CN1621821A - Structure and method for measuring thermal-expansion coefficient of polycrystalline silicon thin film - Google Patents

Abstract

The measurement structure and measurement method for measuring the thermal expansion coefficient of polysilicon thin films are based on the online detection structure of the thermal expansion coefficient of polysilicon thin films based on surface processing technology. The structure is composed of a polysilicon double straight beam structure and two polysilicon curved beam structures. Partially coated with aluminum film, the polysilicon curved beam structure is composed of two identical curved beams, the top of the curved beam is provided with a tip, and its tip is facing the aluminum film; the measurement method is: prepare the measuring beam structure; measure the straight beam at room temperature Pass a small current I ₁ and I ₀ respectively, measure the voltages V ₁ and V ₀ at both ends, and obtain the resistivity ρ ₁ and ρ ₀ ; choose any one of the two curved beam structure groups, and the total length is L ₂ , pass the current I ₂ to it, measure the voltage V ₂ at both ends, measure the resistivity ρ ₂ , pass a slowly increasing current to the two ends of the curved beam respectively, and observe the ohmmeter connecting the anchorage area of the curved beam and the straight beam Whether there is a jump from infinity to finite value in the reading of the reading; the coefficient of thermal expansion α can be obtained.

Description

Measure the measurement structure and the measuring method thereof of polysilicon membrane thermal expansivity

Technical field

The present invention is based on the online detection architecture of the polysilicon membrane thermal expansivity of surface processing technique, belongs to the technical field of MEMS (microelectromechanical systems) technological parameter test.

Technical background

The film thermal expansivity is a very important parameter for the design of MEMS device.On the one hand, the thermal expansion of membraneous material has considerable influence to device performance, and for example, the mismatch of film and substrate thermal expansivity can produce thermal stress, causes malformation or damage; On the other hand, thermal expansion is the power resources of low-grade fever actuator.Many documents have provided body material coefficient of thermal expansion coefficient, but the thermal expansivity of body material coefficient of thermal expansion coefficient and membraneous material and incomplete same, therefore can not the phase trans-substitution.And, even with a kind of membraneous material through different process, thermal expansivity also may be different.Therefore, it is significant that the MEMS structure of micromechanics film thermal expansivity can be accurately measured in proposition.

The test structure that several polysilicon membrane thermal expansivity based on the MEMS technology had been arranged before the present invention.Yet these test structures are more or less some following problems of existence always, make them can not realize online detection.For example, certain structures need detect in vacuum or annular seal space; Some needs comparatively complicated testing tool; Some relies on other too many material parameter; The movement locus of some test structure is curve rather than straight line, makes troubles to test; The measurand of certain structures is difficult to accurate measurement; A lot of testing schemes adopt traditional optical detection method, rather than measure with electrical quantities, therefore, are difficult to carry out other expansion utilization of the encapsulation of road, back and some.

Summary of the invention

Technical matters: the object of the present invention is to provide a kind of measurement structure and measuring method thereof of measuring the polysilicon membrane thermal expansivity, this structure and measuring method can realize the purpose of the required technological parameter of monitoring device manufacturing process at test surfaces processing polysilicon membrane thermal expansivity under the physical environment.

Technical scheme: the measurement structure of measurement polysilicon membrane thermal expansivity of the present invention is on forming, and this measurement structure is made of the two straight beam structures of a polysilicon and two polysilicon camber beam structures; Wherein, in the two straight beam structures of polysilicon, the two ends of polysilicon straight beam are separately fixed in the anchor district on both sides, are coated with the aluminium film at the center section of straight beam, are coated with the aluminium film at the center section of straight beam; Polysilicon camber beam structure is made up of two identical camber beams, and the two ends of camber beam are separately fixed in the anchor district, and the two ends of camber beam are separately fixed in two anchor districts, and the top in the middle of camber beam is provided with the tip, and it is most advanced and sophisticated facing to the aluminium film; Top in the middle of camber beam is provided with the tip, and it is most advanced and sophisticated facing to the aluminium film; The anchor district is positioned on the plane of same layer-of-substrate silicon.

