Calculation method of dispersion and characteristic impedance of silicon-based integrated gap waveguide, terahertz circuit design method and system

Abstract

The present invention relates to the field of wireless communication technology, and is a calculation method for dispersion and characteristic impedance of silicon-based integrated gap waveguide, a terahertz circuit design method and system. The calculation method is based on a silicon-based integrated gap waveguide (Silicon Substrate Integrated Gap Waveguide, SSIGW) model, an equivalent circuit method is used to study the plasma wave number of a silicon-based electromagnetic bandgap structure, a transverse resonance method is used to solve the propagation constant in the y direction of SSIGW, and a mode matching method is used to solve the SSIGW dispersion equation; the closed expression of the SSIGW characteristic impedance is solved in combination with the definition of field distribution and impedance. The present invention can achieve rapid determination of the SSIGW operating frequency band and band width while ensuring accuracy, and improve the design efficiency of terahertz devices based on SSIGW.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a method for calculating dispersion and characteristic impedance of a silicon-based integrated gap waveguide, and a terahertz circuit design method and system. Background Art

[0002] Terahertz waves have good penetration, low energy and broadband properties, and have important application prospects in high-speed space communications, medical detection, non-destructive testing and national defense security. Waveguide transmission technology is an indispensable and important part of the terahertz system. The performance of the terahertz waveguide determines the signal transmission efficiency and integration of the terahertz system. At present, terahertz circuits generally have defects such as surface waves and high interconnection losses.

[0003] Thanks to the development of semiconductor technology, the new silicon substrate integrated gap waveguide (SSIGW) technology has the advantages of low loss, wide bandwidth and easy integration, which effectively solves the above problems. At present, when designing circuits based on SSIGW, simulation software (High Frequency Structure Simulator, HFSS and CST Microwave Studio, CST) is used to model and simulate SSIGW to optimize its performance. However, due to the multi-layer complex structure of SSIGW, the frequency band and stripline width of SSIGW cannot be efficiently determined in a short time, and there is a lack of theoretical guidance for the efficient design of the device. Summary of the invention

[0004] In order to solve the problems of the prior art, the present invention provides a method for calculating the dispersion and characteristic impedance of a silicon-based integrated gap waveguide, which can ensure accuracy while quickly determining the SSIGW operating frequency band and bandline width, thereby improving the design efficiency of terahertz devices based on SSIGW.

[0005] Based on the same inventive concept, the present invention also provides a terahertz circuit design method and system.

[0006] An embodiment of the present invention provides a method for calculating dispersion and characteristic impedance of a silicon-based integrated gap waveguide, which is based on a SSIGW model. The SSIGW model includes a silicon-based electromagnetic bandgap structure array and a strip line etched on the silicon-based electromagnetic bandgap structure array for transmitting electromagnetic waves.

[0007] The calculation method comprises the following steps:

[0008] Establish an equivalent circuit model of silicon-based electromagnetic bandgap structure array, and deduce and calculate the plasma wave number of silicon-based electromagnetic bandgap structure array by applying circuit theory and anisotropic medium theory;

[0009] Combined with the plasma wave number, the reflection characteristics of the silicon-based electromagnetic bandgap structure array are analyzed, the reflection coefficients of transverse electric TE and transverse magnetic TM waves are derived according to the boundary conditions, and the y-direction propagation constant of SSIGW is derived and calculated using the transverse resonance method;

[0010] Combined with the y-direction propagation constant, the field distribution in different regions of SSIGW is analyzed, and the field distribution expression is derived through Maxwell equations; the z-direction propagation constant of SSIGW is derived based on boundary conditions and pattern matching method;

[0011] According to the field distribution expression and in combination with the characteristic impedance definition, the characteristic impedance closed expression of the strip line in the SSIGW is derived and calculated.

[0012] Preferably, the silicon-based electromagnetic bandgap structure array comprises a dielectric substrate, the dielectric substrate comprises at least a first silicon dielectric layer, a second silicon dielectric layer and a third silicon dielectric layer arranged from the bottom; a silicon dioxide isolation layer is arranged between two adjacent silicon dielectric layers;

[0013] A silicon dioxide isolation layer is provided on both the upper and lower surfaces of the first silicon dielectric layer, a column is inserted into the first silicon dielectric layer and the silicon dioxide isolation layers on its upper and lower surfaces, a thin slice is etched on the silicon dioxide isolation layer on the upper surface of the first silicon dielectric layer, the width of the thin slice is greater than the cross-sectional width of the column, and then a layer of silicon dioxide isolation layer is wrapped outside the column to form a silicon-based electromagnetic bandgap structure unit, wherein the copper cylinder sequentially penetrates the silicon dioxide isolation layer on the upper surface of the first silicon dielectric layer, the first silicon dielectric layer, and the silicon dioxide isolation layer on the lower surface of the first silicon dielectric layer; a plurality of the silicon-based electromagnetic bandgap structure units are provided on the silicon-based electromagnetic bandgap structure array;

[0014] The stripline is etched in a silicon dioxide isolation layer above the second silicon dielectric layer.

