The effect of vertical vibration of the ampoule on the directional solidification of InSbGaSb alloy

........

CRYSTAL GROWTH

Journal of Crystal Growth 151 (1995) 235-242

ELSEVIER

The effect of vertical vibration of the ampoule on the directional solidification of InSb-GaSb alloy Weijun Yuan *, Mohsen Banan 1, L.L. Regel, W.R. Wilcox International Center for Gravity Materials Science and Applications, Clarkson University, Potsdam, New York 13699-5700, USA

Received 1 October 1993; manuscript received in final form 9 March 1995

Abstract

The effects of vertical vibration of the ampoule on the directional solidification of InSb-GaSb alloy in the vertical Bridgman-Stockbarger configuration were investigated. The microstructure and compositional profile of In0.2Ga0.8Sb grown with and without vibration were studied. The axial composition profile with and without vibration corresponded to complete mixing of the melt. No significant radial composition variations were observed. Though twins were slightly increased by the application of vibration, the number of grain boundaries in the ingots grown with vibration was less than in ingots grown without vibration, especially in the first-to-freeze parts. With the application of vertical vibration with 20 Hz frequency/0.5 mm amplitude to the growth ampoule, the ingots had the fewest grain boundaries. Vibration did not change the interface shape significantly during the first part of the ingots. However, the interface became more concave during the last part of the solidification when vibration was applied. Twinning mostly initiated from the edge of the ingot where they contacted with the ampoule wall.

1. Introduction

The compounds GaSb and InSb are totally miscible in both liquid and solid phases. The physical properties vary continuously with composition [1]. The change of the band gap of I n S b GaSb crystal with composition makes it have a bright future in device fabrication. After the observation of the G u n n effect in I n S b - G a S b [2], many efforts were m a d e to improve the microstructure and compositional uniformity of this

* Corresponding author. 1Present address: MEMC Electronic Materials, 501 Pearl Drive, St. Peters, Missouri 63376, USA.

material [3,4], such as by t e m p e r a t u r e gradient freeze [5], Czochralski [6] and Bridgman [7] methods, with vibration [8], accelerated crucible rotation technique (ACRT) [9] or application of magnetic fields [10], and growing the crystal in space [11,12]. Because of the unavoidable buoyancy-driven convection in the liquid, compositional inhomogeneity and polycrystallinity are associated with the crystal growth from the melt. There has been an increased interest in applying forced convection to suppress the free convection in crystal growth from melt, such as application of A C R T and vibration. Vibration has been used to crystal growth from the melt over a wide range of frequency and amplitude. For example, ultrasonic vibration was

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236

W. Yuan et al. /Journal of Crystal Growth 151 (1995) 235-242

used to grow InSb [13,14] and InSb-GaSb [15,16]. In the Czochralski growth of Te-doped InSb, the distribution of impurity in the crystal was made more uniform by the introduction of ultrasonic vibration [13]. However, because of its high energy, ultrasonic vibration can induce cavitation and turbulence in the melt, and thereby degrade the microstructure of the crystal [14]. Ultrasonic vibration applied to the growth of InSb-GaSb suppressed the variation of the temperature in the melt [17]. The coupled vibration stirring (CVS) technique, which applied orthogonal low frequency mechanical vibration to the growth ampoule, was developed by Liu et al. [18] and applied to the vertical Bridgman-Stockbarger (VBS) growth of CdTe [19] and Ag-doped PbBr 2 [20]. It is found that CVS can move the fluid rapidly without turbulence and at a velocity significantly faster then ACRT. Vibration at 10-100 Hz frequency and low amplitude (0.05-1.5 mm) resulted in the improvement of the grain size and grain selection in CdTe [21] and InSb-GaSb [8] crystals grown by the Bridgman-Stockbarger technique. It was shown that low frequency vibration can suppress the thermal convection [22,23]. The grain selection was improved, but twins were increased when low frequency was used [8,21]. How vibration affects crystal growth from the melt is still unclear. In this work, experiments on the growth of InSb-GaSb alloy in the VBS technique with axial vibration of the ampoule were carried out to improve our understanding of the effect of vibration.

