CN116469793A - Method and device for determining uncertainty of measurement of reworked depth in wafer laser reworking - Google Patents
Method and device for determining uncertainty of measurement of reworked depth in wafer laser reworking Download PDFInfo
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Abstract
The invention relates to the field of semiconductor processing equipment, in particular to a method and equipment for determining the uncertainty of the reform depth measurement in the process of wafer laser reform, wherein the method determines the component of the uncertainty of the reform depth measurement of a reform groove wafer to be calculated according to a wafer laser reform device and reform depth measurement equipment, and comprises a static uncertainty component and a dynamic uncertainty component; calculating the static uncertainty component and the dynamic uncertainty component; and determining the synthesis standard uncertainty by utilizing the static uncertainty component and the dynamic uncertainty component. According to the invention, a relatively perfect uncertainty source analysis is formed by decomposing the structure of the wafer laser reconstruction, so that the total uncertainty components are synthesized to obtain the synthetic standard uncertainty, and the main component influencing the uncertainty can be obtained by evaluating and analyzing the uncertainty components, so that the main component is controlled, and the method can be used for precisely controlling the wafer reconstruction depth.
Description
Technical Field
The invention relates to the field of semiconductor processing equipment, in particular to a method and equipment for determining uncertainty of measurement of a reworked depth in wafer laser reworking.
Background
Along with the vigorous development of electronic information technology, the importance of a semiconductor chip in social production and life is remarkably improved, the semiconductor chip is generally made of monocrystalline silicon, monocrystalline silicon materials have the characteristics of high hardness, high brittleness and the like, the processing difficulty is high, the traditional processing method generally adopts mechanical micromachining, however, along with the higher and higher integration level of the semiconductor chip, the volume is lighter and lighter, the traditional processing method is difficult to be applied to chips with large size and low thickness, along with the development of ultra-fast laser technology, a picosecond laser is used in wafer surface processing, mechanical stress and high-temperature environment are not generated when the surface of the wafer is modified, and micron-sized surface focusing is realized, so that the problems of hardness reduction caused by laser thermal ablation and easiness in fracture caused by mechanical processing in the traditional method can be solved. This "cold working" approach (i.e., laser chill cracking technique) provides a new solution for achieving surface processing of large-sized wafers.
In the process of processing the surface of the wafer by ultra-fast laser, errors inevitably occur due to the influence of various external factors and the limitation of processing conditions, so that uneven aperture depth of laser reconstruction is caused, and the subsequent processing of the wafer is influenced. Further, the laser reconstruction process has higher requirements on the moving speed of the displacement table, and simultaneously requires that the displacement table is deformed by inertia force to be lower, and the rotation direction of the displacement table is adjusted in time, so that the rigidity and other characteristics of the displacement table are required to be analyzed, and the processing efficiency is improved. In the current laser reconstruction process, related national standards and industry standards are not formed, which leads to uneven surface consistency obtained after laser cold cracking in the market.
Because the error sources of laser reformation are more, the related factors are more complex, and the prior art does not perform error analysis and measurement uncertainty evaluation on the wafer reformation depth during laser reformation at present, so that the wafer reformation depth during the laser reformation process cannot be accurately controlled.
Disclosure of Invention
The application provides a method and equipment for determining uncertainty of wafer modification depth measurement in wafer laser modification, so as to solve the technical problem of inaccurate wafer modification depth control in the prior art.
According to an aspect of an embodiment of the present application, there is provided a method for determining uncertainty of measurement of a reworked depth in wafer laser reworking, the method including:
determining components of uncertainty of wafer modification depth measurement to be calculated according to a wafer laser modification device and a related system, wherein the components comprise a static uncertainty component and a dynamic uncertainty component;
calculating the static uncertainty component and the dynamic uncertainty component;
and determining the synthesis standard uncertainty by utilizing the static uncertainty component and the dynamic uncertainty component.
Optionally, after determining the synthesis criterion uncertainty, further comprising:
the expansion uncertainty is determined using the following:
，
wherein ,to expand uncertainty, ++>For the synthesis of standard uncertainty, +.>The value of the factor is positive.
