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Determination of measurement uncertainty in nano measurement and three-dimensional measurement

overview

in precision measurement, people have reached a broad consensus on the importance of correctly evaluating measurement uncertainty. However, as the party to consider traceability, the industry has improved its understanding of general measurement and evaluation, while the dispute about traceability and uncertainty is still ongoing. In terms of length and shape measurement, when using general measuring instruments for length measurement, the following factors need to be considered (see Table 1): the uncertainty of the measuring instrument, the uncertainty of the measuring instrument after calibration (including the standard parts as the calibration benchmark), the uncertainty of the measurement process, the influence of the environment (especially the influence of temperature), etc. It is possible and simple to evaluate the uncertainty of general length measurement

Table 1 Determination of uncertainty in general length measurement

main factors of uncertainty - Determination Method

① measuring instrument: repeatability, scale error, etc. - JIS, manufacturer's technical specifications

② calibration: benchmark/standard - calibration certificate; Repeatability - Experiment

③ measurement: Environment: temperature, etc. - experiment and theoretical analysis; Repeatability - Experiment

this paper describes the evaluation of uncertainty in nano measurement and three-dimensional measurement. In nano measurement, if the measurement uncertainty is evaluated according to table 1, the standard parts as the calibration benchmark become an important issue. Therefore, when evaluating the uncertainty of nano measurement, it is necessary to focus on the establishment and determination of nano standard parts. In three-dimensional measurement, the measurement steps are complex, and many factors must be considered. The uncertainty evaluation depending on the measurement strategy is very important. The uncertainty of three-dimensional measurement is determined by considering the measurement strategy. In this regard, this paper will clarify the trend of ISO standardization

evaluation of uncertainty in nano measurement

(1) nano standard

nano measurement is very important for the semiconductor industry, and the industry strongly requests to establish the benchmark/standard of nano measurement. As the nano benchmark/standard, the one-dimensional step gauge, step gauge, line value gauge and two-dimensional step gauge shown in Figure 1 are used to determine and establish the nano benchmark/standard

in line with this, various countries have put forward various schemes for measuring machines used to establish nano benchmarks/standards. Npl (British Standards Institute) has researched and developed four measuring machines (see Table 2), which play an important role in the establishment of nano standards. Among them, AFM (length measuring atomic force microscope) is the most widely used. AFM is an atomic force microscope combined with laser length measuring instrument, which is being developed in various countries

Table 2 NPL four important measuring instruments used to establish nano benchmarks/standards

① surface roughness measuring instrument of combined laser length measuring instrument: nanosurf

② atomic force microscope of combined laser length measuring instrument: metrological afm

③ optical interferometer and pay more attention to improvement Combination of improved production process X-ray interferometer: coxi

④ high precision CMM: small CMM

(2) composition of length measuring AFM

the length measuring AFM developed by the metrology standards Department of Japan Institute of industrial technology has the highest performance in the world today. 10. The Y and Z axes are equipped with laser interferometers, which use optical path reflection and electrical subdivision, and the resolution reaches 0.04nm. The measuring object is placed on the workbench with a five sided mirror, and the measurement uncertainty of the instrument is reduced because there is no Abbe error. The laser interferometer is compared with the iodine stabilized laser as the national length standard to ensure traceability. In this way, a complete and traceable measuring machine is formed for the detection benchmark/standard

(3) assign a value to the step gauge benchmark with the length AFM

Table 3 shows the main uncertainty factors when assigning a value to the 240nm step gauge benchmark shown in Figure 3 with the length AFM. It can be seen from the table that for the 240nm step gauge, the nonlinear error of the laser interferometer is the most important factor in the uncertainty of the AFM instrument itself. For the 240nm step gauge, which avoids the narrow measurement range due to impurities such as water, the pentahedral mirror is used in the mechanism, which avoids the influence of large uncertainty factors such as mechanism error (such as Abbe error)

Table 3 main factors of uncertainty when measuring 240nm step gauge with length AFM

main factors of uncertainty - standard deviation

① measuring instrument: nonlinearity of interferometer - 0.12nm; The resolution of the interferometer is - 0.02nm; Abbe error - 0.01nm

② measurement object and operation: material inhomogeneity - 0.09nm; Repeatability of measurement - 0.05nm

due to the discreteness of reference/standard parts manufacturing and different places, the difference of step gauge reference/standard has become a major factor of uncertainty except for the measuring machine. This is a typical problem in nano benchmarks/standards. Even if a good measuring machine is developed, it is difficult to assign a value to the benchmark/standard because the shape deviation of the measured object is too large or the stability is too poor. The example of assigning value to the benchmark/standard of 240nm step gauge shows that the expanded uncertainty can reach ± 0.04nm

