Temperature oscillations in silicon melts

Journal of Crystal Growth 98 (1989) 667—678 North-Holland, Amsterdam

667

TEMPERATURE OSCILLATIONS IN SILICON MELTS Dennis ELWELL Hughes Aircraft Co., 500 Superior Avenue, Newport Beach, California 92658, USA

Erik ANDERSEN Physics Departmen4 Montana State University, Bozeman, Montana 59717, USA

and R.R. DILS Accufiber, Inc., 9550 S. W. Nimbus Avenue, Beaverton, Oregon 97005, USA Received 12 January 1989; manuscript received in final form 27 June 1989

Optical fiber thermometry has been used to study temperature oscillations in silicon melts contained in quartz crucibles of standard design. Fourier analyses of the time—temperature data show the temperature oscillations to be extremely dependent on location in the crucible and crucible rotation speed. A single frequency was observed near the crucible edge at 1 RPM rotation while the temperature fluctuation measured at the crucible center at 8 RPM was composed of over twenty discrete Fourier components. This complex spectrum was the result of combinations of three or four fundamental frequencies which were stable over several crucible rotations. The data suggest that in-Situ monitoring of the temperature fluctuations during crystal growth may be useful in improving crystal quality.

I. Introduction Temperature fluctuations in crystal growth melts are of great importance because of their adverse effects on crystal quality. Large, irregular temperature variations at the crystal—melt interface can lead to high concentrations of non-equilibrium point defects. Clusters of vacancies, which are frozen-in during the rapid cooling portion of the oscillations, can act as the nuclei for oxide precipitates. Fine oxide precipitates are probably the major cause of the microdefects which can be seen when the crystals or wafers are etched. The correlation between microdefects and temperature fluctuations was well established by the work of Kuroda et al. [1], who attached a thermocouple to a silicon seed crystal and demonstrated a strong increase in microdefect concentration with the amplitude of the oscillations. An increase in the

oscillation amplitude from 0.5 to 1.5°Cwas found to increase the microdefect concentration from iO~to iO~cm The details of temperature oscillations in the melts used for Czochralski crystal growth are poorly understood. Although computer simulations [2,3] and analytical calculations [4] have given valuable information on two basic flow patterns, with and without an applied magnetic field, there have been no numerical simulations of the amplitude and frequency of oscillations. A major problem is the complexity of the Czochralski geometry, especially if the real shape of standard crucibles, with rounded bottom surfaces, is considered. Elwell and Andersen [5] originally suggested the optical fiber thermometer as an experimental tool to help understand the origin of oscillations in Czochralski silicon melts and to indicate oper-

0022-0248/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

—

D. Elwell et al.

/

Temperature oscillations in silicon melts

669

1422

I

1416 ~

I

I

1414

0 1412 1410 ~1406 ~1406

1396 0

125

250 TIME

.

375

SEC

Fig. 1. Temperature versus time plot with sensor held for 125 s in each of 4 locations on an arc from the melt center to a point near its edge (5 kg melt; zero crucible rotation). Movement of sensor is from center to edge corresponding to left-right on figure.

observation in fig. 1 is the difference in the character of the oscillations at the center and edge of the melt. The temperature fluctuations due to thermal convection near the edge of the melt were much smaller than those at the center. The crucible was located at its normal position for crystal growth through the experiments. In this location, the maximum temperature due to radial heating from the cylindrical graphite element is expected to be at a distance from the melt surface of about

2/3 of the melt depth [8]. This temperature distribution causes convection cells in which the melt flows up the crucible wall and then inward. The small amplitude of the temperature fluctuations near the edge of the crucible suggest that this flow is rather stable with time. In contrast, the central region where these cells meet experiences much larger and more erratic temperature fluctuations. When the same crucible was rotated at 12 RPM, the average center-edge temperature difference re-

1428

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1422 U

1420

1416 0

1416 1414 1412 1410

~1406~ 1406 1404 1402 1400 1396

________________

0

125

250 TIME

.

37S

SEC

Fig. 2. Same arrangement as fig 1, but with 12 RPM crucible rotation.

