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Temperature, composition and microstructure variations during pulsed laser irradiation of a deposited film on a substrate
Acta metall, mater. Vol. 43, No. 12, pp. 4411~4420, 1995
~
Pergamon
Elsevier Science Ltd Copyright 9 1995 Acta Metanurgica Inc. Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00
0956-7151(95)00121-2
TEMPERATURE, COMPOSITION A N D MICROSTRUCTURE VARIATIONS D U R I N G PULSED LASER IRRADIATION OF A DEPOSITED FILM ON A SUBSTRATE I. T. H. CHANG and B. CANTOR Oxford Centre for Advanced Materials and Composites, Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, England
(Received 3 August 1994; in revisedform 24 February 1995)
Abstract--A computer model has been developed to describe melting and resolidification during laser irradiation of elemental and alloy films on a substrate. The computer model predicts the temperature profile, maximum melt depth, maximum solidification rate, onset of cellular breakdown and the final resolidified composition profile. The computer model has been compared with measurements [I. T. H. Chang and B. Cantor, J. Thin Solid Films 230, 167 (1993)] made on cross-section TEM specimens of 1.15 J/cm 2 irradiated 400 nm thick Sn and 0.96-1.17 J/cm 2 irradiated 120 nm thick Ge-50 at.% Sn films on single crystal Ge substrates. The predicted results give good agreement with the measured data. The maximum melt depth increases with increasing laser energy density. Cellular breakdown takes place at increasing depth with increasing laser energy density.
1. INTRODUCTION Pulsed laser irradiation of a material produces structural changes near the surface as a result of rapid heating and melting, followed by cooling and solidification. Structural changes caused by pulsed laser irradiation include the removal of ion implantation damage [1, 2] and the formation of metastable supersaturated solid solutions [3,4], compounds [5,6] and amorphous phases [7, 8]. Understanding these effects requires detailed knowledge of the thermal evolution in the material during and after irradiation, including the temperature profiles, melt depth, melt duration and cooling and solidification rates. This information can then be used to predict the structure and composition of the final solidified material. Temperature and composition changes in irradiated materials have previously been calculated from separate one-dimensional heat and mass balance equations, giving good agreement with experimental results on dilute alloys [9-15]. However, this approach becomes invalid when applied to concentrated alloys, because temperature changes are then strongly influenced by compositional changes in the liquid. This paper presents a computer model of surface melting and solidification during pulsed laser irradiation of a binary alloy, using combined one-dimensional heat and mass balance equations with a solute distribution coefficient which is dependent on the solidification rate. The model is applied to the pulsed laser irradiation of a deposited film on a substrate, in order to predict the solidification rate, melt depth and duration, and temperature and composition variations as a function of pulse energy
density and initial film composition. These results are used to assess the final irradiated microstructures, as found experimentally for pure Sn and Ge-50 at.% Sn alloy films on a Ge substrate.
2. COMPUTERMODEL 2. I. Heat and mass flow equations Consider a pulsed laser beam incident normally along the z-axis on a sample consisting of a deposited film supported by a substrate as shown schematically in Fig. 1. The deposited film can be either an alloy or an elemental material. The laser beam energy is absorbed near the surface of the sample, and is instantaneously converted into heat, which diffuses into the bulk by thermal conduction. If sufficient energy is absorbed by the sample, the deposited film and adjacent regions of the underlying substrate melt and then resolidify after the radiation pulse. Redistribution of solute takes place by interdiffusion between the film and substrate, and by partitioning across the liquid/solid interface during melting and solidification. When the width of the laser beam is greater than the depth of surface heat treatment, heat and mass flows are confined to the z-axis, as shown in Fig. 1. Under these conditions, the laser treatment can be described by two, linked one-dimensional differential equations as follows: The temperature profile is given by a one-dimensional heat balance equation
4411
dr PC-d-f =
dt
d . + ~z\
.(Kdr + dz ] pL-~
(1)
4412
CHANG and CANTOR: PULSED LASER IRRADIATION solid/liquid interfaces can be expressed as dC/ dt = (dC/dT)(dT/dt), where dT/dt is the same as in equation (1), and d C / d T can be obtained from the slope of the liquidus curve on the equilibrium phase diagram. 2.2. Numerical solutions An explicit forward finite difference method was used to solve equations (1) and (2). The spatial dimension of the sample along the z-axis was divided into many blocks, and the time dimension representing the thermal and compositional histories of the sample was divided into many time steps. The ith block thickness and the j t h time interval were Azi and At respectively. The temperature and the liquid and solid compositions within each block remained constant over each time step and were T4, C~ and C~ respectively for the ith block at timejAt. Material parameters with subscript i were used to define the temperature-and composition-dependent physical properties of the ith block. Equations (1) and (2) were then solved iteratively for all i , j by assuming no heat loss at the surface, constant temperature in the bulk of the sample and mass diffusion only in fully molten blocks. The numerical solution of equation (1) is
Fig. 1. Schematic diagram of a sample irradiated with a laser pulse. where T is the temperature, t is the time, p is the density, c is the specific heat capacity, (dQabs/dt) is the rate of heat absorbed per unit volume from the laser beam, Kis the thermal conductivity, L is the latent heat of melting, df/dt is the rate of change of solid fraction during melting or solidification and the convection is ignored here because it is relatively slow. The composition profile is given by a one-dimensional mass balance equation dC dt
(DdC)+
d dz
dz ]
pici(T~ + ' - - T~) At - P~[1 - exp(-c
(2)
C(1-k)~ft
where C is the melt composition, D is the solute diffusion coefficient, and k is the partition coefficient. The heat and mass balance equations (1) and (2) are linked, since the variation in melt composition at the
~ ~ i .._~__ I r ~ I mug.... I
~ ~ | L
Ahoyor element
element
alloy
1
l
usingVon Neumann's stabilitycriteria
of ith block
f
+p,L,
Calculatetime interval with given block thickness
]~(~ Examinecomposition )'
+ x,)
~(
CheckTI i§ >--or < Tin,calculatetrueTI ~+1 ! accordinglyand calculatef, V and C ( onlywheninterdiffusionbetweenelements oocurs).
Check Ti j+l > or < Tin,calculatetrueTI I+1 accordingly and calculatef, V, C, C s and k
(f~+'
,,z,+41
tie, + K,+,)/
- f4)
At
(3)
Initializeall variables, do time step Harations and calculatelaser power density at given time t
CalT:~ hTesil:;~; eming
!
(,,z,
Do block iteiation for near surfaceregion (z = 20nm - 200Onto)
L
Do blockiterationfor region(200Ohm< z < 300,000nm) and calculatedQ abs/dt, d/dz(Kd'T/dt)for a time intervalof (:It and TII+I
I Endof program~ _
Fig. 2. Block diagram of the computer model.
fore time intervalof dt.
f __
ReeeiTi j to TII+I , and cil to C 11+1
1
Printand store calculateddata
CHANG and CANTOR: PULSED LASER IRRADIATION
4413
Table 1. Polynomial expressions for c, K and ct as a function o f temperature for G e ForGe(300
K
For Ge (T>
K ) : c ( T ) = 5 . 7 6 7 • 10 2(5.16+ 1 . 4 x 1 0 - t T ) J/g K K ( T ) =0.6(300/T) 114 W / c m K ~ ( T ) = 8 • 1@ exp [1.1 • 103(T - 300)] c m -L 1211 K): c ( T ) = 0 . 3 8 0 4 J/g K K(T)=0.25 W/cm K ct(T)= 1 x 106 c m J
where P4 is the power of the laser beam transmitted to the ith block at timejAt, ctiis the absorption coefficient andf~ is the solid fraction. For the surface block i = 1, P~ = P6(I - R) where P~ the laser output power and R is the reflectivity of the surface. Similarly, the numerical solution of equation (2) is
(c ~+'- co At
D {(c~_,- c~) (c~- c~+,)'] -aZ, + -As ]
-
Az, \
+ C4(1 - k) (f4+l - f ~ ) At
(4)
where k varies with the solidification rate VJi, and is given by [16]
k -
(5)
(~)
of the liquid/solid interface. This gives df/dt in equation (I) as f~+~ - f ~ = M(Ti +l - Tm)At
where Tm and M are the melting temperature and the liquid/solid interface mobility respectively. The new temperature Ti + ~ is calculated by the eliminating (f~+l -f~)/At from equations (3) and (7): For an alloy, the melting begins at the solidus temperature (Ts) and ends at the liquidus (T0 temperature. Therefore, the rate of solid fraction molten (df/dt) depends on the heating rate (dT/dt) and the change of solid fraction with temperature (df/dT), according to a simple relationship of df/dt = (df/dT)(dT/dt). The deviation from equilibrium is assumed to be small with little effect on the final solidified microstructure. The lever rule can then be used to give
+ 1 - (1 - xo)C,
(f~+,_f~)_
where a is the interatomic distance of the growing solid, xo = kA/ko,ko = Cs/C is the equilibrium partition coefficient of the solute atoms and k f = ( 1 - C 0 ( 1 - C0 is the equilibrium partition coefficient of the solvent atoms. The solidification rate V4 is given by VI- (f~+'-f~) At
Az,.
