CN103268064B - Analog calculation method of ablating silicon nitride by ultrashort pulse laser - Google Patents

Abstract

The invention discloses an analog calculation method of ablating silicon nitride by ultrashort pulse laser, and Matlab is utilized to perform analog calculation and analysis on processing parameters. The analog calculation method mainly comprises the following steps that an ablating model of ablating silicon nitride by ultrashort pulse laser is established, and calculating parameters are initialized; boundary conditions of the plasma density are defined, and an ablating threshold, depth and volume with different analog parameters are calculated through the model; and on the basis of calculation results and a residual height model, the laser ablated residual height is analyzed and evaluated, and guiding parameters are given. By using the analog calculation method, the process of obtaining the processing parameters by repeated experiment can be avoided, analog results can be utilized to optimize the processing parameters, thereby shortening the product cycle, reducing the processing cost and increasing the production efficiency, and therefore, the analog calculation method has an important guiding value for the actual manufacturing process of ablating silicon nitride by ultrashort pulse laser.

Description

A kind of simulation method of mechanism of ultrashort-pulse laser ablation silicon nitride

Technical field

The invention belongs to ultra-short pulse laser Micrometer-Nanometer Processing Technology field, particularly a kind of simulation method of mechanism of ultrashort-pulse laser ablation silicon nitride.

Background technology

Along with the high speed development of advanced manufacturing technology and industrial level, the research of silicon nitride material is also received much concern.Because silicon nitride material has high chemical stability, high-heat resistance shock resistant, high rigidity, high temperature resistant, radiation hardness, the characteristic such as corrosion-resistant, thermohardening good, excellent optical performance.Therefore be widely applied in industries such as photoelectron, machinery, atomic energy, Aero-Space, and be widely used in the accurate and ultraprecise fields such as microelectronics along with it, microfabrication is carried out to it and seems particularly important.But silicon nitride belongs to high hard easy crisp material, existing processing method is difficult to carry out Precision Machining to it, therefore will realize then becoming key issue urgently to be resolved hurrily to its controlled fine removal.

Ultra-short pulse laser Micrometer-Nanometer Processing Technology a kind ofly utilizes that femtosecond laser is ultrafast, superpower, unique machining feature of superelevation, cause local microexplosion by producing the plasma of HTHP in very short time, thus realize the micro pipes method of material being carried out to accurately removal.Little owing to having the zone of action when femtosecond laser and matter interaction, without fuel factor, machining accuracy is high, can break through the unique advantages such as diffraction limit, therefore makes Precision Machining silicon nitride become possibility.This not only overcomes the difficulty in the process that its high rigidity characteristic brings, and provides a kind of precision machining method of high hard easy crisp material, thus improves crudy.But because removal precision when femtosecond laser carries out ablation to silicon nitride is wayward, and find optimal procedure parameters separately through repetition test and seem very loaded down with trivial details, working (machining) efficiency also can not get ensureing simultaneously, therefore just in the urgent need to a kind of method that can facilitate precision of prediction and don't lose working (machining) efficiency.Based on this, the present invention proposes a kind of simulation method of mechanism of ultrashort-pulse laser ablation silicon nitride, the evaluation of analog computation result when its key is then foundation and the different parameters of ablating model.About theoretical model and the correlation modeling method of mechanism of ultrashort-pulse laser ablation dielectric substance, all there is report with Publication about Document:

American scholar: M.D.Perry, B.C.Stuart, P.S.Banks, et al.Ultrashort-pulse laser machining of dielectric materials [J] .J Appl Phys, 1999,85 (9): 6803-6810.

France scholar: L.Sudrie, A.Couairon, M.Franco, et al.Femtosecond laser-induced damage and filamentary propagation in fused silica [J] .Phys Rev Lett, 2002,89 (18): 186601.

American scholar: C.H.Fan, J.Sun, J.P.Longtin.Plasma absorption of femtosecond laser pulses in dielectrics [J] .J Heat Transfer, 2002,124 (2): 275-283.

Chinese scholar: Liu Qing, Cheng Guanghua, Wang Yishan etc. the three-dimensional mangement of femtosecond pulse in transparent material and mechanism [J] thereof. photon journal, 2003,32 (3): 276-279.

Chinese scholar: Li Xiaoxi, Jia Tianqing, Feng Donghai etc. ablative mechanism and ultra-fast dynamics research [J] thereof of lower lithium fluoride are irradiated in ultrashort pulse. Acta Optica, 2005,25 (11): 1526-1530.

