CN102222142A - Scale-span design method for interface structure of micro/nano/photoelectronic device - Google Patents
Scale-span design method for interface structure of micro/nano/photoelectronic device Download PDFInfo
- Publication number
- CN102222142A CN102222142A CN2011101643917A CN201110164391A CN102222142A CN 102222142 A CN102222142 A CN 102222142A CN 2011101643917 A CN2011101643917 A CN 2011101643917A CN 201110164391 A CN201110164391 A CN 201110164391A CN 102222142 A CN102222142 A CN 102222142A
- Authority
- CN
- China
- Prior art keywords
- interface
- molecular dynamics
- finite element
- interface element
- zone
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Abstract
The invention discloses a scale-span design method for an interface structure of a micro/nano/photoelectronic device, which comprises the following steps of: designing a coupling area of a finite element and an interface element, and an interface element coupling area of molecular dynamics; constructing a finite element, interface element and molecular dynamics coupled model; solving a finite element equation in the finite element area by using a finite element method, and converting the finite element equation to a boundary of the interface element area to solve the interface element area; assigning atoms in the finite element coupling area of the molecular dynamics and converting the solution of the finite element area into a boundary condition of the atoms in the molecular dynamics area; initiating molecular dynamics solving in the molecular dynamics area, and solving new positions of atoms by using a non-equilibrium molecular dynamics model; and finally determining system balance of the molecular dynamics area. By the method, the energy coupled transfer is realized systematically, the macro/micro/nano simulation of interface characteristics of the micro/nano/photoelectronic device is realized, and the method has the characteristics of precision, scientific property and high efficiency.
Description
Technical field
The present invention relates to microcosmic to macroscopical numerical simulation, refer in particular to a kind of be used for little/receive/optoelectronic device microstructure interface stride the yardstick coupling design method.
Background technology
Sandwich construction and many interfaces are ubiquitous phenomenons in electron device itself and device interconnection and the encapsulation, and interface debonding lost efficacy becomes the major issue of properties of product and the care of reliability aspect.The foreign study person finds that by a large amount of experiments the interface is micro-system manufacturing and operating key component, and a lot of destructions and defective all occur near interface.But the research of microcosmic material interface rule is at the early-stage, and is no longer suitable based on the macroscopic theory of continuum mechanics.The surface physics feature is not only relevant with the distribution of material form with the geometry of microstructure, and also with the macroscopic boundary condition of structure, various load etc. are all multifactor relevant.
By the microcosmic approach, can set up basic understanding to the material behavior, it becomes the indispensable important means of development new material and high performance device just gradually.(Molecular Dynamics is one of the main means of microcosmic modeling MD) to molecular dynamics, and many micro details that can't obtain in experiment can be observed in molecular dynamics simulation easily.Molecular dynamics has the higher time than additive method on atomic scale and ability is found the solution in the space, therefore can't can effectively study with molecular dynamics with the microphysics phenomenon that the continuous medium analytical approach is found the solution.But the defective of molecular dynamics simulation is: calculating needs the huge time, sharply increase along with the increase of atomicity its computing time, in order to reduce computing time, the used atomic quantity of molecular dynamics emulation is generally fewer, even if supercomputer also can only simulate 10
9Individual atom, just less than the material of 1 square micron, such range scale obviously is not enough to the emulation as crack propagation, energy impact etc.Therefore, macroscopic view how to utilize the microcosmic of molecular dynamics to find the solution ability and continuum mechanics is found the solution ability, strides the yardstick coupling process effectively and is designed to a current difficult problem.
Summary of the invention
The objective of the invention is for overcome the defective of molecular dynamics simulation in the prior art propose a kind of efficient and little cheaply/receive/the scale Design method of striding of optoelectronic device interfacial structure.
