TW202009479A - System and method for measuring a thermal expansion coefficient - Google Patents

Abstract

A system and a method for measuring a thermal expansion coefficient are provided to solve the problem where the conventional measuring method cannot provide a real-time measurement. The system includes a test member having a tested sample and a substrate, a measuring module generating a heating current flowing into the tested sample which remains a period of time, and a data processing module coupled with the measuring module. The measuring module applies a voltage difference between the tested sample and the substrate and measures a capacitance value. The data processing module obtains a limited current value, a stable time and an absorption voltage value which between the tested sample and the substrate by analyzing the heating current, the heating time, the voltage difference and the capacitance value. The data processing module introduces an equation to calculate the thermal expansion coefficient of the tested sample.

Description

Thermal expansion coefficient detection system and method

The invention relates to a material detection method, in particular to a thermal expansion coefficient detection system and method for semiconductor thin film materials.

Microelectromechanical system (MEMS) is a micro-system that integrates the functions of micro-devices manufactured through semiconductor manufacturing processes and confidential mechanical technologies. It can include micro-sensors, microprocessors, micro-actuators and other components. Microelectromechanical structures are generally manufactured by surface micromachining technology, which is formed by stacking multiple layers of thin films using semiconductor process methods such as evaporation, sputtering or chemical deposition. Therefore, the composition, thickness, and Process differences, such as mechanical properties, will affect the function and quality of MEMS, and through microscopic measurement and analysis techniques, the characteristics of film materials such as stress, deformation and thermal expansion coefficient can be further used to adjust process parameters, and Improve product yield.

The general method of detecting thin film materials is to use the image interference (Interference) principle to measure the bending amount of thin film materials, and the thin film materials are subjected to heat treatment to measure the bending amount of thin film materials at different temperatures, and the thermal expansion coefficient of thin film materials can be further calculated However, the conventional thin film material thermal expansion coefficient detection method needs to capture the interference image multiple times, which is enough to calculate the thermal expansion coefficient through the formula, resulting in the detection process does not meet the immediate needs of the production line. In addition, the production line must be equipped with a light source to emit The light beam is on the thin film material and the image capturing device to collect the interference image, which leads to a significant increase in the cost of production equipment, and the detection process is incompatible with the electrical test process, resulting in additional manpower requirements.

In view of this, the conventional thermal expansion coefficient detection method does still need to be improved.

In order to solve the above problems, the object of the present invention is to provide a thermal expansion coefficient detection system and method, which can instantly detect the thermal expansion coefficient of the thin film material and improve the inspection speed of the production line.

The next object of the present invention is to provide a thermal expansion coefficient detection system and method, which has a simple and fast operation process, which can save manpower and equipment requirements.

The thermal expansion coefficient detection system of the present invention includes: a test piece having a test sample and a substrate, the test sample is electrically insulated from the substrate, the test sample has a same length, a same width and a same thickness, the test sample Before being deformed by heat, there is an initial gap between the test sample and the substrate; a measurement module is electrically connected to the test piece, and the measurement module is used to generate a heating current into the test sample and maintain a heating time, and Applying a potential difference between the test sample and the substrate and measuring the capacitance between the test sample and the substrate; and a data processing module coupled to the measurement module, the data processing module analyzes the The heating current, the heating time, the potential difference and the capacitance value, the maximum heating current allowed by the test piece is a limit current value, and the time for the test sample to reach stability after heating is a stable time, and the test sample and For an adsorption voltage value between the substrates, the data processing module calculates a coefficient of thermal expansion of the detected sample by an empirical formula.

其中，α為該檢測樣本之熱膨脹係數；B _L 為該檢測樣本之樣本長度；B _W 為該檢測樣本之樣本寬度；B _T 為該檢測樣本之樣本厚度；g ₀為該檢測樣本與該基板之間的初始間隙；I為該加熱電流；I _cr 為該極限電流值；t為該加熱時間；t _st 為該穩定時間；V _pi 為該吸附電壓值；k為該測試件之熱傳導係數；β為該測試件之電阻溫度係數；ρ為該測試件之電阻率；E為該測試件之楊氏係數；ε為空氣之介電係數；N1為第一待定係數；N2為第二待定係數；N3為第三待定係數；N4為第四待定係數；N5為第五待定係數。 The thermal expansion coefficient detection method of the present invention uses the thermal expansion coefficient detection system described above, and includes: a heating step to stabilize the heating current into the test piece and continue the heating time, the detection sample is thermally deformed; a measurement step to The gradually increasing potential difference acts between the detection sample of the test piece and the substrate, and simultaneously measures the capacitance value to find the adsorption voltage value; and a calculation step, the heating current, the heating time and The adsorption voltage value is imported into the empirical formula to calculate the thermal expansion coefficient of the test sample. The empirical formula is as follows:

Where α is the thermal expansion coefficient of the test sample; B _{L is} the sample length of the test sample; B _{W is} the sample width of the test sample; B _{T is} the sample thickness of the test sample; g _{0 is} the test sample and the substrate The initial gap between; I is the heating current; I _{cr is} the limit current value; t is the heating time; t _{st is} the stabilization time; V _{pi is} the adsorption voltage value; k is the thermal conductivity coefficient of the test piece; β is the temperature coefficient of resistance of the test piece; ρ is the resistivity of the test piece; E is the Young's coefficient of the test piece; ε is the dielectric coefficient of air; N 1 is the first undetermined coefficient; N 2 is the second Undetermined coefficient; N 3 is the third undetermined coefficient; N 4 is the fourth undetermined coefficient; N 5 is the fifth undetermined coefficient.

According to this, the thermal expansion coefficient detection system and method of the present invention is to heat-deform the detection sample by a stable heating current, and detect the adsorption voltage value of the detection sample, and then import the adsorption voltage value into the empirical formula to Calculate the thermal expansion coefficient of the test sample. Since the test process only uses electrical signals to heat and detect the electrical signal, the thermal expansion coefficient can be obtained quickly and instantly, which can be easily applied to the production line of thin film material components. Thus, the present invention has improved The efficiency of detection speed and production capacity can also save manpower and equipment requirements.

Wherein, the test piece has two electrode ends respectively connected to the two ends of the detection sample, and a supporting layer is provided between each electrode end and the substrate. In this way, the test sample is overhead on the substrate and the test piece forms a bridge structure, which has the effects of electrical insulation and capacitance value generation.

The distance between the two electrode ends of the test piece is the length of the sample, the width of the contact surface between the test sample and the electrode end is the width of the sample, and the height of the contact surface is the thickness of the sample. In this way, the sample length, sample width and sample thickness can represent the state of the test sample deformed by heat, and it has the effect of establishing an empirical formula.

Wherein, the measuring module has a set of current wires electrically connected to the two electrode terminals of the test piece respectively. In this way, the heating current can enter the detection sample through the current wire and the two electrode ends, which has the effect of controlling the current to heat the detection sample.

Wherein, the measurement module has a set of measurement wires electrically connected to one of the electrode terminals and the substrate respectively. In this way, the potential difference may exist between the detection sample and the substrate, which has the functions of measuring the capacitance value and observing the change of the gap.

Among them, the first undetermined coefficient is 1.4~1.5. In this way, the first undetermined coefficient can be adjusted according to different sample thicknesses and sample lengths, which has the effect of improving the calculation accuracy of the empirical formula.

Among them, the second undetermined coefficient is 0.4~0.5. In this way, the second undetermined coefficient can be adjusted according to different sample lengths and sample widths, which has the effect of improving the calculation accuracy of the empirical formula.

Among them, the third undetermined coefficient is 1.8 to 1.9. In this way, the third undetermined coefficient can be adjusted according to different sample thicknesses and sample widths, which has the effect of improving the calculation accuracy of the empirical formula.

Among them, the fourth undetermined coefficient is 1.6 to 1.7. In this way, the fourth undetermined coefficient can be adjusted according to different heating currents and limiting current values, which has the effect of improving the calculation accuracy of the empirical formula.

Among them, the fifth undetermined coefficient is 0.9~1.0. In this way, the fifth undetermined coefficient can be adjusted according to different heating time and stabilization time, which has the effect of improving the calculation accuracy of the empirical formula.