2. Experimental procedures The experimental set-up included a thermally stable vertical Bridgman-Stockbarger growth apparatus with provision for axial vibration of the growth ampoule. Details of the experimental setup were discussed in the previous paper [24]. The growth ampoule was vibrated parallel to the earth's gravity with the square wave oscillation. The growth material was prepared by weighing the proper amount of 6N purity In, Ga and Sb to give a starting composition of In0.zGa0.sSb with a diameter of 9 mm and a length of 6-8 cm. Tern-

perature at the hot zone and the cold zone of the furnace are 800°C and 480 ° C, respectively. Temperature profile was measured using a K-type thermocouple in an empty ampoule. The average temperature in the adiabatic zone was about 33° C/cm. The ampoule lowering rate is 8 m m / day for all solidification. Prior to growth, the ampoule was placed in the hot zone and heated at 800° C overnight to completely mix the materials. After finishing the growth, the furnace temperature was lowered to room temperature at 20°C/h to minimize the thermal stress in the ingots. A quenched interface demarcation technique was used to reveal the interface shape during directional solidification. For demarcation, the heater temperature was lowered quickly from 800 to 750°C and maintained at 750°C for 5 min, then the ampoule was rapidly moved down 1 mm in the furnace, followed by raising the heater temperature to 800° C. The combination of temperature lowering and the rapid movement of the ampoule resulted in fast freezing and hence caused a striation in the resulting ingot. The average growth rate could be calculated from the distance between each pair of striations. The grown ingot was sectioned longitudinally and cut into 2 or 3 cross sectional pieces. The samples were mounted in an epoxy resin mould and ground with 320 and 600 mesh SiC disk paper and mechanically polished with a suspension of 5, 0.3 and 0.05 /xm alumina polishing powder in distilled water, respectively. Energy dispersive X-ray spectroscopy (EDS) in a scanning electron microscopy was used to measure the composition of the polished samples. The axial compositional profile was measured at a spacing of 2 mm along the center of the longitudinal sections, and the radial compositional profile was measured at 1 mm interval across the radius of the sample. The concentration of InSb was calculated from the spectra of pure InSb, pure GaSb and the InSb-GaSb samples [7]. The axial distance z was converted to mole fraction solidified by the relationship: g=

(s;-)/(s:CsAcdz

CsA~dz

)

,

(1)

W. Yuan et al. / Journal of Crystal Growth 151 (1995) 235-242

where A c is the cross-sectional area of the ingot at position z, L is the length of the ingot, and C s is the total concentration (in m o l / m 3) of the solid at position z, calculated by Cs=a/(NAa3),

(2)

where NA is Avogadro's number, and a is the lattice spacing, which depends on the mole fraction of InSb, Xs, as [25]: a = 6.1 × 10 -s + 3.9 × 10-9Xs (cm),

(3)

Both axial and radial compositional profiles were measured. The axial compositional profile was plotted as mole fraction of InSb in the InSb-GaSb ingot versus mole fraction solidified. The mechanically polished samples were etched in a 1 : 1 : 1 solution of HNO 3 + HAc + H 2 0 for 10 s at room temperature to reveal the microstructure. The microstructure of the samples was examined using a Nikon optical microscope. The number of boundaries was counted at 2 mm intervals along the ingots across the diameter. It has been found that twin boundaries could be kinked on microscale and had the curved appearance [26]. Many efforts have been made to distinguish the twin boundaries from grain boundaries [7]. The number of total boundaries (curved boundaries + straight boundaries) was also counted for comparison.

