CN109933917A - The molding research method of three-D photon crystal inner spherical defect quantitative - Google Patents
The molding research method of three-D photon crystal inner spherical defect quantitative Download PDFInfo
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Abstract
Present invention relates particularly to the molding research methods of three-D photon crystal inner spherical defect quantitative that can be acted on based on surface, the surface of the three-D photon crystal has two-dimensional array cylindrical hole, and the research method is the following steps are included: step 1: establishing the phase field model of three-D photon crystal；Step 2: system surfaces energy equation is established；Step 3: the diameter D and aperture distance D of selected two-dimensional array cylindrical holesIt is constant, constantly change the depth H of cylindrical hole, adjusts the maximum conditions of H/D, it can be with the quantitative relationship that is formed by ball defects cavity to obtain the system surfaces of three-D photon crystal.The present invention utilizes the thermal diffusion campaign of three-D photon crystal insulating particles, it realizes in the case where system surfaces can act on to the molding research of photonic crystal inner spherical defect quantitative, the inner link between system surfaces energy E and ball defects number of cavities N is established, provides new idea and method for the stable molding of three-D photon crystal internal microstructure.
Description
Technical field
The invention belongs to micro nano structure studying technological domains, and in particular to the three-D photon crystal that can be acted on based on surface
The molding research method of inner spherical defect quantitative.
Background technique
With the continuous improvement of microelectronic component integrated level, device technology line width just tends to theoretical limit, electricity consumption
Son will face the bottleneck for being difficult to go beyond as the microelectric technique of information carrier.Therefore, use photon as the collection of information carrier
At photoelectronics increasingly by concern both domestic and external.Wherein, the silicon substrate processing of modern large scale integrated circuit maturation is inherited
Technology, and have both the silicon based photon crystal device of photonic crystal perfection control light ability, become naturally the hot spot of research with
Forward position.Currently, mostly using the technologies such as nano impression, electron beam lithography, inductively coupled plasma body (ICP) etching greatly to carry out silicon
Base is one-dimensional, 2 D photon crystal device preparation, and technology comparative maturity, especially introduces defect in the photonic crystal
After forming Defect Modes, photon crystal micro cavity may be used as.The distinguishing feature of photon crystal micro cavity is with the ultrahigh quality factor
Q.With one-dimensional, two-dimensional phase ratio, photonic band gap effects are all may be present in all directions in space in silicon based three-dimensional photonic crystal, can be with
More ideally control light.It is different from conventional round hole photonic crystal and annulus hole photonic crystal, inside is spherical hollow space
Photon crystal micro cavity has higher Q value.
In practical study three-D photon crystal, in value theory research and two aspect of device technology production, currently all deposit
In serious limitation.In terms of value theory research, accurately analyzing the structure must be considered using complete three-dimensional vector, this
Mean that numerical simulation and emulation are carried out to it to be generally required to expend very big computing resource, this carries out three-D photon crystal deep
Enter theory and researchs and proposes very high condition requirement.More important question is that sizable difficulty is prepared with to three-D photon crystal
Degree, especially when to be artificially introduced specific defect sturcture in three-D photon crystal, under existence conditions, not yet
Mature manufacture craft and means.Therefore it urgently needs to carry out the formation problems of silicon based three-dimensional photonic crystal in depth theoretical
Analysis proposes more scientific and effective processing method.
During the experiment, need the array micropore of clear silicon based three-dimensional photon crystal surface in certain circumstances can shape institute
The ball defects needed, and need to carry out ball defects quantitative control.It is well known that the two-dimentional battle array on three-D photon crystal surface
Column micropore is converted into stable ball defects, will receive the influence of some parameters, such as the diameter of array micropore, height and pitch of holes
Deng.But when studying ball defects quantity, it has to an important parameter of consideration be exactly array micropore in z-direction
Hole depth.So in the case where controlling the diameter and pitch of holes of micropore, to study the height of array micropore to three-D photon crystal
The influence of inner spherical defect molding quantity.
Summary of the invention
Based on the above deficiencies in the existing technologies, the present invention is provided in the three-D photon crystal that can be acted on based on surface
Portion's ball defects quantify molding research method.