Optionally, the wafer laser remanufacturing device comprises a laser, a displacement table and a guide rail pair, wherein the guide rail pair comprises a transverse moving guide rail pair and a longitudinal moving guide rail pair which are placed in an overlapping mode, the transverse moving guide rail pair and the longitudinal moving guide rail pair are respectively provided with two guide rails, any guide rail is provided with two sliding blocks, and the displacement table is provided with a displacement sensor; the displacement table is connected with one of the transverse moving guide rail pair or the longitudinal moving guide rail pair through the sliding block, the transverse moving guide rail pair is connected with the longitudinal moving guide rail pair through the sliding block, and the sliding block slides on the guide rail pair; the laser is used for emitting laser to reform the wafer, the displacement table is used for bearing the wafer, the guide rail pair is used for moving the wafer, and the displacement sensor is used for measuring the wafer reform depth.
Optionally, calculating the static uncertainty componentFurther comprises:
calculating uncertainty caused by measurement of the displacement sensorUncertainty caused by the laser output +.>And uncertainty caused by shape and position errors of the wafer, the displacement table and the guide rail +.>At least one of (a) and (b);
by means of、/>、/>Is calculated by->。
Optionally, calculating uncertainty caused by the displacement sensor measurementFurther comprises:
calculating uncertainty caused by repeatedly measuring the surface of the wafer by the displacement sensorAnd the displacement sensor repeatedly measures uncertainty caused by depth of wafer remanufacturing grooveDegree of certainty->Resolution-induced uncertainty->Uncertainty due to perpendicularity error +.>Uncertainty due to temperature drift +.>Uncertainty caused by zero drift +.>Uncertainty due to sensitivity drift +.>Uncertainty due to electromagnetic compatibility>Uncertainty due to return error->At least one of (a) and (b);
by means of、/>、/>Is calculated by->。
Optionally, calculating uncertainty caused by the displacement sensor measurementFurther comprises:
calculating uncertainty caused by repeatedly measuring the surface of the wafer by the displacement sensorAnd the displacement sensor repeatedly measures uncertainty +.>Resolution-induced uncertainty->Uncertainty due to perpendicularity error +.>Uncertainty due to temperature drift +.>Uncertainty caused by zero drift +.>Uncertainty due to sensitivity drift +.>Uncertainty due to electromagnetic compatibility>Uncertainty due to return error->At least one of (a) and (b);
by means of、/>、/>、/>、/>、/>、/>、/> and />Is calculated by->。
Optionally, calculating uncertainty caused by the laser outputFurther comprises:
calculating uncertainty caused by depth of focus of the laserAnd uncertainty caused by focusing aberrationAt least one of (a) and (b);
by means of and />Is calculated by->。
Optionally, calculating uncertainty caused by shape and position errors of the wafer, the displacement table and the guide railFurther comprises:
using the uncertainty caused by the uniformity of the wafer surfaceUncertainty due to the flatness of the surface of the abutment +.>Uncertainty of temperature-induced displacement table and guide rail>Uncertainty caused by rail straightness error>At least one of (a) and (b);
calculation of、/>、/> and />Is calculated by->。
Optionally, calculating the dynamic uncertainty componentFurther comprises:
calculating vibration-induced uncertaintyDegree of uncertainty in displacement caused by amount of deformation of slider of lateral guide railAnd measurement uncertainty caused by bending deformation of the guide rail +.>At least one of (a) and (b);
by means of、/> and />Is calculated by->。
Alternatively, the synthesis criterion uncertainty is determined using the following:
,
wherein ,for the synthesis of standard uncertainty, +.>For static uncertainty->
According to another aspect of the embodiments of the present application, there is also provided an apparatus for determining uncertainty of measurement of a reworked depth in wafer laser reworking, including: a processor and a memory coupled to the processor; the memory stores instructions executable by the processor, so that the processor executes the determination method of the depth measurement uncertainty in the wafer laser reconstruction.
