Method for improving accuracy of propagation delay parameters of tlr calibration

Abstract

The application provides a method for improving the accuracy of a propagation delay parameter in TRL calibration, different effective dielectric constants exist in different frequency ranges of a transmission line calibration piece, different propagation delay parameters are obtained according to the effective dielectric constants corresponding to the different frequency ranges of the transmission line calibration piece, and the propagation delay parameters are corrected by correcting the effective dielectric constants, so that the accuracy of the propagation delay parameter in TRL calibration can be improved.

Description

Technical Field

[0001] This invention relates to the field of semiconductor manufacturing, and more particularly to a method for improving the accuracy of propagation delay parameters in TRL calibration. Background Technology

[0002] The Vector Network Analyzer (VNA) is one of the most important measurement instruments in the field of radio frequency and microwave measurement. It is primarily used to measure the scattering parameters (S-parameters) of components, and further, other parameters such as gain, matching, impedance, and isolation can be derived. Vector network analyzers require calibration before measurement. Common calibration methods include: Short-Open-Load-Thru calibration (SOLT) and Thru-Reflect-Line calibration (TRL).

[0003] The measurement reference plane of a network analyzer is located at the interface of the instrument cable. Therefore, when using a fixture to measure a device, the test result is a combination of the device under test (DUT) and the fixture. To obtain the S-parameters of the DUT, the influence of the fixture needs to be eliminated. TRL calibration can eliminate the influence of the fixture on the results by moving the measurement reference plane from both ends of the fixture to both ends of the DUT, ultimately obtaining the S-parameters of the DUT and enabling direct measurement of the DUT.

[0004] Existing TRL calibration components are not fabricated directly on the wafer, but rather on other substrates. In actual testing, the Device Under Test (DUT) is fabricated on the wafer, resulting in differences in the measurement environment between the TRL calibration component and the DUT. For example, the TRL calibration component uses high-resistivity silicon, which differs from the silicon / substrate / redistribution layer stack structure of the DUT, leading to different probe measurement environments. There may be differences in contact resistance between the TRL calibration component and the probe, and between the DUT and the probe. The pad sizes of the TRL calibration component and the DUT may also differ. Over time, the TRL calibration component wears down; however, each calibration uses the values ​​of a brand-new TRL calibration component as a reference, failing to account for wear and tear, leading to inaccurate calibration. Furthermore, feed lines exist between the DUT and the signal during testing, and the influence of these feed lines must be considered when using the TRL calibration component. These differences prevent accurate calibration using existing TRL calibration components directly.

[0005] The current solution is to fabricate the TRL calibration kit on a wafer to provide the same measurement environment as the device under test. In TRL calibration, the propagation delay T... delayAs an important reference parameter for importing into the vector network analyzer, it needs to have very precise values. Propagation delay T delay The calculation formula is as follows:

[0006]

[0007] Where ΔL is the difference in electrical length between the through calibration element and the line calibration element in TRL calibration, and ε eff is the effective dielectric constant, and c is the speed of light. Therefore, the propagation delay T... delay It is related to the effective dielectric constant. However, obtaining the accurate effective dielectric constant directly on the wafer is difficult and the accuracy is low, thus making it impossible to obtain the accurate propagation delay T. delay This value limits the application of TRL calibration. Summary of the Invention

[0008] To address the aforementioned problems, this invention provides a method for improving the accuracy of propagation delay parameters in TRL calibration. This method corrects the propagation delay parameters by adjusting the effective dielectric constant, thereby improving the accuracy of propagation delay parameters in TRL calibration.

[0009] An embodiment of the present invention provides a method for improving the accuracy of propagation delay parameters in TRL calibration, comprising: providing a stacked structure model, the stacked structure model including a substrate and a transmission line calibration element disposed on the surface of the substrate, the substrate having a first height in a direction perpendicular to the substrate, and the transmission line calibration element having a first width in a direction parallel to the substrate, the substrate being made of the same material as the substrate of the device under test; obtaining a first effective dielectric constant based on the first height, the first width, and the dielectric constant of the substrate, the first effective dielectric constant being the effective dielectric constant of the transmission line calibration element when the contact interface between the substrate and the transmission line calibration element is a smooth interface; obtaining the transmission delay parameter at the contact interface between the substrate and the transmission line calibration element. The transmission line calibration component has a ten-point average roughness. A second effective dielectric constant is obtained based on the first effective dielectric constant, the first height, and the ten-point average roughness. The second effective dielectric constant is the effective dielectric constant of the transmission line calibration component at a first frequency. A third effective dielectric constant is obtained based on the ten-point average roughness. The third effective dielectric constant is the effective dielectric constant of the transmission line calibration component at a second frequency, which is greater than the first frequency. Using the second effective dielectric constant as a parameter, a propagation delay parameter of the transmission line calibration component at the first frequency is obtained. Using the third effective dielectric constant as a parameter, a propagation delay parameter of the transmission line calibration component at the second frequency is obtained.