The distance of the top of two camber beams to the promptly most advanced and sophisticated top of the initial distance of straight beam to the aluminium film is 2 μ m～8 μ m, and it is unequal that the top of two camber beams separates the initial distance of two straight beams of other distance; The width of polysilicon beam is 2 μ m～8 μ m, and thickness all is 1.5 μ m～3 μ m; The overall width of two straight beams equals the width of every camber beam in the polysilicon camber beam structure in the dual poly straight beam structure.

The length of polysilicon straight beam is 300 μ m～600 μ m, and camber beam length is 300 μ m～600 μ m, and all camber beams and straight beam angle are 0.01～0.05rad; And the length of the length of polysilicon camber beam and polysilicon straight beam is inequality.

The method of measuring is:

Measure current value and shift value in the two camber beam structures respectively, just can obtain thermal expansivity by calculating again.

1. at first calculate the medial temperature increment of every camber beam by the calorifics relational expression:

$\mathrm{\ΔT}=\frac{J^2{\mathrm{\ρ}}_0}{k_p{m}^2}\left[\frac{\frac{\mathrm{mL}}{2}-\tanh \left(\frac{\mathrm{mL}}{2}\right)}{\frac{\mathrm{mL}}{2}}\right]-------------\left(1\right)$

$m=\sqrt{\frac{\mathrm{\η}}{k_{p}h}-\frac{J^2{\mathrm{\ρ}}_0\mathrm{\ξ}}{k_p}}---------\left(2\right)$

Δ T is the medial temperature increment, and m is middle parameter, κ _pBe the thermal conductivity of polysilicon, η is the equivalent heat transfer coefficient of bent beam lower surface and substrate, and J is the current density by bent beam, ρ ₀The resistivity of polysilicon when being room temperature, ξ is the temperature coefficient of polysilicon resistance, L is the total length of bent beam.

2. then by displacement--medial temperature increment relation formula calculates thermal expansivity

$\mathrm{\δ}=\mathrm{\α\ΔT}\frac{\frac{L}{2}\cos \left(\mathrm{\θ}\right)(\frac{L^2}{4}-w^2)}{\frac{L^2}{4}{\tan }^2\left(\mathrm{\θ}\right)+w^2}------------\left(3\right)$

Wherein w is the width of camber beam, and θ is the angle of camber beam and level, and α is a thermal expansivity, and δ is the displacement on camber beam top.

The two straight beam structures of polysilicon and two polysilicon camber beam structures are used surface processing technique, and its preparation process is;

The preparation silicon substrate,

Deposit layer of silicon dioxide layer on silicon substrate,

Deposit one deck silicon nitride layer on silicon dioxide layer,

Deposit one deck Pyrex (PSG) sacrifice layer on the silicon nitride layer again,

Deposit polysilicon on PSG,

Make the polysilicon beam by lithography,

Deposit layer of aluminum on polysilicon layer,

Make aluminium lamination in the anchor district and the aluminium film on the straight beam by lithography,

Releasing sacrificial layer.

This measuring method is specially:

Girder construction is measured in a, preparation, promptly prepares two straight beam structures and two polysilicon camber beam structures, and the geometry of these two camber beams is identical, but the top is from the initial distance difference of straight beam;

B, when room temperature, the straight beam in the straight beam structure is fed a Weak current I ₀, measure the voltage V at its two ends ₀, according to relational expression $\frac{V_0}{I_0}={\mathrm{\ρ}}_0\frac{L_1}{\mathrm{wh}}$ Draw that length is L when room temperature ₁The electricalresistivity of polysilicon straight beam ₀, again to feeding another Weak current I in the straight beam ₁, measure its both end voltage V ₁, according to relational expression $\frac{V_1}{I}={\mathrm{\ρ}}_1\frac{L_1}{\mathrm{wh}}$ Measuring feeding electric current is I ₁The time, length is L ₁The electricalresistivity of polysilicon beam ₁,

Any camber beam in c, the selection two camber beam structural group, length overall is L ₂, it is fed electric current I ₂, measure the voltage V at its two ends ₂, and according to relational expression $\frac{V_2}{I}={\mathrm{\ρ}}_2\frac{L_2}{\mathrm{wh}}$ Measuring and feeding electric current is I ₂The time, length is L ₂The electricalresistivity of polysilicon camber beam ₂,