In order to achieve the above object of the invention, the invention adopts the following technical scheme:
The molding research method of three-D photon crystal inner spherical defect quantitative, the surface of the three-D photon crystal have
Two-dimensional array cylindrical hole, the research method the following steps are included:
Step 1: the phase field model of three-D photon crystal is established；
Step 2: system surfaces energy equation is established；
Step 3: the diameter D and aperture distance D of selected two-dimensional array cylindrical holesIt is constant, constantly change the depth of cylindrical hole
H adjusts the maximum conditions of H/D, with obtain three-D photon crystal system surfaces can be formed by determining for ball defects cavity
Magnitude relation.
Preferably, the phase field model includes energy, power and at split-phase.
Preferably, the energy includes free energy, chemical energy and interface energy；The power include atom diffusion and
Transition process；Described at split-phase includes medium phase and air phase.
Preferably, the phase field model for establishing three-D photon crystal, comprising:
Define c1(x, y, z, t) indicates medium phase, c2(x, y, z, t) indicates air phase；Parameter c1、c2At any time in space
On variation reflect the evolutionary process of three-D photon crystal internal microstructure；
Total free energy G of microscopic system is indicated are as follows:
G=∫V[Fbulk+Fint]dV (1)
Wherein, FbulkRepresent the volume energy in system, FintRepresent the surface energy of system；
Total free energy G needs to meet the inequality reached under equilibrium state in system:
It is that total free energy needs change over time and reduce that i.e. system, which reaches equilibrium state to need the condition met,；
For medium phase c1, for this field variable, above-mentioned inequality (2) is rewritten are as follows:
Concentration of medium c1Change over time the diffusion flux that diffusion is spatially generated with itRelationship have:
Then above-mentioned inequality (3) conversion are as follows:
In conjunction with identity:Above-mentioned inequality (5) conversion are as follows:
Equation is obtained in conjunction with above-mentioned inequality (4) and (6):
Wherein,For medium phase c1Mobility；DefinitionFor the chemical potential energy in system, U is usedchIt indicates, then system
In field variable c1The functional equation changed over time are as follows:
It is preferably, described to establish system surfaces energy equation, comprising:
The surface energy equation of system is E=FA；Wherein, F is surface tension, i.e. insulating particles are when being oriented movement
Driving force is constant；A is the surface area of cylindrical hole；
By surface areaDerive the relational expression between system surfaces energy and cylindrical hole depth H are as follows:
Preferably, the two-dimensional array cylindrical hole formed quantification of N=1 ball defects maximum conditions be 5≤
H/D≤10。
Preferably, it is 10 < that the two-dimensional array cylindrical hole, which forms the ball defects maximum conditions of quantification of N=2,
H/D≤20。
Preferably, it is 20 < that the two-dimensional array cylindrical hole, which forms the ball defects maximum conditions of quantification of N=3,
H/D≤30。
Preferably, the ratio of the H/D and two-dimensional array cylindrical hole are formed between the quantity N of ball defects cavity
Relational expression:
Preferably, in conjunction with above-mentioned formula (9) and (10) obtain three-D photon crystal system surfaces can with formed
Ball defects cavity quantitative relationship are as follows:
Compared with prior art, the present invention beneficial effect is:
The present invention utilizes the thermal diffusion campaign of three-D photon crystal insulating particles, realizes in the case where system surfaces can act on to light
Sub- crystals ball defects quantify molding research.The present invention starts with from the angle of energy, and it is brilliant to propose control three-dimensional photon
Internal portion's ball defects form quantitative research method, it is established that between system surfaces energy E and ball defects number of cavities N
Inner link provides new idea and method for the stable molding of three-D photon crystal internal microstructure.
Detailed description of the invention
Fig. 1 is the three-D photon crystal micro-structure heat of surface two-dimensional array cylindrical hole 5≤H/D≤10 of the embodiment of the present invention
Schematic diagram of structural changes before and after the processing；
Fig. 2 is the three-D photon crystal micro-structure of 10 H/D≤20 < of surface two-dimensional array cylindrical hole of the embodiment of the present invention
It is heat-treated the schematic diagram of structural changes of front and back；
Fig. 3 is the three-D photon crystal micro-structure of 20 H/D≤30 < of surface two-dimensional array cylindrical hole of the embodiment of the present invention
It is heat-treated the schematic diagram of structural changes of front and back.
Specific embodiment
In order to illustrate more clearly of the present invention, Detailed description of the invention a specific embodiment of the invention will be compareed below.It is aobvious and easy
Insight, the accompanying drawings in the following description are only example of the invention, for those of ordinary skill in the art, are not paying wound
Under the premise of the property made is worked, it is also possible to obtain other drawings based on these drawings, and obtain other embodiments.
