Spray plate, temperature measurement method and thin film deposition device

Abstract

The invention provides a spraying plate, a temperature measuring method of the spraying plate and a thin film deposition device. The spraying plate comprises a spraying plate body, a plurality of air holes and at least one groove are formed in the spraying plate body, and the groove is located in the upper surface, opposite to a process cavity, of the spraying plate body; the FBG sensor is arranged in the groove and used for determining the temperature of the corresponding area of the spraying plate body according to the transmission spectrum obtained by the output end; and the insertion strip is used for fixing the FBG sensor in the groove.

Description

Technical Field

[0001] The present invention relates to the field of semiconductor manufacturing technology, and particularly to a shower plate, a temperature measurement method for a shower plate, and a thin film deposition apparatus. Background Art

[0002] In semiconductor manufacturing processes, plasma enhanced chemical vapor deposition (PECVD) equipment is widely used in thin film deposition processes. The shower plate and heater in chemical vapor deposition equipment are core components, and their surface temperatures directly affect the growth quality, uniformity, and performance of thin films. To ensure the stability and consistency of thin film deposition, it is crucial to precisely control the surface temperatures of the shower plate and heater. However, during the process, plasma is formed between the shower plate and the heater, and this high-energy environment poses a severe challenge to traditional temperature measurement techniques.

[0003] In chemical vapor deposition processes, the presence of plasma interferes with traditional thermocouple temperature measurement techniques. The high-frequency electromagnetic field generated by the plasma causes thermocouple signal distortion, thereby affecting the accuracy of temperature measurement. In addition, chemical vapor deposition processes are usually carried out in high-temperature environments, and thermocouple wires are prone to carbonization after long-term high-temperature exposure, which not only leads to temperature measurement failure but also contaminates the reaction chamber due to the shedding of carbides, affecting the purity of thin film deposition and the service life of the equipment.

[0004] To overcome the above-mentioned defects existing in the prior art, there is an urgent need in the art for a shower plate technology for precisely measuring the temperature of the shower plate under plasma interference and high-temperature environments, thereby improving the quality of thin film deposition. Summary of the Invention

[0005] The following presents a brief overview of one or more aspects to provide a basic understanding of these aspects. This overview is not an exhaustive survey of all contemplated aspects, and is neither intended to identify key or decisive elements of all aspects nor to attempt to define the scope of any or all aspects. Its sole purpose is to present some concepts of one or more aspects in a simplified form as a prelude to a more detailed description to follow.

[0006] To overcome the above-mentioned defects existing in the prior art, the present invention provides a shower plate, a temperature measurement method for a shower plate, and a thin film deposition apparatus for precisely measuring the temperature of the shower plate under plasma interference and high-temperature environments, thereby improving the quality of thin film deposition.

[0007] Specifically, a spray plate provided according to the first aspect of the present invention includes: a spray plate body, on which a plurality of air holes and at least one groove are provided, wherein the groove is located on the upper surface of the spray plate body facing away from the process chamber; an FBG sensor disposed in the groove for determining the temperature of the corresponding area of the spray plate body according to the transmission spectrum obtained at the output end; and a strip for fixing the FBG sensor in the groove.

[0008] Further, in some embodiments of the present invention, the FBG sensor includes: a core on which at least one grating is provided for filtering light of a characteristic wavelength corresponding to a temperature from the core to obtain a transmission spectrum representing the temperature of the corresponding area of the spray plate body at the output end of the FBG sensor; and a cladding wrapped around the outside of the core for protecting the core.

[0009] Further, in some embodiments of the present invention, the spray plate further includes: an incident light source located at the input end of the FBG sensor for providing a broad-spectrum incident light adapted to the temperature detection range to the FBG sensor to obtain corresponding transmitted light at the output end of the FBG sensor; and a first optical fiber demodulator located at the output end of the FBG sensor for analyzing the transmitted light to determine its transmission spectrum.

[0010] Further, in some embodiments of the present invention, the spray plate further includes: a second optical fiber demodulator located at the input end of the FBG sensor for analyzing the reflected light output from the input end to determine its reflection spectrum, and the FBG sensor also determines the temperature of the corresponding area of the spray plate body according to the reflection spectrum.