[0010] In one embodiment, the step of providing a stacked structure model includes: obtaining structural parameters of a device under test substrate; and forming the stacked structure model based on the structural parameters of the device under test substrate.

[0011] In one embodiment, the step of providing a stacked structure model, wherein the first width is greater than or equal to the first height, and the step of obtaining a first effective dielectric constant based on the first height, the first width, and the dielectric constant of the substrate, includes:

[0012] In one embodiment, the first effective dielectric constant is obtained according to the following formula:

[0013]

[0014] Where, ε eff_no_Roughness It is the first effective dielectric constant, ε r is the dielectric constant of the substrate, h is the first height, and w is the first width.

[0015] In one embodiment, the first frequency is less than or equal to 15 GHz, and the second frequency is greater than 15 GHz.

[0016] In one embodiment, obtaining the second effective dielectric constant of the transmission line calibrator based on the first effective dielectric constant, the first height, and the ten-point average roughness includes:

[0017] The second effective dielectric constant of the transmission line calibrator is obtained according to the following formula:

[0018]

[0019] Where, ε eff_Roughness The second effective dielectric constant is h, the first height is Rz, the ten-point average roughness is ε. eff_no_Roughness It is the first effective dielectric constant.

[0020] In one embodiment, the step of obtaining the third effective dielectric constant of the transmission line calibrator based on the ten-point average roughness includes: obtaining the third effective dielectric constant using a snowball model, wherein the microsphere radius of the snowball model is obtained based on the ten-point average roughness.

[0021] In one embodiment, the propagation delay parameter is obtained using the following formula:

[0022]

[0023] Among them, T delay The propagation delay parameter is ΔL, which is the difference in electrical length between the through-line calibrator and the transmission line calibrator in TRL calibration, and ε is the propagation delay parameter. eff ε is the effective dielectric constant, c is the speed of light, and at the first frequency, ε eff It is the second effective dielectric constant, ε at the second frequency. eff It is the third effective dielectric constant.

[0024] In one embodiment, the method further includes: providing a plurality of stacked structure models, and obtaining a first tolerance of the second effective dielectric constant and a second tolerance of the third effective dielectric constant for the plurality of stacked structure models; using the first tolerance as the phase shift tolerance of ΔL at the first frequency, and using the second tolerance as the phase shift tolerance of ΔL at the second frequency.

[0025] The present invention provides a method for improving the accuracy of propagation delay parameters in TRL calibration. The transmission line calibration component has different effective dielectric constants for different frequency ranges. Different propagation delay parameters are obtained based on the effective dielectric constants corresponding to the different frequency ranges of the transmission line calibration component. The propagation delay parameters are corrected by modifying the effective dielectric constants, thereby improving the accuracy of the propagation delay parameters in TRL calibration. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a schematic diagram of the steps of a method for improving the accuracy of the propagation delay parameter of TRL calibration according to an embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of a stacked structure model provided in an embodiment of the present invention;

[0029] Figure 3 This is a diagram of the contact interface between the substrate and the transmission line calibration component of a stacked structure model provided in an embodiment of the present invention;

[0030] Figure 4 This is a schematic diagram of a snowball model. Detailed Implementation

[0031] The following detailed description, in conjunction with the accompanying drawings, illustrates the specific implementation of the method for improving the accuracy of propagation delay parameters in TRL calibration provided by the present invention.

[0032] Figure 1 This is a schematic diagram illustrating the steps of a method for improving the accuracy of propagation delay parameters in TRL calibration according to an embodiment of the present invention. Please refer to [link / reference]. Figure 1 The method includes:

[0033] Step S10: Provide a stacked structure model, the stacked structure model including a substrate and a transmission line calibration member disposed on the surface of the substrate, the substrate having a first height h in the direction perpendicular to the substrate, and the transmission line calibration member having a first width W in the direction parallel to the substrate, the substrate being made of the same material as the substrate of the device under test.

[0034] Please see Figure 2 This is a schematic diagram of a stacked structure model provided in an embodiment of the present invention. The stacked structure model includes a substrate 200 and a transmission line calibration element 210 disposed on the surface of the substrate 200. In the direction perpendicular to the substrate 200 (e.g., ... Figure 2 In the Z direction (as shown in the image), the substrate has a first height h, and in a direction parallel to the substrate (e.g., ... Figure 2 In the X direction, the transmission line calibration element 210 has a first width W, and the first height h and the first width W can be obtained by simulation software.