According to the uncertainty determination method and the uncertainty determination equipment provided by the invention, the related uncertainty components are calculated through decomposing the structure of the laser reformation of the wafer, so that relatively perfect uncertainty source analysis is formed, all uncertainty components are synthesized to obtain the synthesized standard uncertainty, and the main component influencing the uncertainty can be obtained through evaluating and analyzing the uncertainty components, so that the main component is controlled.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic view of a wafer laser remanufacturing apparatus according to one embodiment of the present invention;
FIG. 2 is a schematic diagram showing another state of the wafer laser trimming apparatus according to the embodiment of the present invention;
FIG. 3 is a flow chart of a method for determining uncertainty of measurement of a reworked depth in wafer laser reworking according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a laser-modified wafer-modified depth traceability system.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention.
In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; the two components can be directly connected or indirectly connected through an intermediate medium, or can be communicated inside the two components, or can be connected wirelessly or in a wired way. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In addition, the technical features of the different embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
As shown in fig. 1, the embodiment of the invention provides a wafer laser remanufacturing device, which comprises a laser 1, a displacement table 3 and a guide rail pair 4, wherein the guide rail pair 4 comprises a transverse moving guide rail pair 5 and a longitudinal moving guide rail pair 6 which are overlapped, the transverse moving guide rail pair and the longitudinal moving guide rail pair are respectively provided with two guide rails, and any guide rail is provided with two sliding blocks. The displacement table 3 is connected with one of the transverse moving guide rail pair 5 or the longitudinal moving guide rail pair 6 through a sliding block, the transverse moving guide rail pair 5 is connected with the longitudinal moving guide rail pair 6 through the sliding block, and the sliding block slides on the guide rail pair.
The displacement platform 3 is used for bearing the wafer 2, the laser 1 is used for sending out laser and carrying out the reform to the wafer 2, and the guide rail pair 4 is used for removing the wafer 2. The displacement table 3 is provided with a displacement sensor for measuring the reworked depth of the wafer 2.
As shown in fig. 1 and 2, the working modes specifically include: the laser 1 is controlled to emit laser, the laser is focused on the surface of the wafer, and the distance from the position of the laser light source read by the displacement sensor to the surface of the wafer isThen, the focusing depth of the laser 1 is adjusted to a preset depth, and meanwhile, the displacement table 3 fixed on the sliding block of the guide rail drives the wafer 2 to axially move according to a set serpentine route, and the laser continuously reforms the wafer 2 in the uniform movement process, so that a plurality of reform grooves 7 with the preset depth are obtained. At this time, the distance from the light source position of the laser 1 to the deepest position of the reforming groove 7 is read again by the displacement sensor to be +.>Thereby, the modified groove depth value d, # is calculated>。
As shown in fig. 3, an embodiment of the present invention provides a method for determining uncertainty of depth measurement during wafer laser modification, where the method may be executed by an electronic device such as a computer or a server, and specifically includes the following operations:
s110, determining components of uncertainty of wafer reform depth measurement to be calculated according to the wafer laser reform device and a related system, wherein the components comprise a static uncertainty component and a dynamic uncertainty component.
For the wafer laser remanufacturing apparatus of fig. 1, the related systems include a wafer track system, a wafer displacement table system, a laser system, and a displacement sensor system. For other retrofit devices, the corresponding system may be selected based on the actual components. Therefore, the uncertainty component of the wafer rework slot depth to be calculated should be determined based on the configuration of the rework apparatus and the measurement transfer chain.
Taking the remanufacturing device shown in fig. 1 as an example, according to the characteristics of the geometric quantity transmission chain, the geometric quantity transmission is divided into the following parts: wafer track system, wafer displacement table system, laser system and displacement sensor system, and the uncertainty sources described above have the following aspects: the uncertainty caused by the measurement of the displacement sensor, the uncertainty caused by the laser output, the uncertainty caused by the shape and position errors of the wafer, the displacement table and the guide rail, the uncertainty caused by the vibration of the displacement table and the uncertainty caused by the inertia force during the swinging of the displacement table are all called as static uncertainty components, and the uncertainty caused by the shape and position errors of the wafer, the displacement table and the guide rail are all called as dynamic uncertainty components.
Further, it may also be determined whether each transfer link has a coupling association, whether each link has a cross-correlation is determined by correlation analysis, the associated components establish their correlation coefficients, and the uncorrelated components are processed according to independent variables. Based on the mathematical model and uncertainty source analysis, each uncertainty component is independent, and the correlation coefficient is negligible.