[0011] Further, in some embodiments of the present invention, the incident light source uses an ultraviolet light source.

[0012] Further, in some embodiments of the present invention, a plurality of the grooves are provided on the upper surface of the spray plate body, wherein the grooves are distributed in parallel and / or crosswise, and / or each of the grooves extends in a linear and / or wavy line shape.

[0013] Further, in some embodiments of the present invention, the strip fixes the FBG sensor in the groove through interference fit with the groove.

[0014] In addition, the thin film deposition apparatus provided according to the second aspect of the present invention includes: a process chamber, which includes a shower plate as described in any one of the first aspects of the present invention, and a heating plate, wherein the shower plate is used to transport gas from the outside to the process chamber, and the heating plate is used to carry and heat a wafer to be processed; and a radio frequency generator, which provides a high-frequency alternating electric field to the process chamber via a radio frequency coil disposed on the top and / or side wall of the process chamber to excite in-situ plasma between the shower plate and the heating plate.

[0015] In addition, the method for measuring the temperature of the shower plate provided according to the third aspect of the present invention includes the following steps: determining the initial temperature of the shower plate as described in any one of the first aspects of the present invention, and obtaining a first transmission spectrum from the output end of its FBG sensor; according to the first transmission spectrum, determining a first Rayleigh scattering spectrum of the cross-section of Rayleigh scattering over the entire core of the FBG sensor, wherein the Rayleigh scattering cross-section is distributed along the direction of the core length; at the working temperature to be measured, obtaining a second transmission spectrum from the output end of the FBG sensor, and determining the corresponding second Rayleigh scattering spectrum therefrom; via a local matching algorithm, locally matching the second Rayleigh scattering spectrum with the first Rayleigh scattering spectrum to determine the spectral peak offset between the two; according to the spectral peak offset, calculating the corresponding temperature change; and according to the initial temperature and the temperature change, determining the working temperature of the corresponding region of the FBG sensor.

[0016] In addition, the method for measuring the temperature of the shower plate provided according to the fourth aspect of the present invention includes the following steps: determining the initial temperature of the shower plate as described in any one of the first aspects of the present invention, and obtaining a first reflection spectrum from the input end of its FBG sensor; according to the first reflection spectrum, determining the first reflection wavelength of the FBG sensor; at the working temperature to be measured, obtaining a second reflection spectrum from the input end of the FBG sensor; according to the second reflection spectrum, determining the second reflection wavelength of the FBG sensor; according to the first reflection wavelength and the second reflection wavelength, calculating the corresponding wavelength offset; according to the wavelength offset, calculating the corresponding temperature change; and according to the initial temperature and the temperature change, determining the working temperature of the corresponding region of the FBG sensor.

[0017] Further, in some embodiments of the present invention, the expression for calculating the corresponding temperature change according to the wavelength offset is:

[0018] ΔT = Δλ B / λ B0 ·(α + ξ)

[0019] wherein, ΔT is the temperature change, Δλ B is the wavelength offset, λ B0is the first reflection wavelength, α is the coefficient of thermal expansion, and ξ is the thermo-optic coefficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] After reading the detailed description of the embodiments of the present disclosure in conjunction with the following drawings, the above features and advantages of the present invention can be better understood. In the drawings, the components are not necessarily drawn to scale, and components with similar relevant characteristics or features may have the same or similar reference numerals.

[0021] Figure 1 Shows a schematic cross-sectional structure diagram of a spray plate provided according to some embodiments of the present invention.

[0022] Figure 2 Shows a schematic structural diagram of a strip provided according to some embodiments of the present invention.

[0023] Figure 3 Shows a schematic structural diagram of an FBG sensor provided according to some embodiments of the present invention.

[0024] Figure 4A Shows a schematic diagram of an incident spectrum provided according to some embodiments of the present invention.

[0025] Figure 4B Shows a schematic diagram of a reflection spectrum provided according to some embodiments of the present invention.

[0026] Figure 4C Shows a schematic diagram of a transmission spectrum provided according to some embodiments of the present invention.

[0027] Figures 5A to 5C Shows a schematic structural diagram of a groove provided according to some embodiments of the present invention.