(6)
The dimensions of the variables used in the present computer model are listed in the Nomenclature in the Appendix.
2.3. Phase change F o r fully molten or solid blocks, the last terms in equations (1) and (2) are zero, so the temperature and composition can be calculated directly from equations (3) and (4) respectively. During melting or freezing, the propagation of the liquid/solid interface is treated differently for an elemental material compared to an alloy. For an elemental material, a linear kinetics approximation [17] is used to describe the movement
- ( T ~ + ~ - T~) ( T I - Ts)
(8)
where T~ and Ts are the liquidus and solidus temperatures on the equilibrium phase diagram. The new temperature, TJ,.§ is calculated by eliminating (f~+l -f~)/At from equations (3) and (8). For an alloy during solidification, the lever rule cannot be used because equilibrium is not maintained. Instead, equations (1) and (2) can be solved simultaneously by eliminating df/dt, and taking k from equation (5) and using dC/dt = (dC/dT)(d T/dt), where dC/dT is taken from the equilibrium phase diagram.
2.4. Computer calculations A computer program was written in F O R T R A N to calculate the temperature and composition profiles during and after laser irradiation of pure Sn and Ge-Sn alloy films on a Ge substrate, using the treatment described in the previous sections. A block diagram of the computer program is shown in Fig. 2. It is divided into several parts for handling the heat and mass flows: (l) without any phase changes; (2) at the initiation of a phase change; and (3) during a phase change. Values of At and Azi were chosen using Von Neuman's stability criterion [18] (At < 0.5
Table 2. Polynomialexpressionsfor c, K and ~ as a function of temperaturefor Sn For SN (300 K< T < 505 K): c(T)=3.528 x 10-2(5.16+ 4.3 x 10-3T) J/g K K(T)=2.295(I/T)~ W/cm K otT= 1 • 106 cm
For Sn (T_> 505 K): c(T)=0.2397 J/g K K(T)=2.49 • 10 ~2T3- 5.64 • 10-gT2 + 2 . 0 8 • 1 0 - 4 T + 0.1997 W / c m K c t ( T ) = l x 106cm -~ AM 43/12--N
(7)
4414
CHANG and CANTOR: PULSED LASER IRRADIATION
Table 3. Polynomial expressions for C and dC/dT as a function o f temperature for G e - S n alloys
Table 5. Numerical expressions for Dsn as a function o f temperature T < 1090 K: D = 3 , 2 4 x 10-4exp ( - 1 3 8 9 / T ) T > 1090 K: D = 1 . 3 9 x 10-3exp ( - 2 0 1 3 / T )
C = 0.22792 + 2.75 x 1 0 - 3 T - 2.4299 x 1 0 - 6 T z 9 d C / d T = 2 . 7 5 x 1 0 - 3 - 4 . 8 5 9 8 x 10 6T
piciAz?Ki-~). F o r each computer simulation, the sample was assumed to have a total thickness in excess of 300 #m, with Az = 20 nm for the first 2/~m below the surface, followed by a gradually increasing A z i = 1.4Azi_l. The value of At was 0.24 ns. Tables 1-5 show the material parameters used in the computer program for pure Ge and Sn. Average values were assumed for the Ge-50 at.% Sn alloy. A value of 0.745 was chosen as the reflectivity of Ge-50 at.% Sn, to correspond to the measured melt depth of a Ge-50 at.% Sn sample. The simulated temperature and composition profiles were compared with experimental measurements obtained by pulsed laser irradiation of thermally evaporated 400 nm thick pure Sn, and 120 nm thick Ge-50 at.% Sn alloy films on single crystal Ge substrates, using a ruby laser operating with a pulse length of 24 ns, wavelength of 694 nm and an energy density in the range 0.96-1.17 J/cm 2. Film thicknesses were measured using an Alphastep. The pulsed laser energies delivered to the samples were measured using an Apollo energy calorimeter. The resulting microstructural variations across the irradiated samples were observed by cross-sectional transmission electron microscopy (TEM) [19] using a Philips CM12 fitted with L I N K energy dispersive X-ray microanalyser (EDX).
3. RESULTS 3.1. 400 nm Sn Figure 3 shows calculations of melt depth vs time for the 400 nm Sn sample irradiated with a 1.15 J/cm 2 laser pulse. The Sn film began to melt after 10 ns, and the melt depth then increased with time, i.e. melting proceeded up to a maximum depth of 562 nm after a time of 50 ns. The melt depth then decreased with time, i.e. the substrate and film resolidified. The shoulder on the plot in Fig. 3 is at a melt depth of 400 nm, at the Sn/Ge interface, and corresponds to a delay in melting as the temperature rises to the high melting point of the Ge substrate. Figure 4 shows the corresponding calculations of temperature vs time at depths of 20, 410 and 570 nm. The temperatures at these depths increased with increasing time, reached maximum values after ~ 30 ns, and then decreased as cooling commenced. The maximum temperatures were 2309, 1487 and
1212 K at depths of 20, 410 and 570 nm respectively, i.e. below the boiling temperature of Sn (2543 K) but above the melting point of Ge (1211 K). The initial cooling rates were 4.6 • 10 ~~ 7.7 • 109 and 1.4 x 109 K / S at depths of 20, 410 and 570 nm respectively. The cooling rates decreased gradually with time until they converged after ~ 100 ns. Figure 5 shows corresponding calculated temperature profiles after times of 30 and 50 ns. After 30 ns, corresponding to the maximum temperature as shown in Fig. 4, there was a steep temperature gradient of 2.39 x 109 K/m within the sample. However, after 50 ns, corresponding to the maximum melt depth as shown in Fig. 3, there was a much smaller temperature gradient of 0.3 x 109 K/m between the surface and the substrate. Figure 6 shows calculated variations of solidification rate for the irradiated 400 nm Sn sample. The solidification rate increased with time, reached a maximum value of 3.4 m/s after 60 ns, and then dropped sharply to a much lower value of ~ 0.1 m/s after ~ 100 ns. Figure 7 shows the calculated Sn solid composition profile after 225 ns, together with corresponding Sn compositions measured by EDX in cross-section TEM specimens [19]. Regions of different microstructure observed by cross-section TEM [19] are also labelled in Fig. 7. The 1.15 J/cm 2 irradiated 400 nm Sn microstructure consisted of: (i) a 257 nm thick Sn overlayer; (ii) a 100 nm thick layer of polycrystals of ct-Ge(Sn) embedded in Sn; (iii) a 100 nm thick layer of cellular ct-Ge(Sn); and (iv) a 70 nm thick layer of segregation-free ~-Ge(Sn), as shown in Fig. 8. The computer model predicted that after 225 ns, the region at depths between 450 and 550 nm solidified with a Sn
600
I
5O0 A
40O .el 3O0 ID
200 ID
100 0
Table 4. T e m p e r a t u r e independent parameters for G e and Sn Ge R = 0.44 (solid Ge, 2 = 694 nm) R = 0.7 (liquid Ge, 2 = 694 nm) p = 5.35 x 106 g / m 3
Sn R = 0 . 6 9 (solid Sn, 2 = 694 nm) R = 0 . 6 9 (liquid Sn, ~. = 694 nm) p = 7.31 x 106 g / m 3
I
0
I 50
I 100 Time
I 150
200
(nn)
Fig. 3. Calculated melt depth vs time for a 400 nm Sn sample irradiated with a 1.15 J/cm 2 laser pulse.
CHANG and CANTOR: PULSED LASER IRRADIATION 2500
(8)
1
4
i
4415
I
I
2000
3
b< r 0
1500 IJ k ID
la,
6
I000
III 6
500 II
0
I
0
50
]
I
100
150
0
200
50
T i m e (ns)
[
i
100
150
200
Time (na)
Fig. 4. Calculated temperature vs time profiles at depths of (a) I0 nm, (b) 410 n m and (c) 530 n m from the surface of a 400 n m Sn sample irradiated with a I.15 J/cm 2 laser pulse.
Fig. 6. Calculated solidification rate vs time during the solidification of a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse.
content less than 2 at. %. This agrees with experimentally measured compositions in the irradiated sample, as shown in Fig. 7.
different times between 40 and 395 ns, i.e. during the solidification stage for 120nm G e - 5 0 a t . % Sn irradiated with a 1.08 J/cm 2 laser pulse. Figure 1l shows corresponding calculations of temperature vs time at depths of 10, 90 and 250 nm. The curves had a similar shape to those shown in Fig. 4 for the 400 nm Sn sample irradiated with a 1.15 J/cm 2 laser pulse. The temperatures at these depths increased with increasing time, reached to a maximum after ~ 30 ns, and then decreased as cooling commenced. The maximum temperatures were 1731, 1556 and 1213 K and the initial cooling rates were calculated as
3.2. 120 nm Ge-50 a t . % Sn
Figure 9 shows calculations of solid fraction vs depth at different times in the first 35 ns, i.e. during the melting stage for 120 nm Ge-50 at.% Sn irradiated with a 1.08 J/cm 2 laser pulse. After 15 ns, all of the deposited Ge-50 at.% Sn alloy film had begun to melt. Melting continued until the melt front was held up at the Ge-50 at.% Sn/substrate boundary. After 25 ns, the Ge substrate began to melt and the melt front then continued to penetrate into the Ge substrate, reaching a maximum melt depth of 255 nm after 40 ns before resolidification began. Figure 10 shows similar calculations of solid fraction vs depth at
(i)
I
I
(ii) i(iii)l(iv) [substrate
1.0
9 measured Z~ p r e d i c t e d
data data
o 0.8 2500
I
eo
F
(a) ~-, M
0.8
2000
0.4 g o
O
1500
0.2 0
1000
O
0
0.0 0
500 1
0
200
I
200
[
300
i . . . .