D, according to the relational expression of resistivity-medial temperature increment:

$\frac{\frac{{\mathrm{\ρ}}_1}{{\mathrm{\ρ}}_0}-1}{\frac{{\mathrm{\ρ}}_2}{{\mathrm{\ρ}}_0}-1}=\frac{{\mathrm{\ΔT}}_1}{{\mathrm{\ΔT}}_2}[\frac{\frac{m{L}_1}{2}-\tan \left(\frac{m{L}_1}{2}\right)}{\frac{{\mathrm{mL}}_1}{2}}/\frac{\frac{{\mathrm{mL}}_2}{2}-\tan \left(\frac{{\mathrm{mL}}_2}{2}\right)}{\frac{{\mathrm{mL}}_2}{2}}]$ Draw m, m is middle parameter;

E, mistake relational expression $m=\sqrt{\frac{\mathrm{\η}}{k_{p}h}-\frac{J^2{\mathrm{\ρ}}_0\mathrm{\ξ}}{k_p}}$ Draw η, ρ ₀, ξ; η is the equivalence of polysilicon beam lower surface

F, the coefficient of heat transfer, ρ ₀Be polysilicon beam resistivity at room temperature, ξ is a polysilicon beam temperature coefficient at room temperature, and h is the thickness of beam, κ _pBe the thermal conductivity of polysilicon, J is the current density in the beam;

G, the two ends of camber beam are fed the electric current of slow increase respectively, whether the reading of observing the ohmmeter that connects camber beam and straight beam anchor district has a saltus step from the infinity to the finite value; As not having, illustrate that then two beams also do not come in contact, continue to increase current value; If any saltus step, illustrate that then contact has taken place two beams, note this moment size, according to relational expression by current value $J=\frac{I}{\mathrm{wh}}$ Calculate current density, J ₁, the displacement of camber beam is δ 1+ Δ δ, and wherein, δ 1 is the actual displacement of camber beam, and Δ δ is an error term;

H, camber beam is repeated above step f, write down another group current density, J again ₂With displacement δ 2+ Δ δ, with above parameter substitution relational expression $\mathrm{\ΔT}=\frac{J^2{\mathrm{\ρ}}_0}{k_p{m}^2}\left[\frac{\frac{\mathrm{mL}}{2}-\tanh \left(\frac{\mathrm{mL}}{2}\right)}{\frac{\mathrm{mL}}{2}}\right],$ And two formulas are subtracted each other, promptly

$({\mathrm{\δ}}_1+\mathrm{\Δ\δ})-({\mathrm{\δ}}_2+\mathrm{\Δ\δ})=\mathrm{\α}({\mathrm{\ΔT}}_1-{\mathrm{\ΔT}}_2)\frac{\frac{L}{2}\cos \left(\mathrm{\θ}\right)(\frac{L^2}{4}-w^2)}{\frac{L^2}{4}{\tan }^2\left(\mathrm{\θ}\right)+w^2}$

According to following formula, just can draw thermalexpansioncoefficient again.

Technique effect: advantage of the present invention is as follows

(1) this structure is used surface processing technique, and test structure is based on the combination of common straight beam and camber beam structure, so technology and structure are all comparatively simple;

(2) this structure does not relate to some special measurement means, so method of testing is simple;

(3) this structure has been considered the influence of fabrication error to measuring, so precision is higher;

(4) because other unknown material parameter that measurement is relied on is less, therefore the independence of measuring is better;

(5) owing to consider that various forms of heats run off in physical environment, so it need not measure under particular surroundingss such as vacuum or seal hatch, and lower to the requirement of measuring equipment;

(6) Ce Shi result can show with the electricity scale, therefore can realize online detection.

Description of drawings

Fig. 1 is the floor map of thermal expansivity test structure of the present invention.

Fig. 2 is the schematic perspective view of thermal expansivity test structure in the embodiment of the invention.

