Observation of Plasma Effect in Nanosecond Pulsed Laser Annealing ...

CHINESE JOURNAL OF PHYSICS

AUGUST 1998

VOL. 36, NO. 4

Observation of Plasma Effect in Nanosecond Pulsed Laser Annealing on Silicon Prior to Melting

D. M. Hsieh, Y. N. Lin, and Andy Y. G. Fuh’ Department of Physics, National Cheng h’ung Tainan, Taiwan 701, R.O.C.

University,

(Received May 8, 1998) A silicon wafer with two sides polished was annealed by a Q-switched Nd:YAG laser of 0.532-pm wavelength. The laser, having a pulse duration of 16 N 18 ns, was incident onto the front surface of the sample. A 1.311-pm-wavelength CW diode laser incident on the back surface of the annealed spot was used as a probe beam. A significant change of the probe beam’s reflectance with time prior to the melting of the sample was observed. The result was analyzed using the heat conduction model together with the assumption of the existence of excess carrier concentration, which is much larger in number than that in equilibrium with the lattice temperature. A good agreement between the calculated and experimental results was obtained. PACS. 61.72.-c - Laser beam annealing. - Optical absorption in plasma. PACS. 52.25 - Semiconductors optical properties. PACS. 78.66

I. Introduction .

The mechanism of laser annealing on silicon was a subject of debate in the early 1980’s [l]. The hot carriers of electron-hole pairs generated by pulsed lasers act as a mediator that

transforms the photon energy into the heat energy. Recently, we have reported an in-situ method that can be used to monitor the movement of the liquid/solid (e/s) interface during pulsed-laser annealing of a silicon crystal wafer [3]. In this method, the reflectance of the CW probe beam, directed onto the back surface of the annealed spot, varies in time due to the interference between light reflected from the moving e/s interface and that reflected from the back surface. During annealing, the melted part together with the solid part of the sample silicon, as seen by the 1.311-pm-wavelength probe beam, can be considered as a thick dielectric coated with a thin metallic layer. Due to the interference of light reflected from the air/dielectric interface and that from the dielectric/metal interface, the probe beam’s reflectance varies with the distance between the two interfaces. With the back surface remaining still, the time-dependent reflected intensity of the probe beam provides in-situ monitoring of the moving e/s interface in real time. The change of the probe beam’s reflectance prior to the melting of the sample silicon was also observed and reported in Ref [3]. In this paper, a further investigation on the cause that makes the probe beam’s reflectance to change with time before melting was carried out. Prior to melting, the 635

@ 1998 THE PHYSICAL SOCIETY OF THE REPUBLIC OF CHINA

OBSERVATION OF PLASMA EFFECT IN . . .

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resultant reflectance due to the interference between light reflected from both the front and back surfaces of the annealed spot changes with the optical path length between the two surfaces. The optical path length is changed because of the presence of the heat and free carriers within the sample, which are induced by the annealing beam. The equation of heat conduction within the silicon wafer during annealing was solved numerically to account for the temperature effect on the optical path length. The classical approach to the absorption of the free carriers as outlined by Smith [4] was used to estimate the influence on the refractive index of the sample. The reflectance of the silicon wafer was finally calculated using Airy summation method [5], and was compared to the experimental data. II. Theory The equation of heat conduction is

dH(T)

~ = at

d da:

(A-g ) •t

aJ(z,t),

where H(T) is the volumetric heat content or enthalpy, Ke is the thermal conductivity, of is the absorption coefficient of silicon at wavelength of 0.532 pm, and I(z, t) is the incident laser flux with a temporal Gaussian profile having a width of N 16 ns. The parameters shown in Eq. (1) are defined as follows: T

H(T) = Ho t

J

PC,& (Jlcm3>,

(2)

3000K

where p(= 2.32g/cm3) is the density of the crystal silicon, H, is the volumetric enthalpy at 300”K, and assumed to be zero in the present calculations. C, is the specific heat of silicon, and its value is [6] C,(T > 300°K ) = 4.185 x 0.166exp(2.375 x 10m4T). (J/(g.‘K))

(3)

The thermal conductivity varies with temperature as follows [6], I 1200°K) = 4.185 x 2.15/T0.502. (J/(s.~rn.~K))

(5)

and

The absorption coefficient of silicon at wavelength of 0.532 pm is [7] Q!(T) = 5.02 x 103exp(T/430). cm-’

(6)

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III. Numerical met hod

The Crank-Nicholson method [8] was used to solve Eq. (1). Because the equation is nonlinear, iteration [9] is required at each time step to make the solution correct. The slab of 5 pm is divided into 500 sublayers and the time step is 0.2 ns. The boundary conditions used were at t = 0, T = 300°K at any depth and T = 300°K at any time for depth larger than 5 pm [lo]. IV. Free carrier absorption and airy summation

We need to know the index of refraction in each layer in order to calculate the probe ’s beam reflectance. The following formulas derived by Smith [4] were used to calculate the refractive index n and the extinction coefficient ri in the presence of free carriers:

n2

Pee2 _ 62 = ni _ -

2nr; =

(

2

)