[0015] Preferably, the derivation and calculation of the plasma wave number of the silicon-based electromagnetic bandgap structure array specifically includes:

[0016] The impedance is calculated based on the equivalent circuit model of the silicon-based electromagnetic bandgap structure array;

[0017] According to the capacitance calculation formula and the inductance calculation formula, calculate the inductance and capacitance values;

[0018] The dielectric constant is calculated based on the relationship between electric displacement flux and electric polarization intensity;

[0019] According to the relationship between the dielectric constant tensor and the plasma wave number, the plasma wave number of the silicon-based electromagnetic band gap structure array is calculated.

[0020] Preferably, deriving and calculating the y-direction propagation constant of SSIGW comprises the following steps:

[0021] According to the characteristics of the SSIGW structure, the upper surface of the lower equivalent dielectric layer is taken as the interface to determine the boundary conditions of the magnetic field, electric field and current density.

[0022] According to the boundary conditions, the reflection coefficients at TE and TM incidence are calculated;

[0023] According to the transverse resonance method, the y-direction propagation constant of SSIGW is calculated for TE and TM incidence.

[0024] Preferably, deriving and calculating the z-direction propagation constant of SSIGW comprises the following steps:

[0025] The SSIGW model structure is divided into three different regions, the quasi-TEM mode is transmitted in the stripline region, and the other regions are TE mode and TM mode;

[0026] Combined with the propagation constant in the y direction, the field distribution of different modes is calculated according to Maxwell's equations;

[0027] Determine the boundary conditions of electric and magnetic fields based on SSIGW electromagnetic characteristics;

[0028] According to the mode matching method, the z-direction propagation constant of SSIGW is calculated.

[0029] A terahertz circuit design method provided by an embodiment of the present invention comprises the following steps:

[0030] According to the design requirements of terahertz circuit, determine its operating frequency band and circuit impedance value;

[0031] According to the method for calculating the dispersion and characteristic impedance of the silicon-based integrated gap waveguide according to the embodiment of the present invention, the dispersion of the silicon-based integrated gap waveguide is calculated to optimize the structural parameters of the SSIGW model so that it works in a determined working frequency band;

[0032] According to the method for calculating the dispersion and characteristic impedance of a silicon-based integrated gap waveguide according to an embodiment of the present invention, the stripline widths corresponding to different impedance values ​​of a terahertz circuit based on a SSIGW model are further calculated through the characteristic impedance.

[0033] A terahertz circuit design system provided by an embodiment of the present invention includes the following modules:

[0034] The circuit parameter determination module determines the operating frequency band and circuit impedance value according to the terahertz circuit design requirements;

[0035] A dispersion calculation module, which calculates the dispersion of the silicon-based integrated gap waveguide according to the calculation method for the dispersion and characteristic impedance of the silicon-based integrated gap waveguide provided in an embodiment of the present invention, so as to optimize the structural parameters of the SSIGW model so that it works in a determined working frequency band;

[0036] The impedance calculation module further calculates the stripline width corresponding to different impedance values ​​of the terahertz circuit based on the SSIGW model through the characteristic impedance according to the method for calculating the dispersion and characteristic impedance of the silicon-based integrated gap waveguide provided by the embodiment of the present invention.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] In order to solve the dispersion calculation problem of SSIGW, the present invention first uses the equivalent circuit method to study the plasma wave number of the silicon-based electromagnetic bandgap structure; then, the lateral resonance method is used to solve the propagation constant of SSIGW in the y direction; finally, the mode matching method is used to solve the SSIGW dispersion equation. For the calculation of the SSIGW characteristic impedance, the present invention combines the definition of field distribution and impedance to solve the closed formula of the SSIGW characteristic impedance. Compared with the simulation software, the embodiment of the present invention has good consistency. In addition, the embodiment of the present invention uses a mathematical method to calculate the characteristic impedance, which can save the time of blind optimization and improve the design efficiency of the terahertz circuit based on SSIGW. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of a flow chart of a method for calculating dispersion and characteristic impedance of a silicon-based integrated gap waveguide in an embodiment of the present invention;