[0028] Reference Numerals:

[0029] 10 Spray plate body

[0030] 11 Air holes

[0031] 20 FBG sensor

[0032] 21 Core

[0033] 211 Grating

[0034] 22 Cladding

[0035] 30 Strip DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] The following specific embodiments illustrate the implementation manners of the present invention, and those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. Although the description of the present invention will be introduced in conjunction with preferred embodiments, this does not mean that the features of this invention are limited to this implementation manner. On the contrary, the purpose of introducing the invention in conjunction with the implementation manner is to cover other alternatives or modifications that may extend based on the claims of the present invention. In order to provide a deep understanding of the present invention, many specific details will be included in the following description. The present invention can also be implemented without using these details. In addition, in order to avoid confusing or obscuring the key points of the present invention, some specific details will be omitted in the description.

[0037] In the description of the present invention, it should be noted that unless otherwise clearly specified and defined, the terms "mounted", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0038] In addition, the "upper", "lower", "left", "right", "top", "bottom", "horizontal", and "vertical" used in the following description should be understood as the orientations shown in this paragraph and the related drawings. This relative term is only for convenience of description, and it does not mean that the device described needs to be manufactured or operated in a specific orientation, so it should not be construed as a limitation to the present invention.

[0039] It can be understood that although terms such as "first", "second", and "third" can be used herein to describe various components, regions, layers, and / or parts, these components, regions, layers, and / or parts should not be limited by these terms, and these terms are only used to distinguish different components, regions, layers, and / or parts. Therefore, the first component, region, layer, and / or part discussed below can be referred to as the second component, region, layer, and / or part without departing from some embodiments of the present invention.

[0040] In semiconductor manufacturing processes, plasma-enhanced chemical vapor deposition equipment is widely used in the thin film deposition process. The showerhead and heater in the chemical vapor deposition equipment are core components, and their surface temperatures directly affect the growth quality, uniformity, and performance of the thin film. In order to ensure the stability and consistency of thin film deposition, it is crucial to precisely control the surface temperatures of the showerhead and heater. However, during the process, plasma will be formed between the showerhead and the heater, and this high-energy environment poses a severe challenge to traditional temperature measurement techniques.

[0041] In a chemical vapor deposition process, the presence of plasma interferes with traditional thermocouple temperature measurement techniques. The high-frequency electromagnetic field generated by the plasma causes distortion of the thermocouple signal, thereby affecting the accuracy of temperature measurement. In addition, the chemical vapor deposition process is usually carried out in a high-temperature environment, and the thermocouple wire is prone to carbonization after long-term exposure to high temperatures, which not only leads to the failure of temperature measurement, but also pollutes the reaction chamber due to the shedding of carbides, affecting the purity of thin film deposition and the service life of the equipment.

[0042] To overcome the above-mentioned defects of the existing technology, the present invention provides a shower plate, a temperature measurement method for a shower plate, and a thin film deposition device, which are used to accurately measure the temperature of the shower plate under plasma interference and high-temperature environment, thereby improving the quality of thin film deposition.

[0043] In some non-limiting embodiments, the shower plate provided in the first aspect of the present invention can be configured in the thin film deposition device provided in the second aspect of the present invention. The temperature measurement method for the shower plate provided in the third aspect and the fourth aspect of the present invention can be implemented based on the shower plate provided in the first aspect of the present invention.

[0044] Specifically, the thin film deposition device provided in the second aspect of the present invention includes a process chamber and a radio frequency generator. Specifically, the process chamber includes a shower plate as described in any one of the first aspects of the present invention, and a heating plate, wherein the shower plate is used to transport gas from the outside to the process chamber, and the heating plate is used to carry and heat the wafer to be processed. The radio frequency generator provides a high-frequency alternating electric field to the process chamber via a radio frequency coil provided on the top and / or side wall of the process chamber to excite in-situ plasma between the shower plate and the heating plate.

[0045] Please refer to Figures 1 to 2 , Figure 1 which shows a schematic cross-sectional structure diagram of a shower plate provided according to some embodiments of the present invention. Figure 2 which shows a schematic structure diagram of a strip provided according to some embodiments of the present invention.

