CN115186621B - Design method and structure of through hole structure of superconducting quantum circuit - Google Patents
Design method and structure of through hole structure of superconducting quantum circuit Download PDFInfo
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Abstract
The invention discloses a design method and a structure of a through hole structure of a superconducting quantum circuit, which comprises the following steps: determining equivalent impedance of a first via structure, wherein the first via structure comprises a signal via and a ground via; the equivalent impedance of the first through hole structure is abnormal to the magnitude relation of the target impedance, an insulation through hole is additionally arranged between a signal through hole and a grounding through hole, the equivalent impedance of the through hole structure of the superconducting quantum circuit is increased by changing the layout of the insulation through hole, the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed; the signal through hole, the grounding through hole and the insulating through hole form a second through hole structure, and insulating media with relative dielectric constants smaller than that of the substrate where the through holes are located are filled in the insulating through holes. The technical scheme provided by the invention improves the matching degree of the equivalent impedance of the superconducting quantum circuit and the preset standard under the condition of not increasing the size of the superconducting quantum circuit.
Description
Technical Field
The invention relates to the technical field of microwave engineering, in particular to a design method and a structure of a through hole structure of a superconducting quantum circuit.
Background
The quantum computing utilizes the characteristics of superposition, entanglement and the like of the quantum, has the characteristic of obvious parallel computing, and has great advantages in the analysis of specific problems in the fields of finance, traffic, medicine and the like. The quantum computing system based on the superconducting circuit has the characteristics of easy design, integrated preparation by utilizing a micro-nano manufacturing technology and large-scale processing and packaging, and becomes a research hotspot direction of quantum computing. In 11 months 2021, international business machines corporation or international business machines corporation (IBM) released processors with 127 qubits, which are expected to at least double the number of on-chip bits per year in the future. Superconducting quantum computing systems are made up of a number of different critical components. To achieve non-destructive reading of quantum states, the resonant frequency of the read cavity (whose qubits are coupled by capacitance) is probed to indirectly obtain the state of the qubit. Researchers have developed studies on quantum coherent mechanisms, device coupling, material action, information transfer, and the like in the system, and have been advancing toward practical superconducting quantum circuit systems. With the development of superconducting quantum chips, effective calculation on a larger scale can be realized only by remarkably improving the bit quantity, the quantum volume, the circuit depth and the like. The achievement of these phased goals presents new challenges to quantum chip physical design. At present, researchers have proposed a design scheme of a multilayer chip, various components such as a bit, a read resonator, a filter and the like are distributed on different chip layers, and a large number of metal thin films between the layers are electromagnetically shielded to reduce signal interference. In order to meet the requirement of efficient signal transmission of each layer, the design of the through hole with good microwave transmission performance and compact structure is very important.
The working frequency band of the superconducting quantum circuit is 1-20 GHz, and the distributed inductance L and the distributed capacitance C on the transmission line play an important role in the effective transmission of microwave signals. At present, researchers can realize the connection of circuit transmission signals on the front side and the back side of a substrate by preparing through holes on a silicon (Si) or sapphire substrate. Considering the film as a superconducting state and the monoplanar transmission line as a regular transmission system (coplanar waveguide structure), the transmission line impedance thereof is defined by
Determination of where Z 0 L is the transmission line impedance, L is the inductance, and C is the capacitance. In the different layer switching area, the transmission carrier of microwave gradually changes from a coplanar waveguide structure to a plurality of through hole structures and then to a coplanar waveguide structure of another layer. Compared with the regular transmission system, the electromagnetic field distribution near the switching region is obviously changed, so that the impedance fluctuation characteristic of the transmission line of the part is presented, and the microwave signal is lost.
In order to ensure better microwave transmission performance in the current design scheme, the through hole structure occupies a large space generally, and the plane area reaches 300 multiplied by 400 mu m 2 . The current scheme significantly reduces the integration level of qubits, considering the integration of other resonators, bits, filters, etc. on the chip. How to effectively reduce the space of the through hole and maintain the excellent transmission performance of the through hole is a big problem for realizing the large-scale superconducting quantum chip. To improve the design, researchers are well versed inAnd the impedance matching is realized by adjusting the central distance D between the signal through holes and the grounding through holes and increasing or decreasing the number of the surrounding grounding through holes. It is noted that most substrates are Si or sapphire, which have a relative dielectric constant ε r>10, thereby resulting in a more pronounced distributed capacitance. Reducing the distributed capacitance is possible by increasing the center distance D between the signal and ground vias, but this behavior can lead to an increase in via size, which is contrary to the scaled integration of superconducting quantum circuits. While a smaller number of ground vias may result in a diffuse distribution of the electromagnetic field that causes radiation.
Disclosure of Invention
The invention provides a design method and a structure of a through hole structure of a superconducting quantum circuit, which are used for enabling the equivalent impedance of the superconducting quantum circuit to meet a preset standard under the condition of not increasing the size of the superconducting quantum circuit.
According to an aspect of the present invention, there is provided a method for designing a via structure of a superconducting quantum circuit, including:
determining an equivalent impedance of a first via structure, wherein the first via structure comprises a signal via and a ground via;
the equivalent impedance of the first through hole structure is abnormal to the target impedance, an insulation through hole is additionally arranged between a signal through hole and a grounding through hole, the equivalent impedance of the through hole structure of the superconducting quantum circuit is increased by changing the layout of the insulation through hole, wherein the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed;
the signal through hole, the grounding through hole and the insulation through hole form a second through hole structure, and insulation media with relative dielectric constants smaller than that of the substrate where the through holes are located are filled in the insulation through holes.