S120, calculating a static uncertainty component and a dynamic uncertainty component. According to the influence mechanism of the change depth in each link, the factors influencing the change depth are classified into two types, namely an uncertainty component can be obtained by a statistical method, and an uncertainty component can not be obtained by a statistical method. Different calculation methods may be employed for the two types of uncertainty components.
S130, determining the synthesis standard uncertainty by utilizing the static uncertainty component and the dynamic uncertainty component. The static uncertainty component includes uncertainty caused by displacement sensor measurementsUncertainty caused by the laser output +.>And uncertainty caused by shape and position errors of the wafer, the displacement table and the guide rail +.>According to->、、/>These three components calculate a total static uncertainty component +.>The method comprises the steps of carrying out a first treatment on the surface of the The dynamic uncertainty component comprises vibration induced uncertainty +.>Degree of uncertainty in displacement caused by the amount of deformation of the slide of the transverse rail>And measurement uncertainty caused by bending deformation of the guide rail +.>According to->、/> and />These three components calculate a total dynamic uncertainty component +.>And according to the static uncertainty component +.>And dynamic uncertainty component->The total synthesis criterion uncertainty is calculated and, as previously described, correlation coefficients may also be introduced for the various components in the calculation process.
It should be noted that, for other reform devices, such as reform devices including more related subsystems, more uncertainty components and thus the uncertainty of the synthesis standard may be calculated.
In an alternative embodiment, after the synthetic criteria uncertainty is determined, an extended uncertainty may be further calculated.
Specifically, the uncertainty is extended，/>To expand uncertainty, ++>For the synthesis of standard uncertainty, +.>The value of the factor is positive. Comprises factor->The value of (2) is related to the confidence probability, and the confidence probability can be improved by setting a proper inclusion factor.
In addition, for ease of calculation, the uncertainty in this scheme may be a relative uncertainty, and the final uncertainty calculation is expressed in terms of a percentage.
The static uncertainty component and the dynamic uncertainty component of the wafer laser reclamation apparatus shown in fig. 1 are described below by way of several embodiments.
With respect to static uncertainty componentsUncertainty caused by measurement of the displacement sensor in (2)>Further comprises:
S1211A, calculating uncertainty caused by the repeatability of the displacement sensor to measure the surface of the waferAnd institute(s)The displacement sensor repeatedly measures uncertainty ++caused by depth of wafer remanufacturing groove>Resolution-induced uncertainty->Uncertainty due to perpendicularity error +.>Uncertainty due to temperature drift +.>Uncertainty caused by zero drift +.>Uncertainty due to sensitivity drift +.>Uncertainty due to electromagnetic compatibility>Uncertainty due to return error->At least one of them.
Specifically, the laser is repeatedly measured to the deepest position of the wafer surface and each reworked groove through a displacement sensor, the measurement times are n, and the average value is respectively and />Standard deviation is +.> and />Its repeatability measurement leads toUncertainty of onset-> and />Respectively is
，
，
Resolution refers to the minimum input amount change value that produces an observable change in output amount over the measurement range of the instrument. The minimum graduation value of the sensor isThe full scale is FS, the uncertainty is a rectangular distribution, therefore, the uncertainty due to resolution error is
，
In the process of measuring the surface of the wafer and remanufacturing the groove through the sensor, the measuring head of the displacement sensor and the surface of the wafer need to be in a strict vertical state, namely Abbe's principle needs to be satisfied, however, due to the limitation of the resolution of human eyes and the influence of mechanical vibration, the measuring head of the sensor and the surface of the wafer are not always in a complete vertical state during the measurement, and therefore, the angle deviation generated during the measurement is set asObeying uniform distribution, uncertainty due to perpendicularity errors is:
，
the full scale range of the displacement sensor is FS, the ambient temperature is T ℃, the temperature drift coefficient is alpha (the unit is FS/DEGC), and the uncertainty caused by the temperature drift is:
，
uncertainty caused by displacement sensor zero drift is:
，
wherein ,for the relative change in temperature, +.>The maximum rate of change of the zero point output at the time of temperature change.
Uncertainty caused by displacement sensor sensitivity drift is:
，
wherein ,for the relative change in temperature, +.>Is the rate of change of sensitivity with respect to temperature.