Have among the above figure: anchor district 11,12,13,14,15,16, straight beam 31,32, camber beam 21,22, tip 211,221, aluminium film 311,321; Aluminum lead layer 41, polysilicon layer 42, silicon nitride layer 43, silicon dioxide layer 44, layer-of-substrate silicon 45.

Embodiment

This measurement structure is made of the two straight beam structures of a polysilicon and two polysilicon camber beam structures; Wherein, in the two straight beam structures of polysilicon, the two ends of polysilicon straight beam 31,32 are separately fixed at the anchor district 13,16 on both sides) on, be coated with aluminium film 311 at the center section of straight beam 31, be coated with aluminium film 321 at the center section of straight beam 32; Polysilicon camber beam structure is made up of two identical camber beams 21,22, the two ends of camber beam 21 are separately fixed in the anchor district 11,12, the two ends of camber beam 22 are separately fixed in two anchor districts 14,15, and the top in the middle of camber beam 21 is provided with tip 211, and its tip 211 is facing to aluminium film 311; Top in the middle of camber beam 22 is provided with tip 221, and its tip 221 is facing to aluminium film 321; Anchor district 11,12,13,14,15,16 is positioned on the plane of same layer-of-substrate silicon.The top of two camber beams to the initial distance of straight beam promptly most advanced and sophisticated 211 top be 2 μ m～8 μ m to the distance of aluminium film 311, it is unequal that the top of two camber beams separates the initial distance of two straight beams of other distance; The width of polysilicon beam is 2 μ m～8 μ m, and thickness all is 1.5 μ m～3 μ m; The overall width of two straight beams 31,32 equals the width of every camber beam 21,22 in the polysilicon camber beam structure in the dual poly straight beam structure.The length of polysilicon straight beam 31,32 is 300 μ m～600 μ m, and camber beam 21,22 length are 300 μ m～600 μ m, and all camber beams and straight beam angle are 0.01～0.05rad; And the length of the length of polysilicon camber beam and polysilicon straight beam is inequality.

On forming, it is made of the two straight beam structures of polysilicon and two polysilicon camber beam structural group.On the relation of position, two camber beam structures are at the two ends of two straight beam structures, and the top of two camber beams is all towards two straight beam structures.On physical dimension, two camber beams are identical, and just their tops separately are inequality from the initial distance of two straight beams; The thickness of all polysilicon beams is all identical; The width of straight beam is 1/2 of a camber beam width; The length of all camber beams is all identical, and the length of all straight beams is also identical; The length of camber beam and the length of straight beam are inequality; All camber beams are all identical with the angle of level.The present invention is a kind of online detection architecture of the polysilicon membrane thermal expansivity based on surface processing technique, and as shown in Figure 2, its process structure layer is made up of layer-of-substrate silicon, silicon dioxide layer, silicon nitride layer, polysilicon layer, aluminum lead layer.The manufacturing process steps of camber beam and two straight beams is as follows:

The preparation silicon substrate,

Deposit layer of silicon dioxide layer,

Deposit one deck silicon nitride layer,

Deposit one deck PSG is as sacrifice layer,

The deposit polysilicon,

Make the polysilicon beam by lithography,

The deposit layer of aluminum,

Photoetching aluminium,

Releasing sacrificial layer.

Concrete testing procedure is as follows:

(1) extraction of parameter m in the middle of:

1. when room temperature, straight beam is fed a Weak current I ₀(0.1mA～0.5mA guarantees that the temperature of camber beam does not almost change) measures the voltage V at its two ends ₀, according to relational expression

$\frac{V_0}{I_0}={\mathrm{\ρ}}_0\frac{L_1}{\mathrm{wh}}$ Can draw the electricalresistivity of the polysilicon when room temperature ₀,

Wherein h is the thickness of two straight beams, and w is the overall width of two straight beams, L ₁Be the length of two straight beams,

2. above two straight beams are fed another Weak current I again ₁(this moment, resistivity was along with variation has taken place in the rising of beam temperature) measures its both end voltage V ₁, and according to relational expression $\frac{V_1}{I}={\mathrm{\ρ}}_1\frac{L_1}{\mathrm{wh}}$ Just can measure feeding electric current is I ₁The time, length is L ₁The electricalresistivity of polysilicon beam ₁,