Technical scheme of the present invention is to adopt following steps: (1) design finite element Interface Element coupling regime and molecular dynamics Interface Element coupling regime, Hamiltonian is decomposed into the Hamiltonian of different scale at coupling regime, realize the coupling of different scale, the coupling model of structure finite element, Interface Element and molecular dynamics; (2) utilize the finite element model for solving finite element equation in the finite element zone
, the macro-size of computation model,
,
,
Be respectively finite element method stiffness matrix, transposed matrix and loading matrix,
fIt is the unit of finite element; (3) at finite element Interface Element coupling regime, the finite element equation that utilizes excessive Interface Element Method that (2) step was tried to achieve is separated the border that is transformed into the Interface Element zone and then is solved separating of Interface Element zone; (4) separating according to the Interface Element zone, adopt mapping operator technology that the atom in the molecular dynamics Interface Element coupling regime is carried out assignment, make the Hamiltonian of the atom in this zone equate, separating of Interface Element zone is converted into the boundary condition of the atom in the molecular dynamics zone with the energy of Interface Element gained; (5) in the molecular dynamics zone, according to the result in (4) step, start molecular dynamics and find the solution, adopt the nonequilibrium state Molecular Dynamics Model to find the solution the reposition of atom; (6) judge the system balancing in molecular dynamics zone,, then carry out the molecular dynamics in (5) step and find the solution until balance if there is not balance to continue.
The invention has the beneficial effects as follows: the present invention is directed to little/receive/the optoelectronic device structure interface, observe the differentiation of micro interface material structure, analyze the generation mechanism of thermal defect, explore the influence of fault in material to the microstructure physical characteristics, micro-analysis method and Interface Element with molecular dynamics, the macroanalysis method of finite element realizes the coupling transmission of energy in system, and then form an energy integral body and find the solution, realized little/receive/the optoelectronic device structure interface feature grand/little/receive simulation, have accurately, science, the characteristics that efficient is high have solved the design challenges of little/nanometer electronic device structural interface preferably.
Description of drawings
Fig. 1 is the coupling mechanism synoptic diagram of finite element-Interface Element-molecular dynamics different scale;
Fig. 2 is based on the finite element-Interface Element coupling mechanism synoptic diagram of transition interface unit;
Fig. 3 strides the scale Design process flow diagram;
Fig. 4 is the figure as a result of the temperature variation on the Z direction of Cu-Cu interface in the embodiment of the invention;
Among the figure: 1. finite element zone; 2. finite element Interface Element coupling regime; 3. Interface Element zone; 4. molecular dynamics Interface Element coupling regime; 5. molecular dynamics zone; 6. transition interface unit.
Embodiment
Referring to Fig. 1, the present invention is with molecular dynamics (Molecular Dynamics, MD), Interface Element (Interface Stress Element, ISE) and finite element method (Finite Element FE) couples together to have the calculating of atom and macro-scale with a kind of unified method.When calculating, the computing information of accepting other two zones is as boundary condition.For example, at molecular dynamics zone (MD Area, A
MD) when describing characteristic variations such as interface temperature, accept Interface Element and finite element provide boundary temperature etc. for Molecular Dynamics Model boundary condition with molecular dynamics simulation.When the analog computation of molecular dynamics, provide the macroscopic boundary condition of behaviors such as temperature for Molecular Dynamics Model.With Hamiltonian (macroscopic view is the kinetic energy and the potential energy sum of system) coupling mechanism is described; Describing Interface Microstructure with molecular dynamics develops and the fault in material feature; Macroscopic boundary conditions such as temperature are provided for Molecular Dynamics Model with Interface Element, finite element, carry out the yardstick of striding of interface feature (temperature) and simulate.
In striding the scale Design method, the coupling of different scale is unusual important problem.For discrete atom and continuous medium are connected, should mix atomic model and continuous model with a kind of appropriate mode.At coupling regime, the transmission that utilizes energy connects the independent energy equation in coupling regime median surface unit, finite element, molecular dynamics zone, thereby the energy (as heat energy) that Interface Element, finite element zone are produced propagates in the molecular dynamics zone and goes.Adopt mapping operator technology, can obtain continuous temperature equation for molecular dynamics simulation provides information (as atom speed, displacement).
