Dynamic simulation on the preparation process of thin films by pulsed laser

Vvol. 44 Sio. 11 .SCIENCE IN CHINA (Series A)Novenber 2001Dynamic simulation on the preparation process of thin filmsby pulsed laserZHANG Duanming (张端明), LI Zhihua (李智华)', YU Boming (郁伯铭)',HUANG Mingtao (黄明涛)', GUANLi(关丽)',ZHONG Zhicheng (钟志成)2 & L Guodong (李国栋)=1. Depatment of Physics, Huazhong University of Science and Technology, Wuhan 430074. China;2. Departnent of Physics. Xiangfan Universily. Xiangfan 410000 ChinaCorespondence should be adresed to Zhang Duanming ( email: zhangd @ public. wuhan. cngb. com)Received March 20, 2001AbstractAn ablation model of targets iradiated by pulsed laser is established. By using the simpleenergy balance conditins, the relationship between ablation surface location and time is derived. Byan adiabatic approximation, the continuous-temperature condition, energy conservation and all bound-ary conditions can be established. By applying the analytical method and integral-. approximationmethod, the solid and liquid phase temperature distributions are obtained and found to be a function oftime and location. The interface of solid and liquid phase is also derived. The results are comparedwith the other published data. In additin, the dynamics process of pulsed laser deposition of KTN(Kta. sNb, xsO,) thin fim is simulated in detail by using fluid dynamics theory. By combining the ex-pression of the target ablation ratio and the dynamic equation and by using the experimental data, theeffects of laser action parameters on the thickness distrbution of thin film and on the thin film compo-nent characterstics are discussed. The results are in good agreement with the experimental data.Keywords: ablation ratio, KTN thin flm, plasma. pulsed laser deposition (PLD).In recent years，with the development of the high-density pulsed laser technique, the PulsedLaser Deposition (PLD) technigue shows its special advantages,2. ，such as high-deposition ve-locity, low substrate temperature and similarity between target and thin flm components. Although many kinds of functional thin flms'. . have been prepared and great progresses in experi-menls have been made, lttle attention was paid to the understanding of the mechanism of thePLD. Singh and Narayan'SI proposed a theoretical model for plasma expansion, but the systemati-cal study in this area was still very limited. lIt is very important 10 prepare the high-quality thinfilm and study the thin flm physics for better understanding the mechanism and dynamie process-es of the interactions between a pulsed laser and a target. In this paper, the PLD mechanism isstudied systematically ，including the ablation process , expansion process and deposition process .First, according to the energy balance conditions, the ablation surface Jocation as a function oftime is derived; then by using the appropriate boundary conditions , we calculate the temperaturedistribution and the interface location of solid and liquid phases . Secondly, based on the modifiedS-N model and on the hydrodynamie theory, the motion equation of plasma generated by pulsedlaser is derived. By combining the ablation process with the spatial-expansion process of plasma，the process equations are obtained which can be used to describe the process of the quasi- molecu-lar deposition for KTN thin films .中国煤化工MYHCNMHG1486SCIENCE IN CHINA (Series A)Vol. 441 Theoretical modelThe process of PLD is generally casified into three separate regimes: (i) the high densityand high lemperature existing on the larget surface iluminated by pulsed laser; (ii) the plasmaexpanding into the vacuum space; (ii) then the plasma depositing on the substrate. We now de-scribe the three processes in the fllowing.1.1 Pulsed-laser ablation modelWhen a high-powered laser beam iradiates on a target surface, the target will absorb thelaser energy and sputter out high-lemperalure and high pressure plasma, and meanwhile, a pantof the target will be liquated. A sketch of the laser- solid interaction is shown infig. I.Fig.1 shows that during the incidence of alaser pulse, three separate purts can be distin-Laser beams guished. (a) High-temperature and high-pressureplasma cloud which can be divided into two re-gions: corona region and conduction region6 ( seec) (b) (a)regions A and B in fig. 1). Ninety-eight percentFig. 