[0040] Figure 2 This is a schematic diagram of the structure of a silicon-based integrated gap waveguide in an embodiment of the present invention;

[0041] Figure 3 This is a schematic structural diagram of a silicon-based electromagnetic bandgap structure in an embodiment of the present invention;

[0042] Figure 4 Schematic diagram of an equivalent structure of a silicon-based electromagnetic bandgap structure in an embodiment of the present invention;

[0043] Figure 5 Schematic diagram of an equivalent circuit of a silicon-based electromagnetic bandgap structure in an embodiment of the present invention;

[0044] Figure 6 Schematic diagram of an equivalent structure of a silicon-based electromagnetic bandgap structure array in which TM and TE waves are incident in an embodiment of the present invention;

[0045] Figure 7 Schematic diagram of an equivalent structure of region division of a silicon-based integrated substrate gap waveguide in an embodiment of the present invention;

[0046] Figure 8 4 is a comparison diagram of the dispersion results of the calculation method in the embodiment of the present invention and the simulation software (CST and HFSS);

[0047] Fig. 94 is a comparison diagram of characteristic impedance results of the calculation method in the embodiment of the present invention and the simulation software (CST and HFSS);

[0048] Fig.10 The figure is a comparison chart of the calculation time of dispersion and characteristic impedance of the calculation method in the embodiment of the present invention and the simulation software (CST and HFSS). DETAILED DESCRIPTION

[0049] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] It should be noted that the step numbers in the text are only for the convenience of explaining the specific embodiments and are not used to limit the order in which the steps are executed.

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment provides a method for calculating dispersion and characteristic impedance of a silicon-based integrated gap waveguide, comprising the following steps:

[0053] Step S1, establishing a SSIGW model, wherein the established SSIGW model includes a silicon-based electromagnetic bandgap structure array and a strip line etched on the silicon-based electromagnetic bandgap structure array for transmitting electromagnetic waves.

[0054] like Figure 2 As shown, the silicon-based electromagnetic bandgap structure array includes a dielectric substrate, and the dielectric substrate includes three silicon dielectric layers (i.e., a first silicon dielectric layer 1, a second silicon dielectric layer 2, and a third silicon dielectric layer 3, with thicknesses from bottom to top being h 1 、h 2 、h 3) and four layers of silicon dioxide isolation layers 6 (all with a thickness of T), and copper is coated on the top and bottom layers of the dielectric substrate to form a copper-clad layer 5; a silicon dioxide isolation layer 6 is set between the copper-clad layer and the silicon dielectric layer, and between two adjacent silicon dielectric layers. A silicon dioxide isolation layer is set on the upper and lower surfaces of the first silicon dielectric layer 1, and a metal column 8 is inserted into the silicon dioxide isolation layer 6 on the first silicon dielectric layer and its upper and lower surfaces, and a metal sheet 7 is etched on the silicon dioxide isolation layer on the upper surface of the first silicon dielectric layer. The width of the sheet is greater than the cross-sectional width of the column, and then a layer of silicon dioxide isolation layer is wrapped around the copper cylinder to form a silicon-based electromagnetic bandgap structure unit, wherein the copper cylinder sequentially penetrates the silicon dioxide isolation layer on the upper surface of the first silicon dielectric layer, the first silicon dielectric layer, and the silicon dioxide isolation layer on the lower surface of the first silicon dielectric layer. A plurality of the above-mentioned silicon-based electromagnetic bandgap structure units are arranged on the silicon-based electromagnetic bandgap structure array.

[0055] In this embodiment, the metal cylinder 8 is preferably a copper cylinder with a radius of r; the metal sheet 7 is preferably a circular sheet with a radius of R, and the radius of the circular sheet is greater than the radius of the cylinder. In fact, the metal sheet 7 can be in any shape, such as a rectangle or a triangle, and the metal cylinder can also be in any shape, such as a rectangular column or a triangular column.

[0056] In the model established in this embodiment, the strip line 4 is etched into the silicon dioxide isolation layer above the second silicon dielectric layer 2, and the strip line can preferably be a rectangular metal layer.

[0057] Step S2: Establish an equivalent circuit model of the silicon-based electromagnetic bandgap structure array, and deduce and calculate the plasma wave number of the silicon-based electromagnetic bandgap structure array by applying circuit theory and anisotropic medium theory.