Uncertainty caused by electromagnetic compatibility of the displacement sensor is:
，
wherein ,for the change of the indication after EMC change, +.>Is the current indication. The uncertainty can pass EMC electromagnetic detection standard EN61000-6-3 and EMC electromagnetic interference detectionThe measurement standard is EN 61000-6-2.
The return error refers to the situation that different coordinate values appear for the same position in the process and the return process, so uncertainty caused by the return error of the displacement sensor is as follows:
，
wherein ,for the coordinate difference of the current same position between the trip and the return, +.>Is the coordinate value of the position.
S1212A, utilize、/>、/>、/>、/>、/>、/>、/>Andis calculated by->. Taking the example of using all components here, the following calculation method may be adopted:
，
in the present embodiment will、/>、/>、/>、/>、/>、/>、/>Andas mutually independent components, no correlation coefficient is introduced in the above calculation formula. For uncertainty components that are considered to be associated, correlation coefficients may be added to the above-described calculation.
It should be noted that this calculation is only for illustrating how to calculate a total component by combining the uncertainty components of the displacement sensor, and it does not mean that all the components must be introduced in practical application. The person skilled in the art can choose the components influencing the measurement result according to the actual situation, and different errors may exist for different displacement sensors, so as to choose and calculate according to the actual situation.
With respect toStatic uncertainty componentUncertainty caused by the laser output in +.>Further comprises:
S1211B, calculating uncertainty caused by depth of focus of laserAnd uncertainty caused by focusing aberrationAt least one of them.
In particular, the depth of focus (i.e., depth of focus) of the laserAnd laser wavelength->Focusing mirror focal length +.>The deviation of the above parameters directly affects the accuracy of the depth of focus in relation to the spot radius D of the laser beam incident on the focusing lens surface, as follows:
，
when the above formula is fully differentiated, because the wavelength, focal length and spot radius are mutually independent components, the correlation can be regarded as 0, and the uncertainty caused by the focusing depth of the laser is as follows:
，
wherein Uncertainty for laser wavelengthDegree(s),>uncertainty for the focal length of the focusing mirror, < >>Is the uncertainty caused by the spot radius.
In the laser surface reconstruction process, the existence of aberration can cause the deviation of the intensity distribution of a focused light field and the intensity distribution of a target light field, thereby affecting the three-dimensional distribution of the light field during processing and reducing the processing precision. The depth deviation of the groove due to aberration isObeying a uniform distribution, the uncertainty due to the focusing aberrations is:
，
S1212B, utilize and />Is calculated by->. Taking the example of using all components here, the following calculation method may be adopted:
，
in the present embodiment will and />As mutually independent components, no correlation coefficient is introduced in the above calculation formula. For uncertainty components considered to be associated, one can count as described aboveAnd adding a correlation coefficient into the formula.
It should be noted that this calculation is only for illustrating how to calculate a total component by combining the uncertainty components of the laser, and it does not mean that all the components must be introduced in practical application. The person skilled in the art can choose the components influencing the measurement results according to the actual situation, and there may be different errors for different lasers, but there may be other error problems as a result, so that the components are chosen and calculated according to the actual situation.
With respect to static uncertainty componentsUncertainty caused by shape and position errors of wafer, displacement table and guide railFurther comprises:
S1211C, calculating uncertainty caused by wafer surface uniformityUncertainty due to the flatness of the surface of the abutment +.>Uncertainty of temperature-induced displacement table and guide rail>Uncertainty caused by rail straightness error>At least one of them.
Specifically, the shape and position errors of the wafer and the displacement table include the total thickness deviation of the wafer, the straightness error of the guide rail, and the error generated by the temperature expansion deformation of the displacement table and the guide rail.
Because of the limitation of the processing technology, the surface of the wafer is difficult to be absolutely leveled and smooth, when the surface of the wafer to be ground is uneven, the deviation of the focusing position of the laser is caused, and then the depth deviation of laser reconstruction is caused, and the flatness condition of the surface of the wafer is generally represented by TTV: TTV (Total Thickness Variation), which characterizes the total thickness deviation of the wafer surface, refers to the difference between the maximum and minimum thickness of the wafer from the reference plane under clamping.
