On-chip calibration device parasitic parameter extraction method based on particle swarm optimization

Abstract

The invention discloses an on-chip calibration part parasitic parameter extraction method based on a particle swarm algorithm. The method comprises the following steps: calculating a propagation constant of a transmission line to be measured through a TRL, calculating a direct-current resistance and a reflection coefficient of a calibration part to calculate line capacitance of the transmission line to be measured, establishing a calibration part parasitic parameter equivalent circuit model, and calculating a real scattering parameter of the calibration part according to a parasitic parameter; 12 error terms are calculated according to the real scattering parameters of the calibration piece and the scattering parameter measurement values; and setting a target function as a constraint condition to enable the calibration value of the transmission line to be measured to approach the real scattering parameter of the transmission line to be measured, optimizing the parasitic parameter by using a particle swarm algorithm, and outputting a group of optimal parasitic parameters. According to the method, the real scattering parameters of the transmission line are calculated by modeling the transmission line model, and the parasitic parameters are optimized by using the particle swarm optimization to aim at enabling the calibrated transmission line parameters to approach the real values, so that the accuracy of the parasitic parameters of the calibration piece is effectively ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wafer-level semiconductor device microwave characteristic measurement, and particularly relates to a method for extracting on-chip calibration piece parasitic parameters based on a particle swarm algorithm. BACKGROUND

[0002] With the development of high-frequency integrated circuits towards wafer-level multifunctional chips, the related manufacturing processes and measurement technologies are also constantly improving. Accurate measurement of scattering parameters (S parameters) is a key basis for high-frequency integrated circuit performance evaluation, model extraction and circuit design. In engineering applications, SOLT calibration is widely used for calibration of on-chip S parameter measurement systems, but its calibration accuracy is heavily dependent on the accuracy of calibration piece definition. Definition errors of calibration pieces will directly affect the final accuracy of system calibration, and therefore, improving the accuracy of calibration piece definition is of great significance for improving the reliability of high-frequency integrated circuit on-chip testing.

[0003] Currently, common calibration piece types include open circuit, short circuit and load calibration pieces, and their performance is usually characterized by lumped parameter models (such as capacitance, inductance or resistance values). However, in the value traceability process of traditional methods based on impedance parameter extraction (such as SOLT calibration), definition errors of calibration pieces will be transmitted to the final measurement results through error terms, thereby affecting the overall accuracy of the test system. In contrast, TRL calibration has become a recognized calibration standard in the field of high-frequency on-chip testing due to its high calibration accuracy and low dependence on calibration piece definition values. Traditional methods usually use TRL calibration to preliminarily calibrate the test system, and then extract impedance parameters by measuring on-chip open circuit, short circuit and load calibration pieces. However, this method still has the problem of error transmission in value traceability, which limits the accuracy of the measurement results.

[0004] Therefore, there is an urgent need for a new method that can reduce the influence of calibration piece definition errors and improve the accuracy of on-chip S parameter measurement to meet the higher requirements of high-frequency integrated circuit development on testing technology. Therefore, a method for extracting on-chip calibration piece parasitic parameters based on a particle swarm algorithm is needed. SUMMARY

[0005] The purpose of the present application is to provide a method for extracting on-chip calibration piece parasitic parameters based on a particle swarm algorithm, which can reduce the propagation path of errors in calibration piece parasitic parameter extraction and improve the measurement accuracy of on-chip S parameters.

[0006] To achieve the above purpose, the present application is implemented according to the following technical solutions:

[0007] The present application provides a method for extracting on-chip calibration piece parasitic parameters based on a particle swarm algorithm, comprising the following steps:

[0008] Step S01, calculate the propagation constant of the transmission line to be measured by TRL, calculate the line capacitance of the calibration standard by the DC resistance and the reflection coefficient of the calibration standard, and calculate the characteristic impedance of the transmission line to be measured by using the line capacitance and the propagation constant;

[0009] Step S02, calculate the real scattering parameters of the transmission line to be measured according to the signal flow graph, the characteristic impedance, the propagation constant and the length of the transmission line;

[0010] Step S03, establish an equivalent circuit model of the parasitic parameters of the calibration standard, and calculate the real scattering parameters of the calibration standard according to the parasitic parameters [C o ,L s ,R l ,L l ];

[0011] Step S04, test the scattering parameter measurement values of the on-chip open circuit, short circuit, load and through calibration standard under 20GHz-40GHz, and the scattering parameter measurement values of the on-chip transmission line to be measured;

[0012] Step S05, calculate 12 error terms according to the real scattering parameters of the calibration standard and the scattering parameter measurement values;

[0013] Step S06, calibrate the transmission line to be measured by using the 12 error terms;

[0014] Step S07, set a target function as a constraint condition to make the calibration values of the transmission line to be measured approximate to the real scattering parameters of the transmission line to be measured, optimize the parasitic parameters by using a particle swarm algorithm, and output a set of optimal parasitic parameters.