3. Results and discussion

Vibration of the ampoule resulted in modulation of acceleration in the direction of the applied vibration. Dynamic acceleration induced by vibration had a sinusoidal form. The frequency of the major peak of the power spectra of dynamic acceleration was very close to the frequency applied to the growth ampoule, and there were no other peaks in the power spectra. Table 1 shows the dynamic acceleration at different frequencies and amplitudes. The ampoule was vibrated axially parallel to the earth's gravity. Vibration-induced dynamic acceleration resulted in the periodic gravity deviation. This time-periodic vertical gravitational acceleration could affect the stability of

237

Table 1 Dynamic acceleration induced by vertical vibration Frequency (Hz)

Amplitude (mm)

Dynamic acceleration (g a)

0 10 20 30 40 60 100

0 0.5 0.5 0.5 0.1 0.05 0.01

0 0.09 0.18 0.25 0.10 0.09 0.05

a g =

9.81

m/s

2.

solute convection during direction solidification [27]. The average growth rate for InSb-GaSb was measured from the interface demarcations. The result is shown in Fig. 1. During the first half of the ingots, the average growth rate was greater than the ampoule lowering rate, and then decreased with the progress of solidification. In the second half of the ingot, the average growth rate becomes less than the ampoule lowering rate. There was a small increase at the last-to-freeze parts of the ingots. Vibration did not significantly change the growth rate for solidification of InSb-GaSb, as shown in Fig. 1. The relative interface velocity was calculated from the interface demarcation. The relative interface velocity is defined such that the interface velocity is positive if the interface moves down in the furnace. If the interface remains at the same position in the furnace during solidification, the

* * * * * 20 0000040

Hz/0.5 Hz/0.1

mm mm

a~a~ no vibration -- - Ampoule Lowering

Rate

o

~6,o . . . . . . . . . . . . .

~

_

_ o _a

. . . . . . . . . . . . . . . . o

4.0

o

*

o

0"00.0

0.2

0.4

0.6

08

Length fraction Solidified Fig. 1. Average growth rate for solidification of InSb-GaSb.

W. Yuan et al. /Journal of Crystal Growth 151 (1995) 235-242

238 i0

~D

~

,/3'

" *~*** no vibration - 0 0 0 0 0 20 H z / 0 . 5 m m . ooooo 40 Hz/O.I mrn - -

predicted

from

a well-mixed

melt

model

0,8

/c

c'C6 O

D// / ~0.4 c/

0.0

O0

0.2

0.4

0,6

0.8

1.0

Molar F r a c t i o n S o l i d i f i e d Fig. 2. Axial compositional profile for InSb-GaSb ingots.

relative interface velocity is equal to zero. The interface velocity increased with the progress of solidification. It changed from slightly less than zero in the first half to greater than zero in the second half of the ingot. This means the interface first moved upwards and then moved downwards in the furnace when solidification proceeded. The melting temperature of In0.2Ga0.8Sb changed from 690 to 525°C during solidification. This caused most of the interface velocity change during solidification. When 20 Hz frequency/0.5 mm amplitude vibration was applied to the growth ampoule, interface movement was a little slower than without vibration. However, when the frequency of vibration was increased, interface velocity increased to the value without vibration. Fig. 2 shows axial composition profiles measured by EDS. It also shows the theoretical composition profile calculated from a well-mixed melt model, which assumes no composition gradient in the melt and equilibrium at the interface. As shown in Fig. 2, vertical vibration of the growth ampoule did not affect the axial compositional profile for InSb-GaSb. The axial compositional profile from all the ingots grown with and without vibration corresponded to the complete mixing model. No significant radial composition variations were observed, whether vibration was used or not. A higher temperature gradient at the melt/solid interface and a lower growth rate must be used for directional solidification in or-