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Temperature oscillations in silicon melts

ating parameters that will minimize their amplitude. They reported on the use of optical fiber thermornetry and on Fourier analysis of the ternperature versus time data as a means of revealing the oscillation spectrum. Fourier analysis of thermocouple data has also been reported by Barber et al. [6] on (Pb, Sn) Te and by Juhasz and Szabo [7] on Bi 4Ge2O12 melts. In this paper, a more detailed analysis of the temperature behavior of a silicon melt is presented with some insights which result from spectral and probabilistic analysis of optical fiber thermometer data.

2. Experimental arrangement The data presented were obtained in a Siltec 860C Crystal Puller, using a 20 cm diameter fused silica crucible of standard shape, with a curved bottom surface of 14 inch radius, and periphery of 2 inch radius. An optical fiber thermometer (OFT), AccufiberTM Model 310, was inserted into the furnace by modifying the viewport. The 20 cm diameter quartz disc was replaced by a brass disc fitted with a smaller viewport and a SwagelokTM fitting to allow the introduction and repositioning of the OFT. The OFT sensor consists of a detector, digital voltmeter, and computer. Since the maximum obtainable length of the sapphire fiber was 30 cm, and the sapphire-glass fiber junction contained a low temperature epoxy, it was necessary to protect the junction from radiation and convective heat flow inside the furnace chamber, A water-cooled jacket was constructed to enclose the fiber junction. The jacket could be rotated and raised or lowered to position the tip of the sapphire fiber Just below the surface of the melt. Due to the angle of the viewport, the temperature could be measured along an arc from the center of the melt to about 2 cm from its edge. Melts of 3 and 5 kg were used in this investigation, To prevent corrosion of the sapphire by the molten silicon, the sapphire fiber was inserted into a thin-walled sheath of fused silica. Silica is slowly dissolved by molten silicon, but the deterioration in the immersed silica sheath was negligible during the course of the experiment.

The Accufiber OFT used in the investigation has a resolution of 1 x 106at 1000°Cand 1 Hz bandwidth, an absolute accuracy of 2°Cat 1000°C and 4°Cat 1500 °C, and a measurement rate up to 50 s’. Its range of measurement was from 500 to 1900°C.Data from the OFT were recorded on a floppy disc and subsequently processed with a standard FFT program. A typical data set consisted of 1000 points recorded at 1 or 0.5 s intervals. In this application, the resolution of the OFT technology was limited by the digital resolution of the Model 310 digital voltmeter. The analog5°C, signal-to-noise 1000° is actually 2 X or 2 x 108ratio overat the 0—1C Hz bandwidth. 10 unusual signal-to-noise ratio is obtained by This using a low noise current to voltage first stage amplifier and a short wavelength which results in a large change in measured radiance for a small change in temperature. For example, using a 950 nm wavelength at 1000°C there will be an 11.89% increase in measured radiance for a 1% increase in temperature. The practical resolution of a standard digital voltmeter is only 1 x 10—s and, therefore, for simple measurements, the temperature resolution is limited to approximately 1 x 1o 6 However, the Accufiber Model 310 has a differential mode of operation in which the majority of the signal is subtracted from the original signal and the remainder is subsequently amplified and measured with the same 10 ~ resolution. In this case, the resolution of the instrument is limited by the analog electrical noise and varies from 8 X 10~to 5 X 105°C or 25 to 27 bits over the 1000—1900°Ctemperature range.

3. Data 3.1. Radial position dependence Fig. I shows temperature versus time plots with the OFT tip in four locations, approximately equally spaced on an arc from the center of the melt to a point near the edge. The melt mass was 5 kg, maximum melt depth about 7 cm, and the crucible was not rotated. No crystal was present. The average temperature difference across the melt was approximately 17°C. The most interesting

1424

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TIME

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t=

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300

360

420

TIME

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250

375

0; OFT tip located near to e

TIME

240

_____________________________

sudden change in crucible rotation rate from I to 8 RPM at Similar to (a) but with a change in rotation rate from 8 to 1 RPM.

SEC

360

1395

0

.

300

1365

1390

1390,

1400

1405

1410

-

Fig. 4. Effect of a growing crystal on melt oscillations: (a) readings taken along an arc as in fig. 1. No crystal. 5 kg melt; 12 RPM crucible rotation. (I same as in (a), but in the presence of a growing 2 inch diameter crystal.

S

U 0 1~1 0

TIME

240

temperature of a

180

a

3 14 F’

16 S

14 0

U 0

1415

1420-

1425

1438

melt

120

effect on

60

—

1440

Fig. 3. (a) Showing the

14

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16 S

0 S 0

O

1462

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1466

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D. Elwell et al.