[0015] Further, the real scattering parameters of the transmission line to be measured are solved as follows:

[0016]

[0017] Wherein:

[0018] Γ1=(Z c -Z0) / (Z c +Z0)

[0019] Wherein Z0=50Ω is a reference impedance, and Z c is a characteristic impedance of the transmission line, which is solved as follows:

[0020]

[0021] Wherein ω=2πf, and C is a line capacitance of the transmission line, which is solved as follows:

[0022]

[0023] Wherein Γload R is the reflection coefficient of the load calibration component after TRL calibration. load,dc It is the DC resistance of the load calibrator, Re() represents the real part, and γ is the propagation constant of the transmission line. Its solution expression is as follows:

[0024]

[0025] Where l is the transmission line length For direct Thru measurements, For the measured values ​​of the transmission line Line, solving the equation yields information about e. -γl The two solutions are used to determine the solution when |α| is much less than 1, and γ is calculated from these solutions.

[0026] Furthermore, based on the parasitic parameters [C] of the open-circuit, short-circuit, and load calibrators... o ,L s ,R l ,L l Calculate the true scattering parameters of the calibration piece. The expression to be solved is as follows:

[0027]

[0028]

[0029] Furthermore, the particle swarm optimization algorithm minimizes the objective function by optimizing x to find the minimum objective function. and Based on the differences, the objective function of the particle swarm optimization algorithm is established as follows:

[0030]

[0031] Where f(x) represents the calibration value of the transmission line under test in step six. And the actual value of the transmission line under test in step two The difference, x represents a set of [C o ,L s ,R l ,L l [], k represents the k-th frequency point, the population size of the particle swarm optimization algorithm is set to 1000, the number of iterations is set to 200, and the inertia weight w decreases linearly with the number of iterations. max =0.9,w min =0.2, both individual learning factor c1 and social learning factor c2 are set to 2, maximum speed V max Set it to 6.

[0032] Compared with the prior art, the embodiments of the present invention have at least the following advantages or beneficial effects:

[0033] The present application calculates the real scattering parameters of a transmission line model by modeling, and uses a particle swarm algorithm to optimize the parasitic parameters, so as to effectively ensure the accuracy of the parasitic parameters of the calibration piece. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 A key step flowchart of the embodiment of the present application;

[0035] Figure 2 A 12-item error model diagram in the embodiment of the present application;

[0036] Among them, Figure 2 (a) is a 12-item forward error model diagram in the embodiment of the present application; Figure 2 (b) is a 12-item backward error model diagram in the embodiment of the present application;

[0037] Figure 3 An algorithm flowchart of the embodiment of the present application;

[0038] Figure 4 A calculated propagation constant result diagram in the embodiment of the present application;

[0039] Among them, Figure 4 (a) is a calculated propagation constant real part diagram in the embodiment of the present application; Figure 4 (b) is a calculated propagation constant imaginary part diagram in the embodiment of the present application;

[0040] Figure 5 An open circuit, short circuit, load calibration piece equivalent open circuit capacitance, short circuit inductance, load resistance and load inductance extraction result diagram of an actual extracted aluminum oxide sheet in the embodiment of the present application;

[0041] Figure 6 An S21 calibration result diagram of a to-be-measured transmission line calibrated using the extracted parasitic parameters in the embodiment of the present application;

[0042] Among them, Figure 6 (a) is an S21 calibration result amplitude diagram of a to-be-measured transmission line calibrated using the extracted parasitic parameters in the embodiment of the present application; Figure 6 (b) is an S21 calibration result phase diagram of a to-be-measured transmission line calibrated using the extracted parasitic parameters in the embodiment of the present application DETAILED DESCRIPTION

[0043] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0044] Referring to Figure 1 As shown in the figure, the present application provides a method for extracting parasitic parameters of on-chip calibration based on particle swarm algorithm, comprising the following steps:

[0045] As shown in the figure, the above-mentioned parasitic parameter extraction method can comprise the following steps: Figure 1

[0046] Step S01, using TRL to calculate the propagation constant of the measured transmission line, in this embodiment, the Thru length is 200um, the Line length is 900um, the DC resistance and the reflection coefficient of the measured Load calibration are calculated according to the measured Load calibration, and then the line capacitance and the propagation constant are used to calculate the characteristic impedance of the measured transmission line. The propagation constant of the measured transmission line is obtained from the analytical method of TRL calibration, and in this method, the e -γl The analytical expression of the binary linear equation is as follows:

[0047]

[0048] Where γ is the propagation constant of the transmission line, l is the length of the transmission line, is the Thru measurement value, is the Line measurement value, and the equation can be solved to obtain two solutions about e -γl , and the solution when |α| is much smaller than 1 is finally taken after discrimination, and γ is calculated.

