CN112652574B - Three-position TSV based on carbon nano tube and parameter extraction method thereof - Google Patents
Three-position TSV based on carbon nano tube and parameter extraction method thereof Download PDFInfo
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- 239000002041 carbon nanotube Substances 0.000 title claims abstract description 76
- 229910021393 carbon nanotube Inorganic materials 0.000 title claims abstract description 75
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- 239000002048 multi walled nanotube Substances 0.000 claims abstract description 55
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- 239000010410 layer Substances 0.000 claims description 28
- 238000010521 absorption reaction Methods 0.000 claims description 12
- 229910021389 graphene Inorganic materials 0.000 claims description 12
- 230000005684 electric field Effects 0.000 claims description 9
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- 229910052710 silicon Inorganic materials 0.000 description 7
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- 241000724291 Tobacco streak virus Species 0.000 description 6
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- 239000002109 single walled nanotube Substances 0.000 description 4
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- 238000003780 insertion Methods 0.000 description 3
- 230000037431 insertion Effects 0.000 description 3
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 description 2
- 239000003575 carbonaceous material Substances 0.000 description 2
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- 150000001875 compounds Chemical class 0.000 description 1
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- 239000000945 filler Substances 0.000 description 1
- 235000020640 mackerel Nutrition 0.000 description 1
- 238000004377 microelectronic Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 230000008646 thermal stress Effects 0.000 description 1
- WFKWXMTUELFFGS-UHFFFAOYSA-N tungsten Chemical compound [W] WFKWXMTUELFFGS-UHFFFAOYSA-N 0.000 description 1
- 229910052721 tungsten Inorganic materials 0.000 description 1
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Abstract
The invention discloses a three-position TSV based on a carbon nano tube and a parameter extraction method thereof, wherein the three-position TSV comprises a TSV structure arranged in a substrate and three signal pads arranged at the top of the TSV structure, and the TSV structure comprises a through hole formed in the substrate and a plurality of bundles of carbon nano tubes uniformly filled in the through hole; the three signal pads are paved at different positions on the top of the TSV structure in a mutually-spaced mode and are respectively communicated with the multi-wall carbon nanotubes below the three signal pads so as to form three signal transmission channels on one TSV structure. The three-bit TSV enables one TSV structure to simultaneously transmit three independent signals through the three signal pads, so that the number of I/O pins between an upper layer chip and a lower layer chip connected with the three-bit TSV is doubled, the chip integration level is improved, the process cost is reduced, and the three-bit TSV has better transmission characteristics.
Description
Technical Field
The invention belongs to the technical field of microelectronics, and particularly relates to a three-position TSV based on a carbon nano tube and a parameter extraction method thereof.
Background
The three-dimensional (3D) integration technology can realize heterogeneous integration while reducing cost, which provides a wide development platform for realizing supermoore's law, and facilitates the integration of different materials (silicon, iii-v compounds, carbon nanotubes, etc.) and processes (memory, logic circuits, radio frequency circuits, micromechanical systems, etc.) into one chip. TSV (Through Silicon Via, through-silicon via) technology has advanced the development of three-dimensional integrated circuits that can reduce the limitations of conventional planar integrated circuits, shorten interconnect lengths, increase integration density, and reduce power consumption.
TSVs have proven to be critical components affecting the overall performance of 3D ICs as conductive vias connecting the upper and lower chips. Carbon Nanotubes (CNT) are an emerging material that, due to their superior electrical, thermal, and mechanical properties, can generally replace copper (Cu) and tungsten (W) as TSV fill materials. The resistance of the CNT bundles per micron is about 2.5 times lower than Cu in the conduction direction, whereas the resistance between adjacent CNTs within the bundle is on the order of megaohms. However, TSVs occupy much more area than on-chip channels. Furthermore, the number of TSVs within any substrate is limited by the difference between the coefficients of thermal expansion of the TSV filler material and the substrate. In order to prevent cracking of the substrate due to thermal stress, the area occupied by the TSVs in the silicon substrate is limited to about 2% of the substrate area. Therefore, how to solve the I/O (input/output) limitation between layers in a three-dimensional structure is a major problem.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a three-position TSV based on a carbon nano tube and a parameter extraction method thereof. The technical problems to be solved by the invention are realized by the following technical scheme:
one aspect of the present invention provides a carbon nanotube-based three-bit TSV, including a TSV structure disposed in a substrate and three signal pads disposed on top of the TSV structure, wherein,
the TSV structure comprises a through hole formed in the substrate and a plurality of bundles of carbon nanotubes uniformly filled in the through hole;
the three signal pads are paved at different positions on the top of the TSV structure in a mutually-spaced mode and are respectively communicated with the multi-wall carbon nanotubes below the three signal pads so as to form three signal transmission channels on one TSV structure.