The concrete steps of method for designing of the present invention are as follows:
The first step: by design two grip range (Handshake, HS), i.e. finite element Interface Element coupling regime 2 and molecular dynamics Interface Element coupling regime 4, the coupling model of structure finite element, Interface Element and molecular dynamics.At coupling regime Hamiltonian is decomposed into the Hamiltonian of different scale, thereby realizes the coupling of different scale.For example, at molecular dynamics Interface Element coupling regime 4(HS
ISE-MD) can represent with the potential-energy function in the object.As shown in Figure 2, at finite element Interface Element coupling regime 2(HS
ISE-FE) adopt transition interface unit 6 that finite element zone 1 and Interface Element zone 3 are effectively linked.Can get transition interface S by generalized variational principle
j 0Stiffness matrix
For:
Wherein, be the interface
, N
FEAnd N
ISEBe respectively the interface node shape function of finite element and Interface Element.L is the transition matrix that the cosine of block unit's local coordinate axle and whole coordinate axis angle is formed; D is the elastic matrix under the transition interface unit local coordinate; T is any array formed to stress and tangential stress of one point method on the interface; N is the shape function matrix of unit; DS is the differential at the interface.Finite element and Interface Element coupling model can link together finite element and Interface Element by transition interface unit method as shown in Figure 2.
At molecular dynamics Interface Element coupling regime, the Hamiltonian (H of system that this is regional
MD-ISE) can resolve into:
Wherein,
The Hamiltonian component of representing the Hamiltonian and the Interface Element of molecular dynamics in this coupling regime respectively;
For this coupling regime Hamiltonian weights coefficient, get 0.5; The Hamiltonian of molecular dynamics can and be represented by the kinetic energy of atom and potential energy.The computing method of these three kinds of yardsticks can be coupled based on said method, effectively couple together.
Second step: at finite element zone 1(FE Area, A
FE) utilize the finite element model for solving finite element equation
,
,
,
Be respectively the stiffness matrix of finite element method, transposed matrix and loading matrix, f are represented the unit of finite element.Calculate the macro-size of multiple dimensioned model and with finite element solving.
The 3rd step: at finite element Interface Element coupling regime 2(H
ISE-FE), utilize excessive Interface Element Method that the second step finite element equation of trying to achieve is separated, comprise the temperature, speed, displacement of node etc., be transformed into Interface Element zone (ISE Area, A
ISE) the border so that solve separating of Interface Element zone, comprise parameters such as at the interface temperature, speed, displacement.
The 4th step:, adopt mapping operator technology to molecular dynamics Interface Element coupling regime 4(HS according to the 3rd step result calculated
ISE-MD) in atom carry out assignment, calculate the initial velocity and the displacement of molecular dynamics Interface Element coupling regime 4.Make the Hamiltonian of this zone atom equate, separating of Interface Element zone 3 is converted into the boundary condition of molecular dynamics zone 5 atoms with the energy of Interface Element gained.
The 5th step:,, start molecular dynamics and find the solution AMD) according to the result in the 4th step at molecular dynamics zone 5(MD Area.Adopt the nonequilibrium state Molecular Dynamics Model to find the solution the new position of atom, calculate the speed and the displacement of molecular dynamics zone 5 all atoms.
The 6th step: judge the system balancing in molecular dynamics zone 5, if the molecular dynamics that does not have balance to proceed for the 5th step is found the solution until balance.After the balance, then can calculate the hot-fluid of all atoms, draw the feature of micro interface, as associated hot mechanics parameters such as the Temperature Distribution at atom interface, thermal conductivities.Simultaneously, the final position of the atom of coupling place of molecular dynamics Interface Element coupling regime 4 is converted into the displacement of Interface Element, utilizes Interface Element Method, finite element method to find the solution Interface Element zone 3, finite element Interface Element coupling regime 2, the node temperature of finite element zone 1 after the built-in system balance again.
Below provide 1 embodiment to further specify the present invention.