[0058] The derivation and calculation process of the plasma wave number of the silicon-based electromagnetic bandgap structure array includes first establishing an equivalent circuit of the silicon-based mushroom-shaped electromagnetic bandgap structure array, and then applying the anisotropic medium theory to calculate the plasma wave number. Figure 3 As shown, the equivalent physical model is as follows Figure 4 As shown, the equivalent circuit is Figure 5 As shown in Figure 2, the period of the silicon-based electromagnetic bandgap structure unit is p, and the spacing between the discs is g. Figure 4 The equivalent physical model includes three equivalent dielectric layers, which are the lower layer, the middle layer and the upper layer from bottom to top, with thicknesses of h, m, d, and equivalent dielectric constants of ε eff1 , ε eff2 , ε eff2 , that is, the equivalent dielectric constant of the middle layer and the upper layer is the same, and copper is applied to the top and bottom layers of the dielectric substrate. The voltage between the top copper layer and the bottom copper layer is U, and the electric field strength is E yThe gap capacitance between two adjacent silicon-based electromagnetic bandgap structure units is C 2 , the capacitance from the thin film to the top copper layer is C 1 , the column inductance is L.

[0059] In this embodiment, the plasma wave number of the silicon-based electromagnetic bandgap structure array is derived and calculated, specifically including:

[0060] S21, calculating the impedance according to the equivalent circuit model of the silicon-based electromagnetic bandgap structure array;

[0061] S22, calculating the inductance and capacitance values ​​according to the capacitance calculation formula and the inductance calculation formula;

[0062] S23. Calculate the dielectric constant based on the relationship between the electric displacement flux and the electric polarization intensity;

[0063] S24. According to the relationship between the dielectric constant tensor and the plasma wave number, the plasma wave number of the silicon-based electromagnetic band gap structure array is calculated as follows:

[0064]

[0065] Where p is the period of the silicon-based electromagnetic bandgap structural unit, ω is the angular frequency, μ 0 is the magnetic permeability of free space; ε eff1 is the relative dielectric constant of the lower equivalent dielectric layer, which can be calculated using the following formula:

[0066]

[0067] The relative dielectric constants of the middle layer and the upper equivalent dielectric layer are calculated as follows:

[0068]

[0069] Among them, ε o is the equivalent dielectric constant of the silicon dioxide isolation layer, ε s is the equivalent dielectric constant of the silicon dielectric layer.

[0070] The relationship between the dielectric constant tensor and the plasma wave number is expressed by the following equation:

[0071]

[0072] in, represents the unit vector in the x direction, represents the unit vector in the y direction, represents the unit vector in the z direction, K 1 is the wave number in the region y<0, K y represents the propagation constant in the y direction, K prepresents the plasma wave number.

[0073] Step S3: Combined with the plasma wave number of step S2, the reflection characteristics of the silicon-based electromagnetic bandgap structure array are analyzed, and the reflection coefficients of transverse electric (TE) and transverse magnetic (TM) waves are derived according to the boundary conditions. The y-direction propagation constant of SSIGW is derived and calculated using the transverse resonance method.

[0074] In this embodiment, the derivation and calculation of the y-direction propagation constant of SSIGW in this step includes calculating the reflection coefficient according to the boundary conditions, and then calculating the y-direction propagation constant by applying the transverse resonance theory. The side view when TM and TE waves are incident on the silicon-based electromagnetic bandgap structure array is shown in FIG. Figure 6 shown.

[0075] Specifically, the y-direction propagation constant of SSIGW is derived and calculated, including the following steps:

[0076] S31. According to the SSIGW structural characteristics, the upper surface of the lower equivalent dielectric layer is taken as the interface to determine the boundary conditions of the magnetic field, electric field and current density.

[0077] The three boundary conditions determined are: the magnetic field is continuous at y=0; the electric field is continuous at y=0; and the current density is 0 at y=0.

[0078] S32. According to the boundary conditions, the reflection coefficients at TE and TM incidence are calculated; the reflection coefficients at TM and TE incidence are calculated as follows:

[0079]

[0080]

[0081] In the formula, K 1 is the wave number in the region y<0, K 2 is the wave number in the region y>0, K || is the parallel wave number of the incident wave, K TE is the propagation constant in the y direction when TE is incident, γ 0 is the incident wave propagation constant, γ TM is the propagation constant of the silicon-based electromagnetic bandgap structure region TM; h represents the thickness of the underlying equivalent dielectric layer.