[0046] As Figures 1 to 2 shown, the shower plate includes a shower plate body 10, an FBG sensor 20, and a strip 30. The shower plate body 10 is provided with a plurality of air holes 11 and at least one groove, wherein the groove is located on the upper surface of the shower plate body 10 facing away from the process chamber. The FBG sensor 20 is disposed in the groove and is used to determine the temperature of the corresponding area of the shower plate body 10 according to the transmission spectrum obtained at the output end. The strip 30 is used to fix the FBG sensor 20 in the groove.

[0047] In some embodiments, the strip 30 and the groove fix the FBG sensor 20 in the groove by interference fit.

[0048] Please refer to Figure 3 , Figure 3 which shows a schematic structural diagram of an FBG sensor provided according to some embodiments of the present invention.

[0049] As Figure 3 shown, the FBG sensor 20 includes a core 21 and a cladding 22. At least one grating 211 is provided on the core 21 for filtering light of a characteristic wavelength corresponding to the temperature from the core 21, so as to obtain a transmission spectrum characterizing the temperature of the corresponding area of the spray plate body 10 at the output end of the FBG sensor 20. The grating 211 can be formed by an etching or mechanical scribing process. The cladding 22 wraps around the outside of the core 21 for protecting the core 21.

[0050] Please refer to Figures 4A to 4C , Figure 4A which shows a schematic diagram of an incident spectrum provided according to some embodiments of the present invention. Figure 4B which shows a schematic diagram of a reflection spectrum provided according to some embodiments of the present invention. Figure 4C which shows a schematic diagram of a transmission spectrum provided according to some embodiments of the present invention.

[0051] As Figures 4A to 4C shown, the spray plate further includes an incident light source, a first optical fiber demodulator, and a second optical fiber demodulator. The incident light source, located at the input end of the FBG sensor 20, is used to provide a broad-spectrum incident light adapted to the temperature detection range to the FBG sensor 20, so as to obtain corresponding transmitted light at the output end of the FBG sensor 20. The first optical fiber demodulator, located at the output end of the FBG sensor 20, is used to analyze the transmitted light to determine its transmission spectrum. The second optical fiber demodulator, located at the input end of the FBG sensor 20, is used to analyze the reflected light output from the input end to determine its reflection spectrum, and the FBG sensor 20 also determines the temperature of the corresponding area of the spray plate body 10 according to the reflection spectrum.

[0052] In some embodiments, the incident light source uses an ultraviolet light source.

[0053] In this way, by pre-burying an FBG sensor on the surface of the spray plate and using ultraviolet exposure technology to form a periodic refractive index distribution in the core of the FBG sensor, high-precision measurement of the surface temperature of the spray plate can be achieved. Compared with the traditional thermocouple temperature measurement technology, the fiber Bragg grating temperature measurement technology has the advantages of strong anti-electromagnetic interference ability, good high-temperature resistance performance, and high measurement accuracy.

[0054] Please refer to Figures 5A to 5C , Figures 5A to 5C which shows a schematic structural diagram of a groove provided according to some embodiments of the present invention.

[0055] Specifically, a plurality of grooves are provided on the upper surface of the spray plate body 10, wherein the grooves are distributed in parallel and / or crosswise, and / or the grooves extend in a linear shape of a straight line and / or a wavy line.

[0056] As Figure 5A shown, the grooves on the surface of the spray plate are distributed in a wavy shape along the radial direction and extend outward from the center of the disc. The positions of the grooves avoid a plurality of air holes and are evenly distributed on the spray plate. Thus, this structure can confirm the temperature distribution during the film deposition process through measurement methods at a plurality of different points.

[0057] As Figure 5B shown, the grooves on the surface of the spray plate are arranged in parallel at different height positions of the disc. The positions of the grooves avoid a plurality of air holes and are evenly distributed on the spray plate. Thus, this structure can simply and directly measure the temperature distribution of the spray plate during the deposition process, thereby improving the measurement efficiency.

[0058] As Figure 5C shown, the grooves on the surface of the spray plate are distributed in a parallel and obliquely crossed manner to form a grid-like structure. Each groove avoids a plurality of air holes and is evenly distributed on the spray plate. Thus, this structure can accurately match the film measurement points and perform point-to-point analysis of film measurement, thereby improving the accuracy and precision of the evaluation of the temperature distribution on the surface of the spray plate during the film deposition process.