The molding research method of three-D photon crystal inner spherical defect quantitative of the embodiment of the present invention, specifically includes following
Step:
Firstly, determining that the initial parameter of the three-D photon crystal micro-structure of two-dimensional array cylindrical hole, including circle are carved in surface
The diameter D of post holes, the depth H of cylindrical hole, the distance D between apertureS。
Step 1: the phase field model of three-D photon crystal is established
In order to study the diffusion motion of microcosmic medium, we establish phase field model, in this model (such as comprising multiple kinds of energy
Free energy, chemical energy, interface can), a variety of dynamics (such as diffusion, migration) and Multiple components phase (medium phase, air phase).
Define c1(x, y, z, t) indicates medium phase, c2(x, y, z, t) indicates air phase.Parameter c1、c2At any time in space
On variation reflect the evolutionary process of three-D photon crystal internal microstructure.Total free energy of microscopic system can indicate
Are as follows:
G=∫V[Fbulk+Fint]dV (1)
Wherein, FbulkRepresent the volume energy in system, FintRepresent the surface energy of system.The surface of system can it is big
It is small and be defined as:
Wherein, h11、h22That indicate is the surface energy coefficient of each phase, h12Indicate that medium phase and air are in contact interface
It surface can coefficient.Indicate Laplace operator:
Total free energy G needs to meet the inequality reached under equilibrium state in system:
It is that total free energy needs change over time and reduce that i.e. system, which reaches equilibrium state to need the condition met,.For being situated between
Matter phase c1, for this field variable, above-mentioned inequality (3) be can be rewritten as:
Concentration of medium c1Change over time the diffusion flux that diffusion is spatially generated with itRelationship have:
Then inequality (4) can convert are as follows:
In conjunction with identity:Inequality (6) can convert are as follows:
In conjunction with above-mentioned formula (5) and (7), available equation:
Wherein,That indicate is medium phase c1Mobility；DefinitionFor the chemical potential energy in system, U is usedchIt indicates,
The then field variable c in system1The functional equation changed over time are as follows:
Nonlinear partial differential equation are introduced, and the elements such as total free energy of addition system and surface energy in the equation,
Microstructure change process can be effectively studied from energy point of view.Change phase field parameters, to change system surfaces energy, surface energy
Reduction so that the cylinder hole shape on three-D photon crystal surface is constantly changed.
Step 2: system surfaces energy equation is established.
The surface energy equation of system is E=FA.Wherein F is surface tension, i.e. insulating particles when being oriented movement
Driving force is constant；A is the surface area of cylindrical hole.
By surface areaThe relational expression between system surfaces energy and cylindrical hole depth H can be released:
Step 3: cylinder bore diameter D and aperture distance D is keptsIt is constant, change the value of cylindrical hole depth H.It can by experiment
Know:
(1) on cylinder hole depth direction, change H (or perhaps changeValue), whenThis ratio is between 5 to 10
Between when, the two-dimensional array micropore on three-D photon crystal surface because surface can variation, ball required for being formed out can be stablized
Shape defect cavity, and quantity is N=1, as shown in Figure 1.
(2) in cylinder hole depth Z-direction, change the value of H, makeThis ratio continues to increase to 10 (not including 10) to 20
Between, three-D photon crystal is heat-treated in the environment of same constant temperature and pressure, determines the two of three-D photon crystal surface
Array micropore is tieed up because of the variation of surface energy, ball defects cavity required for being formed out can be stablized, and quantity is N=2, such as
Shown in Fig. 2.
(3) in cylinder hole depth Z-direction, change the value of H, makeThis ratio, which continues to increase to 20 (not including 20), to be arrived
Between 30, three-D photon crystal is heat-treated in the environment of same constant temperature and pressure, determines three-D photon crystal surface
Two-dimensional array micropore can stablize ball defects cavity required for being formed out because of the variation of surface energy, and quantity is N=3,
As shown in Figure 3.