In one embodiment of the present invention, the carbon nanotubes are multiwall carbon nanotubes, and the three signal pads are all multi-layer graphene materials.
In one embodiment of the present invention, the three signal pads are of a fan-shaped structure with the same diameter, and the fan-shaped angles of the fan-shaped structures are all 120 °.
Another aspect of the present invention provides a method for extracting a parasitic parameter of a three-bit TSV based on a carbon nanotube, which is used for extracting the parasitic parameter of the three-bit TSV based on a carbon nanotube described in any one of the above embodiments, and includes:
s1: constructing a three-position TSV physical model based on the carbon nano tube by using simulation software;
s2: extracting impedance parameters of the three-bit TSV by utilizing an electronic effective mean free path during signal transmission in the three-bit TSV;
s3: extracting the equivalent complex conductivity of the three-bit TSV;
s4: extracting capacitance parameters of the three-bit TSV;
s5: and establishing an equivalent circuit model of the three-bit TSV and carrying out S parameter simulation on a physical model and an equivalent circuit of the three-bit TSV.
In one embodiment of the present invention, the S2 includes:
s21: acquiring the number of walls of the multi-wall carbon nano tube filled in the TSV structure and the diameter of each layer of wall;
s22: obtaining the number of conducting channels of the ith layer wall of the multi-wall carbon nano tube:
wherein D is i Represents the diameter of the i-th wall, T represents the ambient temperature, D T Is constant, D T =1300 nm·k, K representing kelvin temperature units;
s23: acquiring an effective mean free path of electrons in the multiwall carbon nanotube during signal transmission;
s24: obtaining the self-impedance of a single-layer wall in the multi-wall carbon nano tube by utilizing the electron effective average free path;
s25: and obtaining the impedance of the three-position TSV by utilizing the self impedance of the single-layer wall in the multi-wall carbon nano tube.
In one embodiment of the present invention, the S23 includes:
s231: obtaining an average free path of electrons generated by phonon scattering:
wherein D is out The diameter of the outermost wall of the multiwall carbon nanotube, T represents the ambient temperature;
s232: obtaining the mean free path of phonon absorption:
wherein lambda is op Represents the average length of electron emission phonons, f op Following the bose-einstein distribution, f op (300) A glass-einstein distribution function value representing when the temperature is taken at 300K;
s233: acquiring an average free path of phonon emission caused by an electric field:
wherein,representing phonon energy, q representing the charge quantity of electrons, V representing the electric field voltage, and H representing the height of the TSV structure;
s234: acquiring an average free path of phonon emission caused by absorption of optical phonons:
s235: acquiring an effective mean free path of electrons in the multiwall carbon nanotube during signal transmission:
in one embodiment of the present invention, the self-impedance of the single-wall in the multi-wall carbon nanotube is:
wherein R is mc 、R Q 、R S And L K Respectively representing the incomplete contact resistance, quantum contact resistance, scattering resistance and kinetic inductance of a single multiwall carbon nanotube, wherein h represents the Planck constant; v F Representing the fermi velocity, j representing the imaginary part of the complex number, ω representing the angular frequency of the propagating signal within the three-bit TSV.
In one embodiment of the present invention, the impedance of the three-bit TSV is:
wherein N is shell Representing the number of walls of the multiwall carbon nanotubes.
