CN113053622B - Radio frequency inductor with three-dimensional structure and design method thereof - Google Patents
Radio frequency inductor with three-dimensional structure and design method thereof Download PDFInfo
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Abstract
The invention discloses a radio frequency inductor with a three-dimensional structure and a design method thereof, and the radio frequency inductor comprises a first silicon substrate layer and a second silicon substrate layer which are at least arranged in the vertical direction, a first plane spiral metal belt layer arranged on the top of the first silicon substrate layer and a second plane spiral metal belt layer arranged on the top of the second silicon substrate layer, wherein the tail end of the first plane spiral metal belt layer rotating clockwise from an outer ring to an inner ring is electrically connected with the tail end of the second plane spiral metal belt layer rotating clockwise from the outer ring to the inner ring through a first silicon through hole penetrating through the first silicon substrate layer. The invention makes the directions of the electric fields of the upper layer inductance structure and the lower layer inductance structure opposite to each other and offset each other, thereby improving the skin depth, improving the utilization rate of the inductance material and achieving the purposes of improving the quality factor Q and reducing the power consumption.
Description
Technical Field
The invention relates to a radio frequency inductor with a three-dimensional structure and a design method thereof.
Background
In the past decade, wireless communication technology has been rapidly developed, moore's law is still effective today, and communication devices have increasingly become smaller, integrated, and portable. Radio frequency integrated circuits are one of the bases of wireless communication, and the problems to be solved are the present urgent need to solve the problems of integration, miniaturization and high speed. The inductor is a key magnetic energy storage element in many high-performance narrow-band circuits, and is widely used in passive filters, low-noise amplifiers, and the like in radio frequency integrated circuits, and the inductor is also a key performance limiting element in radio frequency integrated circuits, for example, the bandwidth of a low-noise amplifier (LNA), the phase noise of a Voltage Controlled Oscillator (VCO), the loss of a passive filter, and the like, and meanwhile, the size of the inductor is also an important bottleneck limiting the miniaturization of a system. Therefore, how to optimize the performance of the inductor, reduce the size of the inductor, and reduce the cost becomes an important problem in the development of radio frequency integrated circuits.
With the development of deep submicron CMOS technology, the number of metal layers available for the process is increasing, for example, a 0.18 micron process can provide 6 layers of metal, a 0.13 micron process can provide 8 layers of metal, and a 90 nm process can provide 10 layers of metal. The deep submicron CMOS technology is advanced day by day, which is an important technical basis for realizing on-chip multi-layer structure inductance. The general on-chip planar inductor has the advantages of simple structure and excellent performance, can be well supported by design, but has the defects of large volume, poor frequency characteristic and the like, so that the cost is increased, and the development trend of miniaturization and integration is not facilitated. The on-chip multilayer inductor has the main advantages of volume reduction and cost reduction, but because the thickness of the lower layer metal is generally smaller and the parasitic capacitance is generally larger, the performance of the on-chip multilayer inductor is generally considered to be inferior to that of the on-chip planar inductor.
Since Meyer and Nguyen demonstrated for the first time that inductors can be used in silicon-based integrated circuits in 1990, on-chip inductors have gradually gained a great deal of intensive research, and many documents are published on how to optimize the performance of on-chip inductors, and various equivalent circuit models, including lumped and distributed, etc., have been proposed in academia. Nowadays, the planar inductor technology is mature, and the inductor has a high-pass low-resistance current characteristic, which makes the inductor play an important role in many aspects such as filtering, and has been widely used in radio frequency integrated circuits, and the on-chip inductor plays an indispensable role in Low Noise Amplifiers (LNA) and Voltage Controlled Oscillators (VCO), and in addition, the inductor is also used in functional modules such as power amplifiers and mixers, that is, the on-chip inductor is widely used in radio frequency integrated circuits. On-chip inductors have become an integral part of the entire rf integrated circuit.
Only through reasonable application of the inductor, the requirements of high frequency, low noise, low distortion and the like required by modern wireless communication can be correspondingly met. Modern communication usually uses a higher frequency band, and in order to reduce energy loss and increase energy use efficiency, the two module circuits must be impedance-matched, which requires an impedance matching network, and the impedance of the two modules at two ends reaches complex conjugate through the impedance matching network, so as to reduce energy loss to the greatest extent. In the impedance matching network, an inductance is one of indispensable elements, such as an L matching network and a pi matching network.