By testing the comparison with result above, we exact can be obtainedRatio and three-D photon crystal surface
Two-dimensional array micropore forms the relational expression between ball defects number of cavities N:
Convolution (10) and (11) are it can be concluded that its system surfaces of the three-D photon crystal of two-dimensional array micropore are carved on surface
The quantitative relation formula that can and be finally formed by between ball defects cavity:
The molding research method of three-D photon crystal inner spherical defect quantitative of the invention, is situated between using three-D photon crystal
The molding side to photonic crystal inner spherical defect quantitative is realized in the thermal diffusion campaign of plasmid in the case where system surfaces can act on
Method.The present invention starts with from the angle of energy, proposes control three-D photon crystal inner spherical defect molding and determines quantifier elimination side
Method, it is established that inner link between system surfaces energy and ball defects number of cavities is micro- knot inside three-D photon crystal
Structure stable molding provides new idea and method.
The above is only that the preferred embodiment of the present invention and principle are described in detail, to the common skill of this field
For art personnel, the thought provided according to the present invention will change in specific embodiment, and these changes should also regard
For protection scope of the present invention.
Claims (10)
1. the molding research method of three-D photon crystal inner spherical defect quantitative, which is characterized in that the three-D photon crystal
Surface have two-dimensional array cylindrical hole, the research method the following steps are included:
Step 1: the phase field model of three-D photon crystal is established；
Step 2: system surfaces energy equation is established；
Step 3: the diameter D and aperture distance D of selected two-dimensional array cylindrical holesIt is constant, constantly change the depth H of cylindrical hole, adjusts
The maximum conditions of whole H/D, can be with the quantitative pass that is formed by ball defects cavity to obtain the system surfaces of three-D photon crystal
System.
2. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 1, feature exist
In, the phase field model include energy, power and at split-phase.
3. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 2, feature exist
In the energy includes free energy, chemical energy and interface energy；The power includes atom diffusion and transition process；The ingredient
It mutually include medium phase and air phase.
4. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 3, feature exist
In the phase field model for establishing three-D photon crystal, comprising:
Define c1(x, y, z, t) indicates medium phase, c2(x, y, z, t) indicates air phase；Parameter c1、c2Change spatially at any time
Change the evolutionary process for reflecting three-D photon crystal internal microstructure；
Total free energy G of microscopic system is indicated are as follows:
G=∫V[Fbulk+Fint]dV (1)
Wherein, FbulkRepresent the volume energy in system, FintRepresent the surface energy of system；
Total free energy G needs to meet the inequality reached under equilibrium state in system:
It is that total free energy needs change over time and reduce that i.e. system, which reaches equilibrium state to need the condition met,；
For medium phase c1, for this field variable, above-mentioned inequality (2) is rewritten are as follows:
Concentration of medium c1Change over time the diffusion flux that diffusion is spatially generated with itRelationship have:
Then above-mentioned inequality (3) conversion are as follows:
In conjunction with identity:Above-mentioned inequality (5) conversion are as follows:
Equation is obtained in conjunction with above-mentioned inequality (4) and (6):
Wherein,For medium phase c1Mobility；DefinitionFor the chemical potential energy in system, U is usedchIt indicates, then in system
Field variable c1The functional equation changed over time are as follows:
5. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 4, feature exist
In described to establish system surfaces energy equation, comprising:
The surface energy equation of system is E=FA；Wherein, F is surface tension, i.e. driving of the insulating particles when being oriented movement
Power is constant；A is the surface area of cylindrical hole；
By surface areaDerive the relational expression between system surfaces energy and cylindrical hole depth H are as follows:
6. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 5, feature exist
In the ball defects maximum conditions that the two-dimensional array cylindrical hole forms quantification of N=1 are 5≤H/D≤10.
7. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 6, feature exist
In the ball defects maximum conditions that the two-dimensional array cylindrical hole forms quantification of N=2 are 10 H/D≤20 <.
8. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 7, feature exist
In the ball defects maximum conditions that the two-dimensional array cylindrical hole forms quantification of N=3 are 20 H/D≤30 <.
9. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 8, feature exist
In the ratio and two-dimensional array cylindrical hole of the H/D form the relational expression between the quantity N of ball defects cavity:
10. the molding research method of three-D photon crystal inner spherical defect quantitative according to claim 9, feature exist
In, in conjunction with above-mentioned formula (9) and (10) obtain three-D photon crystal system surfaces can be formed by determining for ball defects cavity
Magnitude relation are as follows:
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| CN114289881A (en) * | 2021-12-31 | 2022-04-08 | 杭州电子科技大学 | Method and equipment for forming spherical cavity in silicon-based material |
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