[0049] The solving expression of the transmission line capacitance C is as follows:

[0050]

[0051] Where Γ load is the reflection coefficient of the Load calibration after TRL calibration, R load,dc is the DC resistance of the Load calibration, Re() represents the real part, and the solving expression of the transmission line characteristic impedance Z c is as follows:

[0052]

[0053] Where ω = 2πf

[0054] Step S02, according to the transmission line signal flow diagram, using the characteristic impedance, the propagation constant and the transmission line length obtained in step 1 to calculate the real scattering parameters of the measured transmission line, in this embodiment, the length of the measured transmission line is 900um, and the real scattering parameters of the measured transmission line are calculated ​where γ is the propagation constant of the transmission line under test obtained in step one, l is the length of the transmission line under test, Γ1 and Γ2 represent the reflection coefficients of port 1 and port 2, respectively, and the real scattering parameters of the transmission line under test can be obtained by assuming that Γ1 and Γ2 are equal The expression is solved as follows:

[0055]

[0056] where:

[0057] Γ1 = (Z c -Z0) / (Z c +Z0)

[0058] where Z0 = 50 Ω is the reference impedance, and Z c is the characteristic impedance of the transmission line under test obtained in step one.

[0059] Step S03, a parasitic parameter equivalent circuit model of the calibration piece is established, and the real scattering parameters of the calibration piece are calculated according to the parasitic parameters [C o , L s , R l , L l ].

[0060]

[0061] Step S04, the scattering parameter measurement values of the on-chip open circuit, short circuit, load, and through calibration piece under 20 GHz-40 GHz, and the scattering parameter measurement value of the on-chip transmission line under test are tested.

[0062] Step S05, input the initial parasitic parameters, and calculate 12 error terms according to the real scattering parameters of the calibration piece and the scattering parameter measurement values.

[0063] Step S06, as shown in the figure, a 12-term error model diagram is used to characterize the error terms of the on-chip scattering parameter measurement system, wherein Figure 2 (a) is a 12-term forward error model diagram, which includes 6 forward error terms, namely EDF, ERF, ESF, ELF, ETF, and EXF, Figure 2 (a) is associated with the scattering parameters S11 (reflection coefficient of port 1), S22 (reflection coefficient of port 2), S12 (transmission coefficient from port 2 to port 1), and S21 Figure 2

[0064] (b) is a 12-term backward error model diagram, which includes 6 backward error terms, namely EDR, ERR, ESR, ELR, ETR, and EXR, Figure 2 (b) is associated with the scattering parameters S11 (reflection coefficient of port 1), S22 (reflection coefficient of port 2), S12 (transmission coefficient from port 2 to port 1), and S21 Figure 2 ​(b) Similarly, the scattering parameters S11, S22, S12, and S21 are used to describe the errors generated by the measurement system when the signal is transmitted from port 2 to port 1. The transmission line under test is calibrated using the error terms described in item 12.

[0065] Step S07: Set the objective function as a constraint to make the calibration value of the transmission line under test approximate the true scattering parameters of the transmission line under test. Use the particle swarm optimization algorithm to optimize the parasitic parameters and output a set of optimal parasitic parameters. The objective function of the particle swarm optimization algorithm is established as follows:

[0066]

[0067] Where f(x) represents the calibration value of the transmission line under test in step six. And the actual value of the transmission line under test in step two The difference, x represents a set of [C o ,L s ,R l ,L l [], where k represents the k-th frequency point. The particle swarm optimization algorithm minimizes the objective function by optimizing x to find the minimum objective function. and The differences.

[0068] like Figure 3 As shown, the process of optimizing parasitic parameters of the calibration device based on the particle swarm optimization algorithm is presented. The core is to make the calibrated values ​​approximate the true values ​​through iterative optimization. The specific steps are as follows: input the initial parasitic parameters (open-circuit capacitance Co, short-circuit inductance Ls, load resistance Rl, load inductance Ll), and obtain the calibration device... and the transmission line under test The scattering parameters were measured; the initial parasitic parameters were substituted into the 12-term error model to obtain the calibration values ​​of the transmission line under test. Objective function calculation compares the calibration values ​​of the test piece Compared with the true value (Obtained in step S02), calculate the objective function (difference between the two); iterate to calculate the population-optimal individual (pbest) and the group-optimal (gbest). If the maximum number of iterations has not been reached, update the position and velocity of each particle and repeat steps 2-3; if the maximum number of iterations has been reached (set to 200 in the document), output the optimal parasitic parameters [C]. o ,L s ,R l ,L l ].