400
500
I
600
Depth (nm)
I
400
I
lO0
800
D e p t h (rim) Fig. 5. Calculated temperature vs depth profiles at times of (a) 30 ns and (b) 50 ns for a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse.
Fig. 7. Calculated composition profile in a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse together with corresponding measured compositions. Regions of different microstructure are (i) Sn polycrystals, (ii) polycrystalline ct-Ge(Sn) embedded in Sn, (iii) cellular a-Ge(Sn), (iv) segregation-free a-Ge(Sn), and the Ge single crystal substrate.
4416
CHANG and CANTOR: PULSED LASER IRRADIATION 1.0
0.9 0.8
0.7
~ 0.8 ~
0.5 0.4
e
0.2
0.1
)-
)
0.0 Fig. 8. Cross-section TEM of a 1.15 J/cm~irradiated 400 nm Sn sample, showing (i) a 257 nm thick Sn overlayer, (ii) 100 nm thick polycrystals of ct-Ge(Sn) embedded in Sn, (iii) a 100 nm thick layer of cellular ~-Ge(Sn) and (iv) a 70 nm thick layer of segregation-free ct-Ge(Sn).
2.1 • 10 t~ 1.4 x 10 t~ and 3.6 • 109 K/s at depths of 10, 90 and 250 n m respectively. The cooling rates decreased gradually with time until they converged after ~ 100 ns. Figure 12 shows corresponding calculated temperature profiles after times of 30 and 50 ns. After 30 ns, corresponding to the maximum temperature as shown in Fig. 12, there was a steep temperature gradient of 1.89 • 109K/m within the sample. However, after 50 ns, corresponding to the initial stage of solidification as shown in Fig. 12, there was a much smaller temperature gradient of 2.27 • 108 K / m between the surface and the substrate. Figure 13 shows calculated variations of solidification rate for the irradiated 120 n m G e 50 at.% Sn samples. The solidification rate increased with time, reached a maximum value of 5.6 m/s after
//
1.0 0.9 0.8 0
0
50
100
150
200
250
300
Depth (nm) Fig. 10. Calculated solid fraction vs depth at times of (a) 40 ns, (b) 55 ns, (c) 75 ns, (d) 115 ns and (e) 395 ns for a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm 2 laser pulse.
45 ns and then dropped sharply to a much lower value of 1.4 x 10- 2 m/s after 225 ns. Figure 14 shows the calculated Sn solid composition profile after 595 ns, together with corresponding Sn compositions measured by E D X in cross-section T E M specimens [19]. Regions of different microstructure observed by cross-section T E M [19] are also labelled in Fig. 14. The 1.08 J/cm-' irradiated 120 n m Ge-50 at.% Sn microstructure consisted of: (i) a 90 n m thick Sn overlayer; (ii) a 100 n m thick layer of cellular 9 -Ge(Sn); and (iii) a 65 n m thick layer of segregationfree ~-Ge(Sn), as shown in Fig. 15. The computer model predicted that after 595 ns, the region at depths between 100 and 246 n m solidified with a Sn content ranging from 1 to 20 at.%. This agrees with
2000
(a)
I
I
I
I 50
I 100
I 150
1500
0.7 0.6
t.
1000
0.5 0.4
0
0.3 0.2
/
0.1 0.0 0
50
100 Depth
500
idl (e)
~)
0 50
~00 250
300
(rim)
Fig. 9. Calculated solid fraction vs depths at times of (a) 15 ns, (b) 20 ns, (c) 25 ns, (d) 30 ns and (e) 35 ns for a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse.
0
Time
(ns)
Fig. 11. Calculated temperature vs time profiles at depths of (a) 10 nm, (b) 90 nm and (c) 250 nm from the surface of a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse.
CHANG and CANTOR: PULSED LASER IRRADIATION 2000
[
1
I
[
I
I
(~l ~"
"~
(i)
I
(ii)
1.0
I
(iii)
i subst.
9 Measured data /% P r e d i c t e d d a t a
t/l
1500
4417
,g 0.8 o
I000
as
[-, |
o
500
,~
0.8
a
0.4
a a a
O 0
P
0
I00
I
200
1
300
I
400
"-'
I
500
600
Depth (nm)
A4X
0,2
m o
o
0
Fig. 12. Calculated temperature vs depth at times of(a) 30 ns and (b) 50 ns for a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cmz laser pulse.
experimentally measured compositions in the irradiated sample, as shown in Fig. 14.
3.3. Other samples Two other energy densities of 0.96 and 1.17 J/cm 2 were used with 120 nm thick Ge-50 at.% Sn samples on the computer model to predict the maximum melt depth (Dmax),maximum surface temperature (Tsurf)and maximum solidification rate (Vmax), as shown in Table 6. 4. DISCUSSION
4.1. Maximum melt depth Table 7 shows a list of predicted maximum melt depths together with corresponding maximum depths containing Sn as measured by EDX on 400 nm Sn and 120nm G e - 5 0 a t . % Sn samples [19]. The calculated melt depths agree well with the measured data. The calculated and measured melt depths both increase with increasing energy density, as shown in Table 7.
50
100
150
200
250
Depth (nm)
Fig. 14. Calculated composition profile in a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse, together with corresponding measured compositions. Regions of different microstructure are (i) polycrystalline ct-Ge(Sn) embedded in Sn, (ii) cellular ~t-Ge(Sn), (iii) segregation-free ct-Ge(Sn), and the Ge single crystal substrate.
4.2. Solidification rate In the computer simulations, the temperatures increase rapidly to a maximum during the heating stage as shown in Figs 4 and 11. Subsequently, the liquid resolidifies, with a high initial solidification rate because of steep temperature gradients in both the underlying solid Ge substrate and the molten Ge-Sn alloy liquid, as shown in Figs 5 and 12. However, the release of latent heat during resolidification raises temperatures near the liquid/solid interface, which lowers the temperature gradient and reduces the solidification rate. Ge-Sn alloys exhibit a large freezing range, with limited solid solubility and a large difference in Ge and Sn melting points [20]. As solidification continues, Sn segregates into the liquid at the liquid/solid interface, and this further reduces the solidification rate. The overall increase and then
6
.
4
a
o
3
u
S
2
c
1 0 5O
IOO
150
200
250
Time (ns)
Fig. 13. Calculated solidification rate vs time for a 120 nm Ge--50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse.
Fig. 15. Cross-section TEM micrograph of a 1.08 J/cm 2 irradiated 120 nm Ge-50 at.% Sn sample, showing (i) a 90 nm thick Sn overlayer, (ii) a 100 nm thick layer of cellular ~-Ge(Sn) and (iii) a 65 nm thick layer of segregation-free ct-Ge(Sn).
4418
CHANG and CANTOR: PULSED LASER IRRADIATION Table 6. Summaryof predictedresultsfrom computersimulationsof 400 nm Sn and 120nm Ge-50 at.% Sn irradiatedsamples Maximum
Sample 400 nmSn 120 nmGe-50 at.% Sn
Energy density (J/cm2) 1.15 0.96 1.08 1.17
Maximum melt depth (nm) 562 220 255 300
decrease of the solidification rate with time during resolidification is shown in Figs 6 and 13. The variation in the solidification rate with time for the above cases is different to that predicted for the laser irradiated pure nickel using an analytical method [21]. The difference is caused by the fact that the present computer model takes into account two important effects which are lacking in the previous analytical model [21]. These effects are: (1) the redistribution of solute by interdiffusion between the film and substrate and by partitioning across the liquid/solid interface during melting and solidification, and (2) the evolution of latent heat during solidification. The calculated maximum solidification rate increases initially and then decreases with increasing energy density as shown in Table 6. In the low energy regime, the solidification rate is strongly influenced by the liquid composition prior to resolidification. With a small amount of the Ge substrate being melted, interdiffusion of atoms across the film/substrate boundary leads to a relatively high Sn content liquid with a low liquidus temperature, giving a slow solidification rate. As the energy density increases, the liquid prior to solidification becomes more dilute, giving a higher solidification rate. When more of the underlying Ge substrate is melted, the effect of liquid composition becomes negligible because the liquid is very dilute. Hence at higher energy densities, the solidification rate is controlled by the amount of material being melted, since for a thicker liquid layer, a longer time is required for resolidification.