Analyzed by literature survey, Chinese scholars is when studying induced by ultrashort pulse laser dielectric substance, propose a lot of theoretical model describing avalanche ionization process and photoionization process, and the critical plasma density that conduction band free electron density Evolution and material occur when damaging is described.But these study the discussion that mostly lays particular emphasis on single model and single factors, rarelyr carry out systematically multi-model integrated analysis; And the controling parameters that seldom can relate to the research of ablation threshold and ablation depth in material removal process, lays particular emphasis on experimental analysis to the research of ablation volume then more comprehensively.Domestic scholars research is in this regard mainly for the discussion of interaction mechanism, and carried out lot of experiments, theoretical modeling remains defect, and research object is then in the majority with materials such as quartz glass, analyzes relatively little to the analog computation of silicon nitride material.Due to the weak point of its important application background and at present sunykatuib analysis, therefore find a kind of can the mechanism of accurate characterization ultra-short pulse laser and material, can remove technique to reality again provides the method for guide parameters to seem particularly important.

Summary of the invention

For solving in mechanism of ultrashort-pulse laser ablation silicon nitride process, the present invention removes that the wayward and technological parameter of precision is more difficult the problem such as to determine, for overcoming the deficiency of existing simulation method, study the independent role of unitary variant and the acting in conjunction rule of multiple variable respectively when calculating, its key is:

When 1, pretreatment being carried out to avalanche ionization coefficient and photoionization coefficient, first should determine the relation of ionization rate and electric-field intensity, then determine the relation of itself and energy density, so that follow-up ablation threshold analog computation.

2, laser pulse dimensional energy distribution Gaussian function is described, and Gaussian beam can break through processing diffraction limit, thus improves machining accuracy.

3, accurately should control condition when conduction band electron density reaches critical density, ensure that material calculates ablation depth, volume and residual altitude under the prerequisite that damage occurs.

The object of the present invention is to provide a kind of simulation method of mechanism of ultrashort-pulse laser ablation silicon nitride, not only can realize the optimization of control to ablation precision and technological parameter, and the blindness avoiding repetition test to bring, cut down finished cost, enhance productivity.

For achieving the above object, the present invention adopts following technical scheme:

A, the ablation threshold setting up mechanism of ultrashort-pulse laser ablation silicon nitride, the degree of depth and ablation volume-based model, and parameter initialization is carried out to model constants; Define plasma density boundary condition ρ during silicon nitride generation ablation in institute's established model simultaneously _crbe 1.6 × 10 ²¹cm ^-3, and pretreatment is carried out to the avalanche ionization coefficient of silicon nitride, photoionization coefficient and conduction band free electron density;

B, determine optical maser wavelength, setting pulsewidth computer capacity is 10fs ~ 10ps, calculates silicon nitride ablation threshold.When conduction band electron density exceedes critical plasma density, i.e. ρ _c(x, t) > ρ _crtime, silicon nitride produces damage, works as ρ _c(x, t)≤ρ _crtime, assignment must be carried out again to initializaing variable and calculate;

C, setting laser energy density codomain are 1J/cm ²~ 8J/cm ², based on threshold value result, ablation depth is simulated; Under the modeling volume assumed condition that single pulse ablation pattern is cone shape, and define laser beam waist radius, and then the ablation volume under utilizing ablation depth analog result to obtain corresponding conditions; Described volume-based model is

$V=\frac{x\·{{\mathrm{\π\ω}}_0}^2}{6}\ln \left(\frac{F}{F_{\mathrm{th}}}\right)$

In formula: V is ablation volume, x is ablation depth, ω ₀for waist radius, F _thfor ablation threshold, F is energy density;

D, set up the relational model of sweep speed v, line overlap rate δ and residual altitude Δ x, definition ablation residual altitude boundary condition, and threshold value and depth model result of calculation are loaded in residual altitude model; The relational model of described sweep speed v and residual altitude Δ x is

$v=\mathrm{\ΔL}(f-1)=\mathrm{\ξD}(f-1)=\frac{\mathrm{\Δx}}{x}\×100\%\·D(f-1)$

In formula: Δ L is two pulse distances on sweep speed direction, and ξ is relative residual altitude, and D is ablation diameter, and f is pulse frequency, and x is ablation depth; Δ x is residual altitude, refers to the distance between ablation profile summit line and profile valley line; The relational model of described line overlap rate δ and residual altitude Δ x is

