The semiconductor solid phase epitaxial model of continuous laser-annealing is used to simulate the laser-annealing process of different doping concentration of InP at the continuous Nd:YAG laser. Specially, quasi-static model is used to simulate the radial heat dissipation from radiant region to radiationless region. At the same time, thermal conductivity and optical absorption coefficient varied with temperature is also considered. The method of hidden-form different is used in solving one-dimensional, non-homogeneous, nonlinear partial differential equation of heat conduction. At the room temperature T-0=300K and the power intensity of laser I-0=800W/cm(2), the result is that the temperature of surface reaches about 1290K after 3.8sec

Cai, ZH

Chang, Y

Chaplanov, AM

Chen, C

Chu, JH

Fu, RW

Liu, P

Markevich, MI

陈朝

Xiamen University Institutional Repository

The Numerical Simulation of ContinuousNd:YAG Laser-Annealing of InP*Fu Renwu , Cai Zhihua , Chen Chao(Physics Dept. ofXiamen University, China 361005)MiMarkevich andA.M Chaplanov(Institute ofElectronics, Belarus Academy ofSciences, Mnisk, Belarus, 220080)ABSTRACTThe semiconductor solid phase epitaxial model of continuous laser-annealing is used to simulate the laser-annealingprocess of different doping concentration oflnP at the continuous Nd:YAG laser. Specially, quasi-static model is used tosimulate the radial heat dissipation from radiant region to radiationless region. At the same time, thermal conductivity andoptical absorption coefficient varied with temperature is also considered. The method ofhidden-form different is used insolving one-dimensional, non-homogeneous, nonlinear partial differential equation ofheat conduction. At the roomtemperature T0300K and the power intensity of laser 10800W/cm2, the result is that the temperature of surface reachesabout 1290K after 3.8sec.Keywords : InP, laser-annealing, numerical simulation, quasi-static model.1. INTRODUCTIONThe laser-annealing is widely used in semiconductor materials and making techniques of devices. But the theory is verycomplicated and the process conditions are hard to grasp SC) that a better result can only be obtained by modulating manyexperiments. Ifthe numerical calculative method can be used in the simulation ofthe process oflaser-annealing, it will giveguides in the technology of laser-annealing. In this paper, according to the semiconductor solid phase epitaxial model ofcontinuous laser-annealing, the process of continuous Nd:YAG laser-annealing of InP has been simulated.2. PHYSICAL MODELIf a sample absorbs photons, carriers excited by photons heat the location ofthe sample by colliding. At the same time,heat will be conducted to other regions not irradiated ofthe sample by thermal conduction. The equation ofheat conductionis expressed by:c P ( T I3t )Q-Q- \7• FWhere c is specific heat, P is density, T is the distribution oftemperature in the sample, Q1, and Q is the power intensityof absorption and dissipation ofthe sample respectively, F is the vector of heat flow. When no scanning, F —K V T . Kis the thermoconductivity that is a function of temperature.At normal conditions, the diameter 2a of a laser beam is much greater than the thickness 1 of a sample (ref. to Fig. 1). Sothe three-dimensional equation ofheat conduction can be reduced to a one-dimensional, non-homogeneous, nonlinearpartial differential equation which has no analytical solution.c P ( TIat)- K (3T/aZ2)=Q-Q0 ( 1)Fitting the experimental data of InP[l -2] gives: K ( T ) l .O/(- 1 .24356+8.9072* 1 03*T)Qin depends on optical absorption coefficient. At the conditions of low power intensity of laser and photon energy lowerthan the band gap of InP, the free carrier absorption coefficient a is the main part of optical absorption coefficient.a =N a FCWhere N is the free carrier concentration and a FC is cross section. N is given in[3]:N=N0+4(2 )t kTTh2)312(mm)314exp(-Eg(T)/(2kT))Where N0 is the concentration of ionized impurities and Eg (T) is the band gap of InP given in[4]:Eg (T)' 1 .42 1 -23 .63 1 04T2/(T+l 62)* This project is supported by National and Fujian Science Foundation of ChinaFourth International Conference on Thin Films Physics and Applications, Junhao Chu, Pulin Liu,Yong Chang, Editors, Proceedings of SPIE Vol. 4086 (2000) 2000 SPIE . 