1‧‧‧Test piece

11‧‧‧Electrode

12‧‧‧ substrate

13‧‧‧support layer

2‧‧‧Measurement module

21‧‧‧current wire

22‧‧‧Measurement wire

3‧‧‧Data processing module

B‧‧‧Test sample

B _L ‧‧‧ sample length

B _W ‧‧‧ sample width

B _T ‧‧‧ sample thickness

g‧‧‧Gap

g ₀ ‧‧‧ initial gap

△g‧‧‧Gap change

I‧‧‧Heating current

t‧‧‧heating time

V‧‧‧Potential difference

C‧‧‧Capacitance

I _cr ‧‧‧ limit current value

t _st ‧‧‧ stable time

V _pi ‧‧‧ adsorption voltage value

S1‧‧‧Heating procedure

S2‧‧‧Measurement procedure

S3‧‧‧Calculation procedure

[Figure 1] A system block diagram of a preferred embodiment of the present invention.

[Figure 2a] A partial perspective view of a preferred embodiment of the present invention.

[Figure 2b] The top view as shown in Figure 2a.

[Figure 2c] A side view as shown in Figure 2a.

[Fig. 2d] A partially enlarged view as shown in Fig. 2c.

[Figure 3] A diagram of the operation of a preferred embodiment of the present invention.

[Figure 4a] A graph of the change trend of the capacitance value C in the figure 3 corresponding to the heating time t.

[Figure 4b] A graph of the change trend of the gap change amount converted from the capacitance value C in the figure 4a corresponding to the heating time t.

[Figure 4c] A graph showing the change trend of the capacitance value C corresponding to the potential difference V as shown in Figure 3.

[Figure 5] Step flow chart of a preferred embodiment of the present invention.

In order to make the above and other objects, features and advantages of the present invention more obvious and understandable, the preferred embodiments of the present invention are described below in conjunction with the attached drawings, which are described in detail as follows: Please refer to FIG. 1, It is a preferred embodiment of the thermal expansion coefficient detection system of the present invention, which includes a test piece 1, a measurement module 2 and a data processing module 3, the measurement module 2 is electrically connected to the test piece 1, the data processing The module 3 is coupled to the measurement module 2.

Referring to FIG. 2a, the test piece 1 is connected to the two ends of a test sample B by two electrode terminals 11 respectively. The two electrode terminals 11 are located on a substrate 12 between each of the electrode terminals 11 and the substrate 12 A supporting layer 13 makes the detection sample B overhead on the substrate 12 through the two electrode terminals 11 and the two supporting layers 13, and the test piece 1 forms a bridge structure. The test piece 1 can be formed by stacking and combining semiconductor processes such as lithography, etching, etc., wherein the two electrode terminals 11 are semiconductors and the composition can be silicon, and the substrate 12 can be an SOI wafer (Silicon On Insulator Wafer) ), the supporting layer 13 is an electrical insulator and the composition may be silicon dioxide (Silicon Dioxide).

Please refer to Figures 2b and 2c, the test sample B is a rectangular parallelepiped structure with a sample length B _L , a sample width B _W and a sample thickness B _T , the distance between the two electrode ends 11 of the test piece 1 is The sample length B _L , the width of the contact surface between the test sample B and the electrode terminal 11 is the sample width B _W , and the height of the contact surface is the sample thickness B _T , and the test sample B is overhead on the substrate 12 Above, there is a gap g between the detection sample B and the substrate 12. Please refer to FIG. 2d again. Before the test sample B is deformed by heat, the gap g is equal to an initial gap g _{0. After} the test sample B is deformed by heat, the gap g changes and the initial gap g ₀ minus the gap g is equal to A gap change amount △g.

Referring to FIG. 3, the measurement module 2 may be a semiconductor analyzer, and a set of current wires 21 are respectively electrically connected to the two electrode terminals 11 of the test piece 1, and the measurement module 2 may generate a heating current I is guided by the current wire 21 and the two electrode terminals 11 to cause the heating current I to enter the detection sample B and maintain a heating time t to achieve the effect of heating the detection sample B. In addition, the measurement module 2 is electrically connected to one of the electrode terminals 11 and the substrate 12 by a set of measurement wires 22, and the measurement module 2 may apply one of a gradual increase between the detection sample B and the substrate 12 The potential difference V, and simultaneously measure the capacitance value C between the detection sample B and the substrate 12.