Optionally, when the magnitude relationship between the equivalent impedance of the first via structure and the target impedance is abnormal, the equivalent impedance of the first via structure and the target impedance satisfy the following relationship:
Z TSV0 < Z 0
wherein Z is TSV0 Is the equivalent impedance of the first via structure，Z 0 Is the target impedance.
Optionally, the step of increasing the equivalent impedance of the via structure of the superconducting quantum circuit by changing the layout of the insulating via hole by adding the insulating via hole between the signal via hole and the ground via hole when the magnitude relationship between the equivalent impedance of the first via structure and the target impedance is abnormal includes:
the equivalent impedance of the via structure of the superconducting quantum circuit is increased by changing at least one of the spatial distribution position, the area and the number of the insulating vias.
Optionally, the step of increasing the equivalent impedance of the via structure of the superconducting quantum circuit by changing the layout of the insulating via hole by adding the insulating via hole between the signal via hole and the ground via hole when the magnitude relationship between the equivalent impedance of the first via structure and the target impedance is abnormal includes:
calculating an equivalent impedance of the second via structure;
and adding an insulation through hole between the signal through hole and the grounding through hole, and increasing the equivalent impedance of the through hole structure of the superconducting quantum circuit by changing the layout of the insulation through hole according to the calculation result of the equivalent impedance of the second through hole structure, wherein the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed.
Optionally, calculating the equivalent impedance of the second via structure comprises:
the grounding through holes are symmetrically arranged relative to the signal through holes, and the equivalent impedance of the second through hole structure is calculated through an expression formula of the equivalent impedance of the second through hole structure;
the expression formula of the equivalent impedance of the second via structure satisfies the following relationship:
wherein Z is TSV1 Is the equivalent impedance of the second via structure, Z TSV0 Is the equivalent impedance of the first via structure,
and for the impedance correction coefficient, epsilon r is the relative dielectric constant of the substrate where the through holes are positioned, epsilon r2 is the relative dielectric constant of an insulating medium in the insulating through holes, S1 is the equivalent area of the dielectric space of the first through hole structure, D is the central distance between the signal through holes and the grounding through holes, D is the aperture of the grounding through holes, n2 is the number of the insulating through holes, and S2 is the area of the insulating through holes.
Optionally, calculating the equivalent impedance of the second via structure comprises:
the ground vias are asymmetrically arranged with respect to the signal vias, and the equivalent impedance of the second via structure is calculated by finite elements of electromagnetism.
Optionally, before calculating the equivalent impedance of the second via structure through the expression formula of the equivalent impedance of the second via structure, the method further includes:
obtaining the equivalent impedance of the second through hole structure through finite element calculation;
and if the goodness of fit of the relation between the equivalent impedance of the second through hole structure and the equivalent impedance of the second through hole structure obtained through finite element calculation meets the preset goodness of fit, judging that the accuracy of the expression formula of the equivalent impedance of the second through hole structure meets the preset requirement.
According to another aspect of the present invention, there is provided a via structure of a superconducting quantum circuit, comprising:
the impedance matching circuit comprises a first through hole structure and a second through hole structure, wherein the size relation between the equivalent impedance of the first through hole structure and the target impedance is abnormal;
the first via structure signal vias and ground vias; the second via structure comprises a signal via, a ground via and an insulation via; the insulating through hole is positioned between the signal through hole and the grounding through hole, and insulating media with relative dielectric constants smaller than that of the substrate where the through hole is positioned are filled in the insulating through hole.
Optionally, the equivalent impedance of the first via structure and the target impedance satisfy the following relationship:
Z TSV0 < Z 0
wherein, Z TSV0 Is the equivalent impedance of the first via structure, Z 0 Is the target impedance.
Optionally, the ground vias are symmetrically disposed with respect to the signal vias, and the equivalent impedance of the second via structure satisfies the following relationship:
wherein Z is TSV1 Is the equivalent impedance of the second via structure, Z TSV0 Is the equivalent impedance of the first via structure,
and for the impedance correction coefficient, epsilon r is the relative dielectric constant of the substrate where the through holes are positioned, epsilon r2 is the relative dielectric constant of an insulating medium in the insulating through holes, S1 is the equivalent area of the dielectric space of the first through hole structure, D is the central distance between the signal through holes and the grounding through holes, D is the aperture of the grounding through holes, n2 is the number of the insulating through holes, and S2 is the area of the insulating through holes.
According to the technical scheme provided by the embodiment, when the size relation between the equivalent impedance of the first through hole structure and the target impedance is abnormal, on the premise that the size of the silicon substrate is not increased, on the basis of the first through hole structure, the insulating through hole is arranged between the signal through hole and the grounding through hole, namely, the insulating through hole adjusts the distributed capacitance C and does not change the distributed inductance L, so that the equivalent impedance of the through hole structure of the superconducting quantum circuit is improved. And the equivalent impedance of the via structure of the superconducting quantum circuit can also be increased by changing the layout of the insulating vias. In conclusion, the technical scheme can remarkably improve the impedance matching between the planar transmission line and the through hole structure and ensure the reliability of signal transmission; the spatial dimension of the through hole connecting structure can be effectively reduced, and powerful support is provided for the implementation of a large-scale superconducting quantum circuit; and the trial-and-error cost of the finite element calculation model can be effectively reduced, and the calculation efficiency is improved.