0277-786X100/$1 5.00 199Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/12/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspxU FC given in[5] o FC=e A 2/( m*nc3 t ). A is the wavelength (1 .O6.tm) of laser, m* is the effective mass of carrier. ForInP, electron effective mass m*e0.077m0, hole effective mass mh=O.64m0[61. n is the refractive index, T is the collidingtime ( T m* It le). I-' is the mobility of carrier in InP which is a complicated function of temperature T and dopingconcentration N0. Fitting the experimental data oflnP [7-9] gives the expression for ii (T, N0):1 (T, N0)=2.4* 104(T/300)' 72/(l+(N0/1 7* 1O)°°)1 (T, N0)=3 .85* lO(T/3OO)/( 1 +(N011•7* 1 cr7)° 151)Here, it (T, N0) is mobility of electrons and it (T, N0) is mobility of holes. In the every step of time of numericalcalculation, we assume a model that the irradiated region and its around will put up steady distribution of temperature bythermal conduction. Consequently the heat dissipation of radial conduction can be evaluated. So the model is named asquasi-static model.Irradiated region Region not irradiated1rz' 'T(a, z)fz)T1 T,Fig. 1 The schematic diagram of quasi-static modelIn the cylindrical cycle of a<r<b and O<z<l, the temperature satisfies the Laplace Eq.: LTOaTThe boundary conditions: 0; T(a, z)f(z)T1; T(b,azz=O,lSolving the Laplace Eq. gives:T0 ln(r Ia) + 1 ln(blr) dT T0 —T(r, z) and = (2)ln(b Ia) dr r=a a ln(b I a)Where b/a is 1 .6 for InP. So for unit bottom area of cylinder, the dissipation of unit length of side face is given in:I dTQrout2'J71 (K)radr3. METHOD OF CALCULATIONA partial linear method is used to solve one-dimensional non-homogeneous nonlinear partial differential equation.In detail, we get the difference grid at the axis of space and time and assume z\ z, A t as the variations:Zk=kLz k=O,l,,n+l; tjLt j0,l, mThe backward difference at the axis of time and the central difference at the axis of space are able to get a different formthat is expressed by:(LT) k,J=(Tk-TkJ1)/ L.\t (3.1)(2T) J=(Tk+l-2Tk +Tkl)/( Az)2 (3.2)Thermal conductivity K of each space layer is assumed to be constant in the partial linear method. Consequently thermalconductivity K can be extracted from the symbol of partial differential. At the point of difference grid, the equation (1) canbe expressed by:c (ALT) k,k(Tk,j.I) (62. T)kJ(Q1fl)k1-(Q1OUt)k,1 (4)Here Pk,f (TkJ) At / c c (Az)2 (5)200 Proc. SPIE Vol. 4086Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/12/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspxCombining equation (3.1), (3.2), (4) and (5) we obtain:( 1 + 2 Pk,j-1 ) Pk,-1 Tk1J- Pk,-1 Tk+l= TkJl+Lt/( c P )[(Qin)k,j-1(Qrout)k,j-11 (6)This is a hidden-form equation.Here (Qfl)k,J1=I(1-R)(1-e ak )txexP(za,)(Qrout)k,j-12 K(Tkl)" LtAza ln(bI a)Where I is the power intensity of continuous Nd:YAG laser and R is the coefficient of infrared reflection. The exchangeof radiative heat dissipation and the exchange of natural cooling by air convection is considered. If we select the conditionof adiathermic boundary which is given in ( T Iz ) I the according simulation of difference is expressed byT0=T , TmjTm+i,j . While we select the condition of constant temperature boundary, a condition will be changed toTm+ijT0. The initial condition is given in TkOTO.The equations ( 6 ) and conditions constitute the complete coupled set of equations of one-dimensional nonlinearequation of heat conduction. Using these equations, we can accurately work out the distribution of temperature (T(z, t)) atthe surface and in the bulk ofa sample, So the thickness ofrecrystallization is given in [10]:=0 Jexp[ - ( B a1'KB1'T(t')]C1t'Where Kb is the Boltzmann constant and E is the activation energy. For InP, Ea2.O3ev, 03.2x10'3nmls.4. RESULTSThe rudimentary calculated parameters are: the thickness of InP l300 i m, the coefficient of infrared reflection R0.3,the step of space z\ z0. 