1. A sketch of the laser-solid interacin.of laser energy is deposited in corona by the in-verse bremsstrahlung absorption process, and thena part of the absorbed energy will transfer into the ablation surface because of existence of temper-ature gradient. (b) Liquid phase region generated by the liquated target. (c) Solid phase regionabsorbing the conducting energy。In addition, the heating and meling processes of pulsed laserirrudiation on material constitute a three-dimensional heat flow problem. But in the mlliecondprocess, the short thermal difusion distance and the large dimension of the laser beam comparedto the melt depth limit the thermal gradient parallel to the interface to several orders of magnitudeless than the gradient perpendicular to0 the interface. Thus, the problem can be simplified into aone-dimensional heat flow problem . The solid and liquid phase temperatures , ablation surface po-sition and the dynamic interface are discussed in detail in the next seetion.1.1.1 Ablation ratio and the ablaion process of pulsed laser.The ablation ratio for a tar-get for pulsed laser can be expressed asN = pd/(tm)，(1)where N is the evaporating ratio of particles for a unit dimension,τ is the duration of time of laserpulse, P represents the target density, d is the depth of ablated target, and m is the ablatedAssuming that the power densily of ineident laser pulse is lo, the absorbing coficient is b,the power density 1(x) at the location x satisfiesd/(x)/dx =- 61(x),(2)with the boundary condition: x=0，1(0)= lo, then1(x) = lge~,(3)When a beam of laser transmits to the location x,,中国煤化工reasesto 1,. thelaser cannot evaporale particles any longer. We defing:MYHCNMHGiastheevaporat-ing depth of target by laser pulse. From eq. (3), we havex, = (1/b)In(10/1).(4)4 is the density threshold of an incident laser beam for evaporation, i.e. when the power density.So. IIDYNAMIC SIMULATION ON THE PREPARATION PROCESS 0F THIN FLMS BY PLSED I.ASER1487of the incident laser Io < I, the particles cannol evaporate from the surface of the target by laser.According t0o the principle of energy balance, the energy for evaporation must be equal to thesubliming energy of the material if the evaporated depth per unit dimension is x，i.e.. ρ. E,x= r|, bl(x)dx = rl(1-e-).(5)Because the evaporated depth by a single laser pulse is very small, we expand e~bx at x=0,(6)From eqs. (5) and (6), we havepE,(7)b'τIoAccording t0 ref. [7], the absorbing coficient b can be expressed asb = 4πc/入,(8)where c and λ are the extinction coefficient and laser wavelength, respectively .Substituing eqs. (7) and (8) into eq. (1), the target ablation ratio N can be obtained:N =-p)ρE,λ(9)2πcrm4πct1oFrom eq. (9), we can see that the ablation ratio N is proportional not only to the power density0 but also to the wavelength λ of pulsed laser as well as the component charaterstics of the tar-get. If Io is the original thickness of the target and the coordinate origin is on the back-surface ofthe target, the position of the ablation surface can be expressed asx。(t)= lo-()(10)Subtuting eqs. (1) and (9) into eq. (10) yieldsρEλx。()= b--(11)2π nmt l4πnτ/oand when t= τ，(12)2πnm4πnrlo)Thus，we are the first to derive the relationship of ablation surface to time. Fromeq. (11), wecan see that the ablation surface moves forward at an even speed, which is determined by the pa-rameters of laser and larget. For some kind o[ target and laser, the ablation rate is a constant.This result is in agreement with that of ref. [8], and eq. (11) is more convenient to be used forcomparison with experimental results.1.1.2 Equations and boundary conditions .When high-power pulsed laser iradiates on atarget surface, the high-temperature and high-density plasma spultering will occur on the surlaceand a part of the target will become liquid. The unstable temperature distibution will appear insolid and liquid regions. Moreover, the formation of stochastic density distribution of plasmatakes only several nanosecond!2) , during which the ablation surface advances along the back-sur-face of the