[0035] In this invention, the substrate 200 of the stacked structure model is made of the same material as the substrate of the device under test (DUT), making the measurement environment of the transmission line calibration element 210 approximately the same as that of the DUT, thereby reducing the influence of the test environment and improving the accuracy of the propagation delay parameter of the TRL calibration. For example, if the DUT is a device fabricated on a wafer and its substrate material is silicon, then the substrate 200 of the stacked structure model is also made of silicon. Figure 2 The substrate 200 of the stacked structure model described herein is only a single layer structure. In other embodiments of the present invention, the substrate 200 of the stacked structure model may also be a multi-layer structure, which may be set according to the actual structure of the substrate of the device under test.

[0036] In some embodiments, the method further includes: obtaining structural parameters of the substrate of the device under test (DUT); and forming the stacked structure model based on the structural parameters of the DUT substrate. The structural parameters include the thickness, material, morphology, and dielectric constant of each layer in the DUT substrate. Simulating the stacked structure model in simulation software based on these structural parameters improves the consistency between the transmission line calibration component 210 and the DUT, further reduces the influence of the testing environment, and improves the accuracy of the propagation delay parameters of the TRL calibration.

[0037] Step S11: Obtain the first effective dielectric constant based on the first height h, the first width W, and the dielectric constant of the substrate 200. The first effective dielectric constant is the effective dielectric constant of the transmission line calibration component 210 when the contact interface between the substrate 200 of the stacked structure model and the transmission line calibration component 210 is a smooth interface.

[0038] In some embodiments, since the substrate 200 of the stacked structure model is made of the same material as the substrate of the device under test, the dielectric constant of the substrate of the device under test can be obtained by looking up a table in a known database and used as the dielectric constant of the substrate 200 of the stacked structure model.

[0039] The contact interface between the substrate 200 of the stacked structure model and the transmission line calibration component 210 is typically a rough interface. In this step, a smooth interface between the substrate 200 of the stacked structure model and the transmission line calibration component 210 is an ideal scenario.

[0040] In some embodiments, when the first width W is greater than or equal to the first height h, the first effective dielectric constant is obtained according to the following formula:

[0041]

[0042] Where, ε eff_no_Roughness It is the first effective dielectric constant, ε ris the dielectric constant of the substrate, h is the first height, and w is the first width.

[0043] It is understood that, in order to obtain the first effective dielectric constant using the above formula, the first width W is typically set to be greater than or equal to the first height h when forming the stacked structure model. In other embodiments, the first effective dielectric constant can also be obtained using other known formulas.

[0044] Step S12: Obtain the ten-point average roughness of the transmission line calibrator 210 at the contact interface between the substrate 200 and the transmission line calibrator 210.

[0045] The ten-point average roughness refers to the sum of the average values ​​of the five highest peaks and the five lowest valleys within a predetermined length range of the contact interface between the substrate 200 and the transmission line calibration component 210. In some embodiments, a graph of the contact interface between the substrate 200 and the transmission line calibration component 210 can be obtained using simulation software, and the ten-point average roughness can then be obtained from this graph. For example, as... Figure 3 As shown, it is pattern B of the contact interface between the substrate 200 and the transmission line calibration component 210. Within a set length L, five peaks (Y) are obtained on pattern B. p1 ~Y p5 The value of ) and the five lowest points (Y) v1 ~Y v5 The value of ) is calculated by taking the average of the five highest peaks and the average of the five lowest valleys, and then adding them together. This value is the ten-point average roughness.

[0046] Step S13: Obtain the second effective dielectric constant of the transmission line calibrator 210 based on the first effective dielectric constant, the first height h, and the ten-point average roughness. The second effective dielectric constant is the effective dielectric constant of the transmission line calibrator 210 at the first frequency.

[0047] The first frequency is the frequency of the signal passing through the transmission line calibration element 210. In some embodiments, the first frequency is a low frequency, less than or equal to 15 GHz. The second effective dielectric constant is the effective dielectric constant of the transmission line calibration element 210 at the low frequency.

[0048] In some embodiments, the second effective dielectric constant of the transmission line calibrator 210 is obtained according to the following formula:

[0049]

[0050] Where, ε eff_RoughnessThe second effective dielectric constant is h, the first height is Rz, the ten-point average roughness is ε. eff_no_Roughness It is the first effective dielectric constant.