1 i m, the step of time L\t102 sec, the diameter of a laser beam raO.2cm, the power intensity oflaser 10=800W/cm2. The result is that the temperature of surface reaches about 1290K after 3.8 second.14004.0x1 01200 /3.5x105/..1000 //2.5x105800 /N 2.0x105/ 1.5x10/600 /H / 1.OxlO-7/" . 5.0x10400 ,,—0.0.0 100 200 300 400 -5.0x104 0 100 200 300 400Time t (O.Ols) Time t (0.Ols)Fig. 2 Temperature versus time Fig. 3 The thickness of recrystallization versus timeProc. SPIE Vol. 4086 201Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/12/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx3.Oxl O•12.OxlO00) 1.5x1000000 1.OxlO00- 5.0x10600 0.0.200 400 600 800Temperature T (K)Fig.4 Optical absorption coefficient for different doping concentration (Ne) oflnP versus temperature5. DISCUSSIONContinuous Nd: YAG laser (wavelength Xl .O6im) is used in laser-annealing. Its power intensity is 800W/cm2. Thehighest temperature of InP sample is about 1290K that is lower than the melting point of InP. So the semiconductor solidphase epitaxial model is suitable.The overt-form different equation used in laser-annealing demands the condition of KAt/Cp(Lz)2<O.5. So it can only beused in the pulse laser-annealing. In this paper, the hidden-form different equation is used. Because it does not need thiscondition, the equation can be used in pulse or continuous laser-annealing.No paper reported the optical absorption coefficient of InP varied with temperature and doping concentration until now.We use the classical formula of free carrier absorption to obtain the optical absorption coefficient at photon energy lowerthan the band gap of InP. From Fig.4., we find that at high temperature the excitation of band edge will dominate and thedoping concentration of InP is not important. We have induced Zn into InP by Nd:YAG laser[l 1]. Using this paper's modeland numerical simulation, good results have been obtained. The results in detail ofthis work will be published.In this paper, the exchange ofradiate heat dissipation and the exchange ofnatural cooling by air convection is considered.From the result of calculation, we fmd it has little influence.6. REFERENCE1 . S. A. Aliev et al: Thermal Conductivity and Thermoelectric Power of n-Type Indium Phosphide at low Temperatures,Soviet Phys. —Solid Stare, 7, 1287-1288 (1965).2. I. Kudman et al: Thermal Conductivity and Seebeck Coefficient of Indium Phosphide, Phys. Rev. ,133, A 1665-Al667(1964).3. Kittel, C.: Introduction to Solid State Physics, 5tIed., P. 228 Wiley, New York (1976).4. H. C. Casay, jr and M. B. Panish: Heterostructure Lasers, 1978.5. Handbook on Semiconductors Vol.2, Series editor T.S. Moss optical properties of Solids P.230 RSRE, Malvern Worcs.US, 1980.6. S. M. Sze: "Physics of Semiconductor Devices" Bell Laboratories, Incorporated Murray Hill, New Jersey, P. 849, 1981.7. Manijeh Razeghi: "Semiconductor and Semimetals" (W. T. Tsang) Vol. 22, Chapter 5.8. V.V.Galavanov et al: Thermoelectric Power of p-Type Indium Phosphide, Soviet Phys. —Semiconductor, 3, 1159-1160(1970).9. M. Glicksman et al: Electrical Properties of p-Type Indium Phosphide, Soviet Phys. —Semiconductor, 10, 337-340 (1959).bR. B. Gold et al., Appl. Phys. 51(2)1256 (1980).1 1.Cai Zhihua et al: Diffusion of Zn into InP Induced by YAG Continuous Wave Laser, Abstracts, The 4tI InternationalConference on THIN FILM PHYSICS AND APPLICATIONS, P.118,2000.202 Proc. SPIE Vol. 40861: N0=1019cm32: N0=1018cm33: N0=1017cm34: N0=1016cm3/41000 1200Downloaded From: http://proceedings.spiedigitallibrary.org/ on 04/12/2017 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx

The numerical simulation of continuous Nd : YAG laser-annealing of InP

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The numerical simulation of continuous Nd : YAG laser-annealing of InP

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