der to avoid constitutional supercooling in the melt. However, it has been shown that a high temperature gradient for the solidification of InSb-GaSb can result in a fine grain structure in the resulting ingots [10]. Therefore, in our experiments, a low growth rate was used. The ampoule lowering rate was about 8 mm/day. During solidification, InSb is rejected at the solid/melt interface. Because the density of the rejected InSb is more than the preferentially incorporated GaSb, VBS growth of InSb-GaSb is solutally stable. So in our experiments, all of the ingots were grown under thermally and solutally stable conditions. The well-mixed composition profiles in the ingots grown with vibration might be attributed to the enhancement of mixing by vibration. However, the ingots grown without vibration also had wellmixed composition profiles, which means that there was enough free convection to mix the melt. The same results were obtained by the application of ACRT to the solidification of InSb-GaSb alloy with the same translation rate [9]. Because of the very low growth rate, the buildup of the solute in the melt ahead of the solid/melt might decay by diffusion, as predicted by Gray et al. [28]. Generally, if the characteristic diffusion length (defined by L o = D / l / g , where l/g is the growth rate and D is the diffusivity) is greater than the total length of the melt, L, diffusion alone can completely mix a melt. The diffusivity of InSb in molten InxGal_xSb is unknown. However, if the growth rate is assumed to be the same as the translation rate, and the ingot is 7 mm in length, a diffusivity of 6.5 × 10 -5 c m / s 2 makes L o = L . This diffusivity is well within the range of typical semiconductor melts [29,30]. Therefore, a well-mixed condition in the melt may exist even without convection. The number of grain boundaries decreased with the progress of solidification, while the number of twin boundaries presented a maximum when about 30-40% of the charge was solidified. The number of the boundaries was scattered along the length of the ingots. However, during the second half of the ingots, the number of grain boundaries tended to remain unchanged. The number of grain boundaries in InSb-GaSb ingots was decreased by vibration, especially at the first-

W. Yuan et al. /Journal of Crystal Growth 151 (1995) 235-242

to-freeze part of the ingots. The number of twin boundaries was slightly increased by vibration. Most of the twinning initialized at the edge of the ingots where it contacted with the ampoule wall. Table 2 lists the mean and the standard deviation of the number of the boundaries for InSb-GaSb ingots solidified without and with vibration. An ingot grown with a 20 Hz frequency/0.5 mm amplitude vibration had the fewest number of grain boundaries and the fewest number of total boundaries. The variation of dynamic acceleration affected the number of boundaries, as shown in Fig. 3. The number of grain boundaries at first decreased with increasing dynamic acceleration, with a minimum at about 0.18g, which corresponds to vibration of 20 Hz frequency/0.5 mm amplitude. The number of twin boundaries increased when dynamic acceleration was increased. The increased twinning might have been due to the mechanical stress induced by vibration. T e m p e r a t u r e fluctuations ne a r the melt/solid interface due to periodic mixing caused by vibration may also have contributed to the formation of twins. With vibration, some twin boundaries which initially had a curved appearance might be straightened. This may resulted in the increase of the number of straight boundaries. Statistical analysis was performed on the number of boundaries for some InSb-GaSb ingots solidified with different vibration conditions. A one-side Student's t-test with paired comparisons was used in this analysis by using a commercial software package called the number cruncher statistical system (NCSS). The following is the brief

239

2.9

t

2.4

I

1.9

Total J

1.4

boundaries I

i

,

I

,

J

r

i

__J

i

03

1.4 0 ,.0 1.2

©

Twin

boundaries .

.

.

.

Z 1.0

0.5

0.0

Grain I

o.oo

boundaries I

__1

,

i

I

i

0.05 olo o.15 ozo o.z5 0.30 Dynamic accelerat;ion (±g)

Fig. 3. Effect of dynamic acceleration on the number of boundaries in InSb-GaSb ingots. Error bar represents standard deviation.

description of Student's t-test. Consider two data sets we desire to compare. Each set is arranged in two columns. One column is the length fraction solidified, and the other one is the number of boundaries per mm across the ingot. Two data

Table 2 The mean and the standard deviation of the number of boundaries per mm across the ingot for InSb-GaSb ingots solidified without and with vibration Ingots