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Temperature oscillations in silicon melts

mained unchanged at about 17°C. The average temperatures are also unchanged by the crucible rotation (fig. 2). However, the temperature oscillations are completely different from those in the absence of crucible rotation. The average frequency is clearly much higher and, in contrast to the zero rotation case, the amplitude of the oscillations is greater near the edge of the melt than at the center, 3.2. Transients The effects of changing the crucible rotation rate from 1 to 8 RPM and back from 8 RPM to 1 RPM are shown in fig. 3. In both cases, the OFT tip was located near the edge of the melt, and just below the surface as described before. In fig. 3a, an increase in the frequency of the oscillations and decrease in amplitude is observed as the rotation rate was changed from 1 to 8 RPM. Fig. 3b shows the result of a sudden change in crucible rotation rate from 8 to 1 RPM. The amplitude of the oscillations can be seen to build up with a time constant in the region of 200 s. There is a conesponding and very marked decrease in the frequency of the oscillations. Fig. 3b also shows an increase in the average temperature; this is a transient effect and the difference was observed to decay over about 5 mm. Data of this kind, shown in fig. 3, can be used to evaluate the use of accelerated crucible rotation as a means of stirring a Czochralski silicon melt [91.Transient conditions which result in substantial changes in average melt temperature or cause erratic temperature oscillations are clearly unacceptable. The pattern of oscillations will determine an acceptable program for changing the rotation rate and is an interesting subject for further study. 3.3. Influence of the crystal

OFT in an arc from a point near the center (i.e., near the edge of the crystal) to one near the edge of a melt. The major effects due to the presence of the crystal are a decrease in the temperature difference between the center and the edge of the melt, from about 16°Cto about 6°C, and a small increase in the amplitude of the oscillations. The thermal oscillations depend on the magnitude of the temperature gradients (axial and radial) and the increase in amplitude must result from additional complexity in the flow pattern associated with the crystal rotation. The determination of regimes in which the temperature oscillations are minimized during actual crystal growth is clearly an important practical goal for future work. In this paper, examples of spectral and probabilistic analyses of the melt temperature oscillations are limited to measurements where no crystal was present.

4. Quantitative analysis In the earlier study by Elwell and Andersen [5] Fourier analyses of temperature versus time data for a 3 kg melt with the crucible rotated at 1 and 8 RPM showed marked differences between the two sets of data obtained with the sensor tip located at the center and edge of the melt, respectively. Fourier analysis was shown to be a powerful tool which could distinguish between periodic and random fluctuations and reveal the primary frequency components of the oscillation spectrum. It was suggested that characterization of these components and the study of their variation with system parameters should lead to an understanding of the basic fluid flow patterns which have a crucial role in the crystal growth process. The RMS amplitude of a melt temperature wave, ~T’ can be defined in terms of the power spectral density (PSD) function of the wave, i.e.

The OFT was also used to measure the melt temperature during growth of a small number of 2—3 inch diameter crystals. Fig. 4 shows a comparison of data taken under similar conditions in the absence and presence of a 2 inch crystal. As in fig. 1, the data were taken by moving the tip of the

671

i aT =

~‘t

1

T~( t) d ~

—

p

[F( ~ 2ir

2

dw,

(la)

where F(w) is the Fourier coefficient for angular frequency ~a,is a measurement frequency interval and [F( w ~ 2 is the power spectral density compo-

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__________________________________________________

Fig. 6. Power spectral density for temperature fluctuations in a silicon melt with 8 RPM crucible rotation: (a) near crucible edge; (b) at melt c

so

C60

~70

80

90

100

110

Fig. 5. Power spectral density for temperature fluctuations in a 3 kg silicon melt with 1 RPM crucible rotation: (a) near crucible edge; (b) at me

0

500

1000

1500

‘ZOOO

a

~2500

p3000

3500

4000

4500

5000-

D. Elwell et al.

/

Temperature oscillations in silicon melts

nent. The Fourier components are defined by the relation

T1~t)

=

1rP dca ~ F~co~ exp~icot)—, ~.