It should be understood that the statements in this section are not intended to identify key or critical features of the embodiments of the present invention, nor are they intended to limit the scope of the invention. Other features of the present invention will become apparent from the following description.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flow chart of a method for designing a via structure of a superconducting quantum circuit according to an embodiment of the present invention;
fig. 2 is a top view of a via structure of a superconducting quantum circuit provided in accordance with an embodiment of the present invention;
fig. 3 is a top view of another via structure for a superconducting quantum circuit provided in accordance with an embodiment of the present invention;
FIG. 4 is a simulated view of the first via structure of FIGS. 2 and 3 propagating TEM wave electric field lines;
fig. 5 is a flow chart of a design method of a via structure of a superconducting quantum circuit according to another embodiment of the present invention;
fig. 6 is a flow chart of a method for designing a via structure of a superconducting quantum circuit according to another embodiment of the present invention;
FIG. 7 is a simulated view of the second via structure of FIG. 2 propagating TEM wave electric field lines;
FIG. 8 is a simulated view of the second via structure of FIG. 3 propagating TEM wave electric field lines;
fig. 9 is a simulation of TEM wave electric field lines propagating through a first one of the via structures of another superconducting quantum circuit provided in accordance with an embodiment of the present invention;
FIG. 10 is a simulation of TEM wave electric field lines propagating through a second via structure in a via structure of yet another superconducting quantum circuit provided in accordance with an embodiment of the present invention;
FIG. 11 is a graph of equivalent impedance of the first via structure and the second via structure of FIG. 2 as a function of center distance of the ground via and the signal via;
FIG. 12 is a graph of equivalent impedance of the first via structure and the second via structure of FIG. 2 as a function of the number of ground vias;
FIG. 13 is a graph of equivalent impedances as a function of center distance of a ground via and a signal via in the first via structure, the second via structure of FIG. 2, and the second via structure of FIG. 3;
fig. 14 is a graph of S-parameter versus frequency for the first via structure and the second via structure of fig. 2.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in other sequences than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
In order to meet the signal transmission requirement of a multilayer line of a superconducting quantum circuit and enable the equivalent impedance of the superconducting quantum circuit to meet a preset standard under the condition of not increasing the size of the superconducting quantum circuit, the embodiment of the invention provides the following technical scheme:
referring to fig. 1, the method for designing a via structure of a superconducting quantum circuit includes the steps of:
and S110, determining equivalent impedance of a first through hole structure, wherein the first through hole structure comprises a signal through hole and a grounding through hole.
Referring to fig. 2 and 3, the via structure of the superconducting quantum circuit includes a signal via 001, a ground via 002, and an insulating via 003. In the beginning of designing the via structure of the superconducting quantum circuit, a certain number of signal vias 001 and ground vias 002 are generally provided on a substrate. In the present embodiment, one signal via 001 and four ground vias 002 are taken as an example for description. The signal vias 001 are used to transmit signals of upper and lower layers of the substrate. The ground via 002 is used to access a ground signal. In the present embodiment, the first via structure is denoted by TSV 0. Z for impedance of first through hole structure TSV0 TSV0 To indicate. FIG. 4 is a first via structure of FIGS. 2 and 3 propagating TEM wavesA simulated view of field lines. A TEM Wave (Transverse Electromagnetic Wave) is an Electromagnetic Wave in which an electric field component and a magnetic field component are perpendicular to each other and both are perpendicular to a propagation direction.
S120, the magnitude relation between the equivalent impedance of the first through hole structure and the target impedance is abnormal, an insulation through hole is additionally arranged between the signal through hole and the grounding through hole, the equivalent impedance of the through hole structure of the superconducting quantum circuit is increased by changing the layout of the insulation through hole, the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed;
the signal through hole, the grounding through hole and the insulating through hole form a second through hole structure, and insulating media with relative dielectric constants smaller than that of the substrate where the through holes are located are filled in the insulating through holes;
when the magnitude relation between the equivalent impedance of the first through hole structure and the target impedance is abnormal, the equivalent impedance of the first through hole structure and the target impedance satisfy the following relation:
Z TSV0 < Z 0 （1）
wherein, Z TSV0 Is the equivalent impedance of the first via structure, Z 0 Is the target impedance.
In the embodiment of the present invention, the magnitude relationship between the equivalent impedance of the first through hole structure and the target impedance satisfies the following relationship: z TSV0 = Z 0 The design may be in accordance with the current layout of signal vias 001 and ground vias 002.
When the magnitude relationship between the equivalent impedance of the first via structure and the target impedance is abnormal, only the signal via 001 and the ground via 002 are disposed in the substrate and are limited by the size constraint of the via structure in the substrate, therefore, in this embodiment, on the basis of the first via structure, the insulating via 003 needs to be disposed in the substrate, wherein the insulating via 003 is located between the signal via 001 and the ground via 002, that is, the insulating via 003 adjusts the distributed capacitance C without changing the distributed inductance L, so as to improve the equivalent impedance of the via structure of the superconducting quantum circuit.