In one embodiment of the present invention, the S3 includes:
s31: obtaining the equivalent complex conductivity of the multi-wall carbon nano tube bundle of the three-position TSV in the vertical direction:
s32: obtaining the equivalent complex conductivity of the multi-wall carbon nano tube bundle of the three-position TSV in the horizontal direction:
σ horizontal ＝10 -7 ·σ vertical
in one embodiment of the present invention, the S4 includes:
s41: obtaining the cross-sectional area of the TSV structure along the longitudinal direction of the multi-wall carbon nano tube bundle:
A＝r TSV ·H·N bits ，
wherein N is bits Represents the number of independent signals propagating in the three-bit TSV, r TSV Represents the radius of the TSV structure, and H represents the height of the TSV structure；
S42: acquiring capacitance between any two bits in the three-bit TSV:
where s represents the distance between adjacent signal pads, ε and ε 0 The relative permittivity and vacuum permittivity of the carbon nanotube are shown, respectively.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the three-bit TSV based on the carbon nano tube, the three signal pads are connected through the top, so that one TSV structure can transmit three independent signals at the same time, the number of input/output (I/O) pins between an upper layer chip and a lower layer chip which are connected through the three-bit TSV can be doubled, an extra substrate area is not occupied, the problem of limiting an I/O tube angle between the upper layer chip and the lower layer chip is solved, the chip integration level is improved, the process cost is reduced to a certain extent, and compared with a traditional TSV filled with a Cu conductor, the TSV structure has better transmission characteristics, and the requirement on TSV signal transmission is met.
2. The invention prepares the signal pad by utilizing the multilayer graphene, and the graphene and the carbon nano tube are both covalent bonding carbon-based materials, so that the contact resistance between the original metal and the carbon nano tube can be greatly reduced.
3. In the method for extracting the generation parameters, the mean free path of electrons generated by phonon scattering, the mean free path of phonon absorption, the mean free path of phonon emission caused by an electric field and the mean free path of phonon emission caused by absorption of optical phonons are fully considered, so that the impedance parasitic parameters of the three-bit TSV are extracted more accurately.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic structural diagram of a three-bit TSV based on a carbon nanotube according to an embodiment of the present invention;
fig. 2 is a flowchart of a method for extracting parameters of a three-bit TSV based on a carbon nanotube according to an embodiment of the present invention;
fig. 3 is a flowchart of an impedance parameter extraction process of a three-bit TSV based on a carbon nanotube according to an embodiment of the present invention;
fig. 4 is a flowchart of a three-bit TSV capacitance parameter extraction process based on a carbon nanotube according to an embodiment of the present invention;
fig. 5 is a three-bit TSV equivalent circuit diagram based on a carbon nanotube according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a simulation working principle of a three-bit TSV based on a carbon nanotube according to an embodiment of the present invention;
fig. 7a to 7d are S-parameter diagrams of a three-bit TSV based on carbon nanotubes according to an embodiment of the present invention.
Detailed Description
In order to further illustrate the technical means and effects adopted by the invention to achieve the preset aim, the following is a detailed description of a three-position TSV based on carbon nanotubes and a parameter extraction method thereof according to the invention with reference to the accompanying drawings and the detailed description.
The foregoing and other features, aspects, and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments when taken in conjunction with the accompanying drawings. The technical means and effects adopted by the present invention to achieve the intended purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only, and are not intended to limit the technical scheme of the present invention.
It should be noted that in this document relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in an article or apparatus that comprises the element.
Example 1
Fig. 1 is a schematic structural diagram of a three-bit TSV based on a carbon nanotube according to an embodiment of the present invention. The three-bit TSV comprises a TSV structure 1 arranged in a substrate and three signal pads 2 arranged on top of the TSV structure 1. The TSV structure 1 includes a via 11 opened in the substrate and a plurality of bundles of carbon nanotubes 12 uniformly filled inside the via 11. In the present embodiment, the carbon nanotubes 12 are multiwall carbon nanotubes. It should be understood that the carbon nanotubes may be regarded as being formed by curling graphene sheets, and the number of layers of the graphene sheets may be divided into: single-walled carbon nanotubes (or Single-walled Carbon nanotubes, SWCNTs) and Multi-walled carbon nanotubes (or Multi-layered carbon nanotubes, multi-walled Carbon nanotubes, MWCNTs). The single-wall carbon nanotube is formed by winding one layer of graphene sheets, and the multi-wall carbon nanotube is formed by winding a plurality of layers of graphene sheets.