[0051] Step S14: Obtain the third effective dielectric constant of the transmission line calibrator 210 based on the ten-point average roughness. The third effective dielectric constant is the effective dielectric constant of the transmission line calibrator 210 at a second frequency, which is greater than the first frequency.

[0052] The second frequency is the frequency of the signal passing through the transmission line calibration element 210. In some embodiments, the second frequency is a high-low frequency, the second frequency is greater than the first frequency, and the second frequency is greater than 15 GHz. The third effective dielectric constant is the effective dielectric constant of the transmission line calibration element 210 at high frequencies.

[0053] In some embodiments, the third effective dielectric constant is obtained using a snowball model, wherein the microsphere radius of the snowball model is obtained based on the ten-point average roughness. The snowball model (Hall-Huray Model) is a copper foil roughness model, such as... Figure 4 As shown, this is a schematic diagram of a snowball model, in which multiple microspheres 400 are stacked in a pyramid shape. The snowball model includes the following formula:

[0054]

[0055]

[0056] Where, ε RoughnessFactor is the third effective dielectric constant, Sr is the area ratio of the surface to the base of the pyramid structure composed of microspheres; Rz is the ten-point average roughness, α is the radius of the microsphere, and N / Af is the number of microspheres per unit area.

[0057] The snowball model can be simulated using High Frequency Structure Simulator (HFSS) software to obtain the third effective dielectric constant.

[0058] The microsphere radius α of the snowball model can be obtained through the ten-point average roughness Rz. For example, in some embodiments, the microsphere radius α of the snowball model can be calculated based on the ten-point average roughness Rz using the hexagonal close packing of equal spheres (HCPES) or square close packing of equal spheres (SCPES) in the High Frequency Structure Simulator (HFSS) simulation software. Alternatively, the microsphere radius α of the snowball model can be calculated using both hexagonal close packing of equal spheres and square close packing of equal spheres based on the ten-point average roughness Rz, and the average value is taken as the final microsphere radius α of the snowball model.

[0059] Step S15: Using the second effective dielectric constant as a parameter, obtain the propagation delay parameter of the transmission line calibration element 210 at the first frequency; using the third effective dielectric constant as a parameter, obtain the propagation delay parameter of the transmission line calibration element 210 at the second frequency.

[0060] The transmission line calibration component 210 has different effective dielectric constants for different frequency ranges. This step obtains different propagation delay parameters based on the effective dielectric constants corresponding to different frequency ranges of the transmission line calibration component 210, thereby improving the accuracy of the propagation delay parameters of TRL calibration.

[0061] In some embodiments, the propagation delay parameter is obtained using the following formula:

[0062]

[0063] Among them, T delay The propagation delay parameter is ΔL, which is the difference in electrical length between the through-line calibrator and the transmission line calibrator in TRL calibration, and ε is the propagation delay parameter. eff ε is the effective dielectric constant, c is the speed of light, and at the first frequency, ε eff It is the second effective dielectric constant, ε at the second frequency. eff It is the third effective dielectric constant.

[0064] In some embodiments, the electrical length of the through calibration element in TRL calibration can be approximately zero. Therefore, ΔL in the above formula can be the measured value of the transmission line calibration element 210 in TRL calibration, which is the first width W. In other embodiments, if the electrical length of the through calibration element is not zero, the through calibration element can be further designed in the stacked structure model. The through calibration element has a second width, and ΔL is the difference between the first width W and the second width.

[0065] Referring to the above formula, the propagation delay parameter T delay Also related to ΔL, in some embodiments, the method further includes:

[0066] Multiple stacked structure models are provided, and a first tolerance of the second effective dielectric constant and a second tolerance of the third effective dielectric constant are obtained for each of the multiple stacked structure models. It is understood that the multiple stacked structure models have the same structure. The second effective dielectric constant and the third effective dielectric constant of each of the stacked structure models are obtained according to the above method, thereby obtaining multiple second effective dielectric constants and third effective dielectric constants. The first tolerance is obtained by statistical analysis of the multiple second effective dielectric constants, and the second tolerance is obtained by statistical analysis of the multiple second effective dielectric constants.

[0067] Using the first tolerance as the phase shift tolerance of ΔL at the first frequency, and the second tolerance as the phase shift tolerance of ΔL at the second frequency, the phase shift range of ΔL can be further reduced, and the accuracy of ΔL can be further improved, thereby correspondingly improving the accuracy of the propagation delay parameter. For example, in some embodiments, the phase shift range of ΔL is... in It is the phase shift tolerance.