-

(7)

5$(1+7:yJ+~

(8)

&orne

1+ w”r,”

where ne is the refractive index of the silicon lattice, w is th,e angular frequency of the probe beam, r, and rh are the relaxation times of electron and hole, respectively [lo]. P, (m,) and Ph (mh) are electron and hole concentration (effective masses), respectively [ll]. The refractive index ne varies with temperature as follows [12]: ne = 3.5 + a,(T - 300),

(9)

where a, is the temperature coefficient of the refractive index at wavelength of 1.311 pm, and is N 2.0 x 10m4. The equilibrium carrier concentrations with lattice temperature are [4,101 P; = 5 x 10r5Tr5 exp (-E,/~LBT) ,

(cmm3)

(10)

P, = $ [l + (1 + 4Pf/Nt)3] , (cmF3)

(11)

Ph = iNa [lt (lt 4Pf/Nz)i] , (cmv3)

(12)

a

where Pi is the intrinsic concentration in equilibrium with temperature at T [lo], N, is the impurity concentration, and is N 1 x 1015 cmm3 in our sample. E, is the energy gap of silicon and varies with temperature as follows [13] Eg = 1.170 -

. 4 73 x 10-4T2 . (T-l- 6 3 6 ) ’ (ev)

(13)

The temperature in each sublayer at a particular time step was used to determine the refractive index of the sublayer. The reflectance of the multi-layer structure of the refractive index is then summed up at each time step using the Airy summation method [5].

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V. Experimentals The experimental setup is shown in Fig. 1. Two probe beams were used to monitor the spot on the

sample which was annealed by a Q-switched Nd:YAG laser (Continuum model NY81-10) through a KDP SHG crystal. The sample is a silicon wafer (P type, < l,l, 1 > orientation, N 375 pm thickness) with two sides polished. The annealing beam was directed normally onto the sample from the front surface and had a Gaussian transverse intensity distribution having a radius of N 2 mm. The CW diode laser beam of 0.67-pm wavelength was focused to have a radius of N 150 pm and was incident onto the front surface to monitor if melting has taken place. Upon melting, the molten silicon behaves like a metal, and results in a sudden rise in reflectivity [14]. The other CW diode laser beam of 1.311-pm wavelength was also focused to have a radius of N 150 pm, and directed normally onto the same spot from the back surface to probe the temporal evolution of the annealing process. A beam-splitter and a quarterwave plate were added in the alignment to enable the normal incidence of the IR probe beam. Suitable long pass filters were selected to block the unwanted signals originating from the annealing beam. Photodetectors having a rise time of -1 ns were used to receive the signals from the probe beams, and a TDS680B oscilloscope having 1 GHz bandwidth was used to record the signals after every single shot of the pulsed laser.

Si-sample

Nd:Yag lair team

L4 II4 wave plate

FIG. 1.

Experimental setup is shown schematically. Ml - 7: mirrors; Ll - 5: lens; Dl: red light photo detector, D2: IR photo dector; Fl - 2: long pass filters. A Tektronix TDS680B oscilloscope is used to record the signals.

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639

VI. Results and discussion

The observed temporal evolutions of the reflectance of the 1.311-pm-wavelength probe beam are shown in Fig. 2 and 3 corresponding to the annealing pulse with energies ranging from 7.6 mJ to 29.6 mJ. It should be noted that the sample was not melted under these annealing energies as monitored by the 0.67-pm-wavelength probe beam (the result is not shown). As can be seen from these figures, the temporal profile of the reflectance changes from V-like shape to W-like shape as the annealing energy increases. The change of optical path length between the front and back surfaces of the sample as probed by the 1.311 -pm-wavelength laser beam causes this phenomenon. The optical path length was changed because of the presence of the heat and free carriers, induced by the annealing beam, within the silicon sample. The temperature affects the refractive index through the Eq. (9). Neglecting the presence of the excess carriers generated by the annealing beam, the calculated temporal profile of the surface temperature under the annealing flux of 0.34 J/cm2 and its effect on the reflectance change of the 1.311 -pm-wavelength probe beam are shown in Fig. 4. It can be seen that the temporal evolution of the probe beam’s reflectance, as calculated with a, = 2 x 10m4, does not change as rapidly as the observed ones in Figs. 2 and 3 even when the surface temperature has reached N 1655 °K . Under the irradiation of a high-power laser pulse, the generated carriers of electron-hole pair could be much larger in number than.those exist in equilibrium with the lattice temperature. These excess carrier concentrations can affect the refractive index substantially through the Eqs. (7) and (8). Neglecting the temperature effect, the calculated profiles depicted in Fig. 5 show how the excess carrier concentration can change the probe beam’s reflectance when carrier concentration is 10, 25, 50 times the equilibrium value in succession. The surface temperature is N 1655’K and the surface carrier concentration has reached N 2 x 102r cmF3 at 50 times the equilibrium value. As can be seen in Fig. 5, the

0

FIG. 2. The observed temporal reflectance change of the CW 1.311~pm- wavelength probe beam with the sample being annealed by a SHG Q-switched laser pulse having energy of 7.6 mJ and of 11. 2mJ.