Further, three signal pads 2 are laid at different positions on top of the TSV structure 1 in a spaced manner, and respectively communicate with the multiwall carbon nanotubes 12 thereunder to form three signal transmission channels on one TSV structure 1. In this embodiment, the three signal pads 2 are all made of multiple layers of graphene materials and have a fan-shaped structure with the same diameter, the fan-shaped angles of the fan-shaped structures are 120 degrees, and the spacing s is about 50 nm. Due to the anisotropy of the carbon nanotubes, the TSV is separated into three independent parts by connecting three signal pads 2 on top to constitute the three-bit TSV of the present embodiment, each of which can transmit an independent signal.
According to the three-position TSV based on the carbon nano tube, three signal pads are connected through the top, so that three independent signals can be transmitted simultaneously through one TSV structure, the number of input/output (I/O) pins between an upper layer chip and a lower layer chip which are connected through the three-position TSV can be doubled, an additional substrate area is not occupied, the problem of limiting an I/O tube angle between the upper layer chip and the lower layer chip is solved, the chip integration level is improved, the process cost can be reduced to a certain extent, and compared with a traditional TSV filled with a Cu conductor, the TSV structure has better transmission characteristics, and the requirement on TSV signal transmission is met. In addition, the signal pad is prepared by using the multilayer graphene, and the graphene and the carbon nano tube are both covalently bonded carbon-based materials, so that the contact resistance between the original metal and the carbon nano tube can be greatly reduced.
Example two
On the basis of the above embodiments, the present embodiment provides a method for extracting parameters of three-position TSVs of carbon nanotubes. Referring to fig. 2, fig. 2 is a flowchart of a method for extracting parameters of a three-bit TSV based on carbon nanotubes according to an embodiment of the present invention. The method comprises the following steps:
s1: constructing a three-position TSV physical model based on the carbon nano tube by using simulation software;
the three-bit TSV comprises a TSV structure 1 arranged in a substrate and three signal pads 2 arranged on top of the TSV structure 1. The TSV structure 1 includes a via 11 opened in the substrate and a plurality of bundles of carbon nanotubes 12 uniformly filled inside the via 11. In the specific model building process, firstly, a cuboid model is built in HFSS software to serve as a silicon substrate, two cylinders are etched in the silicon substrate to serve as silicon through holes, and as the HFSS does not contain carbon nano tubes which serve as TSV filling materials, copper conductors with conductivity equal to 4 are used for replacing CNT bundles, then, one cylinder is built to serve as a TSV top layer signal pad, the signal pad is etched in a rectangular mode with three equal lengths and an angle of 120 degrees, the material is multilayer graphene, and building of the three-position TSV physical model is completed.
S2: extracting impedance parameters of the three-bit TSV by utilizing an electronic effective mean free path during signal transmission in the three-bit TSV;
specifically, referring to fig. 3, fig. 3 is a flowchart illustrating an impedance parameter extraction process of a three-bit TSV based on a carbon nanotube according to an embodiment of the present invention. The step S2 specifically comprises the following steps:
s21: obtaining the wall number of the multi-wall carbon nano tube filled in the TSV structure and the diameter of each layer of wall
Specifically, the number of walls (i.e., the number of crimping layers) of the multi-wall carbon nanotube can be expressed as:
wherein, inter [. Cndot.]Represents an integer of D out Represents the outermost wall diameter of the multiwall carbon nanotubes, D in The innermost wall diameter of the multiwall carbon nanotube is represented, m represents the distance between two adjacent layers of walls of the multiwall carbon nanotube, which is van der Waals spacing, and 0.34nm is taken.
Further, the diameter of the i-th wall was calculated as:
D i ＝D out -2m·(i-1),1≤i≤N shell 。
s22: obtaining the number of conducting channels of the ith layer wall of the multi-wall carbon nano tube:
wherein D is i Represents the diameter of the i-th wall, T represents the ambient temperature, D T Is constant, D T =1300 nm·k, K representing kelvin temperature units.
S23: and obtaining an effective mean free path of electrons in the multi-wall carbon nano tube during signal transmission.
There are several scattering mechanisms for electrons in carbon nanotubes that affect their mean free path, including acoustic, optical, and regional boundary phonon scattering, as well as impurity and defect scattering. Since different scattering mechanisms have different scattering lengths and related parameters, the effective mean electron free path λ of a carbon nanotube is the combined effect of all scattering lengths and depends on many parameters, such as tube diameter, height and temperature.