Since the insulating dielectric with a relative dielectric constant smaller than that of the substrate in which the via is located is filled in the insulating via 003, the arrangement of the insulating via 003 is equivalent to increase the equivalent impedance of the entire via structure in the substrate. And the equivalent impedance of the via structure of the superconducting quantum circuit can also be increased by changing the layout of the insulating via 003.
According to the technical scheme provided by the embodiment, when the equivalent impedance of the first through hole structure is abnormal to the target impedance, on the premise that the size of the substrate is not increased, on the basis of the first through hole structure, the insulating through hole 003 is arranged between the signal through hole 001 and the ground through hole 002, namely, the insulating through hole 003 adjusts the distributed capacitance C and does not change the distributed inductance L, so that the equivalent impedance of the through hole structure of the superconducting quantum circuit is improved, specifically, the insulating through hole 003 is filled with the insulating medium with the relative dielectric constant smaller than that of the substrate where the through hole is located, and therefore, the arrangement of the insulating through hole 003 is equivalent to the increase of the equivalent impedance of the whole through hole structure in the silicon substrate. And the equivalent impedance of the via structure of the superconducting quantum circuit can also be increased by changing the layout of the insulating via 003. In conclusion, the technical scheme can obviously improve the impedance matching between the planar transmission line and the through hole structure, and ensure the reliability of signal transmission; the spatial dimension of the through hole connecting structure can be effectively reduced, and powerful support is provided for the implementation of a large-scale superconducting quantum circuit; and the trial-and-error cost of the finite element calculation model can be effectively reduced, and the calculation efficiency is improved.
Alternatively, the substrate on which the Through-hole is formed in the present embodiment includes any one of a Silicon substrate, a sapphire substrate, a Silicon carbide substrate, a diamond substrate, a gallium arsenide (GaAs) substrate, or a Silicon germanium (SiGe) substrate, and when the substrate is a Silicon substrate, the Through-hole may be referred to as a Through Silicon Via (TSV).
Optionally, on the basis of the foregoing technical solution, referring to fig. 5, the step of increasing the equivalent impedance of the via structure of the superconducting quantum circuit by adding an insulating via between the signal via and the ground via and changing the layout of the insulating via when the magnitude relationship between the equivalent impedance of the first via structure and the target impedance is abnormal in S120 includes:
and S220, increasing the equivalent impedance of the through hole structure of the superconducting quantum circuit by changing at least one of the spatial distribution position, the area and the number of the insulating through holes 003.
According to the technical scheme, the equivalent impedance of the through hole structure of the superconducting quantum circuit is increased by changing at least one of the spatial distribution position, the area and the number of the insulating through holes 003, the spatial size of the TSV through hole connecting structure can be effectively reduced on the premise of not increasing the size of the substrate, and powerful support is provided for implementation of large-scale superconducting quantum circuits.
Optionally, on the basis of the foregoing technical solution, referring to fig. 6, the step of increasing the equivalent impedance of the via structure of the superconducting quantum circuit by adding an insulating via between the signal via and the ground via and changing the layout of the insulating via when the magnitude relationship between the equivalent impedance of the first via structure and the target impedance is abnormal in S120 includes:
and S1201, calculating the equivalent impedance of the second through hole structure.
S1202, adding an insulation through hole between a signal through hole and a grounding through hole when the magnitude relation between the equivalent impedance of the first through hole structure and the target impedance is abnormal, and increasing the equivalent impedance of the through hole structure of the superconducting quantum circuit by changing the layout of the insulation through hole according to the calculation result of the equivalent impedance of the second through hole structure, wherein the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed.
In the present embodiment, the second via structure is denoted by TSV 1. Z for impedance of second via structure TSV1 To indicate. The method of calculating the equivalent impedance of the second via structure is described in detail below.
A first method of calculating the equivalent impedance of the second via structure is as follows:
optionally, calculating an equivalent impedance Z of the second via structure TSV1 TSV1 The method comprises the following steps:
referring to fig. 2 and 3, the ground via 002 is symmetrically disposed with respect to the signal via 001, and the equivalent impedance of the second via structure is calculated by an expression formula of the equivalent impedance of the second via structure; the expression formula of the equivalent impedance of the second via structure satisfies the following relationship:
wherein Z is TSV1 Is the equivalent impedance of the second via structure, Z TSV0 Is the equivalent impedance of the first via structure,
and for the impedance correction coefficient, epsilon r is the relative dielectric constant of the substrate where the through holes are positioned, epsilon r2 is the relative dielectric constant of an insulating medium in the insulating through holes, S1 is the equivalent area of the dielectric space of the first through hole structure, D is the central distance between the signal through holes and the grounding through holes, D is the aperture of the grounding through holes, n2 is the number of the insulating through holes, and S2 is the area of the insulating through holes.
Equations (2) - (4) can determine the impedance Z of the second via structure TSV1 TSV1 . Exemplarily, fig. 7 is a simulation diagram of the electric field lines of the propagating TEM wave of the second via structure TSV1 (rectangular) when the insulating via 003 is rectangular. Fig. 8 is a simulation diagram of the electric field lines of the TEM wave propagating through the second via structure TSV1 (circular) when the insulating via 003 is circular.
Referring to equations (2) - (4), the number n2 and the area S2 of the insulating via 003 are variables, and thus the equivalent impedance of the via structure of the superconducting quantum circuit is increased by changing the area S2 of the insulating via 003. Alternatively, the equivalent impedance of the via structure of the superconducting quantum circuit is increased by changing the number n2 of the insulating vias 003.