The total thickness deviation of the wafer surface isObeying the uniform distribution, uncertainty caused by the uniformity of the wafer surface is:
，
flatness error belongs to shape and position error, uncertainty caused by flatness of surface of base stationThe calculation can be performed by a minimum inclusion region method, a diagonal plane method, a least square method and the like. Flatness error->Calculation reference GB/T11337-2004 displacement table surface flatness induced uncertainty +.>The calculation is as follows:
，
when the temperature changes, the displacement table and the guide rail are subjected to linear expansion under the influence of the temperature, and then deformation in the three-dimensional direction is generated, so that deviation occurs in the depth of the modified groove. The linear expansion coefficients of the displacement table and the orthogonal guide rail in the z direction are respectively beta and gamma, the standard temperature is T, the heights are respectively H and H, and the deviation between the current temperature and the standard temperature isObeys toEvenly distributed, the uncertainty of the displacement table and the guide rail caused by temperature is as follows:
，
the guide rail straightness error can be obtained through a level gauge and an auto-collimator, and the guide rail straightness error in the horizontal direction and the vertical direction in the orthogonal guide rail can be respectively obtained through the methods of least square fitting, endpoint connection and the like by obtaining the height deviation of each point on the guide rail relative to the position of 0 point and />The errors follow a uniform distribution, so uncertainty caused by the straightness errors of the guide rail is as follows:
。
S1212C, utilize、/>、/> and />Is calculated by->. Taking the example of using all components here, the following calculation method may be adopted:
，
in the present embodiment will、/> and />As mutually independent components, no correlation coefficient is introduced in the above calculation formula. For uncertainty components that are considered to be associated, correlation coefficients may be added to the above-described calculation.
It should be noted that this calculation is only for illustrating how to calculate a total component by combining the uncertainty components of the laser, and it does not mean that all the components must be introduced in practical application. The person skilled in the art can choose the components influencing the measurement results according to the actual situation, and there may be different errors for different displacement table rails, but there may be other error problems, so the components are chosen and calculated according to the actual situation.
Further, utilize、/>、/>Is calculated by->. Taking the example of using all components here, the following calculation method may be adopted:
，
with respect to dynamic uncertainty componentsUncertainty caused by vibration in +.>Further comprises:
S1221A, calculating vibration-induced uncertainty。
Specifically, vibration of the displacement table, the guide rail and the wafer to be measured is mainly related to three parameters of acceleration, amplitude displacement and frequency, and measurement uncertainty of the vibration is mainly amplitude, the amplitude can be obtained through an acceleration sensor and a dynamic signal analyzer, the uncertainty is evaluated as class B uncertainty, a waveform of general vibration can be decomposed into fundamental waves, second harmonic waves and higher harmonic waves, and the maximum synthesized amplitude of the fundamental waves isThe error distribution follows an arcsine distribution, and the uncertainty caused by vibration is:
，
S1221B calculating the degree of uncertainty in the displacement due to the amount of deformation of the slider of the lateral rail。
Specifically, the guide rail used by the wafer laser remanufacturing device is a rolling guide rail, the guide rail travel is 400mm, the maximum speed is 1m/s, and the acceleration is 1.25m/s2. In the process of moving in the horizontal direction, when the displacement platform moving at high speed is contacted with the edge of the guide rail, the guide rail and the displacement platform can generate bending deformation due to the action of inertia force and gravity, so that the accuracy and the depth uniformity in the laser reconstruction process are affected.
Here, the displacement table may be regarded as a cantilever beam, the guide rail as a constraint of the cantilever beam, and the inertial force is concentrated at the midpoint position of the cantilever beam. As can be seen from calculation of deflection deformation in the material mechanics, when the displacement stage is subjected to the inertial force f=ma, the displacement stage generates deflection in the z directionAnd corner->The method comprises the following steps of:
，
，
wherein E is the Young's modulus of the displacement table,the moment of inertia of the displacement table, H is the height of the displacement table, and the parameter can be obtained through a related manual.