[0069] Figure 4 As shown, by solving e -γlThe binary first order equation (gamma is a propagation constant, and l is a transmission line length) is selected, and a solution when |alpha| is far less than 1 is selected, and finally the propagation constant in the frequency band is obtained.

[0070] Figure 5 As shown in the figure, the open circuit, short circuit, load calibration piece on the alumina sheet in the 20GHz-40GHz frequency band is the extraction result of the parasitic parameter, and the parameter is obtained by optimizing the particle swarm algorithm, which is the key parameter of the equivalent circuit model of the calibration piece.

[0071] Figure 6 As shown in the figure, in the 20GHz-40GHz frequency band, after calibration using the extracted parasitic parameters, the comparison result of the S21 parameter (the transmission coefficient of port 1 to port 2) of the measured transmission line and the true value, and the result shows that after calibration by the parasitic parameters extracted by the method, the amplitude and phase of the S21 parameter are highly consistent with the true value, which verifies the effectiveness of the method.

[0072] The above content is only an example and description of the structure of the application, and those skilled in the art can make various modifications or supplements or use similar ways to replace the described specific embodiments, as long as they do not deviate from the structure of the application or exceed the scope defined by the present claims, and they should belong to the protection scope of the application.

Claims

1. A method for extracting parasitic parameters of on-chip calibration components based on a particle swarm algorithm, characterized in that, The method comprises the following steps: Step S01, calculating the propagation constant of the transmission line to be measured by TRL, calculating the line capacitance of the calibration piece by the DC resistance and the reflection coefficient of the calibration piece, and calculating the characteristic impedance of the transmission line to be measured by using the line capacitance and the propagation constant; Step S02, calculating the real scattering parameters of the transmission line to be measured according to the signal flow graph, the characteristic impedance, the propagation constant and the length of the transmission line; Step S03, establish the equivalent circuit model of the parasitic parameters of the calibration piece, calculate the real scattering parameters of the calibration piece according to the parasitic parameters [C o , L s , R l , L l ] Step S04, testing the scattering parameter measurement values of the on-chip open circuit, short circuit, load and through calibration piece under 20-40 GHz, and the scattering parameter measurement value of the on-chip transmission line to be measured; Step S05, calculating 12 error terms according to the real scattering parameters of the calibration piece and the scattering parameter measurement values; Step S06, calibrating the transmission line to be measured by using the 12 error terms; Step S07, setting a target function as a constraint condition to make the calibration value of the transmission line to be measured approximate to the real scattering parameters of the transmission line to be measured, optimizing the parasitic parameters by using a particle swarm algorithm, and outputting a set of optimal parasitic parameters.

2. The method of claim 1, wherein, Real scattering parameters of a transmission line under test The expression is solved as follows: Wherein: Γ1 = (Z c -Z0) / (Z c +Z0) where Z0= 50 Ω is the reference impedance, Z c is the transmission line characteristic impedance, which is solved by the expression: Wherein ω = 2πf, C is the line capacitance of the transmission line, and the solving expression is as follows: where Γ load is the reflection coefficient of the load calibrator after TRL calibration, R load,dc is the DC resistance of the load calibrator, Re() denotes taking the real part, and γ is the propagation constant of the transmission line, which is solved by the following expression: where l is the length of the transmission line, Thru is the straight-through measurement, Line is the transmission line measurement, solving the equation gives two solutions for e -γl and the final solution is taken when |a| is much smaller than 1, and γ is calculated.

3. The method of claim 1, wherein, The real scattering parameters of the calibration pieces are calculated from the parasitic parameters [C o , L s , R l , L l ] of the open, short and load calibration pieces The expression is solved as follows:

4. The method of claim 1, wherein, The particle swarm algorithm minimizes by optimizing x to find the minimum of the objective function and The objective function for the particle swarm algorithm is established as follows: Where f(x) represents the calibration value of the transmission line under test in step six. And the actual value of the transmission line under test in step two The difference, x represents a set of [C o ,L s ,R l ,L l [], k represents the k-th frequency point, the population size of the particle swarm optimization algorithm is set to 1000, the number of iterations is set to 200, and the inertia weight w decreases linearly with the number of iterations. max =0.9,w min =0.2, both individual learning factor c1 and social learning factor c2 are set to 2, maximum speed V max Set it to 6.

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