[0082] S33. According to the transverse resonance method, the y-direction propagation constant of SSIGW at TE and TM incidence is calculated as follows:

[0083]

[0084]

[0085] In the formula, K TM is the propagation constant in the y direction when TM is incident, is the wave impedance of the y<0 region in the electromagnetic bandgap structure array, is the wave impedance of the y>0 region in the electromagnetic bandgap structure array, m represents the thickness of the intermediate equivalent dielectric layer, and d represents the thickness of the upper equivalent dielectric layer on the strip line. Among them, the y<0 region refers to the lower region of the lower equivalent dielectric layer, and the y>0 region refers to the upper region of the lower equivalent dielectric layer.

[0086] The transverse resonance theory is expressed as follows:

[0087] Z in1 (0)+Z in2 (0) = 0

[0088] Z in1 Z represents the impedance looking down from the interface of the EBG structure array. in2 It represents the impedance viewed upward from the interface of the electromagnetic bandgap structure array, where the interface is the lower surface of the second silicon dielectric layer.

[0089] Step S4, combining the y-direction propagation constant, analyzing the field distribution in different regions of SSIGW, and deriving the field distribution expression through Maxwell equations; deriving the z-direction propagation constant of SSIGW according to boundary conditions and pattern matching method.

[0090] For the calculation of the z-direction propagation constant of SSIGW, the field distribution is first established, and then the mode matching method is used to calculate the z-direction propagation constant, that is, to calculate the dispersion of the silicon-based integrated gap waveguide.

[0091] Specifically, the z-direction propagation constant of SSIGW is derived and calculated, including the following steps:

[0092] S41, divide the SSIGW model structure into three different areas, such as Figure 7 As shown, the quasi-TEM mode is transmitted in the stripline region, and the other regions are TE mode and TM mode.

[0093] S42. Combined with the propagation constant in the y direction, according to Maxwell's equations, the field distribution of different modes is calculated.

[0094] In this embodiment, the field distribution expressions of different modes are as follows:

[0095] (1) Quasi-TEM field (strip line region)

[0096]

[0097]

[0098]

[0099] in is the wave number in the x direction of the quasi-TEM mode, E y1 is the electric field in the y direction of the quasi-TEM mode, H x1 is the magnetic field in the x direction of the quasi-TEM mode, H z1 is the z-direction magnetic field of the quasi-TEM mode, E 0 is the quasi-TEM mode amplitude.

[0100] (2) TM-y field (non-strip line area)

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] in E x2 is the electric field in the x direction of the TM mode, E y2 is the electric field in the y direction of the TM mode, E z2 is the electric field in z direction of TM mode, H x2 is the TM mode x-direction magnetic field, H z2 is the z-direction magnetic field of the TM mode, A TM is the TM mode amplitude, is the TM mode loss in the x direction; y represents the height variable in the y direction.

[0107] (3)TE-y field (non-stripline area)

[0108]

[0109]

[0110]

[0111]

[0112]

[0113] in E x3 is the electric field in the x direction of the TE mode, E z3is the electric field in the z direction of the TE mode, H x3 is the TE mode x-direction magnetic field, H y3 is the TE mode magnetic field in the y direction, H z3 is the TE mode z-direction magnetic field, A TE is the TE modulus amplitude, is the TE mode loss in x direction.

[0114] S43. Determine the boundary conditions of the electric and magnetic fields based on the SSIGW electromagnetic characteristics.

[0115] There are two boundary conditions that must be determined: the electric field is continuous at x = ±w / 2, y = d+m; the magnetic field is continuous at x = ±w / 2, y = d+m.

[0116] S44. Calculate the z-direction propagation constant K of SSIGW according to the pattern matching method. z , calculated as follows:

[0117]

[0118] Step S5: Based on the field distribution expression obtained in step S4 and in combination with the characteristic impedance definition, derive and calculate the closed expression of the characteristic impedance of the strip line in the SSIGW model.

[0119] In this embodiment, the characteristic impedance Z of the strip line of the silicon dioxide isolation layer etched on the upper surface of the second silicon dielectric layer 2 in the SSIGW model is calculated as follows:

[0120]

[0121] Where w is the stripline width.

[0122] The theoretical calculation and simulation results are compared as follows to verify the effectiveness and rapidity of the calculation method of this embodiment:

[0123] like Figure 8 As shown in the figure, the dispersion comparison results of the calculation method of this embodiment and the simulation software (CST and HFSS) are shown. It can be seen that the calculation results of the three are very consistent. Compared with CST, the maximum error of the calculation method of this embodiment in the electromagnetic band gap range is 1.6%, and the maximum error of the propagation constant in the electromagnetic band gap range is 9.6%.