20

so TIME(m)

40

so

loo

FIG. 3. The observed temporal reflectance change of the CW 1.311-pm- wavelength probe beam with the sample being annealed by a SHG Q-switched laser pulse having energy of 16.3 mJ and of 29.6 mJ.

640

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OBSERVATION OF PLASMA EFFECT IN ...

evolution of the shape of the calculated profile changes from V-like to W-like as the excess carrier concentration is increasing. These results resemble those observed experimentally with increasing annealing energy as shown in Figs. 2 and 3. The validity of calculating the probe beam’s reflectance by using a excess carrier concentration that is a multiplier of the equilibrium one is of course questionable, but the coincidence between the calculated and experimental results is reasonable. First, it shows that if the excess carrier concentration, induced by the annealing beam, is large enough, then it affects temporal evolution of the probe beam’s reflectance significantly. Second, the spatial profile of the temperature should not deviate too much from that of the excess carrier concentration. The reason is that the absorption coefficient of the annealing beam in Eq. (6) is proportional to the temperature. The higher the temperature of the silicon layer is, the more photon energy is absorbed. To some extent, the spatial distribution of the temperature should resemble that of the excess carrier concentration. Thus, we believe the excess carriers, induced by the annealing pulse, should be the cause of the observed reflectance change with time of the 1.311 -pmwavelength probe beam prior to the melting of the sample. In conclusion, by calculating the temperature profile in a silicon wafer during the pulsed laser annealing, and by using the model of free carrier absorption together with the Airy summation technique, we can conclude that the temperature effect is not the cause of the observed reflectance change of the probe beam. Rather, the existence of excess carrier

os-

0.,1 w 0

20

40

80

100

TIME (ns)

FIG. 4. The calculated profiles of the surface temperature and the temperatureinduced reflectance change of the 1.311-pm-wavelength probe beam with the sample being irradiated by an annealing beam having fluence of 0.34 J/cm’. The temperature coefficient a, shown in Eq. (9) was set to be 2 x 10m4.

0.0

, 0

, 20

, 40

,

so

m

ml

TIME (ns)

FIG. 5. By using the carrier concentrations 1, 10, 25, and 50 times as large as the equilibrium value in succession, and keeping a, = 0, the calculated reflectance change with time of the 1.311-pm-wavelength probe beam are shown. The temporal profile changes from V-like to W-like shape as the excess carrier concentration is increasing. Theses results resemble those obtained experimentally with increasing annealing energy as shown in Figs. 2 and 3.

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D. M.HSIEH,Y.N. LIN, AND ANDYY.G.FUH

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concentration explains the experimental results satisfactorily. Further investigations by solving the coupled equations describing the laser-annealing mechanism, as proposed by Lietoila and Gibbons [lo], are under way. The observed temporal profiles of the IR probe beam should set another criteria for testing the correctness of the physical model mentioned above. Acknowledgments This work is supported by The National Science Council (NSC) of the Republic of China under Grant NO. NSC 87-2112-M-006-017. References [ 1 ] B. R. Appleton and G. K. Celler, Laser and Electron-Beam Interactions with Solids, (NorthHolland, New York, 1982), p.3. [ 2] K. Seeger, Semiconductors Physics, (Springer, Wien, 1973), p.183. [ 3 ] D. M. Hsieh, J. Y. Wang, and Andy Y. G. Fuh, Jpn. J. Appl. Phys. 36, L457 (1997 ), [ 4 ] R. A. Smith, S emiconductors, (Cambridge University Press, London,1959), p. 85. [ 51 Z. Knittl, Optics of thin Film, (John Wiley & Sons, London,1976), p.47. [ 6 ] S. Unamuno, M. Toulemonde, and P. Siffert, in Laser Processing and Diagnostics (Chemical Physics, Vol. 39), eds. D. Bauerle (Springer-Verlag, Berlin, 1984), p.35. e rson, Jr., and F. A. Modine, Appl. Phys. Lett. 41, 180 (1982). [ 7 ] G. E. J 11’ [ 8 ] A. R. Mitchell, Computational Methods in Partial D, ferential Equations, (Wiley, New York, 1969). [ 91 J. E. Dennis, Jr. and R. B. Schnabel, Numerical Methods For Unconstrained Cptimization & Nonlinear Equations, (Prentice-Hall, New Jersey, 1983), p.147. [LO] A. Lietoila and J. F. Gibbons, J. Appl. Phys. 53, 3207 (1982). [ll] P. A. Schumann, Jr. and R. P. Phillips, Solid-State Electron. 10, 943 (1967). [12] G. E. Jellison, Jr., and H. H. Burke, J. Appl. Phys. 60, 841 (1986). [13] S. M. Sze, Physics of Semiconductor Devices, (John Wiley & Sons, Taiwan, 1985), p.15. [14] D. H. Aust on, J. A. Golovchenko, A. L. Simons, C. M. Surko, and T. N. C. Venkatesan, Appl. Phys. Lett. 34, 777 (1979).