CN106771373B - The research method of laser controlling silicon substrate surface form is utilized based on phase field model - Google Patents
The research method of laser controlling silicon substrate surface form is utilized based on phase field model Download PDFInfo
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- CN106771373B CN106771373B CN201710015449.9A CN201710015449A CN106771373B CN 106771373 B CN106771373 B CN 106771373B CN 201710015449 A CN201710015449 A CN 201710015449A CN 106771373 B CN106771373 B CN 106771373B
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- G—PHYSICS
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- G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
- G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
- G01Q60/24—AFM [Atomic Force Microscopy] or apparatus therefor, e.g. AFM probes
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Abstract
The invention discloses a kind of research methods that laser controlling silicon substrate surface form is utilized based on phase field model, carry out: one, under an atomic force microscope, being clamped the silicon substrate of micro-nano structure using silicon fixture as follows；Two, the several seconds is irradiated with free end of the laser to silicon substrate, observes the silicon substrate surface form of silicon substrate and measures corresponding size；Three, the evolution process of the silicon atom dispersal behavior in the case where phase field model Imitating is based on laser irradiation and nanostructure silicon substrate surface form.
Description
Technical field
The invention belongs to nano-fabrication technique fields, and in particular to one kind utilizes laser controlling silicon substrate table based on phase field model
The research method of face form.
Background technique
In recent years, every subjects field is all insistent attempts various new science and technology to design and manufacture nanometer
Structure silicon-based configuration of surface, and apply it in various micromachines, such as: sensor, resonator etc..End mesh
Before, the research for how to control nanostructure silicon substrate surface form is still blank out.Research both domestic and external is only simple
The silicon atom that describes under thermal processes act thermal diffusion campaign occurs, to form silicon substrate surface form.
In recent years, domestic and foreign scholars are dedicated to using mathematical model come analysis and design nanostructure silicon substrate surface form,
But the research of early stage is all based on the two-dimensional mathematical model of a peacekeeping, this is to understanding that silicon substrate surface form is limited.
Compared to traditional two-dimensional mathematical model of a peacekeeping, next phase-field model (phase field model) proposed by the invention is no
It needs explicitly to track the position of Interface Moving, therefore greatly reduces the complexity of calculating.
Summary of the invention
Based on above-mentioned status, the invention proposes a kind of based on phase field model grinding using laser controlling silicon substrate surface form
Study carefully method.
The present invention includes experiment and emulation two parts, it is specific the technical solution adopted is as follows:
The research method of laser controlling silicon substrate surface form is utilized based on phase field model, is carried out as follows:
One, under AFM (atomic force microscope), the silicon substrate of micro-nano structure is clamped with silicon fixture；
Two, several seconds such as 10s are irradiated with free end of the laser to silicon substrate, observes the silicon substrate surface form of silicon substrate and measures
Corresponding size；
Three, the silicon atom dispersal behavior in the case where Phase-filed model (phase field model) Imitating is based on laser irradiation
With the evolution process of nanostructure silicon substrate surface form.
Step 1, silicon fixture are mainly used for fixed silicon substrate.
The research method that laser controlling silicon substrate surface form is utilized based on phase field model, step 2, the function of laser
Rate P is 75mW, wavelength X 532nm.
The research method that laser controlling silicon substrate surface form is utilized based on phase field model, step 3, the phase of system
Field model includes multiple kinds of energy and power.
The research method that laser controlling silicon substrate surface form is utilized based on phase field model, energy are included thermal energy, changed
Learn energy, surface energy etc..
The described research method that laser controlling silicon substrate surface form is utilized based on phase field model, power include thermal diffusion,
The processes such as migration.
The research method that laser controlling silicon substrate surface form is utilized based on phase field model, step 3, system model
Building process:
There are a kind of in phase-field model (phase field model) into split-phase silicon, defines the volume point that c is silicon atom
Number, c (x, y, z, t) be one spatially and temporally on a phase field parameters, by measure c volume fraction when different
Between and different location on data variation, to simulate the dispersal behavior of silicon substrate surface atom and the differentiation of silicon substrate surface form
Process, according to Cahn-Hilliard model, the free energy equation of system are as follows:
What f (c) was indicated is the chemical energy variation for driving silicon atom to spread；
What is indicated is system surfaces energy variation；
Silicon substrate surface atom occur displacement driving force beWhat wherein u was indicated is chemical potential, by u=δ
G/ δ c determines that during laser irradiation, when silicon substrate to be placed in the temperature field of change of gradient, the flux of silicon atom can be with table
It is shown asM=Da/2kβT.D is thermal diffusion coefficient, kβFor boltzmann's coefficients, a is interfacial area.