[0124] like Fig. 9 The figure shows the comparison results of the characteristic impedance between the calculation method of this embodiment and the simulation software (CST and HFSS). It can be seen that the calculation results of the three are very consistent. The maximum error of the SSIGW characteristic impedance of the calculation method of this embodiment compared with CST is 9.6%; the maximum error of the SSIGW characteristic impedance of the method of this embodiment compared with HFSS is 13.5%.

[0125] like Fig.10 As shown, the comparison results of the unit frequency calculation time of the calculation method of this embodiment and the simulation software (CST and HFSS) are shown. It can be seen that the dispersion calculation time of the calculation method of this embodiment is less than 1 / 100 of the simulation time, and the characteristic impedance calculation time of the calculation method of this embodiment is less than 1 / 55 of the simulation time.

[0126] In general, the calculation method of this embodiment can be applied to the rapid calculation of the dispersion and characteristic impedance of silicon-based integrated gap waveguides. The entire calculation process mainly includes two parts: 1) solving the z-direction propagation constant of SSIGW by the mode matching method, 2) solving the characteristic impedance of SSIGW by the field distribution and the characteristic impedance definition formula; wherein in 1), firstly, an equivalent circuit model of the silicon-based electromagnetic bandgap structure array is established to solve its plasma wave number, and then the y-direction propagation constant of SSIGW is solved by the transverse resonance method, and finally the z-direction propagation constant of SSIGW is solved by combining the mode matching method. This embodiment combines the transverse resonance method with the mode matching method to derive the closed dispersion equation and characteristic impedance formula of SSIGW, providing theoretical guidance for the efficient design of SSIGW terahertz circuits. In addition, this embodiment adopts a mathematical derivation calculation method, which can shorten the calculation time and improve the efficiency of SSIGW terahertz circuit design compared with the existing simulation software using meshing.

[0127] Example 2

[0128] This embodiment provides a terahertz circuit design method, which specifically includes the following steps:

[0129] Step 100: Determine the operating frequency band and circuit impedance value according to the terahertz circuit design requirements.

[0130] Step 200: According to the method for calculating the dispersion and characteristic impedance of the silicon-based integrated gap waveguide proposed in Example 1 of the present invention, the dispersion of the silicon-based integrated gap waveguide is quickly calculated to optimize the structural parameters of the SSIGW model, including the width of the thin film (e.g., the radius R of the circular film), the cross-sectional width of the column (e.g., the radius r of the copper column), the thickness of the silicon dioxide isolation layer, and the period p of the silicon-based electromagnetic bandgap structural unit, so that it operates in the determined working frequency band.

[0131] The process of rapidly optimizing the structural parameters of the SSIGW model includes: different dispersion results can be calculated by changing the structural parameters of the model, that is, different z-direction propagation constants can be calculated; the calculated dispersion results are compared with the required dispersion range to determine whether they meet the design requirements. If not, the model structural parameters are adjusted until the dispersion results meet the design requirements.

[0132] Step 300: According to the method for calculating the dispersion and characteristic impedance of the silicon-based integrated gap waveguide proposed in Embodiment 1 of the present invention, the stripline width corresponding to different impedance values ​​of the terahertz circuit based on the SSIGW model is further calculated through the characteristic impedance.

[0133] Different strip line widths have different characteristic impedances. The characteristic impedances of various strip line widths can be calculated through Example 1.

[0134] Step 400: Establish a circuit model in the simulation software, perform optimization, and obtain the required terahertz circuit simulation model.

[0135] Subsequently, the terahertz circuit simulation model may be processed and tested to verify whether it meets the design requirements.

[0136] Accordingly, this embodiment also provides a terahertz circuit design system, comprising the following modules:

[0137] The circuit parameter determination module determines the operating frequency band and circuit impedance value according to the terahertz circuit design requirements.

[0138] The dispersion calculation module, according to the calculation method of the silicon-based integrated gap waveguide dispersion and characteristic impedance proposed in Example 1 of the present invention, quickly calculates the silicon-based integrated gap waveguide dispersion to optimize the structural parameters of the SSIGW model, including the slice width (e.g., the disc radius R), the cross-sectional width of the column (e.g., the copper column radius r), the thickness of the silicon dioxide isolation layer, and the period p of the silicon-based electromagnetic bandgap structural unit, so that it works in the determined working frequency band. Different dispersion results can be calculated by changing the model structure parameters, that is, different z-direction propagation constants can be calculated; the calculated dispersion results are compared with the dispersion range required for the circuit design, and then the parameters of the SSIGW model structure are adjusted until the dispersion structure meets the circuit design requirements.