And (3) adding an insulating through hole between the signal through hole and the grounding through hole, and increasing the equivalent impedance of the through hole structure of the superconducting quantum circuit by changing the area or the number of the insulating through holes according to the calculation result of the equivalent impedance of the second through hole structure calculated by the formulas (2) - (4), wherein the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed. It should be noted that, the spatial distribution position of the insulating through hole changes, and the equivalent impedance of the through hole structure of the superconducting quantum circuit also changes.
A second method of calculating the equivalent impedance of the second via structure is as follows:
optionally, calculating the equivalent impedance of the second via structure comprises:
the ground vias are asymmetrically arranged with respect to the signal vias, and the equivalent impedance of the second via structure is calculated by finite elements of electromagnetism.
Example 1
In the case that the distribution of the signal vias 001 and the ground vias 002 is asymmetric, the impedance can be optimally designed through finite element calculation in electromagnetism. As shown in fig. 9, the first via structure is asymmetric and includes 3 ground vias 002 and one signal via 001, and the distance and angle between the ground via 002 and the signal via 001 are not uniform. And establishing an analysis model of the electric field and the magnetic field of the structure to obtain the distributed capacitance and the distributed inductance of the structure, and further obtaining the characteristic impedance of the first through hole structure to be 33.3 omega. Since the characteristic impedance is less than the target impedance of 50 omega. On the basis of the structure, the equivalent impedance of the via structure is improved by adding the insulating via 003, i.e., trying to adjust the distributed capacitance C without changing the distributed inductance L. The method specifically comprises the following steps: between the signal via 001 and the ground via 002, 6 insulating vias 003 were additionally provided, and the layout thereof is as shown in fig. 10, so that the insulating vias 003 were located in a region where the electromagnetic field was strong. The characteristic impedance of the second via structure according to this design is 42.0 Ω.
The equivalent impedance of the superconducting quantum circuit through hole structure is increased by changing at least one of the spatial distribution position, area and number of the insulating through holes according to the calculation result of the equivalent impedance of the second through hole structure calculated by finite element of electromagnetism, wherein the distributed inductance of the superconducting quantum circuit through hole structure is not changed, and the distributed capacitance is changed.
Optionally, before calculating the equivalent impedance of the second via structure through the expression formula of the equivalent impedance of the second via structure, the method further includes:
and obtaining the equivalent impedance of the second through hole structure through finite element calculation of electromagnetism.
And if the goodness of fit of the relation between the equivalent impedance of the second through hole structure and the equivalent impedance of the second through hole structure obtained through finite element calculation of electromagnetism meets the preset goodness of fit, judging that the accuracy of the expression formula of the equivalent impedance of the second through hole structure meets the preset requirement.
Before the accuracy of an expression formula of the equivalent impedance of the second through hole structure is judged to meet a preset requirement, the following relation that the equivalent impedance of the first through hole structure meets is introduced:
wherein Z is TSV0 Is the equivalent impedance of the first via structure, Z PTW Impedance, Z, for parallel two-wire model of signal and ground vias Coax The impedance of a coaxial line model is formed by the signal through holes and the grounding through holes, epsilon r is the relative dielectric constant of a substrate where the through holes are located, a1 and a2 are calculation parameters, D is the central distance between the signal through holes and the grounding through holes, D is the aperture of the grounding through holes, and n is the number of the grounding through holes.
Wherein, by fitting a plurality of different sets of (n, Z) TSV0 ) The data yielded a calculated parameter a1 of 0.856 and a calculated parameter a2 of 1.097. Illustratively, set ground viasThe aperture D of the signal through hole 001 is 20 micrometers, the center distance D between the signal through hole 002 and the grounding through hole 002 is 50-80 micrometers, and the relative dielectric constant epsilon r of the substrate where the through holes are located is 11.4.
Example two:
by fitting sets of different (n, Z) TSV0 ) The data obtained in equation (5) had a calculated parameter a1 of 0.856 and a calculated parameter a2 of 1.097. The relative dielectric constant ε r of the substrate having the through-hole was 11.4. The number n2 of the insulating through holes 003 is 4, the number n of the grounding through holes 002 is 4, the aperture D of the grounding through holes 002 is 20 micrometers, and the central distance D between the grounding through holes 002 and the signal through holes 001 is 50 micrometers-80 micrometers; the relative dielectric constant ∈ r2=1 of the insulating medium filled in the insulating via hole 003. Referring to fig. 11, the equivalent impedances of the second through-hole structure TSV1 (rectangle) in fig. 2, which have center distances D of 50 micrometers, 60 micrometers, 70 micrometers and 80 micrometers between the ground via 002 and the signal via 001, are calculated by formula (2) and all fall on the spectral line of the second through-hole structure TSV1 corresponding to the finite element analysis result, and it is determined that the accuracy of the expression formula of the equivalent impedance of the second through-hole structure meets the preset requirement. And the dotted line is a spectral line corresponding to the finite element analysis result of the first through hole structure TSV 0. And the solid line is a spectral line corresponding to the finite element analysis result of the second through hole structure TSV 1.