/

~1b)

2ir

and can be obtained from an FFT analysis of melt temperature data. Fig. 5a shows the PSD function for temperature oscillations measured at the center of the melt with a crucible rotation rate of 1 RPM. The spectrum is dominated by a signal peak at approximately 0.0265 Hz, which corresponds to a period of 42 s. Approximately 55% of the power contamed in the melt temperature oscillation is contamed within this single frequency component. Smaller and broader peaks can also be seen at 0.001, 0.011, 0.017, and 0.041 Hz. The 0.017 Hz component corresponds to the 1 RPM crucible rotation rate and is sharper than the small peaks at 0.011 and 0.041 Hz. The PSD function measured with the sensor at the center of the melt (fig. Sb) is remarkably different from that measured at the edge. The spectrum is much more complex and contains no outstandingly large peak. The 0.0265 Hz peak, which dominates the spectrum at the edge of the melt, is either missing or much reduced and slightly shifted. The 0.017 Hz crucible rotation peak also cannot be distinguished as a separate peak. However, the peaks at 0.011 and 0.041 Hz are now the largest in the spectrum. The very low frequency peak is similar to that observed near the edge of the crucible. Clearly, the power spectrum seen at the center of the melt results from the interaction of a number of convection cells within the melt. The dominant flow cells near the wall cancel or do not reach the central region at the top of the melt intact, but the 0.011 and 0.041 Hz components persist and represent a significant fraction of the measured temperature oscillation at the center of the melt. It is generally accepted that high quality crystals can be best grown from rotating crucibles. Melt temperature oscillations measured with a rotation speed of 8 RPM, which is a typical rotation rate used in practical silicon growth, are shown in fig. 6. These data show that the PSD function is much

673

more complex when a higher crucible rotation rate is used. Although the data measured near the edge of the melt (fig. 6a) indicate a dominant peak at about 0.35 Hz, the power in this largest peak is approximately 27 times lower than that of the large peak of fig. 5a. Therefore, one effect of increasing the crucible rotation is to break up dominant convective flow patterns near the crucible wall and to distribute the energy associated with the temperature fluctuations into a number of discrete frequency components. This motion is still clearly very different from random thermal fluctuations. Initially, it appears that the temperature oscillations measured near the crucible edge at 8 RPM are the product of a complex thermal system with many stable and independent oscillating states. Further inspection suggests that the observed frequencies are the result of only a few fundamental frequencies. For example, in table la, the frequencies of the peaks between 0.05 and 0.50 Hz are listed and assigned to sums of three fundamental frequencies f1, f2 and fr at 0.070, 0.085, and 0.130 Hz respectively. The 0.130 Hz component corresponds to the rotational frequency. The exception is the peak at 0.100 Hz, which is designated f~,but this frequency is not necessary for the assignment of the component frequencies to any of the higher frequency peaks, except for the small peak at 0.189 Hz. Thus, although the assignment of the frequency components is not always unequivocal, the general conclusion that the frequency spectrum consists of coupled oscillations, appears highly convincing. This type of description suggests that the observed melt temperature T( t) is the result of a nonlinear expansion of an input function v ( t); i.e., —

T

~ ‘ /

=

N~Oa ~

vtt “

~“

2

‘ /

where a~is the coefficient of the n th order term and v(t) is composed of a few fundamental frequencies. Fluid motion is generally quite nonlinear, and the suggestion that fluid flows nonlinearly couple within the melt is quite reasonable. In table la, the assignment requires only two funda-

674

D. Elwell et al.

/

Temperature oscillations in silicon melts

Table 1 Fourier spectrum of melt vibrations (8 RPM crucible rotation)

seen that some of the frequencies are slightly different, including the crucible rotation rate, but

(a) Edge of melt

again, all the frequencies can be accounted for as sums of the components of J~,f2~f3 and fr’ The assignment in this case is not always so unequivocal as in the previous case, but an error of ±0.002 Hz was assumed. More use of the 13 oscillation is necessary in this latter case, and the assumption of assignments involving three compo-

Inten- Fre-

(b) Center of melt Assign-

sity (max. 100)

quency ment H2

10 25 35 40

0.070

11 0.086

0.100

f~ f

20 15 65

0.170 0.189 0.199

12+13 f1 + f (2f3?)

20

0.215

12

25 20 10

0.240 0.257 0.277

11 +212

0.130

212

±fr

2fr

4f1

0.302

2f2 + Ir

100

0.348

412(12 + 2f?)

