 in FIG.
When given as a function N(Z) of , the dielectric constant is 2
becomes a function of This is called t−ε(ω, N(Z)l).

To summarize the above explanation, the 1-ta (Δ, ψ) obtained by injecting infrared light into a specific point on the surface and observing the change in polarization of the reflected light is: Angular frequency ω of incident light, carrier concentration distribution N(
is a function of the ray incident angle θ. This is tentatively written as follows.

ψ=f1(ω, N(Z), θ) Δ=etal(ω, N(1), #) Since the specific calculation method for the above functions f, , f, which give ψ and Δ is well known, The explanation is omitted here.

From the above formula, when ω is kept constant and 0 is varied variously, (
It can be seen that the actual measured values of Δ, ψ) reflect N(!1).

Similarly, by keeping θ constant and changing ω, we obtain (Δ, ψ) at nine o'clock.
It can be seen that the actual measured value of N(ri) also reflects N(ri).Using this fact, a method for determining N(Z)t- is shown in the earlier application mentioned above.As one embodiment of this invention, FIG. In the figure, 801 is an infrared light source, 802 is a spectroscope, 803 is a polarizer, 804 is a silicon wafer, and 80
5 is a rotary analyzer, 806Fi rotary encoder, 80
7 is a detector, 80B is an interface, 809 is a minicomputer, and 810 is a large computer. In this example, the light beam emitted from the infrared light source 801 is transmitted to the spectroscope 800.
2, the light is made into monochromatic light, is linearly polarized through an infrared polarizer 803, and is incident on the surface of a cricon wafer 804. 804'' surface passes through a rotating analyzer 805 and is detected by an infrared detector 807. Spectrometer 8
020 wavelength (λ) is sent from the minicomputer 809 via an interface 808, and the detection output of the detector 807 and the angle signal from the rotary encoder 806 are sent to the minicomputer 809 via the interface 808. The obtained ellipso data (Δ(λ), ψ(λ)) is handled by the minicomputer 809, and the obtained data is processed by the large computer 810 to determine the carrier distribution.

FIG. 9 shows another embodiment of the above invention, in which ellipsometric data is measured by arbitrarily changing the incident angle. and enters the silicon wafer 904. The angle of incidence θ is set to a desired value by a rotary stage 913 operated according to instructions from a minicomputer 909. The analyzer 905 and the infrared detector 907 are mounted on the rotating stage 9.
Linked with 13. The detection output of 907, along with the angle signal from rotary encoder 914, is
The processing of the ellipso data (Δ(θ), ψ(θ)) is executed by a large-sized computer 910.

In the above invention, the results of processing a case where the carrier concentration distribution can be approximated by a rectangle using the embodiment in FIG. 9 are also shown. This is shown in FIG. The white circles are actually measured values, and the rectangles are those determined by a large-scale computer that closely match the actual measured values.

The actual carrier distribution (NCZ) within the wafer is not necessarily rectangular, but often has a complex shape. Therefore,
A method for improving the accuracy of application of the invention of the prior application using the present invention will be described below. As an example, we will use the example of the M9 diagram that obtains (Δ(θ), ψ(θ)) as ellipso data, but the example shown in FIG. 8 that obtains (Δ(λ), ψ(λ)) will be used. A similar method can be applied to

In this case, the functions of the large-sized computer 910 and mini-computer 909 in the invention of the prior application shown in FIG. 9 are performed by the computer 150 in FIG. 8g1. Interface 908 in FIG. 9 corresponds to 130 and 140 in FIG. The inspection target 100 in FIG. 1 is the wafer 904 in FIG.
, 913, 914, the output signal observation device 120 is 90
5,907.

Now, the object F (in this example,
As the model f of the physical structure of the carrier distribution measurement site on the silicon wafer, the following f and f shown above are used.

ψ=f1(ω, N(Z), θ) Δ=f, (ωIN("Lθ)) Here, when the carrier distribution N(Z) has various complicated shapes, in order to accurately approximate them, K, N (Z
), the following formula is used.・Here, P・s, 1 mouth, Pts, 1 mouth are all parameters ≧0, and when α>β, Pa+m≧Pha, 14Js-4b node T6゜O(Pts, PIm
) is defined as a function that becomes PI'+'' when 2≧PL and one unit when ``<Ptm.

The above formula is, as shown in the 111th, the normal distribution t-PI*' with asymmetrical spreads PIm and PlJ on the boundary of the median value z=pHt, plus one weight, and the constant Pu t'' It has been added.

Figure 12 shows the parameter P-t for the case ■=2.
〜P*i The shape of the am distribution N(Z, P) when changed to kyuzu is shown (hereinafter, the case where it is written as parameter iP is also used). As shown in the figure, it can be seen that various distribution shapes can be expressed by changing the parameter P.