It should be noted that, referring to fig. 11, for the first via structure TSV0 of the prior art, when the center distance D between the ground via 002 and the signal via 001 is between 50-80 μm, the equivalent impedance of the first via structure TSV0 increases from 26 Ω to 39 Ω. The structure and the target impedance Z 0 A large gap is matched. If the impedance matching degree is further improved by increasing the center distance D between the ground via 002 and the signal via 001, the disadvantage is that a large amount of chip space is required.
Example three:
by fitting sets of different (n, Z) TSV0 ) The data obtained in equation (5) had a calculated parameter a1 of 0.856 and a calculated parameter a2 of 1.097. The relative dielectric constant ε r of the substrate having the through-hole was 11.4. The number n of the ground via 002 is 1, 2, 3, 4, 5, 6, 7 and 8, the aperture D of the ground via 002 is 20 micrometers, and the center distance D between the ground via 002 and the signal via 001 is 50 micrometersRice-80 microns; the relative dielectric constant ∈ r2=1 of the insulating medium filled in the insulating via hole 003. The number of insulating vias 003 is the same as the number of ground vias 002. Referring to fig. 12, with the increase of n, the characteristic impedance of the first via structure TSV0 evolves from the two-wire model to a coaxial line model, the equivalent impedances of the second via structure TSV1 (rectangle) in fig. 2 with the number of insulating vias 003 being 1, 2, 3, 4, 5, 6, 7, and 8 all fall on the spectral line of the second via structure TSV1 corresponding to the finite element analysis result, and it is determined that the accuracy of the expression formula of the equivalent impedance of the second via structure meets the preset requirement. The dotted line is a spectral line corresponding to the finite element analysis result of the first via structure TSV 0. And the solid line is a spectral line corresponding to the finite element analysis result of the second through hole structure TSV 1.
According to the technical scheme, the accuracy of the expression formula of the equivalent impedance of the TSV1 of the second through hole structure is verified, the trial-and-error cost of calculation can be effectively reduced according to the quantized analysis of the evolution trend of the impedance in different structures, a clear direction is provided for optimizing the TSV through hole structure, and the calculation efficiency is improved.
Fig. 13 is a graph showing the relationship between the equivalent impedance of each of the first via structure, the second via structure in fig. 2, and the second via structure in fig. 3, as a function of the center distance D between the ground via 002 and the signal via 001. Fig. 14 is a graph of S-parameter versus frequency for the first via structure and the second via structure of fig. 2.
Referring to fig. 13, verifying that the second via structure TSV1 (rectangular) including the rectangular insulating via 003 in fig. 2 has better transmission, the reflection coefficient thereof can be significantly reduced by about 20dB, referring to fig. 14. Specifically, the area of the insulating via hole 003 in FIG. 2 is 18X 36 μm 2 Compared to the second via structure TSV1 (circular) including the circular insulating via 003 in fig. 3, the electric field distribution is improved better. The area of the air region can be effectively increased by the insulating through hole 003 being rectangular, and the distributed capacitance can be reduced, so that the equivalent impedance of the second through hole structure is better than 45 omega within the parameter range. Compared with the conventional design with the same structure parameter D, the second through hole structure TSV1 in fig. 2 has an impedance improvement effect of 13-100%.
The embodiment of the invention also provides a through hole structure of the superconducting quantum circuit. Referring to fig. 2, the via structure of the superconducting quantum circuit includes: a first via structure and a second via structure; a first via structure signal via 001 and ground via 002; the second via structure comprises a signal via 001, a ground via 002 and an insulating via 003; the insulating through hole 003 is positioned between the signal through hole 001 and the grounding through hole 002, and an insulating medium with the relative dielectric constant smaller than that of the substrate in which the through hole is positioned is filled in the insulating through hole; the arrangement of the insulating through hole enables the distributed inductance of the through hole structure of the superconducting quantum circuit not to change and the distributed capacitance to change. The equivalent impedance and the target impedance of the first via structure satisfy the following relationship:
Z TSV0 < Z 0
wherein Z is TSV0 Is the equivalent impedance of the first via structure, Z 0 Is the target impedance.
According to the technical scheme provided by the embodiment, when the equivalent impedance of the first through hole structure TSV0 is abnormal with the target impedance, on the premise that the size of the silicon substrate is not increased, on the basis of the first through hole structure, the insulating through hole 003 is arranged between the signal through hole 001 and the grounding through hole 002, namely the insulating through hole 003 adjusts the distributed capacitance C and does not change the distributed inductance L, so that the equivalent impedance of the through hole structure of the superconducting quantum circuit is improved, specifically, the insulating through hole 003 is filled with the insulating medium with the relative dielectric constant smaller than that of the substrate where the through hole is located, and therefore the arrangement of the insulating through hole 003 is equivalent to the increase of the equivalent impedance of the whole through hole structure in the silicon substrate. And the equivalent impedance of the via structure of the superconducting quantum circuit can also be increased by changing the layout of the insulating via 003. In conclusion, the technical scheme can remarkably improve the impedance matching between the planar transmission line and the through hole structure and ensure the reliability of signal transmission; the spatial dimension of the through hole connecting structure can be effectively reduced, and powerful support is provided for the implementation of a large-scale superconducting quantum circuit; and the trial-and-error cost of the finite element calculation model can be effectively reduced, and the calculation efficiency is improved.