[0059] Here, by processing grooves on the surface of the spray plate and embedding optical fibers therein by means of interference fit, it can be ensured that the optical fibers are in close contact with the surface of the spray plate, thereby more accurately reflecting the temperature distribution of the spray plate. This technical solution can not only effectively avoid the interference of plasma on temperature measurement, but also prevent the cavity pollution caused by the carbonization of thermocouple wires, providing reliable technical support for the optimization of chemical vapor deposition process and the improvement of film deposition quality.

[0060] The working principles of the above spray plate and film deposition device will be described below in combination with some embodiments of the temperature measurement method of the spray plate. Those skilled in the art can understand that these embodiments of the temperature measurement method of the spray plate are only some non-restrictive implementation manners provided by the present invention, aiming to clearly show the main concept of the present invention and provide some specific solutions convenient for the public to implement, rather than limiting all functions or all working modes of the spray plate and film deposition device. Similarly, the spray plate and film deposition device are also only some non-restrictive implementation manners provided by the present invention, and do not limit the execution subject or execution order of each step in these temperature measurement methods of the spray plate.

[0061] In some embodiments, the method for measuring the temperature of the shower plate may first determine the initial temperature of the shower plate and obtain the first transmission spectrum from the output end of its FBG sensor 20. Then, according to the first transmission spectrum, determine the first Rayleigh scattering spectrum of the cross-section of the entire segment of Rayleigh scattering in the core 21 of the FBG sensor 20, where the Rayleigh scattering cross-section is distributed along the length direction of the core 21. After that, at the working temperature to be measured, obtain the second transmission spectrum from the output end of the FBG sensor 20 and determine the corresponding second Rayleigh scattering spectrum accordingly. Then, through a local matching algorithm (e.g., cross-correlation analysis), locally match the second Rayleigh scattering spectrum with the first Rayleigh scattering spectrum to determine the spectral peak offset between the two. Then, according to the spectral peak offset, calculate the corresponding temperature change. Finally, according to the initial temperature and the temperature change, determine the working temperature of the corresponding region of the FBG sensor 20.

[0062] In some embodiments, the method for measuring the temperature of the shower plate may first determine the initial temperature of the shower plate and obtain the first reflection spectrum from the input end of its FBG sensor 20. Then, according to the first reflection spectrum, determine the first reflection wavelength of the FBG sensor 20. After that, at the working temperature to be measured, obtain the second reflection spectrum from the input end of the FBG sensor 20. Then, according to the second reflection spectrum, determine the second reflection wavelength of the FBG sensor 20. Then, according to the first reflection wavelength and the second reflection wavelength, calculate the corresponding wavelength offset. Then, according to the wavelength offset, calculate the corresponding temperature change. Finally, according to the initial temperature and the temperature change, determine the working temperature of the corresponding region of the FBG sensor 20.

[0063] Further, the expression for calculating the corresponding temperature change according to the wavelength offset is:

[0064] ΔT = Δλ B / λ B0 ·(α + ξ)

[0065] Where, ΔT is the temperature change, Δλ B is the wavelength offset, λ B0 is the first reflection wavelength, α is the coefficient of thermal expansion, and ξ is the thermo-optic coefficient.

[0066] In summary, the shower plate, the method for measuring the temperature of the shower plate, and the thin film deposition device provided by the present invention can be used to accurately measure the temperature of the shower plate under plasma interference and high-temperature environments, thereby improving the quality of thin film deposition.

[0067] Although the methods described above have been illustrated and described as a series of acts for simplicity of explanation, it should be understood and appreciated that the methods are not limited by the order of acts, as some acts may occur in different orders and / or concurrently with other acts not illustrated and described herein or other acts that are understandable to those skilled in the art, in accordance with one or more embodiments.

[0068] The foregoing description of the disclosure has been provided to enable any person skilled in the art to make or use the disclosure. Various modifications to the disclosure will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other variations without departing from the spirit or scope of the disclosure. Thus, the disclosure is not intended to be limited to the examples and designs described herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A spray plate, characterized in that, Comprising: A spray plate body, on which there are a plurality of air holes and at least one groove, wherein the groove is located on the upper surface of the spray plate body facing away from the process chamber; An FBG sensor, disposed in the groove, for determining the temperature of the corresponding area of the spray plate body according to the transmission spectrum obtained at the output end; and A strip for fixing the FBG sensor in the groove.