In this embodiment, the effective mean free path λ of electrons in the carbon nanotubes can be expressed by the law of mackerel:
wherein lambda is ac Is the mean free path of electrons due to phonon scattering; lambda (lambda) op,abs As the mean free path for phonon absorption,an average free path for the electric field to induce phonon emission; />The mean free path of phonon emission is induced for absorption of optical phonons.
Specifically, the mean free path of electrons due to phonon scattering is:
wherein D is out Is the diameter of the outermost wall of the multiwall carbon nanotube, T represents the ambient temperature.
The mean free path of phonon absorption is:
wherein lambda is op Mean length of phonon emitted by high-energy electron, lambda op The value of (2) is related to the diameter of the carbon nano tube and is approximately equal to 56.4D out ，f op (300) The glass-einstein distribution function value when the temperature was taken at 300K was shown.
f op Following the bosch-einstein distribution, it can be expressed as:
wherein k is B Is a boltzmann constant,is approximately 0.19eV for phonon energy.
Further, the mean free path of phonon emission induced by the electric field is:
wherein f op Also following the bose-einstein distribution,for phonon energy, q represents electrons, V represents the magnitude of the electric field voltage, and H represents the height of the TSV structure.
The mean free path of phonon emission due to absorption of optical phonons is:
wherein f op The bose-einstein distribution was also followed.
S24: obtaining self-impedance of single-wall in multi-wall carbon nano tube by utilizing electron effective average free path
Specifically, the self-impedance of the single-wall in the multi-wall carbon nanotube is:
wherein R is mc 、R Q 、R S And L K The method respectively represents the incomplete contact resistance, the quantum contact resistance, the scattering resistance and the kinetic inductance of the single multi-arm carbon nano tube, wherein the incomplete contact resistance and the quantum contact resistance are resistances generated by unsmooth contact surfaces, the scattering resistance is the resistance caused by impurity defects, and the kinetic inductance is the inherent inductance of the carbon nano tube; h represents the height of the TSV structure; n (N) i Representing the number of conductive channels of the ith layer wall of the multiwall carbon nanotube; h is the Planck constant; v F (＝8×10 5 m/s) is the fermi speed; λ is the electron effective mean free path of the multiwall carbon nanotubes, j represents the imaginary part of the complex number, ω represents the angular frequency of the propagating signal within the TSV.
S25: obtaining the impedance of the three-position TSV by utilizing the self impedance of the single-layer wall in the multi-wall carbon nano tube
The impedance of the three-bit TSV, namely the impedance of the multiwall carbon nanotube is as follows:
wherein N is shell The number of walls of the multiwall carbon nanotubes is represented.
S3: extracting the equivalent complex conductivity of the three-bit TSV;
specifically, the equivalent complex conductivity of the multi-wall carbon nanotube bundles of the three-position TSV in the vertical direction is obtained:
obtaining the equivalent complex conductivity of the multi-wall carbon nano tube bundle of the three-position TSV in the horizontal direction:
σ horizontal ＝10 -7 ·σ 2vertical 。
s4: extracting capacitance parameters of the three-bit TSV;
in this embodiment, the capacitance between any two of the three-bit TSVs can be approximated by an expression of parallel plate capacitance, and the width S of the space between two adjacent bits can be analogous to the distance d between the parallel plates, and the area of the parallel plates is the cross-sectional area of the TSV structure along the longitudinal direction of the carbon nanotube bundles.
Specifically, referring to fig. 4, fig. 4 is a flowchart of a three-bit TSV capacitance parameter extraction process based on a carbon nanotube according to an embodiment of the present invention. The step S4 includes:
s41: obtaining the cross-sectional area of the TSV structure along the longitudinal direction of the multi-wall carbon nano tube bundle:
A＝r TSV ·H·N bits ，
wherein N is bits Represents the number of independent signals propagating in the three-bit TSV, r TSV And representing the radius of the TSV structure, and H represents the height of the TSV structure.