Grain boundaries

Twin boundaries

Total boundaries

Dl(no vibration) VI(10 Hz/0.5 ram) V2(20 Hz/0.5 mm) V3(30 Hz/0.5 ram) V4(40 Hz/0.1 mm) V5(100 Hz/0.01 mm)

1.16 + 0.62 + 0.35 + 0.80 + 0.65 + 0.67 +

1.20 + 0.17 1.48 + 0.15 1.39 + 0.15 1.45 + 0.23 1.50 + 0.15 1.30:1:0.19

2.36 + 0.56 2.10 _+0.28 1.72 + 0.32 2.25 + 0.34 2.15 _+0.30 1.97 + 0.32

0.42 0.14 0.19 0.14 0.15 0.15

W. Yuan et aL /Journal of Crystal Growth 151 (1995) 235-242

240

Although the number of straight boundaries was increased, the number of curved boundaries was decreased by vibration, especially in the first half part of the ingot. In ingots grown with vibration, fewer small grains were observed in the first-to-freeze part compared to the ingots grown without vibration. It was found that the direction of the melt motion in the vibrational convection region was opposite to the direction of the melt motion caused by buoyancy [22,23]. Thermal convection could be completely suppressed by vibrational convection according to the frequency and amplitude of vibration [23]. Therefore, the temperature fluctuation induced by thermal convection in the melt could be suppressed. The thermal field near the interface of melt/solid may also be changed by vibration. During crystal growth from the melt, because of the separation of the liquidus and solidus in the phase diagram, at a finite growth rate, constitutional supercooling may occur due to the buildup of solute ahead of the interface. The condition

sets are paired based on the equal length fraction solidified. A one-sided t-test is performed on these two data sets and the probability (confidence) level is calculated. We could say at the probability level, the number of boundaries in one data set (C1) is greater than the number of boundaries in another data set (C2). 1 minus this value is the probability level that C1 is less than C2. Table 3 show the probability level that the number of grain boundaries, twin boundaries and total boundaries per mm width of the ingots listed in the rows were greater than that of the ingots listed in the columns. Table 3 shows that, with 99% confidence, ingots grown with vibration had fewer grain boundaries than those grown without vibration. Ingots grown with vibration also had fewer number of total boundaries. With the application of 20 Hz frequency/0.5 mm amplitude vibration to the growth ampoule, both the number of grain boundaries and the number of total boundaries were the least.

Table 3 Probability level that the number of boundaries per mm across the ingot in the ingots listed in the row was greater than that of the ingots listed in the column (comparison was made along the full length of the ingot) Ingots

D1

V1

V2

V3

V4

V5

0.01 0.01 0.01 0.01 0.01

> 0.99 < 0.01 0.45 > 0.99 0.97

> 0.99 > 0.99 > 0.99 > 0.99 > 0.99

> 0.99 0.55 < 0.01 0.97 0.97

> 0.99 < 0.01 < 0.01 0.03 0.59

> 0.99 0.03 < 0.01 0.03 0.41 -

> 0.99 0.62 0.95 > 0.99 0.52

< 0.01 < 0.01 0.28 0.62 < 0.01

0.38 > 0.99 0.95 0.25 > 0.99

0.05 0.72 0.05 0.59 0.07

< 0.01 0.38 0.75 0.41 < 0.01

0.48 > 0.99 < 0.01 0.93 > 0.99 -

0.07 < 0.01 < 0.01 0.32 < 0.01

0.93 < 0.01 0.29 0.87 < 0.01

> 0.99 > 0.99 > 0.99 > 0.99 > 0.99

> 0.99 0.71 < 0.01 0.76 < 0.01

0.68 0.13 < 0.01 0.24 < 0.01

> > < > >

Grain boundaries D l ( n o vibration) VI(10 Hz/0.5 mm) V2(20 H z / 0 . 5 mm) V3(30 H z / 0 . 5 mm) V4(40 H z / 0 . 1 mm) V5(100 Hz/0.01 mm)