The error is subject to uniform distribution, and thus the uncertainty is
，
The displacement platform is connected with the guide rails through the sliding blocks, and due to the influence of inertia force and gravity of the displacement platform, the two sliding blocks on each guide rail are unevenly stressed and respectively receive upward and downward acting forces, so that the sliding blocks are elastically deformed under the axial compression action.
According to the principle of material mechanics, if the rigidity of the sliding block is k, the stresses to which the sliding blocks 1 and 2 are subjected are:
，
，
wherein the F1 direction is vertically downward and the F2 direction is vertically upward. b is the distance between the slide 1 and the slide 2, v is the maximum speed during the acceleration movement, and t is the time during the acceleration movement. Taking b=0.4m, v=1 m/s, t=0.8 s, a=1.25 m/s2, g=10 m/s2, substituting the above formula:
，
，
from this, the axial deformations generated by the forces applied to the slider 1 and the slider 2 are respectively:
，
，
the resulting angular deviation is:
，
the uncertainty of displacement caused by the deformation of the sliding block of the horizontal guide rail is as follows:
，
S1221C calculating measurement uncertainty due to rail bending deformation。
Specifically, due to uneven stress of the sliding block, uneven stress of the guide rail is further caused, and due to direct contact between the guide rail and the sliding block, acting force between the sliding block and the wafer displacement table is concentrated on the sliding block. The slide block is set as two mass points, and the acting force of the slide block on the guide rail is F3 and F4 respectively, wherein F3=0.25 mg+F1 and F4=0.25 mg-F2.
The total length of the guide rail is 2b, and the maximum bending stress to which the guide rail is subjected during the reciprocating motion of the guide rail is concentrated at the center position x of the guide rail:
，
measurement uncertainty due to bending deformation of the railThe method comprises the following steps:
，
further, utilize、/> and />Is calculated by->. Taking the example of using all components here, the following calculation method may be adopted:
，
in step S130, to calculate the synthesis standard uncertainty by integrating the static uncertainty component and the dynamic uncertainty component, the following manner may be adopted:
，
wherein ,for the synthesis of standard uncertainty, +.>Is static uncertainty.
Further on this basis, an expansion uncertainty is calculatedWhen k takes a value of 2.
Therefore, by evaluating and analyzing the uncertainty component, the main component affecting the uncertainty can be obtained, and then the main component is controlled, so that errors in the processing process are reduced, and the processing precision, the processing efficiency and the surface consistency are improved.
In the magnitude transfer and tracing system, the magnitude transfer is respectively from top to bottom: metering references, metering standards and work metering appliances. Wherein the measurement standard is divided into international standard and national standard.
In order to ensure that uncertainty components in the synthesis standard uncertainty evaluation process of the reform device can be traced one by one, a magnitude tracing system shown in fig. 4 can be established.
According to the system, each link of the consistency control of the reform depth in the laser reform process corresponds to the corresponding metering standard of the national metering system respectively:
physical quantity of a base station system forming a wafer bearing part can trace to national length standard and angle standard; physical quantity forming a guide rail system for driving the base station to move can trace to national length standard, angle standard and time standard; physical quantity of a laser system forming a wafer processing part can trace to national length standard; the physical quantity of a wafer system forming the wafer processing depth can trace to the national length standard; physical quantity of a sensor system forming wafer parameter output can trace to national length standard and angle standard; the physical quantity of the ambient temperature throughout the entire measurement system can be traced to national temperature standards.
The national standard throughput is traced back to the national standard, and the physical constant of the basic unit is redefined according to the international metering system, so that the wafer reconstruction depth under the reconstruction depth consistency control system in the laser reconstruction process is traced back to the basic physical constant finally.
It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.
Claims (10)
1. A method for determining uncertainty of measurement of a reworked depth in laser reworking of a wafer, comprising:
determining components of uncertainty of wafer modification depth measurement to be calculated according to a wafer laser modification device and a related system, wherein the components comprise a static uncertainty component and a dynamic uncertainty component;
calculating the static uncertainty component and the dynamic uncertainty component;
and determining the synthesis standard uncertainty by utilizing the static uncertainty component and the dynamic uncertainty component.
2. The method of claim 1, further comprising, after determining the synthesis criterion uncertainty:
the expansion uncertainty is determined using the following:
,
wherein ,to expand uncertainty, ++>For the synthesis of standard uncertainty, +.>The value of the factor is positive.