3. (length overall is L to select any camber beam in the two camber beam structural group ₂), it is fed electric current I ₂, measure the voltage V at its two ends ₂, and according to relational expression $\frac{V_2}{I}={\mathrm{\ρ}}_2\frac{L_2}{\mathrm{wh}}$ Just can measure and feed electric current is I ₂The time, length is L ₂The electricalresistivity of dual poly beam ₂,

4. according to the relational expression of resistivity-medial temperature increment:

$\frac{\frac{{\mathrm{\ρ}}_1}{{\mathrm{\ρ}}_0}-1}{\frac{{\mathrm{\ρ}}_2}{{\mathrm{\ρ}}_0}-1}=\frac{{\mathrm{\ΔT}}_1}{{\mathrm{\ΔT}}_2}=[\frac{\frac{m{L}_1}{2}-\tan \left(\frac{{\mathrm{mL}}_1}{2}\right)}{\frac{{\mathrm{mL}}_1}{2}}/\frac{\frac{{\mathrm{mL}}_2}{2}-\tan \left(\frac{{\mathrm{mL}}_2}{2}\right)}{\frac{{\mathrm{mL}}_2}{2}}]$

Just can obtain m, pass through relational expression: $m=\sqrt{\frac{\mathrm{\η}}{k_{p}h}-\frac{J^2{\mathrm{\ρ}}_0\mathrm{\ξ}}{k_p}}$ Just can draw η, ρ ₀, ξ; η is the equivalent heat transfer coefficient of polysilicon beam lower surface, ρ ₀, ξ be respectively polysilicon beam resistivity at room temperature with and temperature coefficient.

(2) measurement of thermalexpansioncoefficient:

1. the two ends of camber beam A are fed the electric current that slowly increases, the top that the thermal effect that electric current produces can make beam generation thermal expansion and promote beam travels forward.

Whether the reading of 2. observing the ohmmeter that connects camber beam and straight beam anchor district has a saltus step from the infinity to the finite value; As not having, illustrate that then two beams also do not come in contact, continue to increase current value; If any saltus step, illustrate that then contact has taken place two beams, note this moment size, according to relational expression by current value $J=\frac{I}{\mathrm{wh}}$ Calculate current density, J ₁, the displacement of camber beam is δ 1+ Δ δ, and wherein, δ 1 is the actual displacement of camber beam, and Δ δ is an error term.

3. to camber beam group B repeating step 1,2.Note J ₂, δ 2+ Δ δ.

4. with above parameter substitution relational expression $\mathrm{\Δ\&Tgr;}=\frac{J^2{\mathrm{\ρ}}_0}{k_p{m}^2}\left[\frac{\frac{\mathrm{mL}}{2}-\tanh \left(\frac{\mathrm{mL}}{2}\right)}{\frac{\mathrm{mL}}{2}}\right]$ And two formulas are subtracted each other, $({\mathrm{\δ}}_1+\mathrm{\Δ\δ})-({\mathrm{\δ}}_2+\mathrm{\δ\Δ})=\mathrm{\α}({\mathrm{\ΔT}}_1-{\mathrm{\ΔT}}_2)\frac{\frac{L}{2}\cos \left(\mathrm{\θ}\right)(\frac{L^2}{4}-w^2)}{\frac{L^2}{4}{\tan }^2\left(\mathrm{\θ}\right)+w^2},$ Wherein w is the width of camber beam, and θ is the angle of camber beam and level, and α is a thermal expansivity, and δ is the displacement on camber beam top.

According to following formula, just can draw thermalexpansioncoefficient.

Object lesson:

Two camber beam tops are respectively 3.5 μ m, 4 μ m from the initial top of straight beam distance among Fig. 1,2.The width of polysilicon straight beam all is 2 μ m, and the width of polysilicon camber beam is 4um; The thickness of all beams all is 2 μ m; The length overall of straight beam is 450 μ m, the length overall 500 μ m of camber beam; The angle of all camber beams and level is 0.05rad.