surface Maximum temperature solidificationrate (K) (m/s) 2222.6 3.6 1603.5 5.68 1731.0 5.58 1842.0 5.40
is the upper limit where the surface energy of the liquid/solid interface becomes dominant in stabilizing the planar growth. In pulsed laser irradiation, the solidification rate has been shown to be extremely fast initially and decreases with time. Therefore, the cellular breakdown is defined by the following absolute stability criterion
V,b- m D ( k - 1)Co k2TmF
(9)
where k is the equilibrium partition coefficient, Tm is the melting temperature, F is the ratio of surface energy to the latent heat of freezing, m is the liquidus slope on the equilibrium phase diagram and Co is the overall composition of the liquid prior to solidification. Figures 16 and 17 show predicted variations of solidification rate R (full line) and absolute stability velocity V,b (dashed line) during resolidification of 1.15 J/cm ~ irradiated 4 0 0 n m Sn and 1.08 J/cm 2 irradiated 120 nm Ge-50 at.% Sn samples respectively. In Figs 16 and 17, the solidification rate R is given directly by the computer simulation at each time, and the absolute stability velocity V~b is calculated from the liquid composition Co just ahead of the liquid/solid interface at each time, using equation (9) and the constants in Table 8. The corresponding liquid
4
0.20
l
m
4.3. Cellular breakdown Cellular growth is stable when the solidification rate lies between V~ and Vab for a given temperature gradient in the liquid. V,~ is the lower limit where the solute gradient in the liquid unstablizes the planar liquid/solid interface (i.e. constitutional supercooling [22]). V,b, known as the absolute stability velocity [23],
/ / /
/ ~a
0.10
o"~ ,,o
/ /
r
o
/
0.o5
/
/
o
Table7. Comparisonbetweenpredictedand measuredmaximummelt depths for 400 um Sn and 120 nm Ge--50at.% Su irradiatedsamples Energy Predicted Measured density depth depth Sample (J/cm2) (nm) (nm) 400 nm Sn 1.15 562 557 120 nm Ge-50 at.% Sn 0.96 220 -1.08 255 246 1.17 300 296
0.1fi ~. .,3
/
9 /
0
50
o
(b)
I
0.00 tO
55
Time
(las)
Fig. 16. (a) Calculated solidification rate vs time (--) for a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse, and (b) absolute stabilityvelocity for planar growth (- - -) for the corresponding liquid composition ( 0 ) ahead of the liquid/solid interface during resolidification of the irradiated sample.
4419
CHANG and CANTOR: PULSED LASER IRRADIATION 35
I
1.5
I
A
.~
m 30 /
"--'25
I
2
1.0 .d ,~
/ / /
o
/
o 15 /
:(b)
0.5
"d o
Table 9. Comparison between predicted and measured depths for transition from planar to cellular solidificationfor 400 nm Sn and 120 nm Ge-50 at.% Sn irradiated samples Energy Predicted Measured density depth depth Sample (J/cm2) (nm) (nm) 400 nm Sn 1.15 450 457 120 nm Ge-50 at.% Sn 0.96 75 75 1.08
180
190
1.17
200
208
/
~
g~
d
5 O0
4,0
0.0
.... 45
50
55
Time (ns) Fig. 17. (a) Calculated solidification rate vs time (--) for a 120 nm Ge-50 at% Sn sample irradiated with a 1.08 J/cm2 laser pulse, and (b) absolute stability velocity for planar growth (- - -) for the corresponding liquid composition (@) ahead of the liquid/solid interface during resolidification of the irradiated sample.
compositions Co are shown by full circles on Figs 16 and 17. For each sample, the solidification rate R rises and then falls, as discussed in Section 4.2. The absolute stability velocity Vab rises sharply with increasing Co, as Sn is segregated into the liquid ahead of the liquid/solid interface. In Figs 16 and 17, when the solidification rate R is greater than lab for the corresponding liquid composition Co, a planar liquid/solid interface is predicted to be stable during resolidification of the irradiated sample. The transition from planar to cellular solidification takes place when R equals lab, and this is predicted to be at a depth which can be obtained from Figs 3, 10, 16 and 17. Table 9 shows the resulting predicted and measured [19] depths for the onset of cellular microstructures in 1.15 J/cm 2 irradiated 400 n m Sn and 1.08 J/cm 2 irradiated 120 n m Ge-50 at.% Sn samples. The predicted depths agree well with the measured data. Cellular breakdown takes place at greater depth with increasing energy density, as shown in Table 9. 4.4. Equiaxed structure The formation of polycrystalline cr occurs when the liquid ahead of the cellular solidification front is constitutionally supercooled because of solute segregation. This leads to fresh nucleation of equiaxed e-Ge(Sn) crystals. However, the present computer model does not include the effect of nucleation undercooling in the liquid, and is therefore unable to predict the transition from cellular to equiaxed structure. Table 8. Constantsused to calculatethe absolutestabilityvelocity Vab from equation (9) k D (m2/s) Tm(K) m (K/at.% Sn) r (m) 0.02 2.0 x 108 1211 -480 9.122 x 10-9
5. CONCLUSIONS A computer model has been developed to describe melting and resolidification during laser irradiation of elemental and alloy films on a substrate. The computer model predicts the temperature profile, m a x i m u m melt depth, maximum solidification rate, onset of cellular breakdown and the final resolidified composition profile. The computer model has been compared with measurements [19] made on cross-section T E M specimens of 1.15 J/cm 2 irradiated 400 n m thick Sn and 0.96-1.17 J/cm 2 irradiated 120 n m thick G e 50 at.% Sn films on single crystal Ge substrates. The predicted results give good agreement with the measured data. The maximum melt depth increases with increasing laser energy density. Cellular breakdown takes place at increasing depth with increasing laser energy density. Acknowledgements--The authors would like to thank Dr A. G. Cullis for helpful discussions and the U.K. Science and Engineering Research Council and DRA Malvern for financial support of the research programme. REFERENCES
1. F. S. Spaepan and D. Turnbull, in Laser Annealing of Semiconductors (edited by J. M. Poate and J. W. Mayer), p. 15. Academic Press, New York (1982). 2. A.G. Cullis, H. C. Webber and N. G. Chew, Appl. Phys. Lett. 36, 547 (1980). 3. J. M. Poate, in Laser and Electron Beam Processing of Materials (edited by C. W. White and P. S. Peercy), p. 691. Academic Press, New York (1980). 4. F. Catalina, C. N. Afonso and E. Rollan, J. less-common Metals 145, 209 (1988). 5. G. J. van Gurp, G. E. J. Eggermont, Y. Tamminga, W. T. Stacy and J. R. M. Gijsbers, Appl. Phys. Lett. 35, 273 (1979). 6. K. G~irtner, G. G6tz, C. Kaschner, I. Kasko, A. Witzmann and Z. Zentgraf, Physica status solidi (a) 112, 747 (1989). 7. A. G. Cullis, N. G. Chew, H. C. Webber and D. J. Smith, J. Cryst. Growth 68, 624 (1984). 8. U. Kambli, M. von Allmen, N. Saunders and A. P. Miodownik, Appl. Phys. A 36, 189 (1985). 9. P. Baeri, G. Campisano, G. Foti and E. Rimini, J. appl. Phys. 50, 788 (1979). 10. J. R. Meyer, M. R. Kruer and F. J. Bartoli, J. appl. Phys. 51, 5512 (1980). 11. A. Bhattacharyya, B. G. Streetman and K. Hess, J. appl. Phys. 52, 3611 (1980). 12. R. F. Wood, J. C. Wang, G. E. Giles and J. R. Kirkpatrick, in Laser and Electron Beam Processing of Materials (edited by C. W. White and P. S. Peercy), p. 37. Academic Press, New York (1980).
4420
CHANG and CANTOR:
PULSED LASER IRRADIATION
13. A. K. Jain, V. N. Kulkarin and D. K. Sood, Appl. Phys. 25, 127 (1981). 14. H.C. Webber, A. G. Cullis and N. G. Chew, Appl. Phys. Lett. 43,.669 (1983). 15. W.J. Boettinger, S. R. Coriell and R. F. Sekerka, Mater. Sci. Engng 65, 27 (1983). 16. M.J. AzizandT. Kaplan, Actametall. 36,2335(1988). 17. D. Turnbull, Thermodynamics in Metallurgy. Am. Soc. Metals, Metals Park, Ohio (1949). 18. B. W. Arden and K. N. Astill, in Numerical Algorithms: Origins and Applications, p. 280. Addison-Wesley, London (1970). 19. I. T. H. Chang and B. Cantor, J. Thin Solid Films 230, 167 (1993). 20. R. W. Olesinski and G. K. Abbaschian, Bull. Phase Diagram 5, 265 (1984). 21. E. M. Breinan and B. H. Kear, in Laser Materials Processing (edited by M. Bass), p. 236. North Holland, Amsterdam (1983). 22. W.A. Tiller, K. A. Jackson, W. Rutter and B. Chalmers, Acta metall. 1, 428 (1953). 23. W. J. Boettinger, R. J. Schaefer and F. S. Biancaniello, Metall. Trans. 15A, 55 (1984).