(4) on the subject of nano measurement uncertainty

there is an example. When assigning a value to the 70nm step gauge benchmark/standard, the uncertainty caused by the poor surface morphology exceeds 1nm, accounting for more than 1% of the step difference, which is equivalent to 1mm unevenness on the surface of 100mm gauge block. This shows that factors that do not need to be considered in micron scale measurement will become a major problem in nano scale measurement

in nano measurement, scanning electron microscope or general AFM is usually calibrated with nano benchmark/standard, and then bioamber company is selected as the supplier of biological hupernic acid for measurement. In this case, the uncertainty of measurement is evaluated by adding the uncertainty of nano benchmark/standard with the uncertainty of measuring machine and measurement operation. The uncertainty of nano benchmark/standard accounts for a large proportion

it can be seen that nano benchmark/standard is very important in nano measurement. In Japan in the future, it is very important to prepare Japanese nano benchmarks/standards with the Institute of industrial technology as the center, and it is necessary and indispensable to realize the self supply of high-quality benchmarks/standards

evaluation of uncertainty in three-dimensional measurement

(1) high accuracy of CMM

CMM is used to measure three-dimensional shape, size, etc. in order to achieve high accuracy of measurement, it is necessary to calibrate the CMM with high accuracy first. Then it is necessary to evaluate the measurement uncertainty in order to ensure its traceability when using the CMM with high precision calibration for three-dimensional measurement

now in iso/tc213/wg10 (coordinate measuring machines) standard, the accuracy evaluation of coordinate measuring machines has been specified, and the evaluation specification of measurement uncertainty is being discussed

(2) motion accuracy of CMM

as for the measurement accuracy of CMM, according to the regulations of JIS B in Japan, in the case of dimension measurement, the index adopted is the maximum allowable indication error mpee. Figure 4 shows a CMM with portal structure, which is one of the most accurate models today. The main technical specifications are as follows:

· mpee= (0.35=l/1000) mm (when the measurement length is l=500mm, e=0.85mm)

· temperature range: 18 ~ 22 ℃

· measurement range: 710mm 710mm 610mm

in order to obtain high measurement accuracy in a large temperature range and measurement range, computer compensation technology for instrument motion accuracy is adopted

Figure 5 shows the motion accuracy of the gantry structure CMM. Consider the whole instrument as a rigid body, and evaluate its movement error and rotation error in the X, y, z axes. First, consider the x-axis, the straightness in the Y-axis and z-axis directions and the position (ruler) error of the x-axis as the translation error, while the torsion pendulum, swing and roll pendulum errors belong to the rotation error. There are 6 kinds of errors for each axis, 3 perpendicularity errors between axes, and 21 kinds of motion errors (36+3) included in the instrument

Figure 6 shows the method of calibrating CMM with ball plate gauge. The central position of each ball of the ball plate gauge is measured and assigned with high precision by the inversion method in advance. By measuring the ball plate gauge in 4 different positions and 6 directions, 21 motion errors of CMM can be calculated. From the nature of the ball plate gauge, it can be seen that the interval of the measurement space is large when calculating, and the error between the measurement spaces is calculated by polynomial method

(3) evaluation of the uncertainty of CMM

when using CMM for measurement, in order to ensure traceability, it is necessary to evaluate the measurement uncertainty. See Table 4 for the main factors of measurement uncertainty. After evaluating each error factor, it is necessary to calculate the measurement uncertainty

Table 4 main factors of uncertainty of three-dimensional measurement

① error of CMM: geometric error, repeatability error; Scale resolution; Detect system error; Repeatability error, directivity error

② environmental error: influence of temperature and vibration

③ measuring parts: fixing method and operation method; Surface roughness, shape error

④ measurement strategy

the measurement characteristic of CMM is its measurement strategy. Use a coordinate measuring machine to measure each plane and cylindrical surface of the workpiece shown in Figure 7, and calculate the included angle between the plane normal and the axis of the cylindrical surface (in this example, the included angle is 88.52 °). This is a simple measurement example. In order to obtain the uncertainty of the included angle, in addition to the error factor of the CMM itself, the measurement strategies such as the location and number of measurement points are also of great significance

even if the inner hole diameter of the same measurement object is measured on the same coordinate measuring machine, the lightweight packaging of the measurement results needs to maintain the performance and functional uncertainty of the original packaging under the conditions of uniform or uneven distribution of measurement points and different number of measurement points

a variety of schemes have been proposed for the method of obtaining measurement uncertainty under the consideration of measurement strategy. In iso15530 documents, the following three methods are mainly adopted:

· comparative measurement method (replacement method)

· computer simulation method (computer simulation, virtual coordinate measuring machine method)

· complex measurement method (multiple measurements)

among them, computer simulation method is the most widely used. Figure 8 is an outline of the virtual coordinate measuring machine method using computer simulation. The errors of CMM and detection system are evaluated by using ball plate gauge or standard ball, and the error model of CMM is constructed by computer. In this error model, because the error is recorded statistically, the statistical error measured according to the actual measurement strategy and stored in the computer can be simulated, and the measurement uncertainty can be calculated by Monte Carlo simulation. The virtual CMM method was first proposed by the German Institute of standards. Since then, NEDO has set up a project, and Japan, Germany and Australia have jointly made in-depth and detailed research on it

(4) the subject of evaluating the uncertainty of coordinate measurement

roughness measuring instruments, shape measuring instruments, image measuring instruments and other measuring instruments that use computers for complex measurement have been popularized. And CMM

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