20 20 15

sity

Assign-

quency ment

(max. 100)

20

20

Inten- Fre-

0.385 0 116 0.458 0.476

31r

50 12 40 55 100 15 40

0.068 30 0.107 0.125 0.141 0.159 0.181

f~

45 25 15 40 10 40 10 15 20 15 10 10

0.194 ~ 207 0.216 0.228 0.241 0.250 0.270 0284 0.292 0.308 0.319 0.329

11 + f

15 15 15 15

0.356 0.364 0.378 0.392

5

0.438

0.06812

f~ J~

nents (one of them f2) is necessary to account for two small peaks. However, the general conclusion that the observed temperature oscillations can be explained to be the result of nonlinearly coupled fluid motions within the melt is reinforced by the

i.i,

f1 +f2 212 3f

data from the center of the melt. Similar descriptions of nonlinear systems are available in the literature, from descriptions of combustion oscillations in gas turbine combustors [10], to analyses of thermal oscillations in xenon

f2~fr

13

+ Ir 11 + 212 21r

4f1 1 + 21

.

J

212 + 211+212 12 + 13 + Jr 3f1 + Jr

21+13 f1 + 212 +Jr ~fr 2f + 2fr 212 +21

4f + 2f

r

f~±3f~2 12

~3fr

5

0.466

12 +31r

mental frequencies and lower order harmonics of the fundamental oscillations. Terms involving Jr with f~and 12 appear frequently, indicating that the rotation couples with the thermal convective motions to produce compound oscillations. The PSD function measured at the center of the melt at 8 RPM is presented in fig. 6b. It is observed that the PSD function is shifted towards lower frequencies, i.e., to oscillations of longer periods. In addition, there are more peaks at the center, as in the 1 RPM case. Several of the peaks observed at the edge of the melt at 8 RPM are also observed at the center of the melt. In table lb, it is

gas [11]. Identification of the nonlinear nature of a system leads to the realization that the observation of the many frequency components in a PSD function does not imply that separate oscillations with these characteristic frequencies exist physically, but only that the PSD function is not urnform and that there are discrete fixed phase relationships between some of the Fourier components. To proceed further, it is necessary to measure the dependence of changes in the PSD function on the growth conditions and location in the melt, with special emphasis on the importance of the rotational frequency, J~.,since it can be unambiguously identified. Multiple sensor experiments can also be conducted to characterize the convective flow with the melt.

5.

Q

factor

No speculation has been offered regarding the physical nature of the oscillations except for the identification of the crucible rotation frequency and the suggestion that the dominant peak of fig. 5a is due to thermal convection within the melt. It is possible to draw further conclusions about the nature of the oscillations without additional speculation. The stability of a linearly damped

D. Elwell et al.

/

Temperature oscillations in silicon melts

oscillator can be described in terms of a factor, defined as:

Q,

Q =f~/&(~

(3)

and ~1f~is the width of the peak of frequency f~at half the maximum intensity. The oscillation will

From these is it possible to define the first moment, m1, the second central moment (or van0T by the ance) m2, and the standard deviation, relations m 1

decay to 1/e of its initial value in a time T~= l/(2~f~). Analyzing the melt temperature oscillation with a spectrum analyzer of 5 x io~Hz bandwidth results in a value of Q for the 0.0265 Hz component of fig. 5a of approximately 12. The corresponding r 1 is 115 s, which is greater than the time required for one revolution of the crucible. The Q of the main peaks in fig. 6a varies from 13 for the peak at 0.130 Hz (JR) to 30 at 0.199 and 0.348 Hz. The corresponding r1 values are 28, 24 and 14 s, respectively. Again, the corresponding values of T1 are much longer than the period of revolution, which at 8 RPM is only 7.5 s, and it can be concluded that the oscillations persist for several revolutions of the crucible, It is perhaps surprising that the Q factors for the 8 RPM oscillations are higher than for those at 1 RPM. This implies that, in spite of the great increase in complexity of the spectrum at the higher rotation frequencies, the oscillation modes are in fact more stable. Such Q factor data may provide confirmation of the desirability of relatively high crucible rotation rates in crystal growth.

675

m2

=

=

=

f

(5a) 2p(T) dT.