S42: acquiring capacitance between any two bits in the three-bit TSV:
where s represents the distance between adjacent signal pads, ε and ε 0 The relative permittivity and vacuum permittivity of the carbon nanotube are shown, respectively. It should be noted that, the capacitance between any two bits is the capacitance between adjacent transmission channels formed by different signal pads and carbon nanotube bundles.
Further, on the basis of the above steps, the parameter extraction method in the embodiment of the present invention further includes:
s5: and establishing an equivalent circuit model of the three-bit TSV, and performing S parameter simulation on the physical model of the three-bit TSV and the equivalent circuit to verify the accuracy of the equivalent circuit and parameter extraction.
Specifically, an equivalent circuit model of the three-bit TSV is built in ADS software, please refer to fig. 5, fig. 5 is a three-bit TSV equivalent circuit diagram based on carbon nanotubes, wherein R inside Corresponding to parasitic resistance inside the three-bit TSV bit, R outside Corresponding to parasitic resistance between three TSV bits, C inside The parasitic resistance between bits is an manifestation of carbon nanotube anisotropy corresponding to the parasitic capacitance inside a three bit TSV, which impedes signal transmission from bit to bit. Referring to fig. 6, fig. 6 is a schematic diagram illustrating a simulation working principle of a three-position TSV based on a carbon nanotube according to an embodiment of the present invention. The terminals T1 to T6 are signal source terminals virtually added in HFSS software, and a total of 6 virtual signal source terminals are respectively added on each bit surface of the TSV. And then, respectively carrying out S parameter simulation on the three-bit TSV physical model based on the carbon nano tube and the equivalent circuit in HFSS and ADS software, and verifying the accuracy of the equivalent circuit and parameter extraction. Referring to fig. 7a to 7d, fig. 7a to 7d are S-parameter diagrams of a three-bit TSV based on carbon nanotubes according to an embodiment of the present invention. Simulating S11, S21, S31 and S41 curves in HFSS software, wherein S11 refers to return loss between a signal sent from a bit corresponding to the terminal T1 and a received signal; s21 refers to the slave terminalThe bit corresponding to the terminal T1 sends out signals, and the bit corresponding to the terminal T2 receives the insertion loss between the signals; s31 refers to the insertion loss between signals sent from the bit corresponding to the terminal T1 and received from the bit corresponding to the terminal T3; s41 denotes an insertion loss between signals received from the bit corresponding to the terminal T1 and the bit corresponding to the terminal T4.
The result shows that the S parameter simulation based on the three-bit TSV of the carbon nano tube in the HFSS software and the S parameter simulation based on the ADS software can form good fitting degree, and the result shows that the S parameter curves of the two are basically fitted, the error is within 1.2%, and the correctness of the physical model and the equivalent circuit of the three-bit TSV based on the carbon nano tube in the whole frequency range provided by the embodiment is further verified.
According to the three-bit TSV based on the carbon nano tube, three signal pads are connected through the top, so that one TSV structure can transmit three independent signals at the same time, the number of input/output (I/O) pins between an upper layer chip and a lower layer chip connected through the three-bit TSV can be doubled, an extra substrate area is not occupied, the problem of limiting an I/O tube angle between the upper layer chip and the lower layer chip is solved, and the chip integration level is improved. In addition, in the parameter extraction method of the present embodiment, the mean free path of electrons generated by phonon scattering, the mean free path of phonon absorption, the mean free path of phonon emission caused by an electric field, and the mean free path of phonon emission caused by absorption of optical phonons are fully considered, so that the impedance parasitic parameters of the three-bit TSV can be extracted more accurately.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.
Claims (7)
1. The parameter extraction method for the three-position TSV based on the carbon nano tube is characterized by being used for extracting parasitic parameters of the three-position TSV based on the carbon nano tube, wherein the three-position TSV based on the carbon nano tube comprises a TSV structure arranged in a substrate and three signal pads arranged on the top of the TSV structure, and the TSV structure comprises a through hole formed in the substrate and a plurality of bundles of carbon nano tubes uniformly filled in the through hole; the three signal pads are paved at different positions at the top of the TSV structure in a mutually spaced mode and are respectively communicated with the multi-wall carbon nanotubes below the three signal pads so as to form three signal transmission channels on one TSV structure; the carbon nano tube is a multi-wall carbon nano tube, and the three signal pads are all made of multi-layer graphene materials;
the method comprises the following steps:
s1: constructing a three-position TSV physical model based on the carbon nano tube by using simulation software;
s2: extracting impedance parameters of the three-bit TSV by utilizing an electronic effective mean free path during signal transmission in the three-bit TSV;
s3: extracting the equivalent complex conductivity of the three-bit TSV;
s4: extracting capacitance parameters of the three-bit TSV;
s5: and establishing an equivalent circuit model of the three-bit TSV and carrying out S parameter simulation on a physical model and an equivalent circuit of the three-bit TSV.