Embodiment
At thickness is 2
UmCu film two ends apply respectively-the temperature boundary condition of 500K and 500K.According to striding the scale Design process flow diagram, at first, at finite element zone (FE Area, A
FE), utilize finite element method that it is dispersed and find the solution its stiffness matrix, load array, having applied up and down, the temperature boundary condition is respectively :-500K, 500K are the step of second in the above-mentioned concrete implementation step; Secondly, utilize transition interface unit method, result and the Interface Element of finite element solving linked together, the separating of calculating Interface Element zone; Then, separating of trying to achieve is applied to interface zone (ISE Area, A
ISE) atom get on, and, be the 3rd step in the above-mentioned concrete implementation step as finding the solution calculating as the starting condition of nonequilibrium state molecular dynamics simulation in the Molecular Dynamics Model; The last step find the solution finish after, give this coupling regime (HS with the interface temperature of gained and strain assignment
ISE-MD) copper atom, adopt nonequilibrium state Molecular Dynamics Model and periodic boundary condition, molecular dynamics simulation is carried out until system balancing in the junction, interface, be the 4th, the 5th step in the above-mentioned concrete implementation step.
Fig. 4 (a) is depicted as after system balancing, the temperature gradient curve at Cu-Cu interface, dT/dZ be in the thermograde value of z direction for the time through the interface, the thermograde of z direction is dT/dZ=-0.2412 * 10
9K/m is still becoming dT/dZ=-0.1903 * 10 through gradient after the interface
9K/m, variation of temperature trend is close to be identical because form the material at interface, but temperature value has a jump, and this is owing to exist the uncontinuity of medium to cause at the interface.This result of study Fig. 4 (b) with people such as external Soon-Ho Choi compares in in-problem at the interface sudden change similar, and the thermograde before and after Fig. 4 (b) interface is respectively dT/dZ=-3.2445 * 10
8K/m, dT/dZ=-4.2128 * 10
8K/m is owing to constitute the material difference at interface.This has shown and utilizes finite element-Interface Element-molecular dynamics to stride accuracy and validity that yardstick is analyzed.
Though Molecular Dynamics Model can be reflected in the molecular evolution of the film interface under the small scale preferably and have very high precision, but, can not truly be reflected in the thermal characteristics of extraneous macroscopical temperature thin-film interfacial structure owing to the restriction of hardware conditions such as computing machine.Therefore, finite element-Interface Element-molecular dynamics is striden the dimensional analysis model and is compared with simple Molecular Dynamics Model and considered the influence of extraneous macroscopical temperature conditions to the film interface structure can reflect the Temperature Distribution of interface under extraneous thermal effect more really.Although striding the yardstick computation model, finite element-Interface Element-molecular dynamics adopted macroscopical analysis means---finite element/Interface Element, on computational accuracy, be lower than simple Molecular Dynamics Calculation model, but stride the external condition that the yardstick model has higher counting yield than molecular dynamics computation model and can consider macroscopic view.The result shows: based on molecular dynamics-Interface Element-finite element stride dimensional analysis model and method for designing be feasible effectively.
Therefore, can utilize and stride the programming of yardstick model and method for designing and calculate, further assay surface defective (as crackle, hole etc.) or microstructure evolution mechanism is to the influence of microstructure characteristic, for little/receive/design of optoelectronic device interfacial structure provides analysis means and basis.