At first surface working dual poly straight beam and arbitrary polysilicon camber beam are fed the electric current of identical size.The voltage of measuring its two ends respectively just can calculate polysilicon resistivity, the temperature coefficient of resistivity and the equivalent heat transfer coefficient of beam and substrate at room temperature, utilizes these data just can ask for the polysilicon beam at a certain medial temperature increment that applies correspondence under the electric current according to the thermal modeling of beam again.

Then two camber beams are fed electric current identical, that increase progressively gradually (unsuitable excessive, as to guarantee that the maximum temperature point of beam is no more than 800K), the reading of observing the ohmmeter that connects camber beam and straight beam anchor district has or not saltus step.If no, then continue to increase electric current; If have, then explanation two beams this moment come in contact, and note this current value of camber beam constantly.The thermal modeling of utilizing the front to narrate just can calculate the medial temperature increment of the camber beam of this electric current correspondence, just can obtain the thermal expansivity of polysilicon again by model of structural mechanics.In concrete processing procedure, the camber beam structure has been adopted the method for error compensation, with cancellation because the influence that unrelieved stress, fabrication error etc. produce test.The thermal expansivity that can draw surface finished polysilicon thin film through measurements and calculations is approximately 2.58510-6, and the error of measurement is greatly about about 5.6%.

Claims (5)