target. After the formation of the plasma system, ninety-eight percent of laser energywill be absorbed by an inverse bremsstrahlung processb，so the heat source term can be neglect-中国煤化工YHCNMHG1488SCIENCE IN CHINA (Series A)Vol. 44 .ed when both solid and liquid phases are considered. For convenience, we set the coordinate ori-gin al the ablation surface, T(x,t) represents the temperature of a faculative point x of the tar-get and a facultaive time l, so the heat flow equation is3T(x,t)p;(T)Cp(T)一)lAT(x,t)](0< 1≤r,0< x≤d)，(13)where the subscript i= 1 ,2 reler to the solid and liquid phase respetively, p(T) and Cg(T)represent the temperature-dependent density and thermal heat capacity per unit length. Assumingthat the thermal conductivity K, is independent o{ lemperature, we define the thermal difusivityas a=k/(pcp), then eq. (13) can be expressed asT(x,t) 1 aT(x,t)(0< l≤t,0< x≤d).(14)8xLet S(l) represent the interface of the solid and liquid phase, L and Tm refer to the latent heatper unit volume and meling temperature of the malerial, respectively, and To be the emperalureat t=0. In the interface position of the solid and liquid phases，the continuous-temperature con-dition and the conservation of energy must be satisfied, s0 the boundary conditions of the interfaceare given by3T(15)T(S) = T,(S) = T(16Moreover, an adiabatic bypothesis is adopted at the back-surface of the target, that is 10 say thatno energy is losing at the back surface of the larget, which is reasonable for the short-pulse laser,because the duration of time of laser pulse is very short ( mllisecond). So it is impossible to losea large amount of energy from the surface. So the boundary condition for the back- surface of thetarget is given byT,K,x= 0,(17)where x。represents the position of the ablation- surface. Because the coordinate origin is placed atthe ablation surface, the back -surface coordinate is xg. When plasma sputering is completed, xcan be expressed aspE,\4πntlo )During the action of the pulsed laser, we consider that the ablation surface remains on the boilingtemperature Tq, and the boundary condition isT,|。= Tq (0< l≤r).(18)After a pulse action, the adiabatic hypothesis can also be adopted, i.e.=0(τ r, where τ is the duration of thelaser pulse. According to ref. [5]， when I≤τ, the expansion process may be considered asisothermnal, and when l> t, the process is adiabatic.We assume that the spatial concentration of plasma is similar to the Gauss distribution in theZ and Y directions, but in the X drection is Poisson-lype distribution. Because a large numberof particles in the y and z directions ejected from the target surface expands feely and is dis-tributed in the Gauss-type while the particles in the x direetion are restricted by the target sur-face, the particle density distibution is Poisson-type, which is dfferent from the model of ref.中国煤化工MHCNMHG\o. I1DITAMIC SIMCLIATIUN 0V THE PREPARATION PROCESS 0F ThIN FIMS BY PLISED LASER1491.5]. So the spatial concentration of plasma can be expressed asn(x.y.z,t) = CNisx exp8(1)- 2y()2- 22(26≤5，(31)where C is the unitary cofficient, ;v represents the larget ablation ratio, s| is the dimension oflaser beam spot, X(i), Y(i) and Z(l) are the spatial sizes of plasma，which are correspond-ing to the sizes when the plasma density decreases to 37.5% of the plasma density on the targetsurface . Integrating eq. (31), the unitary cofficient C can be obtained byC=2πX(1)Y(l)Z(t)(32)Subsituting eqs. (9) and (31) into eq. (32)， the spalial concentration of plasma can be ex-pressed asphts|n(x.y,z,l) =4x2 crmX(t)Y(l)Z(t)4πcr1o)zx exp|X(t) 2Y(t)2 22(t)，i≤t.(33)According to the ideal gas equation, P = nkTo( where n is the plasma density). we can ob-tain the spatial distribution of the plasma pressure P(x,y,z,l) given bypils;KTopEλP(x,y,z,t)=23x(1)Y(t)2(i)( 4πctlo )z2x expX(t)~ 2Y(1)2~ 2Z(l)2'l≤τ.(34)The plasma spatial velocity ean be expressed asdX(t).y_ dY(t).dZ(i)v(x,y,z.t) =dtY(t) dZ(t) duk,(35)where i, j and k are the unit veclors in the x， y and z directions, respectively,dX(t)dY(t)dZ(l)and. are the expansion velocities of plasma edges X, Y and Z. The gas dynamicdi1equations and continuity equation goveming the expansion of plasma are given byi pdV =-!p(v . so)ds+ -(mNu),(36)i 12()+p(v.V)v+ v(V.