The planar spiral inductor integrated with the integrated circuit takes silicon as a substrate, and the silicon substrate is conductive, so that the high-frequency characteristic of the planar spiral inductor is in a considerable relation with the silicon substrate. The structure of the planar spiral inductor causes many parasitic problems, such as parasitic capacitance, proximity effect, skin effect, etc. The energy losses of the planar spiral inductor are high in the frequency range we consider (0-20GHz), and specifically include two losses: substrate losses and metal conductor losses.
The substrate loss can be generally divided into an electric field loss and a magnetic field loss, because a parasitic capacitance exists between the coil and the substrate, when a current flows through the inductor, a part of the current is transmitted to the substrate due to a displacement current, and we define the energy loss caused by the electric field coupling as the electric field loss. Similarly, magnetic field loss is defined as energy loss due to magnetic field coupling. The magnetic field coupling generates eddy currents, and the induced electric field energy is converted into joule heat energy to be dissipated, which causes energy loss. Since most of the materials used for the substrate have low resistivity, eddy current flowing through the inductor causes large energy loss.
The loss of the metal conductor and the impedance of the metal conductor which forms the inductor have two loss forms when the frequency is higher and the current flows through the inductor: ohmic losses and eddy current losses.
The source of ohmic loss is the resistivity of metal, and usually we will use a material with low resistivity as a conductor and increase its thickness to reduce the impedance, thereby reducing joule heat generated by the resistance, i.e. reducing ohmic loss. In practical application, we should select the metal material and thickness to influence the resistance, including the number of turns of the coil and the inner and outer radius of the coil.
The alternating current in the inductance coil can generate an alternating magnetic field, the alternating magnetic field can generate an eddy current in the inductance coil, the eddy current can generate an alternating magnetic field with the direction opposite to that of the original magnetic field, and the total magnetic field intensity is the sum of the alternating magnetic field and the original alternating magnetic field and is smaller than the original alternating magnetic field intensity. Near the inner coil, the eddy current is in the same direction as the primary current, where the total current density increases, while, opposite, near the outer coil, the eddy current is in the opposite direction to the primary current, where the total current density decreases. Therefore, the current density which is originally uniform becomes a current density which is no longer uniform and is large inside and small outside, which causes the occurrence of the proximity effect and the skin effect, which finally increase the equivalent resistance of the coil, thereby causing additional energy loss, i.e., the eddy current loss of the metal conductor.
The conventional planar inductor structure is formed by winding a metal material on a silicon surface, and a barrier layer is generally further provided on the silicon substrate to block an electric field reflected from the substrate from affecting the inductor.
In the design of inductors, there is an important parameter that is the skin depth δ, which is expressed as:
where ρ is the resistivity of the material, μ0Is a vacuum permeability, murFor relative permeability, f is the operating frequency of the inductor.
It can be seen from the formula that the higher the operating frequency, the smaller the skin depth, and the higher the loss of inductance. In order to reduce the loss of the inductor, the resistivity of the material needs to be increased, but the electrical performance of the inductor is often reduced by simply increasing the resistivity of the material. In actual manufacturing, the inductor is often made of a metal material, and the resistivity is generally extremely low, so that the area of the on-chip integrated inductor is extremely large, and the area of the substrate is wasted.
Disclosure of Invention
One object of the present invention is to overcome the disadvantages of the prior art, and the present invention provides a radio frequency inductor with three-dimensional structure, which comprises at least a first silicon substrate layer and a second silicon substrate layer arranged in the up-down direction, and a first planar spiral metal strip layer provided on top of said first silicon substrate layer and a second planar spiral metal strip layer provided on top of said second silicon substrate layer, the tail end of the first plane spiral metal belt layer which rotates clockwise from the outer ring to the inner ring is electrically connected with the tail end of the second plane spiral metal belt layer which rotates clockwise from the outer ring to the inner ring through a first silicon through hole which penetrates through the first silicon substrate layer, the head end of the first plane spiral metal strip layer rotating clockwise is electrically connected with a first external lead, and the head end rotating clockwise with the second plane spiral metal strip layer is electrically connected with a second external lead through a second silicon through hole penetrating through the first silicon substrate layer.