1. A measurement structure for measuring the coefficient of thermal expansion of a polysilicon film is characterized in that in the composition of the structure, the measurement structure is composed of a polysilicon double straight beam structure and two polysilicon curved beam structures; wherein, in the polysilicon double straight beam structure , the two ends of the polysilicon straight beam (31, 32) are respectively fixed on the anchor areas (13, 16) on both sides, and the middle part of the straight beam (31) is coated with an aluminum film (311), and on the straight beam (32) The middle part is coated with an aluminum film (321); the polysilicon curved beam structure is composed of two identical curved beams (21, 22), and the two ends of the curved beam (21) are respectively fixed on the anchorage areas (11, 12), and the curved beam The two ends of (22) are respectively fixed on two anchor areas (14,15), and the top in the middle of the curved beam (21) is provided with a tip (211), and its tip (211) faces the aluminum film (311); The top in the middle of the curved beam (22) is provided with a tip (221), and its tip (221) faces the aluminum film (321); the anchor regions (11, 12, 13, 14, 15, 16) are located on the same silicon substrate layer on flat surface. 2. The measurement structure for measuring the coefficient of thermal expansion of polysilicon thin films according to claim 1, characterized in that the initial distance from the tops of the two curved beams to the straight beams, that is, the distance from the top of the tip (211) to the aluminum film (311) is 2 μm～ 8 μm, the initial distances between the tops of the two curved beams and the two straight beams are not equal; the width of the polysilicon beams is 2 μm to 8 μm, and the thickness is 1.5 μm to 3 μm; in the double polysilicon straight beam structure, the two straight beams (31 The total width of , 32) is equal to the width of each curved beam (21, 22) in the polysilicon curved beam structure. 3. The measurement structure for measuring the thermal expansion coefficient of polysilicon thin films according to claim 1, characterized in that the length of the polysilicon straight beams (31, 32) is 300 μm to 600 μm, and the length of the curved beams (21, 22) is 300 μm to 600 μm. The angle between the curved beam and the straight beam is 0.01-0.05 rad; and the length of the polysilicon curved beam is different from that of the polysilicon straight beam. 4. a measuring method for measuring the measuring structure of polysilicon thin film thermal expansion coefficient as claimed in claim 1, is characterized in that this measuring method is: a. Prepare the measuring beam structure, that is, prepare a double straight beam structure and two polysilicon curved beam structures. The geometric structures of the two curved beams are exactly the same, but the initial distances from the top to the straight beam are different; b. At room temperature, pass a small current I ₀ to the straight beams (31, 32) in the straight beam structure, and measure the voltage V ₀ at both ends, according to the relationship $\frac{V_0}{I_0}={\mathrm{\&rho;}}_0\frac{L_1}{\mathrm{wh}}$ Obtain the resistivity ρ ₀ of the polysilicon straight beam whose length is L ₁ at room temperature, then pass another tiny current I ₁ into the straight beam (31, 32), and measure the voltage V ₁ at its two ends, according to the relationship $\frac{V_1}{I}={\mathrm{\&rho;}}_1\frac{L_1}{\mathrm{wh}}$ Measure the resistivity ρ ₁ of the polysilicon beam whose length is L ₁ when the input current is I ₁ , c. Select any curved beam in the two curved beam structure groups, the total length is L ₂ , pass current I ₂ to it, measure the voltage V ₂ at both ends, and according to the relation $\frac{V_2}{I}={\mathrm{\&rho;}}_2\frac{L_2}{\mathrm{wh}}$ Measure the resistivity ρ ₂ of the polysilicon curved beam with length L ₂ when the input current is I ₂ , d. According to the relationship between resistivity and average temperature increment: $\frac{\frac{{\mathrm{\&rho;}}_1}{{\mathrm{\&rho;}}_0}-1}{\frac{{\mathrm{\&rho;}}_2}{{\mathrm{\&rho;}}_0}-1}=\frac{\mathrm{\&Delta;}{T}_1}{\mathrm{\&Delta;}{T}_2}=[\frac{\frac{{\mathrm{mL}}_1}{2}-\mathrm{the\; tan}\left(\frac{{\mathrm{mL}}_1}{2}\right)}{\frac{{\mathrm{mL}}_1}{2}}/\frac{\frac{{\mathrm{mL}}_2}{2}-\mathrm{the\; tan}\left(\frac{{\mathrm{mL}}_2}{2}\right)}{\frac{{\mathrm{mL}}_2}{2}}]$ Get m, m is an intermediate parameter. e, through the relationship $m=\sqrt{\frac{\mathrm{\&eta;}}{k_{p}h}-\frac{J^2{\mathrm{\&rho;}}_0\mathrm{\&xi;}}{k_p}}$ η, ρ ₀ , ξ are obtained; η is the equivalent heat transfer coefficient of the lower surface of the polysilicon beam, ρ ₀ is the resistivity of the polysilicon beam at room temperature, ξ is the temperature coefficient of the polysilicon beam at room temperature, and h is the thickness of the beam , k _p is the thermal conductivity of polysilicon, J is the current density in the beam; f. To the two ends of the curved beam (21), feed slowly increasing currents respectively, and observe whether the reading of the ohmmeter connecting the curved beam and the anchorage area of the straight beam has a jump from infinity to a finite value; if there is no, it means The two beams have not been in contact yet, continue to increase the current value; if there is a jump, it means that the two beams have been in contact, record the current value passing through at this moment, according to the relationship $J=\frac{I}{\mathrm{wh}}$ Calculate the current density J ₁ , the moving distance of the curved beam is δ1+Δδ, where δ1 is the actual moving distance of the curved beam, and Δδ is the error term; g. Repeat the above step f for the curved beam (22), then record another set of current density J ₂ and moving distance δ2+Δδ, and substitute the above parameters into the relational formula $\mathrm{\&Delta;T}=\frac{J^2{\mathrm{\&rho;}}_0}{k_p{m}^2}\left[\frac{\frac{\mathrm{mL}}{2}-\tanh \left(\frac{\mathrm{mL}}{2}\right)}{\frac{\mathrm{mL}}{2}}\right],$ and subtract the two equations, that is, $<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;\&delta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; L</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$ According to the above formula, the coefficient of thermal expansion α can be obtained. 5. The method for measuring the measuring structure for measuring the coefficient of thermal expansion of polysilicon thin films according to claim 4, characterized in that the preparation method of the measuring beam structure is as follows: a. Prepare the silicon substrate, b. Deposit a layer of silicon dioxide on the silicon substrate, c. Depositing a silicon nitride layer on the silicon dioxide layer, d. Deposit a sacrificial layer of borosilicate glass on the silicon nitride layer, e. Depositing polysilicon on the sacrificial layer of borosilicate glass, f. Photoetching polysilicon beams, g. Deposit a layer of aluminum on the polysilicon layer h, photoetching the aluminum layer on the anchor area and the aluminum film on the straight beam, i. Release the sacrificial layer.

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