[0139] The impedance calculation module further calculates the stripline widths corresponding to different impedance values ​​of the terahertz circuit based on the SSIGW model through the characteristic impedance according to the calculation method of the dispersion and characteristic impedance of the silicon-based integrated gap waveguide proposed in Example 1 of the present invention. Different stripline widths have different characteristic impedances, and the characteristic impedances of various stripline widths can be calculated through Example 1.

[0140] The simulation module establishes a circuit model in the simulation software and optimizes it to obtain the required terahertz circuit simulation model.

[0141] The optimized terahertz circuit simulation model can be processed and tested to verify whether it meets the design requirements.

[0142] The circuit design method and design system of this embodiment are both implemented based on the dispersion and characteristic impedance calculation method proposed in Example 1. The calculation process of the dispersion result and the calculation process of the characteristic impedance refer to the specific steps described in Example 1.

[0143] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, it can be further rewritten and expanded without departing from the principle of the present invention. These improvements and expansions are also regarded as the protection scope of the present invention.

Claims

1. A method for calculating dispersion and characteristic impedance of a silicon-based integrated gap waveguide, characterized in that: The calculation method is based on a SSIGW model, which includes a silicon-based electromagnetic bandgap structure array and a strip line etched on the silicon-based electromagnetic bandgap structure array for transmitting electromagnetic waves; The calculation method comprises the following steps: Establish an equivalent circuit model of silicon-based electromagnetic bandgap structure array, and deduce and calculate the plasma wave number of silicon-based electromagnetic bandgap structure array by applying circuit theory and anisotropic medium theory; Combined with the plasma wave number, the reflection characteristics of the silicon-based electromagnetic bandgap structure array are analyzed, the reflection coefficients of transverse electric TE and transverse magnetic TM waves are derived according to the boundary conditions, and the y-direction propagation constant of SSIGW is derived and calculated using the transverse resonance method; Combined with the y-direction propagation constant, the field distribution in different regions of SSIGW is analyzed, and the field distribution expression is derived through Maxwell's equations; the z-direction propagation constant of SSIGW is derived according to the boundary conditions and mode matching method, that is, the dispersion of silicon-based integrated gap waveguide is calculated; According to the field distribution expression and in combination with the characteristic impedance definition, the characteristic impedance closed expression of the strip line in the SSIGW is derived and calculated.

2. The calculation method according to claim 1, characterized in that: The silicon-based electromagnetic bandgap structure array comprises a dielectric substrate, which comprises at least a first silicon dielectric layer, a second silicon dielectric layer and a third silicon dielectric layer arranged from the bottom; a silicon dioxide isolation layer is arranged between two adjacent silicon dielectric layers; A silicon dioxide isolation layer is provided on both the upper and lower surfaces of the first silicon dielectric layer, a column is inserted into the first silicon dielectric layer and the silicon dioxide isolation layers on its upper and lower surfaces, a thin slice is etched on the silicon dioxide isolation layer on the upper surface of the first silicon dielectric layer, the width of the thin slice is greater than the cross-sectional width of the column, and then a layer of silicon dioxide isolation layer is wrapped outside the column to form a silicon-based electromagnetic bandgap structure unit, wherein the copper cylinder sequentially penetrates the silicon dioxide isolation layer on the upper surface of the first silicon dielectric layer, the first silicon dielectric layer, and the silicon dioxide isolation layer on the lower surface of the first silicon dielectric layer; a plurality of the silicon-based electromagnetic bandgap structure units are provided on the silicon-based electromagnetic bandgap structure array; The stripline is etched in a silicon dioxide isolation layer above the second silicon dielectric layer.

3. The calculation method according to claim 2, characterized in that: The derivation and calculation of the plasma wave number of the silicon-based electromagnetic bandgap structure array specifically includes: The impedance is calculated based on the equivalent circuit model of the silicon-based electromagnetic bandgap structure array; According to the capacitance calculation formula and the inductance calculation formula, calculate the inductance and capacitance values; The dielectric constant is calculated based on the relationship between electric displacement flux and electric polarization intensity; According to the relationship between the dielectric constant tensor and the plasma wave number, the plasma wave number of the silicon-based electromagnetic band gap structure array is calculated.

4. The calculation method according to claim 2, characterized in that: The y-direction propagation constant of SSIGW is derived and calculated, including the following steps: According to the characteristics of the SSIGW structure, the upper surface of the lower equivalent dielectric layer is taken as the interface to determine the boundary conditions of the magnetic field, electric field and current density. According to the boundary conditions, the reflection coefficients at TE and TM incidence are calculated; According to the transverse resonance method, the y-direction propagation constant of SSIGW is calculated for TE and TM incidence.