Tp(T) dT,

o~=(T— rni)ay

=

f00 (T —

m 1)

(Sb) These statistical quantities are useful in the description of the large melt temperature fluctuations which cause microdefects in the grown crystal. It has been shown previously that the statistical characteristics of a wave form produced by a completely random or stochastic process are useful in estimating the number of large excursions in a waveform which is the product of a complex, nonlinear, and nonrandom system [10,12]. For a random wave, the power spectral density is constant over the entire bandwidth of the signal, with random phase relations among the components and the following probability density function 1 p(T) 1/2 exp[ —(T— 7~v)2/2a~J, (6a) aT(21T) where 2, (6b) = (m2 rn1) m 2p(T) dT= T~+ a~. (6c) 2= j T In figs. 7 and 8, the experimental probability density functions measured at 1 and 8 RPM are compared with those expected from a random signal with an equivalent second central moment. In spite of the strong departure from randomness in the data, the plots are quite similar. The experimental values do show some asymmetry, but these types of distortions in probability density func=

—

6. Probabilistic analysis

-00

Each measurement of temperature is a real, positive value, so that the distribution of temperature over a given interval can be described by a probability distribution function P(T) and a related probability density distribution function p (T) such that P(T)

(

=

JTp(T) dt,

(4a)

00

p(T) dt

=

1,

(4b)

—00

where P(— cc)

=

0,

P(cc)

=

1.

(4c)

tions indicate that the waves are a product of a nonlinear system and that there are fixed phase relationships between some of the harmonic cornponents of the waves. This observation is in agreement with the preceding discussions of the spectral characteristics of the waves.

0.07

1445

455 MELT TEMPERATURE 060 C

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MELT TEMPERATURE

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_________________________________________________

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Fig. 8. Probability density functions for temperature fluctuations in a 3 kg silicon melt with 8 RPM crucible rotation: (a) near crucible edge; (b) at i calculated using random wave model; (0) experimental points.

0.

00.06’

0

o

(0_Is, O

I

-

0.2

0.22

Fig. 7. Probability density functions for temperature fluctuations in a 3 kg silicon melt with 1 RPM crucible rotation: (a) near crucible edge; (b) at calculated using random wave model; (0) experimental points.

0.

0.04

~

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0,14

D. Elwell et at.

/

Temperature oscillations in silicon melts

The number of large temperature fluctuations in the melt can be estimated from the number of passages in unit time n ( T1) through a given temperature level T1. For a random wave model, 2/2afl, (7a) n(T1) =0.SNoexp(—T1 where T 1 T ‘;~~ and =

677

Table 2. It can be seen that the random model is useful as a means of predicting to a first approximation the frequency of the larger temperature oscillations. 7. Summary and conclusions

—

00

N0

—

8~

2 ~

w( ~) d ~, W( o.,) d to

(7b)

00 ~,2

—00

N0 is the number of expected zero crossings per second, to is the angular frequency of the harmonic component, and W(to) the power at frequency For a low pass filter of bandwith B, eq. 7(a) becomes ~.

n (i’~)= 0.5775B exp(

—

(8)

T~/2ufl.

The temperature fluctuations in the 3 kg silicon melt are generally contained in a bandwidth from 0.1—1.0 Hz. For a 1000 s measurement interval, GT can be determined to ±3%. Dils [12] has pointed out that, for large fluctuations, the number of crossings of a given temperature level is approximately equal to the number of range pairs. A range pair consists of an alternate crossing in opposite directions, and, therefore, can be used to characterize the large temperature excursions which are most likely to have an adverse influence on crystal growth. Comparisons between the experimental data and the number of large fluctuations predicted by eq. (8) are presented in

Table 2 Large temperature oscillations: comparison between random wave model and experimental data from ref. [5]; the table also

shows a reduction ~ from 1 to 8 RPM 0T

Parameters

(°C)

as the rotational speed is increased

B (Hz)

~T (°C)