ρv)+ Vp)dv =0，(37)where V is the plasma volume, S is the curve surface enveloping the volume V, So is the unitvector of the elementary dimension ds in the normal direction, ρ is the plasma density, m is theaverage mass of atoms, the last term in eq. (36) represents the mass variation of particles ip-ping into plasma .Subsituting the expressions of the plasma density ，pressure and velocity into eqs. (36) and(37) yields{1 dX dx(t)] [」 dY dfY()]X()[-4+12]= Y(t){F4+2-]中国煤化工MYHCNMHG1492SCTENCE IN CHINA (Series A)vol. 448Z(i)] kT。= Z()(38)i p2Eq. (38) describes the variation of the plasma edge size as a function of time during the action ofa laser pulse (t≤τ). Generally speaking, the original size of plasma on the landscape orienta-tion is the magnitude of millimeter, while the portrait original size is the magnitude of micron. Sohe portait acceleration will be larger than that in the landscape orientation. Therefore, a dreichplasma will be formed in space .When l> τ, the action of a laser pulse ceases，s0 the expansion process can be consideredas an adiabatic process which satisfies the thermodynamics equationT! Xx(i)Y(l)Z(t)]Y-I = constant,(39)where y is the ratio of specific heat capacities al conslant pressure and volume, T is the adiabat-ie temperature.During the adiabatic expansion process. the action of laser stops, there are no particleseraporated from the target, so the number of paricles keeps constanl. According to eq. (33),the densily n(x，y，z，t) in plasma can be expressed aspXs!n(x,y,z,t)4π? cmX(t)Y(t)Z(1)4πcr1o)X(l) 2Y(t)2 22(t)2]，l>τ.(40)Since we have assumed that plasma behaves as an ideal gas, the pressure P at any point in theplasma is related to its density by the ideal gas equation (P = nkT) which can be expressed aspAs;KTpEλP(x,y,z.t) =4xr2cmmX(t)Y(t)2(o)(- 4πcr1o)?2x expX(t)~ 2Y(t)2~ 2Z(1)2]，t>t.(41)The adiabatic equation of state and equation of temperature are1 pJFpli+ v.VF]- 1n+v.vn]=o,(42)T+ v.VT= (1- y)TV. v，(43)8respectively .We have assumed thal there is no spatial variation in the plasma temperalure, orVT=0. Ifwe substitute the density, pressure and velocily profiles into the dfferential equations (35),(39). (41) and (43), the solution controling the expansion of plasma in this regime is given byjdX[d2Y[dZ] kTo[XoYoZo1Y-1x(l)|= Y(t)2(2小= m(1(0)(0)2)(44)where Xo, Y。 and Zo are he iniial orthogonal edges of plasma after the lernination o[ the laserpulse (l= t).So far we have oblained a set of dfferential equations (38) and (44) describing the spatialexpansion of plasma. By using the difference method, the two equations can be solved numerical-ly, and the relation of the spalial-expansion size，velocity and lime can be obtained. Using these中国煤化工TYHCNMHG\n.11D) \AMIC SIMLLATION ON THE PREPARATION PHOCESS OF THIN FILMS BY PLLSED LASER1493relations, we will futher simulate a series of deposition characteristics of thin film in the nextsection in detail.2 ExperimentsThe K(0C2H5)s, Nb(0C2H3)s, Ta( OCqHs)s were chosen as the test materials, the pow-der of KTa.6sNbq.3sO3(KTN) was prepared, and then pressed into 030 mmx 3 mm circularslices, finally sintered in the atmosphere of potassium oxide al 100C for 45 h, then the high-quality KTN ceramic targets were obtained. In addition, the volume density of KTN was measuredto be6.14x 103 kg/m'，the rfractivity is 2.23, the sublimation energy is 1.0x 10 J/kg. TheKTN thin fIm was prepared scssully on the P-Si(100) substrate by using the Lambda,WMG201 MSC quasi-molecular laser instrument 135.161 when the laser power density is 1.6 J/cm2and the substrate temperature Ts is 560C，where the duration of time of a laser pulse is 45 ns,and the output wavelength was 308 nmb}l.3 Results and discussionAccording t0 the expressions of the ablation ratio and the spatial dynamic equations (36)and (40) of plasma, and by using some experimental parameters, we have simulated the effectsof different wavelengths and power densities of pulsed laser on the deposition characteristics ofthin films . Because there are many different components with different velocities ，for conveniencewe chose Nb as the representative particles to discuss the distribution characteristics of spatialthickness. When we analyze the efcte of the power densily of pulsed laser on the componentcharacteristics of the KTN thin film, Ta，Nb and K are chosen as the representative particles ，and the proportionof K in the thin film is 1. Lnder general conditions. K:Ta:Nb= 1:0. 