Nomenclature density p (g m 3) absolute temperature T (K) time t (s) heat absorbed per unit volume Q,~ (J m 3) K ( W m - J K ~) thermal conductivity distance from the surface z (m) latent heat of freezing L (J g 1) solid fraction f composition C(at.%) diffusion coefficient D (m 2 s ~) partition coefficient k absorption coefficient ~ (m- ~) reflectivity of the surface R solidification rate V (ms- ~) liquid/solid interface mobility M (K-~s 1) liquidus slope on the equilibrium phase m (K at.% -~) diagram ratio of surface energy to the latent heat of F (m) freezing
~
Pergamon
Elsevier Science Ltd Copyright 9 1995 Acta Metanurgica Inc. Printed in Great Britain. All rights reserved 0956-7151/95 $9.50 + 0.00
0956-7151(95)00121-2
TEMPERATURE, COMPOSITION A N D MICROSTRUCTURE VARIATIONS D U R I N G PULSED LASER IRRADIATION OF A DEPOSITED FILM ON A SUBSTRATE I. T. H. CHANG and B. CANTOR Oxford Centre for Advanced Materials and Composites, Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, England
(Received 3 August 1994; in revisedform 24 February 1995)
Abstract--A computer model has been developed to describe melting and resolidification during laser irradiation of elemental and alloy films on a substrate. The computer model predicts the temperature profile, maximum melt depth, maximum solidification rate, onset of cellular breakdown and the final resolidified composition profile. The computer model has been compared with measurements [I. T. H. Chang and B. Cantor, J. Thin Solid Films 230, 167 (1993)] made on cross-section TEM specimens of 1.15 J/cm 2 irradiated 400 nm thick Sn and 0.96-1.17 J/cm 2 irradiated 120 nm thick Ge-50 at.% Sn films on single crystal Ge substrates. The predicted results give good agreement with the measured data. The maximum melt depth increases with increasing laser energy density. Cellular breakdown takes place at increasing depth with increasing laser energy density.
1. INTRODUCTION Pulsed laser irradiation of a material produces structural changes near the surface as a result of rapid heating and melting, followed by cooling and solidification. Structural changes caused by pulsed laser irradiation include the removal of ion implantation damage [1, 2] and the formation of metastable supersaturated solid solutions [3,4], compounds [5,6] and amorphous phases [7, 8]. Understanding these effects requires detailed knowledge of the thermal evolution in the material during and after irradiation, including the temperature profiles, melt depth, melt duration and cooling and solidification rates. This information can then be used to predict the structure and composition of the final solidified material. Temperature and composition changes in irradiated materials have previously been calculated from separate one-dimensional heat and mass balance equations, giving good agreement with experimental results on dilute alloys [9-15]. However, this approach becomes invalid when applied to concentrated alloys, because temperature changes are then strongly influenced by compositional changes in the liquid. This paper presents a computer model of surface melting and solidification during pulsed laser irradiation of a binary alloy, using combined one-dimensional heat and mass balance equations with a solute distribution coefficient which is dependent on the solidification rate. The model is applied to the pulsed laser irradiation of a deposited film on a substrate, in order to predict the solidification rate, melt depth and duration, and temperature and composition variations as a function of pulse energy
density and initial film composition. These results are used to assess the final irradiated microstructures, as found experimentally for pure Sn and Ge-50 at.% Sn alloy films on a Ge substrate.
2. COMPUTERMODEL 2. I. Heat and mass flow equations Consider a pulsed laser beam incident normally along the z-axis on a sample consisting of a deposited film supported by a substrate as shown schematically in Fig. 1. The deposited film can be either an alloy or an elemental material. The laser beam energy is absorbed near the surface of the sample, and is instantaneously converted into heat, which diffuses into the bulk by thermal conduction. If sufficient energy is absorbed by the sample, the deposited film and adjacent regions of the underlying substrate melt and then resolidify after the radiation pulse. Redistribution of solute takes place by interdiffusion between the film and substrate, and by partitioning across the liquid/solid interface during melting and solidification. When the width of the laser beam is greater than the depth of surface heat treatment, heat and mass flows are confined to the z-axis, as shown in Fig. 1. Under these conditions, the laser treatment can be described by two, linked one-dimensional differential equations as follows: The temperature profile is given by a one-dimensional heat balance equation
4411
dr PC-d-f =
dt
d . + ~z\
.(Kdr + dz ] pL-~
(1)
4412
CHANG and CANTOR: PULSED LASER IRRADIATION solid/liquid interfaces can be expressed as dC/ dt = (dC/dT)(dT/dt), where dT/dt is the same as in equation (1), and d C / d T can be obtained from the slope of the liquidus curve on the equilibrium phase diagram. 2.2. Numerical solutions An explicit forward finite difference method was used to solve equations (1) and (2). The spatial dimension of the sample along the z-axis was divided into many blocks, and the time dimension representing the thermal and compositional histories of the sample was divided into many time steps. The ith block thickness and the j t h time interval were Azi and At respectively. The temperature and the liquid and solid compositions within each block remained constant over each time step and were T4, C~ and C~ respectively for the ith block at timejAt. Material parameters with subscript i were used to define the temperature-and composition-dependent physical properties of the ith block. Equations (1) and (2) were then solved iteratively for all i , j by assuming no heat loss at the surface, constant temperature in the bulk of the sample and mass diffusion only in fully molten blocks. The numerical solution of equation (1) is
Fig. 1. Schematic diagram of a sample irradiated with a laser pulse. where T is the temperature, t is the time, p is the density, c is the specific heat capacity, (dQabs/dt) is the rate of heat absorbed per unit volume from the laser beam, Kis the thermal conductivity, L is the latent heat of melting, df/dt is the rate of change of solid fraction during melting or solidification and the convection is ignored here because it is relatively slow. The composition profile is given by a one-dimensional mass balance equation dC dt
(DdC)+
d dz
dz ]
pici(T~ + ' - - T~) At - P~[1 - exp(-c
(2)
C(1-k)~ft
where C is the melt composition, D is the solute diffusion coefficient, and k is the partition coefficient. The heat and mass balance equations (1) and (2) are linked, since the variation in melt composition at the
~ ~ i .._~__ I r ~ I mug.... I
~ ~ | L
Ahoyor element
element
alloy
1
l
usingVon Neumann's stabilitycriteria
of ith block
f
+p,L,
Calculatetime interval with given block thickness
]~(~ Examinecomposition )'
+ x,)
~(
CheckTI i§ >--or < Tin,calculatetrueTI ~+1 ! accordinglyand calculatef, V and C ( onlywheninterdiffusionbetweenelements oocurs).
Check Ti j+l > or < Tin,calculatetrueTI I+1 accordingly and calculatef, V, C, C s and k
(f~+'
,,z,+41
tie, + K,+,)/
- f4)
At
(3)
Initializeall variables, do time step Harations and calculatelaser power density at given time t
CalT:~ hTesil:;~; eming
!
(,,z,
Do block iteiation for near surfaceregion (z = 20nm - 200Onto)
L
Do blockiterationfor region(200Ohm< z < 300,000nm) and calculatedQ abs/dt, d/dz(Kd'T/dt)for a time intervalof (:It and TII+I
I Endof program~ _
Fig. 2. Block diagram of the computer model.
fore time intervalof dt.
f __
ReeeiTi j to TII+I , and cil to C 11+1
1
Printand store calculateddata
CHANG and CANTOR: PULSED LASER IRRADIATION
4413
Table 1. Polynomial expressions for c, K and ct as a function o f temperature for G e ForGe(300
K
For Ge (T>
K ) : c ( T ) = 5 . 7 6 7 • 10 2(5.16+ 1 . 4 x 1 0 - t T ) J/g K K ( T ) =0.6(300/T) 114 W / c m K ~ ( T ) = 8 • 1@ exp [1.1 • 103(T - 300)] c m -L 1211 K): c ( T ) = 0 . 3 8 0 4 J/g K K(T)=0.25 W/cm K ct(T)= 1 x 106 c m J
where P4 is the power of the laser beam transmitted to the ith block at timejAt, ctiis the absorption coefficient andf~ is the solid fraction. For the surface block i = 1, P~ = P6(I - R) where P~ the laser output power and R is the reflectivity of the surface. Similarly, the numerical solution of equation (2) is
(c ~+'- co At
D {(c~_,- c~) (c~- c~+,)'] -aZ, + -As ]
-
Az, \
+ C4(1 - k) (f4+l - f ~ ) At
(4)
where k varies with the solidification rate VJi, and is given by [16]
k -
(5)
(~)
of the liquid/solid interface. This gives df/dt in equation (I) as f~+~ - f ~ = M(Ti +l - Tm)At
where Tm and M are the melting temperature and the liquid/solid interface mobility respectively. The new temperature Ti + ~ is calculated by the eliminating (f~+l -f~)/At from equations (3) and (7): For an alloy, the melting begins at the solidus temperature (Ts) and ends at the liquidus (T0 temperature. Therefore, the rate of solid fraction molten (df/dt) depends on the heating rate (dT/dt) and the change of solid fraction with temperature (df/dT), according to a simple relationship of df/dt = (df/dT)(dT/dt). The deviation from equilibrium is assumed to be small with little effect on the final solidified microstructure. The lever rule can then be used to give
+ 1 - (1 - xo)C,
(f~+,_f~)_
where a is the interatomic distance of the growing solid, xo = kA/ko,ko = Cs/C is the equilibrium partition coefficient of the solute atoms and k f = ( 1 - C 0 ( 1 - C0 is the equilibrium partition coefficient of the solvent atoms. The solidification rate V4 is given by VI- (f~+'-f~) At
Az,.