Claims (2)
- One kind little/receive/the scale Design method of striding of optoelectronic device interfacial structure, it is characterized in that adopting following steps:(1) design finite element Interface Element coupling regime and molecular dynamics Interface Element coupling regime, Hamiltonian is decomposed into the Hamiltonian of different scale at coupling regime, realize the coupling of different scale, the coupling model of structure finite element, Interface Element and molecular dynamics;(2) utilize the finite element model for solving finite element equation in the finite element zone, the macro-size of computation model, ,
,
Be respectively finite element method stiffness matrix, transposed matrix and loading matrix, fIt is the unit of finite element;
(3) at finite element Interface Element coupling regime, the finite element equation that utilizes excessive Interface Element Method that (2) step was tried to achieve is separated the border that is transformed into the Interface Element zone and then is solved separating of Interface Element zone;(4) separating according to the Interface Element zone, adopt mapping operator technology that the atom in the molecular dynamics Interface Element coupling regime is carried out assignment, make the Hamiltonian of the atom in this zone equate, separating of Interface Element zone is converted into the boundary condition of the atom in the molecular dynamics zone with the energy of Interface Element gained;(5) in the molecular dynamics zone, according to the result in (4) step, start molecular dynamics and find the solution, adopt the nonequilibrium state Molecular Dynamics Model to find the solution the reposition of atom;(6) judge the system balancing in molecular dynamics zone,, then carry out the molecular dynamics in (5) step and find the solution until balance if there is not balance to continue. - 2. according to claim 1 little/receive/the scale Design method of striding of optoelectronic device interfacial structure, it is characterized in that: the described excessive Interface Element Method of step (3) is to adopt transition interface unit to link transition interface S with finite element zone and Interface Element are regional j 0Stiffness matrixFor:
, N FEAnd N ISEBe respectively the interface node shape function of finite element and Interface Element; L is the transition matrix that the cosine of block unit's local coordinate axle and whole coordinate axis angle is formed; D is the elastic matrix under the transition interface unit local coordinate; T is any array formed to stress and tangential stress of one point method on the interface; N is the shape function matrix of unit; DS is the differential at the interface.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 201110164391 CN102222142B (en) | 2011-06-20 | 2011-06-20 | Scale-span design method for interface structure of micro/nano/photoelectronic device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN 201110164391 CN102222142B (en) | 2011-06-20 | 2011-06-20 | Scale-span design method for interface structure of micro/nano/photoelectronic device |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN102222142A true CN102222142A (en) | 2011-10-19 |
| CN102222142B CN102222142B (en) | 2013-03-13 |
Family
ID=44778692
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN 201110164391 Expired - Fee Related CN102222142B (en) | 2011-06-20 | 2011-06-20 | Scale-span design method for interface structure of micro/nano/photoelectronic device |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN102222142B (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104361167A (en) * | 2014-11-04 | 2015-02-18 | 南京航空航天大学 | Finite element prediction method of electrode-containing ferroelectric single crystal based on phase-field method analysis |
| CN105046029A (en) * | 2015-09-08 | 2015-11-11 | 武汉大学 | Pressed steel plate design method based on multiscale analysis |
| CN110210103A (en) * | 2019-05-27 | 2019-09-06 | 北京工业大学 | A kind of multi-dimension analogy method of heterogeneous composite material mechanical behavior |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101515307A (en) * | 2009-02-11 | 2009-08-26 | 江苏大学 | Multi-physical field interface multi-scale design method of structure of micro-nano electronic device |
-
2011
- 2011-06-20 CN CN 201110164391 patent/CN102222142B/en not_active Expired - Fee Related
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101515307A (en) * | 2009-02-11 | 2009-08-26 | 江苏大学 | Multi-physical field interface multi-scale design method of structure of micro-nano electronic device |
Non-Patent Citations (6)
| Title |
|---|
| 《Computer Methods in Applied Mechanics and Engineering》 20040730 Hiroshi Kadowaki, Wing Kam Liu. Bridging multi-scale method for localization problems 3267-3302 1-2 第193卷, * |