The data processing module 3 may be a computer for importing the relevant parameters of the thermal expansion coefficient detection, including: the sample length B _L , the sample width B _W , the sample thickness B _T , the initial gap g ₀ , the heating current I. The heating time t, the potential difference V and the capacitance value C, the data processing module 3 can use the measurement module 2 to use multiple sets of different heating currents I to act on the test piece 1 and observe the capacitance The relationship between the value C and the heating time t; the data processing module 3 can also gradually increase the potential difference V through the measurement module 2 and observe the relationship between the potential difference V and the capacitance value C.

As shown in FIG. 4a, during the process of the heating current I acting on the test piece 1, the capacitance value C corresponds to the change trend of the heating time t, which is different according to the heating current I of different magnitudes. When it is too large, the structure of the test piece 1 is damaged and the capacitance C cannot be measured (as shown by the I ₄ curve in Fig. 4a), and the maximum heating current I that the test piece 1 can withstand is a limit current value I _cr (as shown by the I _cr curve in Figure 4a).

Moreover, as shown in FIG. 4b, the capacitance value C of the test piece 1 can be converted into the gap change amount Δg, then the gap change amount Δg corresponds to the heating time t change, when the gap change amount Δg When the maximum value is reached, the change of the gap change amount Δg tends to be stable, and the process from the beginning of heating the test piece 1 to the gap change amount Δg being stable is a stabilization time t _st .

Moreover, as shown in FIG. 4c, after the process of heating the test piece 1 is completed, the capacitance value C is measured to correspond to the change trend of the potential difference V. The potential difference V at the instant when the capacitance value C rises sharply is an adsorption voltage value V _pi .

其中，k為該測試件1之熱傳導係數；β為該測試件1之電阻溫度係數；ρ為該 測試件1之電阻率；E為該測試件1之楊氏係數；ε為空氣之介電係數；N1係第一待定係數且較佳為1.4~1.5；N2係第二待定係數且較佳為0.4~0.5；N3係第三待定係數且較佳為1.8~1.9；N4係第四待定係數且較佳為1.6~1.7；N5係第五待定係數且較佳為0.9~1.0。 According to the above relationship diagram, the data processing module 3 can import the limit current value I _cr , the stabilization time t _st and the adsorption voltage value V _pi and other characteristic parameters of the test piece 1 into an empirical formula and calculate the To test the thermal expansion coefficient α of sample B, the empirical formula is as follows:

Where k is the thermal conductivity coefficient of the test piece 1; β is the temperature coefficient of resistance of the test piece 1; ρ is the resistivity of the test piece 1; E is the Young's coefficient of the test piece 1; ε is the dielectric of air Coefficients; N 1 is the first undetermined coefficient and is preferably 1.4 to 1.5; N 2 is the second undetermined coefficient and is preferably 0.4 to 0.5; N 3 is the third undetermined coefficient and is preferably 1.8 to 1.9; N 4 is The fourth to-be-determined coefficient is preferably 1.6 to 1.7; N 5 is the fifth to-be-determined coefficient and is preferably 0.9 to 1.0.

Please refer to FIG. 5, which is a preferred embodiment of the method for detecting the thermal expansion coefficient of the present invention, which includes a heating step S1, a measuring step S2, and a calculating step S3.

In the heating step S1, the measurement module 2 causes the stable heating current I to enter the test piece 1 for the heating time t, so that the detection sample B is deformed by heating.

In the measurement step S2, the measurement module 2 applies the gradually increasing potential difference V to the test piece 1, and simultaneously measures the capacitance value C to find the adsorption voltage value V _pi .

The calculation step S3 introduces the heating current I, the heating time t and the adsorption voltage value V _pi into the empirical formula to calculate the thermal expansion coefficient α.

In summary, the system and method for detecting the coefficient of thermal expansion of the present invention heat the deformation of the test sample by a stable heating current, and detect the adsorption voltage value of the test sample, and then import the adsorption voltage value into the empirical formula In order to calculate the thermal expansion coefficient of the test sample, because the detection process only uses electrical signals to heat and detect the electrical signals, the thermal expansion coefficient can be obtained quickly and instantaneously, which can be easily applied to the production line of thin film material components. It has the effect of improving inspection speed and production capacity, and can also save manpower and equipment requirements.

Although the present invention has been disclosed using the above-mentioned preferred embodiments, it is not intended to limit the present invention. Anyone who is familiar with this art without departing from the spirit and scope of the present invention still makes various changes and modifications to the above-mentioned embodiments. The technical scope of the invention is protected, so the scope of protection of the present invention shall be subject to the scope defined in the appended patent application.