Optionally, the ground vias are symmetrically disposed about the signal via, and the equivalent impedance of the second via structure satisfies the following relationship:
wherein Z is TSV1 Is the equivalent impedance of the second via structure, Z TSV0 Is the equivalent impedance of the first via structure,
for the impedance correction coefficient, ε r is the relative dielectric constant of the substrate on which the through hole is located, ε r2 is the relative dielectric constant of the insulating medium in the insulating through hole, S1 is the dielectric space equivalent area of the first through hole structure, D is the center distance between the signal through hole and the ground through hole, D is the aperture of the ground through hole, n2 is the number of the insulating through holes, and S2 is the area of the insulating through holes.
Referring to equations (2) - (4), the number n2 and the area S2 of the insulating via 003 are variables, and thus the equivalent impedance of the via structure of the superconducting quantum circuit is increased by changing the area S2 of the insulating via 003. Alternatively, the equivalent impedance of the via structure of the superconducting quantum circuit is increased by changing the number n2 of the insulating vias 003.
By combining the above analysis, it can be found that the through hole structure of the superconducting quantum circuit provided by the embodiment of the invention is characterized in that an insulating through hole is added between a signal through hole and a ground through hole, the characteristic impedance of the structure is evaluated based on analytic solutions of two types of regular transmission systems, and further the finite element calculation verification is carried out. The through hole structure of the superconducting quantum circuit can obviously improve the impedance matching between the planar transmission line and the through hole structure, and ensures the reliability of signal transmission. Meanwhile, the space size of the through hole structure can be effectively reduced, and powerful support is provided for the implementation of a large-scale superconducting quantum circuit; the provided calculation and analysis method can quantitatively analyze the evolution trend of the impedance in different structures, can effectively reduce the trial and error cost of calculation, provides a clear direction for optimizing the TSV structure, and improves the calculation efficiency.
Optionally, on the basis of the above technical solution, an expression formula of the capacitance of the second via structure satisfies the following relationship:
wherein, C TSV1 Capacitor of the second via structure, C TSV0 A capacitor of the first via structure, C PTW Distributed capacitance, C, for a parallel two-wire model coax Is the distributed capacitance of the coaxial line model,
the impedance correction coefficient is shown as the epsilon r, the epsilon r is the relative dielectric constant of the substrate where the through hole is located, the epsilon r2 is the relative dielectric constant of an insulating medium in the insulating through hole, b1 and b2 are calculation parameters, D is the central distance between the signal through hole and the grounding through hole, D is the aperture of the grounding through hole, n is the number of the grounding through holes, n2 is the number of the insulating through holes, and S2 is the area of the insulating through holes; epsilon isThe dielectric constant of the substrate on which the via is located.
Wherein, the expression formula of the inductance of the first through hole structure satisfies the following relation:
wherein L is TSV0 An inductor of the first via structure, C PTW Distributed capacitance, L, for a parallel two-wire model PTW Distributed inductance, L, being a parallel two-wire model Coax The distributed inductance of the coaxial line model is represented by c1 and c2 as calculation parameters, D is the central distance between the signal through hole and the grounding through hole, D is the aperture of the grounding through hole, and n is the number of the grounding through holes; mu is the magnetic permeability of the substrate where the through hole is located.
The expression formula of the equivalent impedance of the second via structure can satisfy the following relation:
optionally, on the basis of the above technical solution, the magnitude relationship between the equivalent impedance of the first through hole structure and the target impedance satisfies a preset condition, and the equivalent impedance of the through hole structure of the superconducting quantum circuit is changed by changing the layout of the ground through hole.
When the magnitude relation between the equivalent impedance of the first through hole structure and the target impedance meets a preset condition, the equivalent impedance of the first through hole structure is larger than the target impedance.
Optionally, the equivalent impedance of the first via structure satisfies the following relationship:
wherein Z is TSV0 Is the equivalent impedance of the first via structure, Z PTW Impedance, Z, for parallel two-wire model of signal and ground vias Coax The impedance of a coaxial line model is formed by the signal through holes and the grounding through holes, epsilon r is the relative dielectric constant of a substrate where the through holes are located, a1 and a2 are calculation parameters, D is the central distance between the signal through holes and the grounding through holes, D is the aperture of the grounding through holes, and n is the number of the grounding through holes.
Wherein, by fitting a plurality of different sets of (n, Z) TSV0 ) The data yielded a calculated parameter a1 of 0.856 and a calculated parameter a2 of 1.097. Illustratively, the aperture D of the ground via 002 is set to 20 microns, the center distance D between the signal via 001 and the ground via 002 is set to 50-80 microns, and the relative dielectric constant ∈ r of the substrate on which the via is located is set to 11.4.
Optionally, on the basis of the above technical solution, the equivalent impedance of the first via structure is greater than the target impedance, and the equivalent impedance of the via structure of the superconducting quantum circuit may be reduced by reducing the center distance D between the ground via 002 and the signal via 001. And/or the equivalent impedance of the via structure of the superconducting quantum circuit is reduced by increasing the number of ground vias 002.
It should be understood that various forms of the flows shown above may be used, with steps reordered, added, or deleted. For example, the steps described in the present invention may be executed in parallel, sequentially, or in different orders, and are not limited herein as long as the desired results of the technical solution of the present invention can be achieved.