Therefore, the net flux of silicon atom isDefine the mobility of silicon atom are as follows:
For this system model, phase field variable is determined by Cahn-Hilliard nonlinear diffusion equations, and bond quality
Conservation RelationshipObtain equation control as follows:
Wherein,Since the temperature field diffusion equation that laser irradiation generates can
Pass through following equation solution:
In above formula,ρ is density of material, and λ indicates that specific heat, k indicate thermally conductive
Coefficient.What β was indicated is the absorption coefficient of heat source, and R is reflectivity, I0For laser intensity.
Based on above-mentioned mathematical model, emulated in simulation software.
Compared with prior art, the present invention has a characteristic that
1, the method combined with analogue simulation the invention proposes experimental study is to the silicon substrate surface shape under laser irradiation
State is studied.
2, the mathematical model used in the present invention includes multiple kinds of energy and kinematics, can effectively be ground from energy point of view
Study carefully the evolution process of silicon substrate surface form.
3, the mathematical model used in the present invention does not need the position at display tracking interface, greatly reduces the complexity of calculating
Property.
Detailed description of the invention
Fig. 1 is the simple schematic diagram of nanostructure silicon substrate surface form compacting mechanism.
Fig. 2 is the simple schematic diagram of nanostructure silicon substrate surface form under experimental provision.
Fig. 3 is the simple schematic diagram of the energy for including and movement in phase-field model (phase field model).
Fig. 4 A, 4B, 4C are silicon substrate surface metamorphosis figure.
Fig. 5 is the silicon substrate surface form under experimental technique.
Fig. 6 is the silicon substrate surface form under emulation technology.
Specific embodiment
The preferred embodiment of the present invention is described in detail with reference to the accompanying drawing.
The silicon substrate surface moulding mechanism of silicon substrate is simply introduced.When laser (frequency is in Gaussian Profile) photograph
When the left end of radiosilicon substrate, the variation of temperature can occur for silicon substrate surface, thermal diffusion occur so as to cause silicon atom, and along one
Displacement occurs for direction, so that it is in a stable state, ultimately forms silicon substrate surface form as shown in Figure 1.
Experimental provision platform is built under AFM (atomic force microscope), main silicon fixture (the silicon production including micro-nano size
Fixture, for fixing silicon substrate) and laser emitter.The silicon substrate of a piece of micro-nano size is taken, the right end of silicon substrate is clipped in silicon
On fixture, with the left end of laser vertical irradiation silicon substrate.Experimental provision is as shown in Fig. 2, experiment specific step is as follows:
The power P of laser is transferred to 75mW by step 1, and wavelength X is transferred to 532nm, is irradiated to the left end of silicon substrate.
Step 2, laser irradiation silicon substrate 10s.
Step 3 is removed silicon substrate and is placed under AFM (atomic force microscope) and observed, the image observed such as Fig. 2 institute
Show.
The present invention will propose a kind of three-dimensional phase-field model (phase field model) to simulate based on silicon under laser irradiation
The evolution process of the diffusion behavior and nanostructure silicon substrate surface form of atom.There are a kind of ingredients in simulation model of the invention
Phase silicon defines the volume fraction that c is silicon atom.C (x, y, z, t) be one spatially and temporally on a phase field parameters,
By measuring data variation of the volume fraction of c on different time and different location, to simulate silicon substrate surface atom
The evolution process of dispersal behavior and silicon substrate surface form.
As shown in figure 3, when silicon substrate receives laser irradiation, the phase field model of system includes multiple kinds of energy and a variety of dynamic
Power；
The energy includes thermal energy, chemical energy, surface energy etc..
The power includes the processes such as thermal diffusion, migration.
For the model of this system, according to Cahn-Hilliard model, the free energy equation of system are as follows:
What f (c) was indicated is the chemical energy variation for driving silicon atom to spread.What is indicated is system surfaces
Energy variation.
Silicon substrate surface atom occur displacement driving force beWhat wherein u was indicated is chemical potential, by u=δ
G/ δ c is determined.During laser irradiation, when silicon substrate to be placed in the temperature field of change of gradient, the flux of silicon atom can be with
It is expressed asM=Da/2kβT.D is thermal diffusion coefficient, kβFor boltzmann's coefficients, a is interface face
Product.Therefore, the net flux of silicon atom is
Define the mobility of silicon atom are as follows:
For this system model, phase field variable is determined by Cahn-Hilliard nonlinear diffusion equations, and bond quality
Conservation RelationshipObtain equation control as follows:
Wherein,The temperature field diffusion equation generated due to laser irradiation
Following equation solution can be passed through:
In above formula,ρ is density of material, and λ indicates specific heat, and k expression is led
Hot coefficient.What β was indicated is the absorption coefficient of heat source, and R is reflectivity, I0For laser intensity.