65:0.35. In addition, Y is 1 .66 for the adiabatic process .Assuming thal the target location is fixed, and the substrate is parallel to the target, the dis-tance from the substrale to the target is 3 cm, so the deposition thickness of thin fIms can be ex-pressed asd(y) a n(x,y,z,t)u,(t)dt,where l1 is the time when the edge of plasma arrives at the substrate surface, l2 is the total depo-sition time. Simply. we choose z =0.0, and only study the thickness distibution along the y-axis. The zero spot of y-axis corresponds to the center of the irradiated spot on the target surface .3.1 Relation between the thickness distribution and the laser densityFig. 2 gives the thickness distribution under different laser power densities. In fig. 2, thex-axis represents the different location on the substrate, and the vertical axis is the thickness ofthe thin film. .From fig.2, we can see that the thickness distribution of the thin flm in the x direction isnot uniform, independent of power density of laser beam. The thickness of the thin flm reachesits maximum as x=0. The thickness decreases with increase of x. When the power density oflaser becomes higher, the deposition velocity will become much larger, but the effect of the laserpower density on the film thickness is negligible. The reason is that the spatial concentration dis-tribution of plasma is similar to the Gauss-type distribution, so the thickness distribution of thinfilm is also similar to the Gauss distibution. According to eq. (9), the higher the laser power中国煤化工MHCNMHG1494SCIEYCE IN CHINA (Series A)Vnl. 44density, the larger the evaporating velocity and the plasma concentration. So. the thin films willbe much thicker, but the changing of the thickness of thin films with the laser power density isnot significant at the location far away from x = 0，because there the plasma concentration ismuch lower. So the higher laser power density is helpful for inerease of the deposition velocity.But we know that the over high deposition velocity will worsen thin film construction, and it is im-portant to choose the appropriate laser power density in the actual work. In addition, from fig. 2,wecan see that the lower laser power density is of advantage to improve the uniformity of thethickness distribution of thin films.3.2 Relation belween the thin film thickness distribution and the laser wavelengthFig. 3 shows the thickness distribution of KTN thin film prepared under different laser powerdensity，where x-axis represents the dilerent location in the substrate ，and the longitudinal axisrepresents the thin flm thickness. According t0 fig.3, the thickness distribution of thin flm isnot uniform. independent of the wavelength of laser, which is similar 10 fig. 2. The thickness ofthe thin film reaches its maximum as x =0, the thickness decreases with the increase of x，andthe longer the laser wavelength, the worse the uniformity of the thickness distibutin. The .change of thin film thickness with the wavelength is not significant at the location far away from x= 0 either, where the plasma concentration is low . The theoretical results are in good agreenentwith our esperimental resuls13.4.x 10~107) 7rX10'06F... 222X 10'W/em?0.6p一2.89 x l0Wem:05+0.5---i12....人/3040.4-言0.2-差0.201|0.140.0l000.0L00 0.02 0.0406083.000.00 0.02 0.04 006 0.080.0xem .x/mFig. 2Fig.了From the above discussion, we can see that the laser power density and wavelength shouldbe chosen appropriately. Aclually，we find that this problem can be solved by the reyolving lensmethod because the thin film uniformity can be improved by changing laser beam orientation. Wehave prepared large- area and uniform KTN thin filmns on the Si slice by revolving-lens methodsusulyl5.3.3 Relation between the thin film component properties and the laser power densityFig. 