(6)
The dimensions of the variables used in the present computer model are listed in the Nomenclature in the Appendix.
2.3. Phase change F o r fully molten or solid blocks, the last terms in equations (1) and (2) are zero, so the temperature and composition can be calculated directly from equations (3) and (4) respectively. During melting or freezing, the propagation of the liquid/solid interface is treated differently for an elemental material compared to an alloy. For an elemental material, a linear kinetics approximation [17] is used to describe the movement
- ( T ~ + ~ - T~) ( T I - Ts)
(8)
where T~ and Ts are the liquidus and solidus temperatures on the equilibrium phase diagram. The new temperature, TJ,.§ is calculated by eliminating (f~+l -f~)/At from equations (3) and (8). For an alloy during solidification, the lever rule cannot be used because equilibrium is not maintained. Instead, equations (1) and (2) can be solved simultaneously by eliminating df/dt, and taking k from equation (5) and using dC/dt = (dC/dT)(d T/dt), where dC/dT is taken from the equilibrium phase diagram.
2.4. Computer calculations A computer program was written in F O R T R A N to calculate the temperature and composition profiles during and after laser irradiation of pure Sn and Ge-Sn alloy films on a Ge substrate, using the treatment described in the previous sections. A block diagram of the computer program is shown in Fig. 2. It is divided into several parts for handling the heat and mass flows: (l) without any phase changes; (2) at the initiation of a phase change; and (3) during a phase change. Values of At and Azi were chosen using Von Neuman's stability criterion [18] (At < 0.5
Table 2. Polynomialexpressionsfor c, K and ~ as a function of temperaturefor Sn For SN (300 K< T < 505 K): c(T)=3.528 x 10-2(5.16+ 4.3 x 10-3T) J/g K K(T)=2.295(I/T)~ W/cm K otT= 1 • 106 cm
For Sn (T_> 505 K): c(T)=0.2397 J/g K K(T)=2.49 • 10 ~2T3- 5.64 • 10-gT2 + 2 . 0 8 • 1 0 - 4 T + 0.1997 W / c m K c t ( T ) = l x 106cm -~ AM 43/12--N
(7)
4414
CHANG and CANTOR: PULSED LASER IRRADIATION
Table 3. Polynomial expressions for C and dC/dT as a function o f temperature for G e - S n alloys
Table 5. Numerical expressions for Dsn as a function o f temperature T < 1090 K: D = 3 , 2 4 x 10-4exp ( - 1 3 8 9 / T ) T > 1090 K: D = 1 . 3 9 x 10-3exp ( - 2 0 1 3 / T )
C = 0.22792 + 2.75 x 1 0 - 3 T - 2.4299 x 1 0 - 6 T z 9 d C / d T = 2 . 7 5 x 1 0 - 3 - 4 . 8 5 9 8 x 10 6T
piciAz?Ki-~). F o r each computer simulation, the sample was assumed to have a total thickness in excess of 300 #m, with Az = 20 nm for the first 2/~m below the surface, followed by a gradually increasing A z i = 1.4Azi_l. The value of At was 0.24 ns. Tables 1-5 show the material parameters used in the computer program for pure Ge and Sn. Average values were assumed for the Ge-50 at.% Sn alloy. A value of 0.745 was chosen as the reflectivity of Ge-50 at.% Sn, to correspond to the measured melt depth of a Ge-50 at.% Sn sample. The simulated temperature and composition profiles were compared with experimental measurements obtained by pulsed laser irradiation of thermally evaporated 400 nm thick pure Sn, and 120 nm thick Ge-50 at.% Sn alloy films on single crystal Ge substrates, using a ruby laser operating with a pulse length of 24 ns, wavelength of 694 nm and an energy density in the range 0.96-1.17 J/cm 2. Film thicknesses were measured using an Alphastep. The pulsed laser energies delivered to the samples were measured using an Apollo energy calorimeter. The resulting microstructural variations across the irradiated samples were observed by cross-sectional transmission electron microscopy (TEM) [19] using a Philips CM12 fitted with L I N K energy dispersive X-ray microanalyser (EDX).
3. RESULTS 3.1. 400 nm Sn Figure 3 shows calculations of melt depth vs time for the 400 nm Sn sample irradiated with a 1.15 J/cm 2 laser pulse. The Sn film began to melt after 10 ns, and the melt depth then increased with time, i.e. melting proceeded up to a maximum depth of 562 nm after a time of 50 ns. The melt depth then decreased with time, i.e. the substrate and film resolidified. The shoulder on the plot in Fig. 3 is at a melt depth of 400 nm, at the Sn/Ge interface, and corresponds to a delay in melting as the temperature rises to the high melting point of the Ge substrate. Figure 4 shows the corresponding calculations of temperature vs time at depths of 20, 410 and 570 nm. The temperatures at these depths increased with increasing time, reached maximum values after ~ 30 ns, and then decreased as cooling commenced. The maximum temperatures were 2309, 1487 and
1212 K at depths of 20, 410 and 570 nm respectively, i.e. below the boiling temperature of Sn (2543 K) but above the melting point of Ge (1211 K). The initial cooling rates were 4.6 • 10 ~~ 7.7 • 109 and 1.4 x 109 K / S at depths of 20, 410 and 570 nm respectively. The cooling rates decreased gradually with time until they converged after ~ 100 ns. Figure 5 shows corresponding calculated temperature profiles after times of 30 and 50 ns. After 30 ns, corresponding to the maximum temperature as shown in Fig. 4, there was a steep temperature gradient of 2.39 x 109 K/m within the sample. However, after 50 ns, corresponding to the maximum melt depth as shown in Fig. 3, there was a much smaller temperature gradient of 0.3 x 109 K/m between the surface and the substrate. Figure 6 shows calculated variations of solidification rate for the irradiated 400 nm Sn sample. The solidification rate increased with time, reached a maximum value of 3.4 m/s after 60 ns, and then dropped sharply to a much lower value of ~ 0.1 m/s after ~ 100 ns. Figure 7 shows the calculated Sn solid composition profile after 225 ns, together with corresponding Sn compositions measured by EDX in cross-section TEM specimens [19]. Regions of different microstructure observed by cross-section TEM [19] are also labelled in Fig. 7. The 1.15 J/cm 2 irradiated 400 nm Sn microstructure consisted of: (i) a 257 nm thick Sn overlayer; (ii) a 100 nm thick layer of polycrystals of ct-Ge(Sn) embedded in Sn; (iii) a 100 nm thick layer of cellular ct-Ge(Sn); and (iv) a 70 nm thick layer of segregation-free ~-Ge(Sn), as shown in Fig. 8. The computer model predicted that after 225 ns, the region at depths between 450 and 550 nm solidified with a Sn
600
I
5O0 A
40O .el 3O0 ID
200 ID
100 0
Table 4. T e m p e r a t u r e independent parameters for G e and Sn Ge R = 0.44 (solid Ge, 2 = 694 nm) R = 0.7 (liquid Ge, 2 = 694 nm) p = 5.35 x 106 g / m 3
Sn R = 0 . 6 9 (solid Sn, 2 = 694 nm) R = 0 . 6 9 (liquid Sn, ~. = 694 nm) p = 7.31 x 106 g / m 3
I
0
I 50
I 100 Time
I 150
200
(nn)
Fig. 3. Calculated melt depth vs time for a 400 nm Sn sample irradiated with a 1.15 J/cm 2 laser pulse.
CHANG and CANTOR: PULSED LASER IRRADIATION 2500
(8)
1
4
i
4415
I
I
2000
3
b< r 0
1500 IJ k ID
la,
6
I000
III 6
500 II
0
I
0
50
]
I
100
150
0
200
50
T i m e (ns)
[
i
100
150
200
Time (na)
Fig. 4. Calculated temperature vs time profiles at depths of (a) I0 nm, (b) 410 n m and (c) 530 n m from the surface of a 400 n m Sn sample irradiated with a I.15 J/cm 2 laser pulse.