3. The method according to claim 1 or 2, wherein the wafer laser remanufacturing device comprises a laser, a displacement table and a guide rail pair, the guide rail pair comprises a transverse moving guide rail pair and a longitudinal moving guide rail pair which are placed in an overlapping mode, two guide rails are respectively arranged on the transverse moving guide rail pair and the longitudinal moving guide rail pair, two sliding blocks are arranged on any guide rail, and a displacement sensor is arranged on the displacement table; the displacement table is connected with one of the transverse moving guide rail pair or the longitudinal moving guide rail pair through the sliding block, the transverse moving guide rail pair is connected with the longitudinal moving guide rail pair through the sliding block, and the sliding block slides on the guide rail pair; the laser is used for emitting laser to reform the wafer, the displacement table is used for bearing the wafer, the guide rail pair is used for moving the wafer, and the displacement sensor is used for measuring the wafer reform depth.
4. A method according to claim 3, wherein the static uncertainty component is calculatedFurther comprises:
calculating uncertainty caused by measurement of the displacement sensorUncertainty caused by the laser outputAnd uncertainty caused by shape and position errors of the wafer, the displacement table and the guide rail +.>At least one of (a) and (b);
by means of、/>、/>At least one calculation of (a)/>。
5. The method of claim 4, wherein the uncertainty caused by the displacement sensor measurement is calculatedFurther comprises:
calculating uncertainty caused by repeatedly measuring the surface of the wafer by the displacement sensorAnd the displacement sensor repeatedly measures uncertainty +.>Resolution-induced uncertainty->Uncertainty due to perpendicularity error +.>Uncertainty due to temperature drift +.>Uncertainty due to zero driftUncertainty due to sensitivity drift +.>Uncertainty due to electromagnetic compatibility>Uncertainty due to return error->At least one of (a) and (b);
by means of、/>、/>、/>、/>、/>、/>、/> and />Is calculated by->。
6. The method of claim 4, wherein the uncertainty caused by the laser output is calculatedFurther comprises:
calculating uncertainty caused by depth of focus of the laserAnd uncertainty due to focusing aberration +.>At least one of (a) and (b);
by means of and />Is calculated by->。
7. The method of claim 4, wherein uncertainty due to shape and position errors of the wafer, displacement table and guide rail is calculatedFurther comprises:
calculating uncertainty caused by the uniformity of the surface of the waferUncertainty due to abutment surface flatnessUncertainty of temperature-induced displacement table and guide rail>Uncertainty caused by rail straightness error>At least one of (a) and (b);
by means of、/>、/> and />Is calculated by->。
8. A method according to claim 3, wherein the dynamic uncertainty component is calculatedFurther comprises:
calculating vibration-induced uncertaintyDegree of uncertainty in displacement caused by the amount of deformation of the slide of the transverse rail>And measurement uncertainty caused by bending deformation of the guide rail +.>At least one of (a) and (b);
by means of、/> and />Is calculated by->。
9. The method of claim 1, wherein the synthetic standard uncertainty is determined by:
,
wherein ,for the synthesis of standard uncertainty, +.>Is static uncertainty.
10. A determination apparatus for a depth measurement uncertainty in wafer laser rework, comprising: a processor and a memory coupled to the processor; wherein the memory stores instructions executable by the processor to cause the processor to perform the method of determining a reform depth measurement uncertainty in a wafer laser reform as claimed in any one of claims 1-9.
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| CN115344814A (en) * | 2022-10-13 | 2022-11-15 | 北京特思迪半导体设备有限公司 | Down pressure uncertainty calculation method based on flexible air bag |
| CN115831296A (en) * | 2023-02-21 | 2023-03-21 | 北京特思迪半导体设备有限公司 | Method for calculating uncertainty of friction coefficient of material and application |
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| CN115344814A (en) * | 2022-10-13 | 2022-11-15 | 北京特思迪半导体设备有限公司 | Down pressure uncertainty calculation method based on flexible air bag |
| CN115831296A (en) * | 2023-02-21 | 2023-03-21 | 北京特思迪半导体设备有限公司 | Method for calculating uncertainty of friction coefficient of material and application |
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