$\mathrm{\δ}=\frac{(d-\mathrm{\Δd})}{d}\×100\%=(1-\mathrm{\ξ})\×100\%$

In formula: Δ d is ablation distance between centers of tracks, Δ d=ξ d; D is ablation line width, d=D;

E, paired pulses frequency carry out assignment, and are 4.0J/cm in energy density ²~ 8.0J/cm ², sweep speed is calculate residual altitude under 0 ~ 3mm/s condition.If Δ x > Δ x _max, do not meet the demands, variable should be re-entered and calculate, if Δ x≤Δ x _max, meet machining accuracy, export guide parameters, complete analog computation.

Described avalanche ionization coefficient is:

$\mathrm{\η}\left(E\right)=v_s\·\mathrm{\α}\left(E\right)=\frac{v_s\mathrm{eE}}{\mathrm{\Δ}}\exp (-\frac{E_i}{E(1+\frac{E}{E_P})+E_{\mathrm{kT}}})$

In formula: v _sfor saturation drift velocity, α (E) is Townsend coefficient, and e is electron charge, and Δ is energy gap.E _i, E _pand E _kTthat carrier overcomes electric-field intensity needed for ionization, optical phonon and thermal scattering effect respectively.

Described photoionization coefficient is:

In formula: ω is laser frequency, m=m _em _h/ (m _e+ m _h) be the reduction effective mass of electron hole pair, _me, m _hbe respectively the effective mass in electronics and hole; N=< Δ/(h ω)+1> represents the number of photons exciting an electron institute to absorb from valence band to conduction band; U=Δ-e ²e ²/ (4m ω ²), Φ (z) is Dawson integration.

Described ablation threshold model is:

${\mathrm{\&rho;}}_{\mathrm{cr}}(0,\mathrm{\&tau;})=\frac{{\mathrm{\&rho;}}_{a0}[W_{\mathrm{th}}+H_{\mathrm{th}}{\mathrm{\&rho;}}_{c0}]\exp \left[(\frac{{2W}_{\mathrm{th}}}{{\mathrm{\&rho;}}_{a0}}+H_{\mathrm{th}})\mathrm{\&tau;}\right]-W_{\mathrm{th}}({\mathrm{\&rho;}}_{a0}-{2\mathrm{\&rho;}}_{c0})}{{2W}_{\mathrm{th}}+H_{\mathrm{th}}{\mathrm{\&rho;}}_{c0}\exp \left[(\frac{{2W}_{\mathrm{th}}}{{\mathrm{\&rho;}}_{a0}}+H_{\mathrm{th}})\mathrm{\&tau;}\right]+H_{\mathrm{th}}({\mathrm{\&rho;}}_{a0}-{2\mathrm{\&rho;}}_{c0})}$

In formula: ρ _a0, ρ _c0be respectively initial valence band, conduction band electron density, ρ _crfor critical electron density.H _th=η (F _th); W _th=w _pI(F _th), F _thfor ablation threshold, τ is pulse width.

Described ablation depth model is:

In formula: x is ablation depth, h is Planck's constant; N=(< ε >+ Δ)/h ω, < ε > is averaged electron energy in plasma, W _f=[F/F _th] ⁿw _pI(F _th), H _f=[F/F _th] ^1/2η (F _th).

Described conduction band free electron density equation is:

$\frac{{\&PartialD;\mathrm{\&rho;}}_c(x,t)}{\&PartialD;t}={\left(\frac{{\&PartialD;\mathrm{\&rho;}}_c(x,t)}{\&PartialD;t}\right)}_{\mathrm{AI}}+{\left(\frac{{\&PartialD;\mathrm{\&rho;}}_c(x,t)}{\&PartialD;t}\right)}_{\mathrm{PI}}-{\left(\frac{{\&PartialD;\mathrm{\&rho;}}_c(x,t)}{\&PartialD;t}\right)}_{\mathrm{Los}.}$

In formula: AI item and the conduction band electron variable density that PI item represents avalanche ionization respectively, photoionization causes, Los. item represents the loss of carrier.

Described avalanche ionization coefficient and photoionization coefficient pretreatment refer to the relation by light intensity and electric-field intensity, energy density, finally set up function between ionization coefficient and energy density and to its computational analysis; The pretreatment of conduction band free electron density refers to and utilizes it to characterize equation, and the space-time expression form in conjunction with laser is done to derive further, and carries out analog computation by the parameter such as initial conduction band, valence-band electrons density of silicon nitride.