Fig. 6. Calculated solidification rate vs time during the solidification of a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse.
content less than 2 at. %. This agrees with experimentally measured compositions in the irradiated sample, as shown in Fig. 7.
different times between 40 and 395 ns, i.e. during the solidification stage for 120nm G e - 5 0 a t . % Sn irradiated with a 1.08 J/cm 2 laser pulse. Figure 1l shows corresponding calculations of temperature vs time at depths of 10, 90 and 250 nm. The curves had a similar shape to those shown in Fig. 4 for the 400 nm Sn sample irradiated with a 1.15 J/cm 2 laser pulse. The temperatures at these depths increased with increasing time, reached to a maximum after ~ 30 ns, and then decreased as cooling commenced. The maximum temperatures were 1731, 1556 and 1213 K and the initial cooling rates were calculated as
3.2. 120 nm Ge-50 a t . % Sn
Figure 9 shows calculations of solid fraction vs depth at different times in the first 35 ns, i.e. during the melting stage for 120 nm Ge-50 at.% Sn irradiated with a 1.08 J/cm 2 laser pulse. After 15 ns, all of the deposited Ge-50 at.% Sn alloy film had begun to melt. Melting continued until the melt front was held up at the Ge-50 at.% Sn/substrate boundary. After 25 ns, the Ge substrate began to melt and the melt front then continued to penetrate into the Ge substrate, reaching a maximum melt depth of 255 nm after 40 ns before resolidification began. Figure 10 shows similar calculations of solid fraction vs depth at
(i)
I
I
(ii) i(iii)l(iv) [substrate
1.0
9 measured Z~ p r e d i c t e d
data data
o 0.8 2500
I
eo
F
(a) ~-, M
0.8
2000
0.4 g o
O
1500
0.2 0
1000
O
0
0.0 0
500 1
0
200
I
200
[
300
i . . . .
400
500
I
600
Depth (nm)
I
400
I
lO0
800
D e p t h (rim) Fig. 5. Calculated temperature vs depth profiles at times of (a) 30 ns and (b) 50 ns for a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse.
Fig. 7. Calculated composition profile in a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse together with corresponding measured compositions. Regions of different microstructure are (i) Sn polycrystals, (ii) polycrystalline ct-Ge(Sn) embedded in Sn, (iii) cellular a-Ge(Sn), (iv) segregation-free a-Ge(Sn), and the Ge single crystal substrate.
4416
CHANG and CANTOR: PULSED LASER IRRADIATION 1.0
0.9 0.8
0.7
~ 0.8 ~
0.5 0.4
e
0.2
0.1
)-
)
0.0 Fig. 8. Cross-section TEM of a 1.15 J/cm~irradiated 400 nm Sn sample, showing (i) a 257 nm thick Sn overlayer, (ii) 100 nm thick polycrystals of ct-Ge(Sn) embedded in Sn, (iii) a 100 nm thick layer of cellular ~-Ge(Sn) and (iv) a 70 nm thick layer of segregation-free ct-Ge(Sn).
2.1 • 10 t~ 1.4 x 10 t~ and 3.6 • 109 K/s at depths of 10, 90 and 250 n m respectively. The cooling rates decreased gradually with time until they converged after ~ 100 ns. Figure 12 shows corresponding calculated temperature profiles after times of 30 and 50 ns. After 30 ns, corresponding to the maximum temperature as shown in Fig. 12, there was a steep temperature gradient of 1.89 • 109K/m within the sample. However, after 50 ns, corresponding to the initial stage of solidification as shown in Fig. 12, there was a much smaller temperature gradient of 2.27 • 108 K / m between the surface and the substrate. Figure 13 shows calculated variations of solidification rate for the irradiated 120 n m G e 50 at.% Sn samples. The solidification rate increased with time, reached a maximum value of 5.6 m/s after
//
1.0 0.9 0.8 0
0
50
100
150
200
250
300
Depth (nm) Fig. 10. Calculated solid fraction vs depth at times of (a) 40 ns, (b) 55 ns, (c) 75 ns, (d) 115 ns and (e) 395 ns for a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm 2 laser pulse.
45 ns and then dropped sharply to a much lower value of 1.4 x 10- 2 m/s after 225 ns. Figure 14 shows the calculated Sn solid composition profile after 595 ns, together with corresponding Sn compositions measured by E D X in cross-section T E M specimens [19]. Regions of different microstructure observed by cross-section T E M [19] are also labelled in Fig. 14. The 1.08 J/cm-' irradiated 120 n m Ge-50 at.% Sn microstructure consisted of: (i) a 90 n m thick Sn overlayer; (ii) a 100 n m thick layer of cellular 9 -Ge(Sn); and (iii) a 65 n m thick layer of segregationfree ~-Ge(Sn), as shown in Fig. 15. The computer model predicted that after 595 ns, the region at depths between 100 and 246 n m solidified with a Sn content ranging from 1 to 20 at.%. This agrees with
2000
(a)
I
I
I
I 50
I 100
I 150
1500
0.7 0.6
t.
1000
0.5 0.4
0
0.3 0.2
/
0.1 0.0 0
50
100 Depth
500
idl (e)
~)
0 50
~00 250
300
(rim)
Fig. 9. Calculated solid fraction vs depths at times of (a) 15 ns, (b) 20 ns, (c) 25 ns, (d) 30 ns and (e) 35 ns for a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse.
0
Time
(ns)
Fig. 11. Calculated temperature vs time profiles at depths of (a) 10 nm, (b) 90 nm and (c) 250 nm from the surface of a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse.
CHANG and CANTOR: PULSED LASER IRRADIATION 2000
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Fig. 12. Calculated temperature vs depth at times of(a) 30 ns and (b) 50 ns for a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cmz laser pulse.
experimentally measured compositions in the irradiated sample, as shown in Fig. 14.
3.3. Other samples Two other energy densities of 0.96 and 1.17 J/cm 2 were used with 120 nm thick Ge-50 at.% Sn samples on the computer model to predict the maximum melt depth (Dmax),maximum surface temperature (Tsurf)and maximum solidification rate (Vmax), as shown in Table 6. 4. DISCUSSION
4.1. Maximum melt depth Table 7 shows a list of predicted maximum melt depths together with corresponding maximum depths containing Sn as measured by EDX on 400 nm Sn and 120nm G e - 5 0 a t . % Sn samples [19]. The calculated melt depths agree well with the measured data. The calculated and measured melt depths both increase with increasing energy density, as shown in Table 7.
50
100
150
200
250
Depth (nm)
Fig. 14. Calculated composition profile in a 120 nm Ge-50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse, together with corresponding measured compositions. Regions of different microstructure are (i) polycrystalline ct-Ge(Sn) embedded in Sn, (ii) cellular ~t-Ge(Sn), (iii) segregation-free ct-Ge(Sn), and the Ge single crystal substrate.
4.2. Solidification rate In the computer simulations, the temperatures increase rapidly to a maximum during the heating stage as shown in Figs 4 and 11. Subsequently, the liquid resolidifies, with a high initial solidification rate because of steep temperature gradients in both the underlying solid Ge substrate and the molten Ge-Sn alloy liquid, as shown in Figs 5 and 12. However, the release of latent heat during resolidification raises temperatures near the liquid/solid interface, which lowers the temperature gradient and reduces the solidification rate. Ge-Sn alloys exhibit a large freezing range, with limited solid solubility and a large difference in Ge and Sn melting points [20]. As solidification continues, Sn segregates into the liquid at the liquid/solid interface, and this further reduces the solidification rate. The overall increase and then
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150
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250
Time (ns)
Fig. 13. Calculated solidification rate vs time for a 120 nm Ge--50 at.% Sn sample irradiated with a 1.08 J/cm2 laser pulse.
Fig. 15. Cross-section TEM micrograph of a 1.08 J/cm 2 irradiated 120 nm Ge-50 at.% Sn sample, showing (i) a 90 nm thick Sn overlayer, (ii) a 100 nm thick layer of cellular ~-Ge(Sn) and (iii) a 65 nm thick layer of segregation-free ct-Ge(Sn).
4418
CHANG and CANTOR: PULSED LASER IRRADIATION Table 6. Summaryof predictedresultsfrom computersimulationsof 400 nm Sn and 120nm Ge-50 at.% Sn irradiatedsamples Maximum
Sample 400 nmSn 120 nmGe-50 at.% Sn
Energy density (J/cm2) 1.15 0.96 1.08 1.17
Maximum melt depth (nm) 562 220 255 300
decrease of the solidification rate with time during resolidification is shown in Figs 6 and 13. The variation in the solidification rate with time for the above cases is different to that predicted for the laser irradiated pure nickel using an analytical method [21]. The difference is caused by the fact that the present computer model takes into account two important effects which are lacking in the previous analytical model [21]. These effects are: (1) the redistribution of solute by interdiffusion between the film and substrate and by partitioning across the liquid/solid interface during melting and solidification, and (2) the evolution of latent heat during solidification. The calculated maximum solidification rate increases initially and then decreases with increasing energy density as shown in Table 6. In the low energy regime, the solidification rate is strongly influenced by the liquid composition prior to resolidification. With a small amount of the Ge substrate being melted, interdiffusion of atoms across the film/substrate boundary leads to a relatively high Sn content liquid with a low liquidus temperature, giving a slow solidification rate. As the energy density increases, the liquid prior to solidification becomes more dilute, giving a higher solidification rate. When more of the underlying Ge substrate is melted, the effect of liquid composition becomes negligible because the liquid is very dilute. Hence at higher energy densities, the solidification rate is controlled by the amount of material being melted, since for a thicker liquid layer, a longer time is required for resolidification.