And a plurality of concave-convex parts vertical to the upper surface of the base part of the silicon substrate layer are respectively arranged on the tops of the first silicon substrate layer and the second silicon substrate layer.
And the central parts of the first silicon substrate layer and the second silicon substrate layer are provided with soft magnetic material columns along the axial direction.
A design method of a radio frequency inductor with a three-dimensional structure,
for at least a first planar spiral metal belt layer and a second planar spiral metal belt layer, the thickness of metal is increased or metal with low resistivity is used as a conductor, the loss of the metal conductor is reduced, and the quality factor Q value of the inductor is improved, wherein the quality factor Q is as follows:
wherein W represents the energy stored in the inductor, WTRepresenting the energy, omega, dissipated by the inductor per unit time0Representing the angular frequency, P, of the input powerLRepresents the average power loss per unit time;
by using
Wherein f isresIs the self-resonant frequency when the magnetic energy of the inductor is equal to the electric energy thereof, csIs an inductance equivalent capacitance, cpThe inductance is connected with the parasitic equivalent capacitance RSIs an inductive resistance, LSThe actual inductance value of the inductor;
obtain at least the second one ofA planar spiral metal strip layer or a second planar spiral metal strip layer; ensuring that the inductance of at least the first planar spiral metal strip layer or the second planar spiral metal strip layer has a working frequency f lower than the self-resonant frequency fresSo that the inductor is inductive;
setting an inductor at least provided with a first plane spiral metal strip layer or a second plane spiral metal strip layer into an upper and a lower multilayer metal strip structures, wherein the layers of metal strips are connected by adopting a through silicon via; the directions of electric fields of the upper layer inductance structure and the lower layer inductance structure are opposite and mutually offset, and the skin depth is improved;
the soft magnetic material column is arranged in the center of the first silicon substrate layer and the second silicon substrate layer along the axial direction, so that the utilization rate of the magnetic flux of the inductance material is improved, and the quality factor Q is improved;
by providing a plurality of concave-convex portions perpendicular to the upper surface of the base portion of the silicon substrate layer,
by using
Wherein, IWIs a substrate eddy current, and is characterized in that,
induced electromotive force, p, of eddy current electric fieldcResistivity, S, of eddy-current loops in the substrate1Projecting a perimeter, S, for the first or second planar spiral metal strip onto the substrate2The actual perimeter of the concave-convex part projected by the substrate;
by introducing the actual circumference S of the relief2The substrate resistance is increased, and the eddy current loss of the inductive substrate of the first planar spiral metal strip layer or the second planar spiral metal strip layer is reduced;
using HFSS for Ls-f、Q-f、Rs-f、CpF with RPR between the operating frequency f of the inductorpSimulation of the f parameter, RPA simulation model of the radio frequency inductor with a multilayer structure is established for the impedance of the inductor parasitic equivalent capacitor, so that the inductor is obtained.
The working principle of the invention is as follows: setting the inductance of at least a first plane spiral metal belt layer or a second plane spiral metal belt layer as an upper layer and a lower layer to form a multi-metal layer structure, wherein the multi-metal layer structure adopts a Through Silicon Via (TSV) connection mode; the electric field directions of the upper layer inductance structure and the lower layer inductance structure are opposite and mutually offset, the skin depth is improved, the utilization rate of the inductance material is improved, and the purposes of improving the quality factor Q and reducing the power consumption are achieved. The soft magnetic material column is arranged between the central parts of the silicon substrate layers along the axial direction, so that the influence of the proximity effect on the inductor is reduced, the utilization rate of the magnetic flux of the inductor material is improved, and the quality factor Q is improved; by arranging a plurality of concave-convex parts vertical to the upper surface of the base part of the silicon substrate layer, the eddy current loss of the inductance substrate is reduced by utilizing the vertical fin-shaped structure; the substrate resistance value is increased, and the effect of improving the quality factor Q is also obtained.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings;
FIG. 1 is a schematic structural diagram of a three-dimensional radio frequency inductor designed by using TSV;
FIG. 2 is a schematic diagram of a three-dimensional RF inductor and substrate combination using TSV design;
FIG. 3 is a L of the RF inductor with a multi-layer structures-f is a schematic drawing;
FIG. 4 is a schematic diagram of Q-f diagram of a multi-layer RF inductor;
FIG. 5 is a schematic diagram of R of a RF inductor with a multi-layer structures-f is a schematic drawing;