Based on phase-field model (phase field model), 10.0 × 30.0 × 1.5um is established in simulation software3's
Silicon substrate model, wherein the thermal conductivity of silicon substrate model is 150W/m-K, and the thermal conductivity of rest part is 0W/m-K.In the model,
The distance between adjacent heat source is 10um, as shown in Figure 4 A.After simulation in 5 seconds, silicon substrate surface will be shaped on silicon substrate
Form, it is specific as shown in Figure 4 B.After 10 seconds, the silicon substrate surface form of forming is up to stable state, specifically such as Fig. 4 C institute
Show.
Fig. 5 is the silicon substrate surface form under experimental technique, and Fig. 6 is the silicon substrate surface form under emulation technology, comparison discovery
The silicon substrate surface form of emulation and the silicon substrate surface form of experiment are closely similar, demonstrate the correctness of emulation.
Above embodiments are the preferred embodiment of the present invention.The technical staff of this neighborhood is by carrying out above-described embodiment
Modifications and changes on various forms, fall within the scope of protection of the present invention.
Claims (5)
1. based on phase field model utilize laser controlling silicon substrate surface form research method, it is characterized in that in accordance with the following steps into
Row:
One, under an atomic force microscope, the silicon substrate of micro-nano structure is clamped using silicon fixture；
Two, the several seconds is irradiated with free end of the laser to silicon substrate, observes the silicon substrate surface form of silicon substrate and measures corresponding
Size；
Three, the silicon atom dispersal behavior in the case where phase field model Imitating is based on laser irradiation and nanostructure silicon substrate surface form
Evolution process；Step 3, the building process of model:
There are a kind of in phase field model into split-phase silicon, defines the volume fraction that c is silicon atom, c (x, y, z, t) is one in sky
Between a upper and temporal phase field parameters, pass through data of the volume fraction of measurement c on different time and different location and become
Change, so that the dispersal behavior of silicon substrate surface atom and the evolution process of silicon substrate surface form are simulated, according to Cahn-Hilliard
Model, free energy equation are as follows:
F (c) indicates the chemical energy variation that driving silicon atom is spread；
Indicate system surfaces energy variation；
Silicon substrate surface atom occur displacement driving force beWherein, u indicates chemical potential, is determined by u=δ G/ δ c
Fixed, during laser irradiation, when silicon substrate to be placed in the temperature field of change of gradient, the flux of silicon atom is expressed asM=Da/2kβT；D is thermal diffusion coefficient, kβFor boltzmann's coefficients, a is interfacial area；Cause
This, the net flux of silicon atom isDefine the mobility of silicon atom are as follows:
For model, phase field variable is determined by Cahn-Hilliard nonlinear diffusion equations, and bond quality Conservation RelationshipObtain equation control as follows:
Wherein,Since the temperature field diffusion equation that laser irradiation generates passes through such as
Lower equation solution:
Wherein,ρ is density of material, and λ indicates that specific heat, k indicate thermal coefficient；β
What is indicated is the absorption coefficient of heat source, and R is reflectivity, I0For laser intensity；
Based on above-mentioned mathematical model, emulated in simulation software.
2. the research method of laser controlling silicon substrate surface form, feature are utilized based on phase field model as described in claim 1
Be: step 2, the power P of laser are 75mW, wavelength X 532nm.
3. the research method of laser controlling silicon substrate surface form, feature are utilized based on phase field model as described in claim 1
Be: step 3, phase field model include multiple kinds of energy and power.
4. the research method of laser controlling silicon substrate surface form, feature are utilized based on phase field model as claimed in claim 3
Be: the energy includes thermal energy, chemical energy, surface energy.
5. the research method of laser controlling silicon substrate surface form, feature are utilized based on phase field model as claimed in claim 3
Be: the power includes thermal diffusion, transition process.
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| CN108318485A (en) * | 2017-12-14 | 2018-07-24 | 杭州电子科技大学 | Based on laser irradiation different materials to the research method of surface micro-structure shaping influence |
| CN109063262B (en) * | 2018-07-03 | 2022-12-02 | 杭州电子科技大学 | Method for controlling silicon-based internal microstructure based on phase field and temperature field |
| CN111488715B (en) * | 2020-04-10 | 2023-04-28 | 杭州电子科技大学 | Silicon-based inner cavity forming method based on electric field effect |
| CN111705361B (en) * | 2020-06-15 | 2021-05-11 | 杭州电子科技大学 | Preparation method of three-dimensional photonic crystal with stably formed internal spherical cavity array |
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| JP2007091543A (en) * | 2005-09-29 | 2007-04-12 | Canon Inc | Calculating method of grain shape |
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| CN106055887A (en) * | 2016-05-26 | 2016-10-26 | 杭州电子科技大学 | Research method of controlling draw ratio of Ag2Ga nano-needle based on phase field model |
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| JP2007091543A (en) * | 2005-09-29 | 2007-04-12 | Canon Inc | Calculating method of grain shape |
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