5. The calculation method according to claim 2, characterized in that: The z-direction propagation constant of SSIGW is derived and calculated, including the following steps: The SSIGW model structure is divided into three different regions, the quasi-TEM mode is transmitted in the stripline region, and the other regions are TE mode and TM mode; Combined with the propagation constant in the y direction, the field distribution of different modes is calculated according to Maxwell's equations; Determine the boundary conditions of electric and magnetic fields based on SSIGW electromagnetic characteristics; According to the mode matching method, the z-direction propagation constant of SSIGW is calculated.

6. The calculation method according to claim 5, characterized in that: The field distribution expressions of different modes are as follows: Quasi-TEM field in the stripline region: in K z is the propagation constant in the z direction, is the wave number in the x direction of the quasi-TEM mode, K2 is the wave number of the upper region of the lower equivalent dielectric layer of the equivalent model of the electromagnetic bandgap structure array, and E y1 is the electric field in the y direction of the quasi-TEM mode, H x1 is the quasi-TEM mode x-direction magnetic field, H z1 is the z-direction magnetic field of the quasi-TEM mode, E0 is the amplitude of the quasi-TEM mode, η2 is the wave impedance of the upper region of the lower equivalent dielectric layer of the equivalent model of the electromagnetic bandgap structure array; TM-y field in non-stripline region: in K2 is the wave number of the upper region of the lower equivalent dielectric layer of the equivalent model of the electromagnetic bandgap structure array, E x2 is the electric field in the x direction of the TM mode, E y2 is the electric field in the y direction of the TM mode, E z2 is the electric field in z direction of TM mode, H x2 is the TM mode x-direction magnetic field, H z2 is the z-direction magnetic field of the TM mode, A TM is the TM mode amplitude, is the TM mode loss in x direction; K TM is the propagation constant in the y direction when TM is incident, m represents the thickness of the equivalent dielectric layer in the middle layer of the equivalent physical model of the electromagnetic bandgap structure array, and d represents the thickness of the equivalent dielectric layer in the upper layer of the strip line of the equivalent physical model of the electromagnetic bandgap structure array; TE-y field in non-stripline region: in E x3 is the electric field in the x direction of the TE mode, E z3 is the electric field in the z direction of the TE mode, H x3 is the TE mode x-direction magnetic field, H y3 is the TE mode magnetic field in the y direction, H z3 is the TE mode z-direction magnetic field, A TE is the TE modulus amplitude, is the TE mode loss in x direction, K TE is the propagation constant in the y direction when TE is incident, y represents the height variable in the y direction, and w is the stripline width.

7. The calculation method according to claim 6, characterized in that: Propagation constant K in z direction z Calculate as follows: The characteristic impedance Z of the strip line is calculated as follows:

8. The calculation method according to claim 3, characterized in that: The plasma wave number is calculated as follows: Where p is the period of the silicon-based electromagnetic bandgap structural unit, ω is the angular frequency, μ0 is the magnetic permeability of free space; ε eff1 is the relative dielectric constant of the lower equivalent dielectric layer of the equivalent physical model of the silicon-based electromagnetic bandgap structure array; the gap capacitance between the thin sheets of two adjacent silicon-based electromagnetic bandgap structure units is C2, the capacitance from the thin sheet to the top layer of the dielectric substrate is C1, and the column inductance is L.

9. A terahertz circuit design method, characterized in that: The following steps are involved: According to the design requirements of terahertz circuit, determine its operating frequency band and circuit impedance value; According to the method for calculating the dispersion and characteristic impedance of the silicon-based integrated gap waveguide according to any one of claims 1 to 8, the dispersion of the silicon-based integrated gap waveguide is calculated to optimize the structural parameters of the SSIGW model so that it works in the determined working frequency band; The characteristic impedance is calculated, and the strip line width corresponding to different impedance values ​​of the terahertz circuit based on the SSIGW model is further calculated through the characteristic impedance.

10. A terahertz circuit design system, characterized in that: Includes the following modules: The circuit parameter determination module determines the operating frequency band and circuit impedance value according to the terahertz circuit design requirements; A calculation module, which calculates the dispersion of the silicon-based integrated gap waveguide according to the calculation method for the dispersion and characteristic impedance of the silicon-based integrated gap waveguide according to any one of claims 1 to 8, so as to optimize the structural parameters of the SSIGW model so that it works in the determined working frequency band; The characteristic impedance is calculated, and the strip line width corresponding to different impedance values ​​of the terahertz circuit based on the SSIGW model is further calculated through the characteristic impedance.

Images