| 《中国机械工程》 20050831 刘更等. 宏观-微观多尺度数值计算方法研究进展 1493-1498 1-2 第16卷, 第16期 * |
| 《力学进展》 20110325 谭浩等. 微纳米尺度下材料性能多尺度模拟方法进展 155-171 1-2 第41卷, 第2期 * |
| 《湖南科技大学学报（自然科学版）》 20061231 尹伟华,易伟建,刘艳. 有限元-界面元混合模型及其应用 41-45 1-2 第21卷, 第4期 * |
| LI-QIANG ZHANG,PING YANG,XIAO-LIANG WANG,PEI LI,HUAN WANG: "MD-ISE-FE Multi-scale Modeling of Interface Structure in Microelectronic Devices", 《2011 INTERNATIONAL CONFERENCE ON ELECTRIC INFORMATION AND CONTROL ENGINEERING》 * |
| 廖宁波: "不同材料界面传热的多尺度建模及物理机制研究", 《中国博士学位论文全文数据库》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104361167A (en) * | 2014-11-04 | 2015-02-18 | 南京航空航天大学 | Finite element prediction method of electrode-containing ferroelectric single crystal based on phase-field method analysis |
| CN104361167B (en) * | 2014-11-04 | 2017-09-05 | 南京航空航天大学 | A kind of finite element prediction method of monocrystalline containing electrode ferroelectric analyzed based on Phase Field |
| CN105046029A (en) * | 2015-09-08 | 2015-11-11 | 武汉大学 | Pressed steel plate design method based on multiscale analysis |
| CN110210103A (en) * | 2019-05-27 | 2019-09-06 | 北京工业大学 | A kind of multi-dimension analogy method of heterogeneous composite material mechanical behavior |
| US11798658B2 (en) | 2019-05-27 | 2023-10-24 | Beijing Universitry Of Technology | Multi-scale method for simulating mechanical behaviors of multiphase composite materials |
Also Published As
| Publication number | Publication date |
|---|---|
| CN102222142B (en) | 2013-03-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Jin et al. | Three-dimensional exact solution for the free vibration of arbitrarily thick functionally graded rectangular plates with general boundary conditions | |
| Saxena | Synthesis of compliant mechanisms for path generation using genetic algorithm | |
| CN106066913A (en) | Complex composite material structure equivalent material performance multi-dimension computational methods | |
| Shenas et al. | Free vibration of functionally graded quadrilateral microplates in thermal environment | |
| Berger et al. | A comprehensive numerical homogenisation technique for calculating effective coefficients of uniaxial piezoelectric fibre composites | |
| Heydarpour et al. | Thermoelastic analysis of FG-GPLRC spherical shells under thermo-mechanical loadings based on Lord-Shulman theory | |
| CN107451308A (en) | A kind of complex composite material structure effective thermal expansion coefficient multiscale simulation method | |
| Bowen et al. | Trade space exploration of magnetically actuated origami mechanisms | |
| CN107451307A (en) | A kind of method of Multi-Scale Calculation complex composite material structure effective stiffness matrix | |
| Cárdenas et al. | Numerical validation of a finite element thin‐walled beam model of a composite wind turbine blade | |
| CN106021644B (en) | The method for determining mixed dimensional modelling interface constraint equation coefficient | |
| Ganapathy et al. | An effective unit cell approach to compute the thermal conductivity of composites with cylindrical particles | |
| Kentli | Topology optimization applications on engineering structures | |
| Hegde et al. | Design of single-input-single-output compliant mechanisms for practical applications using selection maps | |
| Mosavi et al. | Review on the Usage of the Multiobjective Optimization Package of modeFrontier in the Energy Sector | |
| CN102222142B (en) | Scale-span design method for interface structure of micro/nano/photoelectronic device | |
| CN103455712B (en) | A kind of Forecasting Methodology of three axial woven composite grid mechanical modulis | |
| Zhao et al. | Closed-form solutions of bending-torsion coupled forced vibrations of a piezoelectric energy harvester under a fluid vortex | |
| Chen et al. | Shakedown and optimization analysis of periodic composites | |
| CN101515307A (en) | Multi-physical field interface multi-scale design method of structure of micro-nano electronic device | |
| Zhou et al. | A multi-physics coupling cell-based smoothed finite element micromechanical model for the transient response of magneto-electro-elastic structures with the asymptotic homogenization method | |
| Yadav et al. | Modeling and simulation of piezo-beam structure mounted in a circular pipe using laminar flow as energy harvester | |
| CN107862130A (en) | A kind of analysis method for the inside key factor for causing relay storage to be degenerated | |
| Bayoumy et al. | A relative adequacy framework for multi-model management in design optimization | |
| Wu et al. | Three-dimensional numerical simulation of a flat plate perpendicularly submitted to current with a blockage ratio of 0.214: URANS and detached eddy simulation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20130313 Termination date: 20170620 |