By using this method, the previous model et al.

are, as follows, instead of N(Z), nokudimeta Pt
Since the model can be changed to a variable, this is used as 170 in FIG.

ψ"i (ωp, θ) Δ=f-(ω, P, #) The data table in Figure 5141/'-180 is shown in Figure 13. This table contains the incident glaze by the processing up to No. 2114245. The actual measured value of ellipso data at the corner is stored.

The following equation is used as the deviation function δ of 185 in FIG.

This is the actual measured ellipso data (Δ”(θ), f”(θ)
) and the data (Δ(
θ) and ψ(θ)) for all incident angles added.

As the function δ, in addition to the above formula, it is also possible to use, for example, the following.

This means ψ”(θ) and ψ(θ
) and the absolute value of the difference between Δ"(6) and Δ(θ), which is the size of a mosquito, the larger [- is used as the deviation between the measured data and the calculated data. Ru.

Figure m14 shows the situation when the process MAt of Figure 2 of the present invention is applied to this example. The data read in the process in FIG. 2 2451 (FIG. 13) also reads the incident angular frequency ω shown on the left side of FIG. In the process 250 of FIG. 2, the parameter P is assumed as shown in the case 10 column of the figure, for example. In the process of 255, using the previous model '+, f*, the thrust output Δ=
f t (ω, P1°θ), ψ=f word ω, P3. θ)
Calculate each value of tθ. In process 260, using the function δ shown above, the value of the measured ellipso data and
Calculate the deviation of calculated values. In step 265, it is checked whether δ is larger than a separately given reference value -. FIG. 14 shows an example in which a>6 and the process returns to step 250 to perform the calculation again. Parameter Pi assumed in the first calculation
has been changed to P snow. The following process is the same,
The above process is repeated until the process 2650 judgment condition satisfies δ≦ε.

FIG. 15 shows the results of process 270. The state of the analytical logarithm ψ(P) (in this example, the carrier distribution in the depth direction N(z, P)...see FIG. 12) calculated from the parameters P and 1c and P is shown in FIG. The light is showing.

In one example, the application of the present invention to the method of FIG. 9 for acquiring ellipsodata at various angles of incidence θ was shown.
A similar method can be used to determine the carrier distribution using ellipsodata for various incident light angular frequencies ω (from the relationship λ = 2πC/ω, equivalent to varying the incident wavelength λ, where C is the speed of light). can. In this case, it is good to store in the data table 180 in FIG. 1 ellipso data measured by fixing θ and varying λ. ψ,
Model for calculating Δ ψ=f, (ω, P, θ) Δ=
(ω, P, θ) can be left as they are. However, ψ.

When calculating Δ, a given fixed value is used for θ, and ω is calculated from λ using (ω=2πC/λ, C: speed of light).

According to this embodiment, it is possible to apply the carrier distribution measurement principle t1 shown in the invention of the prior application with high precision when the carrier distribution within the wafer has a complicated shape f.

In addition, in this example, a method was used in which the intra-wafer carrier distribution was expressed as the sum of the number of feet and an asymmetric normal distribution function.
As another example, it is also possible to use an orthogonal function family such as a Fourier series. In this case, the definition formula for N(Z, P) may be changed.

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing the basic configuration of the present invention, FIG. 2 is a flowchart showing the processing procedure of the program in FIG. 1,
3, 4, 5, 6(a) and 6(b) are explanatory diagrams when the present invention is applied to failure diagnosis of combinational logic circuits, and FIGS. 7, 8, and 9 figure. Figure 1θ, Figure 11, Figure 12, Figure 13, Figure 14,
FIG. 15 is an explanatory diagram when the present invention is applied to carrier distribution measurement. 100... Diagnosis target, 110... Input signal generating device, 120... Output signal receiving device, 130... Computer output interface, 140... Calculation input interface, 150... Computer , 160...Processing program, 170...Diagnostic pair [100 model f (output signal calculation program), iso...Data storage table, FIG. 1L
J'￥J3 figure'fJ4 figure ￥36 figure (tλ2n￥J 3 times 1114 I 9 figure % // Figure 11: (l) Figure 11 N (Kn straw IZ figure

Claims (1)

[Claims] 1. A step of applying one input signal (denoted as i) to the target (denoted as F), and a step of obtaining a series of output signals from the series of input signals, Diagnosis target F
The output signal of F (denoted as Q), the model formula f of F that relates the input signal to tIF and the parameter (denoted as P) representing the characteristics of F to be diagnosed, and the output signal value calculated using φ for ft-. A non-destructive diagnostic method consisting of a step of examining the degree of agreement between the actual output signal values of F, and a step of modifying the parameter P of model f to improve the degree of agreement.