< < < < <

Twin boundaries D l ( n o vibration) VI(10 H z / 0 . 5 mm) V2(20 H z / 0 . 5 mm) V3(30 H z / 0 . 5 mm) V4(40 Hz/0.1 mm) V5(100 Hz/0.01 mm)

Total boundaries D l ( n o vibration) VI(10 H z / 0 . 5 mm) V2(20 H z / 0 . 5 mm) V3(30 H z / 0 . 5 mm) V4(40 Hz/0.1 mm) V5(100 Hz/0.01 mm)

0.99 0.99 0.01 0.99 0.99 -

W. Yuan et al. /Journal of Crystal Growth 151 (1995) 235-242

for avoiding the constitutional supercooling in the melt may be represented as: m l C ~ ( k o - 1)

G --

>

(4)

V~

koD

'

where D is the diffusivity of solute in the melt, G is the imposed temperature gradient at the interface, Vg is the growth rate, rn I is the slope of the liquidus in phase diagram, k 0 is the equilibrium distribution coefficient, and Cs* is the concentration of solute in the crystal at the interface. Assuming a diffusivity of 5 × 10 -5 cm2/s, at a growth rate of 8 ram/day, a temperature gradient at the melt/solid interface of 30°C/cm is expected to avoid constitutional supercooling for solidification of InSb-GaSb. This value was less than the imposed temperature gradient in our experiments. As predicted, under these growth conditions, no interface breakdown was observed for InSb-GaSb ingots. Morphological instability did occur during directional solidification of In0.2Ga0.sSb at 21 m m / d a y without vibration [8]. When vertical vibration was applied to the growth ampoule, no morphological breakdown was observed at the same growth rate [8]. If the growth rate is large enough, diffusion and gentle convection are not enough to completely mix the melt. With vibration, enhanced convection would exist in the melt, and the interfacial composition would remain equal to the bulk value. Fig. 4 shows the interface depth for some InSb-GaSb ingots. The interface depth was de-

?eeee

S-

i :2

a~a

241

fined as the difference between the average location of the interface at the edge of the ingot and the location of the interface at the position of maximum depth. The larger the interface depth, the more concave the interface is. Vibration did not appreciably change the interface shape. Near the end of the solidification, vibration made the interface more concave. In this work, fewer grains were observed when vibration was applied to the solidification. Vibration might enhance nucleation at the beginning, so the melt would not be so supercooled and few grains would nucleate.

4. Conclusion The effect of vertical vibration of the ampoule on the InSb-GaSb crystal growth in the vertical Bridgman-Stockbarger furnace was investigated. Vibration had no significant effect on the composition profile and the growth rate for InSb-GaSb ingot. With vibration, the number of grain boundaries was decreased, while twin boundaries were slightly increased. InSb-GaSb ingots solidified with 20 Hz frequency/0.5 mm amplitude vibration had the fewest number of grain boundaries and total boundaries. Vibration improved grain selection, especially in the first-to-freeze part of the solidification. The improved grain selection might have been due to periodic back-melting and regrowth caused by vibration. Increased straight twins might have been induced by the variation of temperature near the melt/solid interface due to periodic mixing caused by vibration.

20 Hz/0,5 m m 40 Hz/0.1 m m no vibration

Acknowledgements

_ ~06

This work was sponsored by NASA's Microgravity Science and Application Division under grant number NAG8-831.

/

References 0"000

0.2

0.4

0,6

0.8

Length fraction Solidified Fig. 4. Interface depth for solidification of InSb-GaSb.

1,0

[1] M. Nuenberger, I I I - V Semiconductor Compounds, Handbook of Electronic Materials, Vol. 2 (Plenum, New York, 1971).

242

W. Yuan et al. ~Journal of Crystal Growth 151 (1995) 235-242

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