The pass of described light intensity and electric-field intensity, energy density is:

$I=\frac{n_0{E}^2}{{2R}_0}=\frac{F}{\mathrm{\&tau;}}$

In formula: R ₀=c μ ₀for vacuum impedance, c is vacuum light speed, μ ₀for space permeability, n ₀for medium refraction index.

Compared with prior art, the present invention has following beneficial effect:

1, the simulation method adopted in the present invention is compared with the scheme in the past reported, take into full account electron ionization mode when ultra-short pulse laser and silicon nitride interact and electron density Evolution, the removal mechanisms at work of material in ablation process can have been reflected more truly;

2, the simulation method adopted in the present invention is compared with the scheme in the past reported, each machined parameters is determined convenient and is convenient in actual production realize, revise with after analog result comparison, technological parameter database can be listed in, to subsequent technique optimization, there is important guiding and be worth;

3, the simulation method adopted in the present invention, compared with the scheme in the past reported, can be applied in a flexible way in the product of processing different accuracy, size, reduce while designing and developing cost and turn improve efficiency, be easier to ensure crudy.

Accompanying drawing explanation

The present invention has 6, accompanying drawing, wherein:

Fig. 1 is a kind of simulation method flow chart of mechanism of ultrashort-pulse laser ablation silicon nitride;

Fig. 2 is the Changing Pattern of silicon nitride ablation threshold with pulse width;

Fig. 3 is the Changing Pattern of silicon nitride ablation depth with energy density;

Fig. 4 is the Changing Pattern of silicon nitride ablation volume with energy density;

Fig. 5 (a), (b) are that sweep speed and line overlap rate affect schematic diagram to residual altitude respectively;

Fig. 6 is the Changing Pattern of residual altitude with sweep speed, energy density and pulse width.

Detailed description of the invention

Below in conjunction with accompanying drawing 1-6 and embodiment, the present invention is further described: as shown in Figure 1, a kind of simulation method flow chart of mechanism of ultrashort-pulse laser ablation silicon nitride, embodiments of the invention require: under optical maser wavelength is 780nm condition, obtain by analog computation the technological parameter being used to guide actual processing.Mainly comprising pulsewidth is damage threshold under 10fs ~ 10ps condition; Energy density is 1J/cm ²~ 8J/cm ², ablation depth when pulsewidth is 12fs, 35fs, 220fs and volume and sweep speed are 0 ~ 3mm/s, and energy density is 4.0J/cm ²~ 8.0J/cm ²time residual altitude.Physical simulation calculation procedure is as follows:

A, the ablation threshold setting up mechanism of ultrashort-pulse laser ablation silicon nitride, the degree of depth and ablation volume-based model, and parameter initialization is carried out to model constants.By Matlab software, in electric field strength E=0 ~ 350MV/cm, during energy gap Δ=5.0eV, can be calculated Townsend coefficient; Another by free electron saturation drift velocity v _s=2 × 10 ⁷cm/s, vacuum impedance R ₀=376.991 Ω, refractive index n0=2.0, can calculate the relation of avalanche ionization speed and energy density; For silicon nitride material, from valence band to conduction band, excite the number of photons n=4 that an electron institute will absorb, and then at electron hole pair reduction effective mass m=0.86m _e=7.833 × 10 ^-31during kg, analog computation goes out photoionization speed.

B, utilize conduction band free electron density EVOLUTION EQUATION ρ _c(x, t) is described the electron density in silicon nitride ablation process, wherein: initial valence-band electrons density p _a0=1.10 × 10 ²³cm ^-3, initial conduction band electron density p _c0=10 ¹⁰cm ^-3, critical electron density ρ _cr=1.6 × 10 ²¹cm ^-3.Work as ρ _c(x, t) > ρ _crtime, meet ablation threshold condition, and then under pulsewidth is 10fs ~ 10ps condition, calculate the short pulse ablation threshold value of silicon nitride, result as shown in Figure 2, wherein during τ > 10ps, is long pulse ablation threshold.