2. The method for extracting parameters of three-bit TSV based on carbon nanotubes according to claim 1 wherein the S2 includes:
s21: acquiring the number of walls of the multi-wall carbon nano tube filled in the TSV structure and the diameter of each layer of wall;
s22: obtaining the number of conducting channels of the ith layer wall of the multi-wall carbon nano tube:
wherein D is i Represents the diameter of the i-th wall, T represents the ambient temperature, D T Is constant, D T =1300 nm·k, K representing kelvin temperature units;
s23: acquiring an effective mean free path of electrons in the multiwall carbon nanotube during signal transmission;
s24: obtaining the self-impedance of a single-layer wall in the multi-wall carbon nano tube by utilizing the electron effective average free path;
s25: and obtaining the impedance of the three-position TSV by utilizing the self impedance of the single-layer wall in the multi-wall carbon nano tube.
3. The method for extracting parameters of three-bit TSV based on carbon nanotubes according to claim 2 wherein the S23 includes:
s231: obtaining an average free path of electrons generated by phonon scattering:
wherein D is out The diameter of the outermost wall of the multiwall carbon nanotube, T represents the ambient temperature;
s232: obtaining the mean free path of phonon absorption:
wherein lambda is op Represents the average length of electron emission phonons, f op Following the bose-einstein distribution, f op (300) A glass-einstein distribution function value representing when the temperature is taken at 300K;
s233: acquiring an average free path of phonon emission caused by an electric field:
wherein,represents phonon energy, q represents the charge amount of electrons, V represents the electric field voltage,h represents the height of the TSV structure;
s234: acquiring an average free path of phonon emission caused by absorption of optical phonons:
s235: acquiring an effective mean free path of electrons in the multiwall carbon nanotube during signal transmission:
4. the method for extracting parameters of three-position TSV based on carbon nanotubes according to claim 3, wherein the self-impedance of the single-wall in the multi-wall carbon nanotubes is:
wherein R is mc 、R Q 、R S And L K Respectively representing the incomplete contact resistance, quantum contact resistance, scattering resistance and kinetic inductance of a single multiwall carbon nanotube, h represents the Planck constant, v F Representing the fermi velocity, j representing the imaginary part of the complex number, ω representing the angular frequency of the propagating signal within the three-bit TSV.
5. The method for extracting parameters of three-bit TSV based on carbon nanotubes according to claim 4, wherein the impedance of the three-bit TSV is:
wherein N is shell Representing the number of walls of the multiwall carbon nanotubes.
6. The method for extracting parameters of three-bit TSV based on a carbon nanotube according to claim 5 wherein S3 includes:
s31: obtaining the equivalent complex conductivity of the multi-wall carbon nano tube bundle of the three-position TSV in the vertical direction:
s32: obtaining the equivalent complex conductivity of the multi-wall carbon nano tube bundle of the three-position TSV in the horizontal direction:
σ horizontal ＝10 -7 ·σ vertical 。
7. the method for extracting parameters of three-bit TSV based on carbon nanotubes according to claim 4 wherein S4 includes:
s41: obtaining the cross-sectional area of the TSV structure along the longitudinal direction of the multi-wall carbon nano tube bundle:
A＝r TSV ·H·N bits ，
wherein N is bits Represents the number of independent signals propagating in the three-bit TSV, r TSV Representing the radius of the TSV structure, and H represents the height of the TSV structure;
s42: acquiring capacitance between any two bits in the three-bit TSV:
where s represents the distance between adjacent signal pads, ε and ε 0 The relative permittivity and vacuum permittivity of the carbon nanotube are shown, respectively.
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