FIG. 6C of RF inductor with multi-layer structurep-f is a schematic drawing;
FIG. 7 is a schematic diagram of R of a RF inductor with a multi-layer structurep-f is a schematic drawing;
101, a second through silicon via, 102, a first through silicon via, 103, a soft magnetic material column, 104, a concave-convex part, 105, a second plane spiral metal strip layer, 106, and a first plane spiral metal strip layer.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention. The following is further explained with reference to the drawings;
in order to overcome the defects of the prior art, the invention provides a radio frequency inductor with a three-dimensional structure in fig. 1 to 7, which comprises at least a first silicon substrate layer and a second silicon substrate layer arranged in the up-down direction, and a first planar spiral metal strip layer 106 arranged on top of said first silicon substrate layer and a second planar spiral metal strip layer 105 arranged on top of said second silicon substrate layer, the tail end of the first planar spiral metal strip layer 106 rotating clockwise from the outer ring to the inner ring is electrically connected with the tail end of the second planar spiral metal strip layer 105 rotating clockwise from the outer ring to the inner ring through a first through silicon via 102 penetrating through the first silicon substrate layer, the first end of the first planar spiral metallic strip layer 106 rotating clockwise is electrically connected to a first external lead, the clockwise rotating head end of the second planar spiral metal strip layer 105 is electrically connected to a second external lead through a second through-silicon via 101 penetrating the first silicon substrate layer.
And a plurality of concave-convex parts 104 vertical to the upper surface of the base part of the silicon substrate layer are respectively arranged on the tops of the first silicon substrate layer and the second silicon substrate layer.
And a soft magnetic material column 103 is arranged at the central parts of the first silicon substrate layer and the second silicon substrate layer along the axial direction.
A design method of a radio frequency inductor with a three-dimensional structure,
for at least the first planar spiral metal strip layer 106 and the second planar spiral metal strip layer 105, the thickness of metal is increased or metal with low resistivity is used as a conductor, so that the loss of the metal conductor is reduced, and the quality factor Q of the inductor is improved, wherein the quality factor Q is as follows:
wherein W represents the energy stored in the inductor, WTRepresenting the energy, omega, dissipated by the inductor per unit time0Representing angular frequency, P, of input powerLRepresents the average power loss per unit time;
by using
Wherein f isresIs the self-resonant frequency when the magnetic energy of the inductor is equal to the electric energy thereof, csIs an inductance equivalent capacitance, cpThe inductance is connected with the parasitic equivalent capacitance RSIs an inductive resistance, LSThe actual inductance value of the inductor;
obtaining the working frequency range of the inductance of at least a first planar spiral metal strip layer 106 or a second planar spiral metal strip layer 105; ensuring that the inductance of at least the first planar spiral metal strip layer 106 or the second planar spiral metal strip layer 105 has a working frequency f lower than the self-resonant frequency fresSo that the inductor is inductive;
setting an inductor at least provided with a first planar spiral metal strip layer 106 or a second planar spiral metal strip layer 105 into an upper and a lower multilayer metal strip structures, wherein the layers of metal strips are connected by silicon through holes; the directions of electric fields of the upper layer inductance structure and the lower layer inductance structure are opposite and mutually offset, and the skin depth is improved;
the soft magnetic material column 103 is arranged in the center of the first silicon substrate layer and the second silicon substrate layer along the axial direction, so that the utilization rate of the magnetic flux of the inductance material is improved, and the quality factor Q is improved;
by providing the asperities 104 perpendicular to the upper surface of the base portion of the silicon substrate layer,
by using
Wherein, IWIs a substrate eddy current, and is,
induced electromotive force, p, of eddy current electric fieldcIs the resistivity, S, of the eddy current circuit of the substrate1Projecting the perimeter, S, onto the substrate for the first or second planar spiral metal strip2The actual perimeter of the relief 104 projected under the substrate;
by introducing the actual circumference S of the relief 1042The resistance of the substrate is increased, and the eddy current loss of the inductance substrate of the first plane spiral metal strip layer 106 or the second plane spiral metal strip layer 105 is reduced;
using HFSS for Ls-f、Q-f、Rs-f、CpF with RPR between the operating frequency f of the inductorpSimulation of the f parameter, RPA simulation model of the radio frequency inductor with a multilayer structure is established for the impedance of the inductor parasitic equivalent capacitor, so that the inductor is obtained.