[0068] The method of the present invention for improving the accuracy of propagation delay parameters in TRL calibration can correct the propagation delay parameters by modifying the effective dielectric constant, thereby improving the accuracy of propagation delay parameters in TRL calibration and benefiting the application of TRL calibration.

[0069] It should be noted that the terms "comprising" and "having," and their variations, used in this invention document are intended to cover non-exclusive inclusion. The terms "first," "second," etc., are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence, unless explicitly indicated by the context; it should be understood that such use of data can be interchanged where appropriate. The term "one or more" depends at least in part on the context and can be used to describe features, structures, or characteristics in a singular sense, or in a plural sense to describe combinations of features, structures, or characteristics. The term "based on" can be understood as not necessarily intended to express an exclusive set of factors, but can instead, also at least in part on the context, allow for the presence of other factors that are not necessarily explicitly described. Furthermore, embodiments and features in embodiments of this invention can be combined with each other without conflict. In addition, descriptions of well-known components and technologies have been omitted in the above description to avoid unnecessarily obscuring the concepts of this invention. In the various embodiments described above, each embodiment focuses on its differences from other embodiments; similar / identical parts between embodiments can be referred to mutually.

[0070] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for improving the accuracy of propagation delay parameters in TRL calibration, characterized in that, include: A stacked structure model is provided, the stacked structure model including a substrate and a transmission line calibration element disposed on the surface of the substrate, the substrate having a first height in a direction perpendicular to the substrate, and the transmission line calibration element having a first width in a direction parallel to the substrate, the substrate being made of the same material as the substrate of the device under test; A first effective dielectric constant is obtained based on the first height, the first width, and the dielectric constant of the substrate. The first effective dielectric constant is the effective dielectric constant of the transmission line calibrator when the contact interface between the substrate and the transmission line calibrator is a smooth interface. The ten-point average roughness of the transmission line calibrator at the contact interface between the substrate and the transmission line calibrator is obtained. The second effective dielectric constant of the transmission line calibrator is obtained based on the first effective dielectric constant, the first height, and the ten-point average roughness. The second effective dielectric constant is the effective dielectric constant of the transmission line calibrator at a first frequency, and is obtained according to the following formula: in, eff_Roughness It is the second effective dielectric constant. h Rz is the first height, and Rz is the ten-point average roughness. eff_no_Roughness It is the first effective dielectric constant; The third effective dielectric constant of the transmission line calibrator is obtained using a snowball model based on the ten-point average roughness. The microsphere radius of the snowball model is obtained based on the ten-point average roughness, and the snowball model includes the following formula: in, RoughnessFactor It is the third effective dielectric constant. Sr It is the ratio of the surface area to the base area of ​​the pyramid structure composed of microspheres, where α is the radius of the microsphere. N / Af It is the number of microspheres per unit area; the third effective dielectric constant is the effective dielectric constant of the transmission line calibrator at a second frequency, where the first frequency is less than or equal to 15 GHz and the second frequency is greater than 15 GHz; Using the second effective dielectric constant as a parameter, the propagation delay parameter of the transmission line calibrator at the first frequency is obtained; using the third effective dielectric constant as a parameter, the propagation delay parameter of the transmission line calibrator at the second frequency is obtained.

2. The method according to claim 1, characterized in that, The steps to provide a layered structure model include: Obtain the structural parameters of the substrate of the device under test; The stacked structure model is formed based on the structural parameters of the substrate of the device under test.

3. The method according to claim 1, characterized in that, In the step of providing a stacked structure model, the first width is greater than or equal to the first height, and the step of obtaining the first effective dielectric constant based on the first height, the first width, and the dielectric constant of the substrate includes: The first effective dielectric constant is obtained according to the following formula: in, eff_no_Roughness It is the first effective dielectric constant. r It is the dielectric constant of the substrate. h It is the first height. w It is the first width.

4. The method according to claim 1, characterized in that, The propagation delay parameter is obtained using the following formula: in, T delay It is the propagation delay parameter, Δ It is the difference in electrical length between the through calibration component and the transmission line calibration component in TRL calibration. It is the effective dielectric constant. c It is the speed of light, at the first frequency. It is the second effective dielectric constant at the second frequency. It is the third effective dielectric constant.

5. The method according to claim 4, characterized in that, Also includes: Multiple stacked structure models are provided, and a first tolerance of the second effective dielectric constant and a second tolerance of the third effective dielectric constant of the multiple stacked structure models are obtained; Let the first tolerance be Δ The phase shift tolerance at the first frequency, with the second tolerance as Δ Phase shift tolerance at the second frequency.

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