2. The spray plate according to claim 1, wherein The FBG sensor includes: A core, on which there is at least one grating for filtering light of a characteristic wavelength corresponding to a temperature from the core, so as to obtain a transmission spectrum characterizing the temperature of the corresponding area of the spray plate body at the output end of the FBG sensor; and A cladding, wrapped around the outside of the core for protecting the core.

3. The spray plate according to claim 1, characterized in that, Further comprising: An incident light source, located at the input end of the FBG sensor, for providing a broadband incident light adapted to the temperature detection range to the FBG sensor, so as to obtain corresponding transmitted light at the output end of the FBG sensor; And A first optical fiber demodulator, located at the output end of the FBG sensor, for analyzing the transmitted light to determine its transmission spectrum.

4. The shower plate according to claim 3, characterized in that Further comprising: A second optical fiber demodulator, located at the input end of the FBG sensor, for analyzing the reflected light output from the input end to determine its reflection spectrum, and the FBG sensor also determines the temperature of the corresponding area of the spray plate body according to the reflection spectrum.

5. The shower plate according to claim 3, wherein, The incident light source uses an ultraviolet light source.

6. The shower plate according to claim 1, characterized in that, The upper surface of the spray plate body is provided with a plurality of the grooves, wherein the grooves are distributed in parallel and / or crosswise, and / or each of the grooves extends in a linear shape of a straight line and / or a wavy line.

7. The shower plate according to claim 1, characterized in that, The strip and the groove fix the FBG sensor in the groove through interference fit.

8. A thin film deposition apparatus, characterized in that, Comprising: A process chamber, which includes a spray plate as described in any one of claims 1 to 7, and a heating plate, wherein the spray plate is used for transporting gas from the outside to the process chamber, and the heating plate is used for carrying and heating a wafer to be processed; And A radio frequency generator, via a radio frequency coil disposed on the top and / or side wall of the process chamber, provides a high-frequency alternating electric field to the process chamber to excite in-situ plasma between the spray plate and the heating plate.

9. A method for measuring the temperature of a spray plate, characterized in that, Comprising the following steps: Determine the initial temperature of the spray plate as described in any one of claims 1 to 7, and obtain a first transmission spectrum from the output end of its FBG sensor; According to the first transmission spectrum, determine a first Rayleigh scattering spectrum of the full-section Rayleigh scattering cross-section in the core of the FBG sensor, wherein the Rayleigh scattering cross-section is distributed along the length direction of the core; At a working temperature to be measured, obtain a second transmission spectrum from the output end of the FBG sensor, and determine a corresponding second Rayleigh scattering spectrum accordingly; Via a local matching algorithm, locally match the second Rayleigh scattering spectrum with the first Rayleigh scattering spectrum to determine the spectral peak offset between the two; According to the spectral peak offset, calculate the corresponding temperature change amount; and According to the initial temperature and the temperature change amount, determine the working temperature of the corresponding area of the FBG sensor.

10. A method for measuring the temperature of a spray plate, characterized in that, Comprising the following steps: Determine the initial temperature of the spray plate according to any one of claims 1 to 7, and obtain the first reflection spectrum from the input end of its FBG sensor; Determine the first reflection wavelength of the FBG sensor according to the first reflection spectrum; At the working temperature to be measured, obtain the second reflection spectrum from the input end of the FBG sensor; Determine the second reflection wavelength of the FBG sensor according to the second reflection spectrum; Calculate the corresponding wavelength shift according to the first reflection wavelength and the second reflection wavelength; Calculate the corresponding temperature change according to the wavelength shift; And Determine the working temperature of the corresponding area of the FBG sensor according to the initial temperature and the temperature change.

11. The temperature measurement method according to claim 10, characterized in that, The expression for calculating the corresponding temperature change according to the wavelength shift is: ΔT = Δλ B / λ B0 ·(α + ξ) where ΔT is the temperature change, and Δλ B is the wavelength shift, λ B0 is the first reflection wavelength, α is the coefficient of thermal expansion, and ξ is the thermo-optic coefficient.

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