surface Maximum temperature solidificationrate (K) (m/s) 2222.6 3.6 1603.5 5.68 1731.0 5.58 1842.0 5.40
is the upper limit where the surface energy of the liquid/solid interface becomes dominant in stabilizing the planar growth. In pulsed laser irradiation, the solidification rate has been shown to be extremely fast initially and decreases with time. Therefore, the cellular breakdown is defined by the following absolute stability criterion
V,b- m D ( k - 1)Co k2TmF
(9)
where k is the equilibrium partition coefficient, Tm is the melting temperature, F is the ratio of surface energy to the latent heat of freezing, m is the liquidus slope on the equilibrium phase diagram and Co is the overall composition of the liquid prior to solidification. Figures 16 and 17 show predicted variations of solidification rate R (full line) and absolute stability velocity V,b (dashed line) during resolidification of 1.15 J/cm ~ irradiated 4 0 0 n m Sn and 1.08 J/cm 2 irradiated 120 nm Ge-50 at.% Sn samples respectively. In Figs 16 and 17, the solidification rate R is given directly by the computer simulation at each time, and the absolute stability velocity V~b is calculated from the liquid composition Co just ahead of the liquid/solid interface at each time, using equation (9) and the constants in Table 8. The corresponding liquid
4
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4.3. Cellular breakdown Cellular growth is stable when the solidification rate lies between V~ and Vab for a given temperature gradient in the liquid. V,~ is the lower limit where the solute gradient in the liquid unstablizes the planar liquid/solid interface (i.e. constitutional supercooling [22]). V,b, known as the absolute stability velocity [23],
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Table7. Comparisonbetweenpredictedand measuredmaximummelt depths for 400 um Sn and 120 nm Ge--50at.% Su irradiatedsamples Energy Predicted Measured density depth depth Sample (J/cm2) (nm) (nm) 400 nm Sn 1.15 562 557 120 nm Ge-50 at.% Sn 0.96 220 -1.08 255 246 1.17 300 296
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50
o
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Fig. 16. (a) Calculated solidification rate vs time (--) for a 400 nm Sn sample irradiated with a 1.15 J/cm2 laser pulse, and (b) absolute stabilityvelocity for planar growth (- - -) for the corresponding liquid composition ( 0 ) ahead of the liquid/solid interface during resolidification of the irradiated sample.
4419
CHANG and CANTOR: PULSED LASER IRRADIATION 35
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Table 9. Comparison between predicted and measured depths for transition from planar to cellular solidificationfor 400 nm Sn and 120 nm Ge-50 at.% Sn irradiated samples Energy Predicted Measured density depth depth Sample (J/cm2) (nm) (nm) 400 nm Sn 1.15 450 457 120 nm Ge-50 at.% Sn 0.96 75 75 1.08
180
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Time (ns) Fig. 17. (a) Calculated solidification rate vs time (--) for a 120 nm Ge-50 at% Sn sample irradiated with a 1.08 J/cm2 laser pulse, and (b) absolute stability velocity for planar growth (- - -) for the corresponding liquid composition (@) ahead of the liquid/solid interface during resolidification of the irradiated sample.
compositions Co are shown by full circles on Figs 16 and 17. For each sample, the solidification rate R rises and then falls, as discussed in Section 4.2. The absolute stability velocity Vab rises sharply with increasing Co, as Sn is segregated into the liquid ahead of the liquid/solid interface. In Figs 16 and 17, when the solidification rate R is greater than lab for the corresponding liquid composition Co, a planar liquid/solid interface is predicted to be stable during resolidification of the irradiated sample. The transition from planar to cellular solidification takes place when R equals lab, and this is predicted to be at a depth which can be obtained from Figs 3, 10, 16 and 17. Table 9 shows the resulting predicted and measured [19] depths for the onset of cellular microstructures in 1.15 J/cm 2 irradiated 400 n m Sn and 1.08 J/cm 2 irradiated 120 n m Ge-50 at.% Sn samples. The predicted depths agree well with the measured data. Cellular breakdown takes place at greater depth with increasing energy density, as shown in Table 9. 4.4. Equiaxed structure The formation of polycrystalline cr occurs when the liquid ahead of the cellular solidification front is constitutionally supercooled because of solute segregation. This leads to fresh nucleation of equiaxed e-Ge(Sn) crystals. However, the present computer model does not include the effect of nucleation undercooling in the liquid, and is therefore unable to predict the transition from cellular to equiaxed structure. Table 8. Constantsused to calculatethe absolutestabilityvelocity Vab from equation (9) k D (m2/s) Tm(K) m (K/at.% Sn) r (m) 0.02 2.0 x 108 1211 -480 9.122 x 10-9
5. CONCLUSIONS A computer model has been developed to describe melting and resolidification during laser irradiation of elemental and alloy films on a substrate. The computer model predicts the temperature profile, m a x i m u m melt depth, maximum solidification rate, onset of cellular breakdown and the final resolidified composition profile. The computer model has been compared with measurements [19] made on cross-section T E M specimens of 1.15 J/cm 2 irradiated 400 n m thick Sn and 0.96-1.17 J/cm 2 irradiated 120 n m thick G e 50 at.% Sn films on single crystal Ge substrates. The predicted results give good agreement with the measured data. The maximum melt depth increases with increasing laser energy density. Cellular breakdown takes place at increasing depth with increasing laser energy density. Acknowledgements--The authors would like to thank Dr A. G. Cullis for helpful discussions and the U.K. Science and Engineering Research Council and DRA Malvern for financial support of the research programme. REFERENCES
1. F. S. Spaepan and D. Turnbull, in Laser Annealing of Semiconductors (edited by J. M. Poate and J. W. Mayer), p. 15. Academic Press, New York (1982). 2. A.G. Cullis, H. C. Webber and N. G. Chew, Appl. Phys. Lett. 36, 547 (1980). 3. J. M. Poate, in Laser and Electron Beam Processing of Materials (edited by C. W. White and P. S. Peercy), p. 691. Academic Press, New York (1980). 4. F. Catalina, C. N. Afonso and E. Rollan, J. less-common Metals 145, 209 (1988). 5. G. J. van Gurp, G. E. J. Eggermont, Y. Tamminga, W. T. Stacy and J. R. M. Gijsbers, Appl. Phys. Lett. 35, 273 (1979). 6. K. G~irtner, G. G6tz, C. Kaschner, I. Kasko, A. Witzmann and Z. Zentgraf, Physica status solidi (a) 112, 747 (1989). 7. A. G. Cullis, N. G. Chew, H. C. Webber and D. J. Smith, J. Cryst. Growth 68, 624 (1984). 8. U. Kambli, M. von Allmen, N. Saunders and A. P. Miodownik, Appl. Phys. A 36, 189 (1985). 9. P. Baeri, G. Campisano, G. Foti and E. Rimini, J. appl. Phys. 50, 788 (1979). 10. J. R. Meyer, M. R. Kruer and F. J. Bartoli, J. appl. Phys. 51, 5512 (1980). 11. A. Bhattacharyya, B. G. Streetman and K. Hess, J. appl. Phys. 52, 3611 (1980). 12. R. F. Wood, J. C. Wang, G. E. Giles and J. R. Kirkpatrick, in Laser and Electron Beam Processing of Materials (edited by C. W. White and P. S. Peercy), p. 37. Academic Press, New York (1980).
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PULSED LASER IRRADIATION
13. A. K. Jain, V. N. Kulkarin and D. K. Sood, Appl. Phys. 25, 127 (1981). 14. H.C. Webber, A. G. Cullis and N. G. Chew, Appl. Phys. Lett. 43,.669 (1983). 15. W.J. Boettinger, S. R. Coriell and R. F. Sekerka, Mater. Sci. Engng 65, 27 (1983). 16. M.J. AzizandT. Kaplan, Actametall. 36,2335(1988). 17. D. Turnbull, Thermodynamics in Metallurgy. Am. Soc. Metals, Metals Park, Ohio (1949). 18. B. W. Arden and K. N. Astill, in Numerical Algorithms: Origins and Applications, p. 280. Addison-Wesley, London (1970). 19. I. T. H. Chang and B. Cantor, J. Thin Solid Films 230, 167 (1993). 20. R. W. Olesinski and G. K. Abbaschian, Bull. Phase Diagram 5, 265 (1984). 21. E. M. Breinan and B. H. Kear, in Laser Materials Processing (edited by M. Bass), p. 236. North Holland, Amsterdam (1983). 22. W.A. Tiller, K. A. Jackson, W. Rutter and B. Chalmers, Acta metall. 1, 428 (1953). 23. W. J. Boettinger, R. J. Schaefer and F. S. Biancaniello, Metall. Trans. 15A, 55 (1984).
Nomenclature density p (g m 3) absolute temperature T (K) time t (s) heat absorbed per unit volume Q,~ (J m 3) K ( W m - J K ~) thermal conductivity distance from the surface z (m) latent heat of freezing L (J g 1) solid fraction f composition C(at.%) diffusion coefficient D (m 2 s ~) partition coefficient k absorption coefficient ~ (m- ~) reflectivity of the surface R solidification rate V (ms- ~) liquid/solid interface mobility M (K-~s 1) liquidus slope on the equilibrium phase m (K at.% -~) diagram ratio of surface energy to the latent heat of F (m) freezing