The above-described embodiments should not be construed as limiting the scope of the invention. It should be understood by those skilled in the art that various modifications, structures, sub-structures, and substitutions may be made in accordance with design requirements and other factors. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A method for designing a via structure of a superconducting quantum circuit, comprising:
determining an equivalent impedance of a first via structure, wherein the first via structure comprises a signal via and a ground via;
when the magnitude relation between the equivalent impedance of the first through hole structure and the target impedance is abnormal, under the condition that the size of the superconducting quantum circuit is not increased, an insulating through hole is additionally arranged between the signal through hole and the grounding through hole, the equivalent impedance of the through hole structure of the superconducting quantum circuit is increased by changing the layout of the insulating through hole, the distributed inductance of the through hole structure of the superconducting quantum circuit is not changed, and the distributed capacitance is changed; the signal through hole, the grounding through hole and the insulating through hole form a second through hole structure, and insulating media with relative dielectric constants smaller than that of the substrate where the through holes are located are filled in the insulating through holes;
the grounding through holes are symmetrically arranged relative to the signal through holes, and the equivalent impedance of the second through hole structure is calculated through an expression formula of the equivalent impedance of the second through hole structure;
the expression formula of the equivalent impedance of the second via structure satisfies the following relationship:
wherein Z is TSV1 Is the equivalent impedance of the second via structure, Z TSV0 Is the equivalent impedance of the first via structure,
for the impedance correction coefficient, ε r is the relative dielectric constant of the substrate on which the through hole is located, ε r2 is the relative dielectric constant of the insulating medium in the insulating through hole, S1 is the dielectric space equivalent area of the first through hole structure, D is the center distance between the signal through hole and the ground through hole, D is the aperture of the ground through hole, n2 is the number of the insulating through holes, and S2 is the area of the insulating through holes.
2. The method of claim 1, wherein when the relationship between the equivalent impedance of the first via structure and the target impedance is abnormal, the equivalent impedance of the first via structure and the target impedance satisfy the following relationship:
Z TSV0 < Z 0
wherein Z is TSV0 Is the equivalent impedance of the first via structure, Z 0 Is the target impedance.
3. The method of claim 1, wherein the equivalent impedance of the first via structure is abnormal with respect to a target impedance, an insulating via is additionally provided between the signal via and the ground via, and the increasing the equivalent impedance of the via structure of the superconducting quantum circuit by changing a layout of the insulating via comprises:
the equivalent impedance of the via structure of the superconducting quantum circuit is increased by changing at least one of the spatial distribution position, the area and the number of the insulating vias.
4. The method according to claim 1 or 3, wherein the equivalent impedance of the first via structure is abnormal in relation to a target impedance, the step of adding an insulating via between the signal via and the ground via, and the step of increasing the equivalent impedance of the via structure of the superconducting quantum circuit by changing a layout of the insulating via comprises:
calculating the equivalent impedance of the second via structure;
the equivalent impedance of the superconducting quantum circuit through hole structure is changed by changing the layout of the insulating through holes according to the calculation result of the equivalent impedance of the second through hole structure, wherein the distributed inductance of the superconducting quantum circuit through hole structure is not changed, and the distributed capacitance is changed.
5. The method of claim 4, wherein calculating the equivalent impedance of the second via structure comprises:
the ground vias are asymmetrically arranged with respect to the signal vias, and the equivalent impedance of the second via structure is calculated by finite elements of electromagnetism.
6. The method of claim 1, wherein the calculating the equivalent impedance of the second via structure according to the expression formula of the equivalent impedance of the second via structure further comprises:
obtaining the equivalent impedance of the second through hole structure through finite element calculation of electromagnetism;
and if the goodness of fit of the relation between the equivalent impedance of the second through hole structure and the equivalent impedance of the second through hole structure obtained through finite element calculation of electromagnetism meets the preset goodness of fit, judging that the accuracy of the expression formula of the equivalent impedance of the second through hole structure meets the preset requirement.
7. A via structure for a superconducting quantum circuit, comprising:
a first via structure and a second via structure;
the first via structure signal vias and ground vias; when the magnitude relation between the equivalent impedance and the target impedance of the first through hole structure is abnormal, under the condition that the size of the superconducting quantum circuit is not increased, the second through hole structure comprises a signal through hole, a grounding through hole and an insulating through hole; the insulating through hole is positioned between the signal through hole and the grounding through hole, an insulating medium with a relative dielectric constant smaller than that of the substrate where the through hole is positioned is filled in the insulating through hole, and the arrangement of the insulating through hole enables the distributed inductance of the through hole structure of the superconducting quantum circuit not to be changed and the distributed capacitance to be changed;
the ground vias are symmetrically arranged with respect to the signal vias, and the equivalent impedance of the second via structure satisfies the following relationship:
wherein Z is TSV1 Is the equivalent impedance of the second via structure, Z TSV0 Is the equivalent impedance of the first via structure,
for the impedance correction factor,. Epsilon.r is the relative dielectric constant of the substrate on which the through hole is formed, ε r2 is the relative dielectric constant of the insulating medium in the insulating through hole, and S1 isThe dielectric space equivalent area of the first through hole structure, D is the center distance between the signal through hole and the grounding through hole, D is the aperture of the grounding through hole, n2 is the number of the insulation through holes, and S2 is the area of the insulation through holes.
8. A via structure for a superconducting quantum circuit according to claim 7,
the equivalent impedance and the target impedance of the first via structure satisfy the following relationship:
Z TSV0 < Z 0
wherein Z is TSV0 Is the equivalent impedance of the first via structure, Z 0 Is the target impedance.
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