The first planar spiral metal strip layer 106 and the second planar spiral metal strip layer 105 are respectively arranged on the corresponding silicon substrates, and conductive plugs are formed between the spaced silicon layers through the arranged silicon through holes, so that the first planar spiral metal strip layer 106 and the second planar spiral metal strip layer 105 are connected in series in the spaced silicon layers.
Inductance generally has three very important criteria, which are: inductance L, quality factor Q, self-resonant frequency fresWhere the calculation of the inductance is difficult to obtain an accurate value, it is usually calculated in the form of a software simulation.
For commonly used rf integrated circuits, the Q value of the inductor is very important, the effective power, noise figure, bandwidth, etc. of the circuit are greatly affected by it, and the performance of the circuit is often limited by it. The magnitude of the loss of the matching network, the performance of the bandpass filter, etc. The quality factor Q characterizes the loss behavior of the inductor, which directly affects the inductor behavior and is proportional to the ratio of the stored energy to the energy lost per unit time.
When the frequency is higher thanfresWhen the frequency is lower than f, the inductor shows the capacityresThe inductance can only exhibit inductive behavior, that is, at frequencies above fresThe inductance becomes a capacitance, therefore, fresThe available working frequency range of the inductor is determined, and when the inductor is used, the working frequency is required to be lower than fresSo that the inductor can work normally.
On the basis of the planar spiral inductor, the radio frequency inductor is designed into a multilayer structure, wherein a plurality of metal layers are connected by TSV, so that the directions of electric fields of upper and lower planar spiral inductor structures are just opposite and can be mutually offset, the skin depth can be effectively improved, the utilization rate of inductor materials is improved, and the purposes of improving quality factors and reducing power consumption are achieved. The method has positive significance for reducing the cost and the volume, and can effectively reduce the area of the substrate and reduce the energy loss.
Fig. 1 and fig. 2 are schematic diagrams of the novel three-dimensional CMOS integrated inductor structure, in which an upper layer inductor and a lower layer inductor are connected by a TSV (through silicon via), and the current directions of the upper layer inductor and the lower layer inductor are opposite to each other, thereby improving the circuit performance. The resistivity of the inductor is improved by the addition of the TSV, the skin depth can be effectively increased on the premise of not influencing the magnetic conductivity, and the purpose of reducing power consumption is achieved. In addition, the soft magnetic material column 103 is arranged between the central parts of the silicon substrate layers along the axial direction, so that the utilization rate of the magnetic flux of the inductance material is improved, the influence of the proximity effect on the inductance is reduced, and the quality factor Q is improved; by arranging the concave-convex parts 104 vertical to the upper surface of the base part of the silicon substrate layer and utilizing the vertical fin-shaped structure, the inductor is suspended on the surface of the substrate, an air gap with very low dielectric constant is introduced, the coupling capacitance of the substrate is reduced, the eddy current path is limited, the resistance value of the substrate is increased, the eddy current loss of the inductor substrate is reduced, and the effect of improving the quality factor Q is also obtained. By using soft ferromagnetic material, such as ferrite material, the inductance value is improved to obtain larger Q value, the distance between the inductance coil and the substrate is increased, and the substrate eddy current is also reduced.
The metal wire of the planar spiral inductor is designed by adopting the following parameters: the metal wire is made of copper material, the number of turns is 3, the outer diameter is 202.5 mu m, the line width is 15 mu m, and the space is 1.5 mu m. The first planar spiral metal strip layer 106 and the second planar spiral metal strip layer are used as a demonstration experiment, the model in practice has strong expansibility, and the model can be simulated by using HFSS of the radio frequency inductor with the multilayer structure.
FIG. 3 is a L diagram of a multilayer RF inductor exemplified by two metal stripss-f schematic representation.
Meanwhile, in combination with other figures, Q-f and R can be obtaineds-f、Cp-f and Rp-image of f:
the Q-f schematic diagram of the multilayer structure RF inductor is shown in FIG. 4;
r of multilayer structure radio frequency inductors-f is schematically shown in figure 5;
c of multilayer structure radio frequency inductorp-f is schematically shown in figure 6;
r of multilayer structure radio frequency inductorp-f is schematically shown in figure 7; RP is the impedance of the equivalent capacitance.