1‧‧‧Test piece

11‧‧‧Electrode

12‧‧‧ substrate

13‧‧‧support layer

2‧‧‧Measurement module

21‧‧‧current wire

22‧‧‧Measurement wire

3‧‧‧Data processing module

B‧‧‧Test sample

I‧‧‧Heating current

t‧‧‧heating time

V‧‧‧Potential difference

C‧‧‧Capacitance

Claims (11)

A thermal expansion coefficient detection system includes: a test piece having a test sample and a substrate, the test sample is electrically insulated from the substrate, the test sample has a sample length, a sample width and a sample thickness, the sample is deformed by heat Previously, there was an initial gap between the test sample and the substrate; a measurement module, electrically connected to the test piece, the measurement module used to generate a heating current into the test sample and maintain a heating time, and in the Applying a potential difference between the detection sample and the substrate and measuring the capacitance between the detection sample and the substrate; and a data processing module coupled to the measurement module, the data processing module analyzes the heating current , The heating time, the potential difference and the capacitance value, the maximum heating current allowed by the test piece is a limit current value, and the time for the test sample to reach stability after heating is a stable time, and the test sample and the substrate Between an adsorption voltage value, the data processing module calculates a thermal expansion coefficient of the detected sample by an empirical formula. The thermal expansion coefficient detection system as described in Item 1 of the patent application range, wherein the test piece has two electrode ends connected to the two ends of the detection sample, and a support layer is provided between each electrode end and the substrate. The thermal expansion coefficient detection system as described in item 2 of the patent application scope, wherein the distance between the two electrode ends of the test piece is the sample length, and the width of the contact surface between the detection sample and the electrode end is the sample width , And the height of the contact surface is the thickness of the sample. The thermal expansion coefficient detection system as described in item 2 of the patent application scope, wherein the measurement module has a set of current wires electrically connected to the two electrode terminals of the test piece, respectively. The thermal expansion coefficient detection system as described in item 2 of the patent application scope, wherein the measurement module has a set of measurement leads electrically connected to one of the electrode terminals and the substrate respectively. A thermal expansion coefficient detection method using the thermal expansion coefficient detection system described in any one of items 1 to 5 of the patent application scope, the method includes: a heating step to stabilize the heating current into the test piece and continue the heating At time, the test sample is deformed by heat; a measuring step, which gradually increases the potential difference between the test sample and the substrate of the test piece, and simultaneously measures the capacitance value to find the adsorption voltage value; and In a calculation step, the heating current, the heating time and the adsorption voltage value are imported into the empirical formula to calculate the thermal expansion coefficient of the test sample. The empirical formula is as follows:

Where α is the thermal expansion coefficient of the test sample; B _{L is} the sample length of the test sample; B _{W is} the sample width of the test sample; B _{T is} the sample thickness of the test sample; g _{0 is} the test sample and the substrate The initial gap between; I is the heating current; I _{cr is} the limit current value; t is the heating time; t _{st is} the stabilization time; V _{pi is} the adsorption voltage value; k is the thermal conductivity coefficient of the test piece; β is the temperature coefficient of resistance of the test piece; ρ is the resistivity of the test piece; E is the Young's coefficient of the test piece; ε is the dielectric coefficient of air; N 1 is the first undetermined coefficient; N 2 is the second Undetermined coefficient; N 3 is the third undetermined coefficient; N 4 is the fourth undetermined coefficient; N 5 is the fifth undetermined coefficient. The thermal expansion coefficient detection method as described in item 6 of the patent application range, wherein the first undetermined coefficient is 1.4-15. The thermal expansion coefficient detection method as described in item 6 of the patent application scope, wherein the second to-be-determined coefficient is 0.4 to 0.5. The thermal expansion coefficient detection method as described in item 6 of the patent application scope, wherein the third undetermined coefficient is 1.8 to 1.9. The thermal expansion coefficient detection method as described in item 6 of the patent application scope, wherein the fourth undetermined coefficient is 1.6 to 1.7. The thermal expansion coefficient detection method as described in item 6 of the patent application scope, wherein the fifth to-be-determined coefficient is 0.9 to 1.0.

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