4 shows the component properties of the KTN thin film under the diferent laser powerdensities. Fig. 4(a) and (b) correspond to the cases when the power densities are 2.22x 10'W/cm2 and 6.67x 10' W/cm2，respectively. For convenience , the proportional curves of Ta andNb in the thin films are drawn nomally, and the solid line represents: Ta:K=0.65:1, Nb:K=0.35:1.Fig.4 shows that when the laser density is very high, the proportion of K, Ta and Nb is very中国煤化工MYHCNMHGDI1SAMIC SIMLLATION ON TIE PREPARATION PROCESS OF THIN FIMS BY PLSED L4SER149500r-n10(b)a●Ta.Ta0-●Nb8040-20-0000005 0.010 0.015 0.020 0.025 0.0300.000 0.005 0.010 0015 0020 0.025 0.030xi10 Wem. (b) Dependence of the film component propeties on the x-dirertional distance when rnergy density is6.67x10' W/em2 .close to the particle compositions in the target. .Moreover. when the laser power density is verylow，the difference is very large between the Ta and Nb proportion and the particle proportion inthe target. That is, when the power density of laser is very low, the keeping-composition charac-teristics of the thin film will be rather worse . The reason is that the ablation velocity will be largerunder the action of higher laser power density. The high-temperature and high-density plasma willbe formed on the target surface. But according tn the kinetic energy E=一mo2, the higher thelaser power density , the higher the particle average kinetice energy. So, the energy is primarilydetermined by particle velocity. On the contary, the effect of the difference of particle mass onenergy will be remarkable, and the keeping composition charactrstics of thin films will be ratherworse. These results are in good greement with the experimental resuls .16) . From the above dis-cussion，in order to keep hin film components consistent with those of the larget, we may in-crease the laser power density . But over high laser power density will make thin film constructionworse, so it is very important to choose the appropriate laser power density in experiments .4 Conclusions1) By using energy balance conditions, we have establshed the ablation model equation andcoresponding boundary conditins. In addition, we have analtically obtained the dynamic equa-tion (11) of the ablation surface for the first time. Compared with the relationship of ref. [8].eq. (11) is more convenient for comparison with experimental results. The relationship of the po-sition of solid and liquid interface with time is derived analtically . The theoretical results are ingood agreement with the numerical data of ref. [12]. By adopting the accurate-resol ing methodand integral-approximation method, we have also obtained the temperature distribution as a func-tion of time and place for the whole system.2) By the bhydrodynamic theory , the motion equation of plasma generaled by pulsed laser hasbeen obtained as well. Combining the ablation process with the spatial-expansion process of theplasma，the process equations are obtained which can describe the process of the quasi- moleculardeposition of thin films .3) Uising the experimental parameters of a target obtained from our experimental work. theefects of laser action parameters on the thickness distribution of thin flm and the thin film com-中国煤化工MHCNMHG1496SCIENCE IY CHINA (Series A)Vol. 44ponent characteristics are discussed. The results are in good agreement with the experimental con.clusions .4) In addition, according to our theoretical and experimental work, many good techniqueconditions for depositing large-dimension and uniform-thickness distribution of thin fiIms are ob-tained , which can offer clues for improving the PLD method .Acknowledgemeats The Buthors would like to thank their teachers and cllegues for ifnrnative discusins.References1. Agosieleli. J. A.. Braunstein. G. H.. Blanton, T. N., Epitaxial LiTaO, flm by pulsed laser ablain. 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Wang Shiming. 7hang Duanming et al.. Depostion of the higl-orientation KTN thin filn on the P-Si ( 100) sub-stralr bhy qusimolecular pulsed laser, Chinese Science Bulein (in Chinrse)，1998, 43(3): 259- 267.16. An Chengwu, Xu Desheng, Preparation of high-temperature superconductivity thin film by quasi- molecular lasr xatteringtmethod. Applird Jaser (in Chinese). 1989, 9(5): 193- -204.中国煤化工MYHCNMHG