From the above simulation results, we can obtain that the maximum Q value can reach 20, Rs is about 7 Ω, Cp is about 0.1fF, Rp is about 0 Ω in this frequency band, and Ls is about 1.7 nH.
Compared with the planar spiral inductor, the inductance value is slightly reduced, the Q value is higher, the Rs and the Cp are slightly reduced, other parameters are acceptable, the Q value is improved after the planar spiral inductor is subjected to the planar spiral inductor, the balance between the Q value and the inductance value is achieved, and the obtained inductor can meet the required requirements.
In the description herein, references to the description of "one embodiment" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (1)
1. A design method of a radio frequency inductor with a three-dimensional structure is characterized in that,
the radio frequency inductor with the three-dimensional structure comprises a first silicon substrate layer and a second silicon substrate layer which are at least arranged in the vertical direction, a first plane spiral metal belt layer arranged on the top of the first silicon substrate layer and a second plane spiral metal belt layer arranged on the top of the second silicon substrate layer, wherein the tail end of the first plane spiral metal belt layer rotating clockwise from an outer ring to an inner ring is electrically connected with the tail end of the second plane spiral metal belt layer rotating clockwise from the outer ring to the inner ring through a first silicon through hole penetrating through the first silicon substrate layer;
a plurality of concave-convex parts vertical to the upper surface of the base part of the silicon substrate layer are respectively arranged on the top of the first silicon substrate layer and the top of the second silicon substrate layer;
the center parts of the first silicon substrate layer and the second silicon substrate layer are provided with soft magnetic material columns along the axial direction;
for at least a first planar spiral metal belt layer and a second planar spiral metal belt layer, the thickness of metal is increased or metal with low resistivity is used as a conductor, the loss of the metal conductor is reduced, and the quality factor Q value of the inductor is improved, wherein the quality factor Q is as follows:
wherein W represents the energy stored in the inductor, WTIndicating the loss of inductance per unit timeEnergy of, omega0Representing the angular frequency, P, of the input powerLRepresents the average power loss per unit time;
by using
Wherein f isresIs the self-resonant frequency when the magnetic energy of the inductor is equal to the electric energy thereof, csIs an inductance equivalent capacitance, cpThe inductance is connected with the parasitic equivalent capacitance RSIs an inductive resistance, LSThe actual inductance value of the inductor is obtained;
obtaining the working frequency range of the inductance of at least a first plane spiral metal strip layer or a second plane spiral metal strip layer; ensuring that the inductance of at least the first or second planar spiral metal strip layer has a working frequency f lower than the self-resonant frequency fresSo that the inductor is inductive;
setting an inductor at least provided with a first plane spiral metal belt layer or a second plane spiral metal belt layer into an upper and a lower multilayer metal belt structures, wherein the layers of metal belts are connected by silicon through holes; the directions of electric fields of the upper layer inductance structure and the lower layer inductance structure are opposite and mutually offset, and the skin depth is improved;
the soft magnetic material column is arranged in the center of the first silicon substrate layer and the second silicon substrate layer along the axial direction, so that the utilization rate of the magnetic flux of the inductance material is improved, and the quality factor Q is improved;
by providing a plurality of concave-convex portions perpendicular to the upper surface of the base portion of the silicon substrate layer,
by using
Wherein, IWIs a substrate eddy current, and is,
induced electromotive force, p, of eddy current electric fieldcFor substrate eddy current circuitResistivity of (S)1Projecting a perimeter, S, for the first or second planar spiral metal strip onto the substrate2The actual perimeter of the concave-convex part projected by the substrate;
by introducing the actual circumference S of the relief2The substrate resistance is increased, and the eddy current loss of the inductive substrate of the first planar spiral metal strip layer or the second planar spiral metal strip layer is reduced;
using HFSS for Ls-f、Q-f、Rs-f、CpF with RPR between the operating frequency f of the inductorpSimulation of the f parameter, RPA simulation model of the radio frequency inductor with a multilayer structure is established for the impedance of the inductor parasitic equivalent capacitor, so that the inductor is obtained.
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