C, based on threshold value analog result, obtain damage threshold when pulsewidth is 12fs, 35fs and 220fs, be respectively 2.0J/cm ², 1.8J/cm ²and 1.4J/cm ²; Setting energy density codomain is 1J/cm ²~ 8J/cm ², and calculating ablation depth, result is as shown in Figure 3.And then at waist radius ω ₀when=30 μm, ablation volume when analyzing distinct pulse widths by volume-based model, as shown in Figure 4; The ablation depth curve utilizing Fig. 3 to obtain, can select the energy density parameter adopted during ablation different depth.

D, set up the relational model of sweep speed v, line overlap rate δ and residual altitude Δ x respectively, modeling schematic diagram is as shown in Fig. 5 (a), (b); Meanwhile, definition ablation residual altitude boundary condition, and the ablation depth result that the ablation threshold result obtained by Fig. 2 and Fig. 3 obtain is loaded in residual altitude model.

E, setting pulse frequency are 1kHz, and energy density is 4.0J/cm ²~ 8.0J/cm ², sweep speed is 0 ~ 3mm/s, and utilize sweep speed model to carry out analog computation analysis to residual altitude, result as shown in Figure 6.According to residual altitude requirement, can determine to add the technological parameters such as sweep speed, energy density and the pulsewidth adopted man-hour, if Δ x > Δ x _max, do not meet the demands, variable should be re-entered and calculate, if Δ x≤Δ x _max, meet machining accuracy, export guide parameters, complete analog computation.

Above-described embodiment is the unrestricted method scheme of the present invention in order to explanation only, and any being equal to according to technical scheme of the present invention and inventive concept thereof replaces or change, and all should be encompassed within protection scope of the present invention.

Claims (1)

1. a simulation method for mechanism of ultrashort-pulse laser ablation silicon nitride, is characterized in that the method comprises the following steps:

A, set up the ablating model of mechanism of ultrashort-pulse laser ablation silicon nitride, and parameter initialization is carried out to model constants, define plasma density boundary condition ρ during silicon nitride generation ablation in institute's established model simultaneously _crbe 1.6 × 10 ²¹cm ^-3;

B, determine optical maser wavelength, setting pulsewidth computer capacity is 10fs ~ 10ps, calculates silicon nitride ablation threshold; When conduction band electron density exceedes critical plasma density, i.e. ρ _c(x, t) > ρ _crtime, silicon nitride produces damage, works as ρ _c(x, t)≤ρ _crtime, assignment must be carried out again to initializaing variable and calculate;

C, setting laser energy density codomain are 1J/cm ²~ 8J/cm ², based on threshold value result, ablation depth is simulated; Under the modeling volume assumed condition that single pulse ablation pattern is cone shape, set up ablation volume-based model, and define laser beam waist radius, and then the ablation volume under utilizing ablation depth analog result to obtain corresponding conditions; Described volume-based model is

$V=\frac{x\&CenterDot;\mathrm{\&pi;}{{\mathrm{\&omega;}}_0}^2}{6}\ln \left(\frac{F}{F_{\mathrm{th}}}\right)$

In formula: V is ablation volume, x is ablation depth, ω ₀for waist radius, F _thfor ablation threshold, F is energy density;

D, set up the relational model of sweep speed v, line overlap rate δ and residual altitude Δ x, definition ablation residual altitude boundary condition, and threshold value and depth model result of calculation are loaded in residual altitude model; The relational model of described sweep speed v and residual altitude Δ x is

$v=\mathrm{\&Delta;L}(f-1)=\mathrm{\&xi;D}(f-1)=\frac{\mathrm{\&Delta;x}}{x}\&times;100\%\&CenterDot;D(f-1)$

In formula: Δ L is two pulse distances on sweep speed direction, and ξ is relative residual altitude, and D is ablation diameter, and f is pulse frequency, and x is ablation depth; Δ x is residual altitude, refers to the distance between ablation profile summit line and profile valley line; The relational model of described line overlap rate δ and residual altitude Δ x is

$\mathrm{\&delta;}=\frac{(d-\mathrm{\&Delta;d})}{d}\&times;100\%=(1-\mathrm{\&xi;})\&times;100\%$

In formula: Δ d is ablation distance between centers of tracks, Δ d=ξ d; D is ablation line width, and ξ is relative residual altitude, d=D;

E, paired pulses frequency carry out assignment, and are 4.0J/cm in energy density ²~ 8.0J/cm ², sweep speed is calculate residual altitude under 0 ~ 3mm/s condition; If Δ x > Δ x _max, do not meet the demands, re-enter variable and calculate; If Δ x≤Δ x _max, meet machining accuracy, export guide parameters, complete analog computation.