Number of excur-

sions per 500 5 Theory

Experiment

1 1 8 8

RPM edge RPM center RPM edge RPM center

3.9 3.0 2.2 2.1

0.1 0.1 0.6 0.4

±6 ±4 ±3 ±3

9 11.8 36.5 41

8

11.5 35.7

30

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strate Examples the value haveofbeen optical presented fiber thennometry which demonin studying temperature oscillations in the melt. Transient analyses indicated that when the crucible rotation rate was changed rapidly, the oscillation pattern changed with a time constant on the order of a few minutes. The presence of crystal reduced the radial temperature gradient but caused larger temperature fluctuations in the melt. Fourier analysis of the data was found to be a particularly valuable tool for studying the melt temperature oscillations and their dependance on crucible rotation. At 1 RPM crucible rotation, over half the energy of the temperature fluctuation measured near the edge of the melt was contained in a single peak at 0.0265 Hz. The peak was not present at the center of the melt, where a more complex spectrum was generated. Increasing the crucible rotation rate to 8 RPM resulted in a significant increase in the complexity of the melt oscillation spectrum, but it was found that all the peaks in the PSD function could be assigned to combinations of three or four fundamental frequency components, including the crucible rotation frequency. The Q of the peaks at 8 RPM was higher than at 1 RPM, indicating the oscillations were more stable at higher rotational speeds. Although the PSD functions of the temperature oscillations indicated the system producing the oscillations was not random, the large excursions in melt temperature could be approximately described a random wave model. The by study reported here is clearly of a preliminary nature and is intended only to demonstrate new experimental techniques and analyses for the investigation of melt temperatures. It would be of interest to conduct more extensive investigations on the influence of crucible rotation and location within the crucible on the PSD function in order to identify the origin of the observed

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/ Temperature oscillations in silicon melts

frequency components. An investigation of the influence of the growing crystal on the temperature oscillations is another obvious extension of the techniques in view of its practical importance Speculation concerning the origin of the motions responsible for the temperature oscillations has generally been avoided. Modeling of the oscillations is a desirable follow up to this experimental study. With regard to modeling, useful additional experimental information on the nature of the fluid flows in the melt can be obtained from the use of multiple sensors. One arrangement consisting of three OFTs with tips separated in the vertical and horizontal direction from a fourth thermal central sensor, would allow the measurement of the time interval for a thermal fluctuation to flow across any pair of tips, and would lead directly to the measurement of the fluid flow velocity components. As pointed out earlier [5], anemometry is a technique which would be particularly useful in the study of fluid flow patterns, but a suitable experimental arrangement has not been available. The development of such an OFT anemometer would be of value for investigating even the most complex flow patterns in silicon and other melts. Optical fiber thermometry is also of potential benefit to silicon crystal production. If the tip of the sensor were left in the melt continuously during growth, the rotation rates could be adjusted to minimize the amplitude of the temperature oscillations. A position as close as possible to the crystal-liquid interface would be desirable in view of the dependence of the oscillation spectrum on position within the melt. Founer analysis of the temperature fluctuations would be of particular value in revealing the frequencies and amplitudes of the largest components in the oscillation spectrum Momtonng, and eventually controlling, the temperature oscillations in silicon melts during

crystal growth will have major beneficial effects for the grower. In addition to the importance of melt temperature oscillations in determining the concentration of microdefects, the yield of crystals is also likely to increase when growth occurs from relatively quiescent melts. In particular, the necking and shouldering stages immediately following introduction of the seed should be easier to accomplish successfully if the major excursions in temperature could be eliminated.

Acknowledgments The experimental data were obtained at J.C. Schumacher Co., and we thank Dr. John Schumacher for permission to use the data. David O’Meara contributed to the experiments.

References [1] E. Kuroda, H. Kozuka and Y. Takano, J. Crystal Growth 68 (1982) 613. [2] W.E. Langlois, J. Crystal Growth 63 (1983) 61. [3] M. Mihel~ié,C. Schrdck-Pauli, K. Wingerath, H. Wenzl, W. Uelhoff and A. van der Hart, J. Crystal Growth 57 (1982) 300. [4] L.J. Hieliming and J.S. Walker, J. Fluid Mech. 164 (1986) 237. [5] D. Elwell and E. Andersen, J. Crystal Growth 84 (1987) [6] PG. Barber, R.K. Crouch, A. Fripp, 1.0. Clark, W.J. Debnam and R. Simchik in: MRS Europe Conf. Proc., 1985, p. 41. [71Z. Juhasz and G. Szabo, J. Crystal Growth 79 (1986) 303. [8] K. E. Benson, W. Lin and P.E. Martin, in: Semiconductor Silicon 1981, Eds. HR. Huff, R.J. Kriegler and Y.Takeishi (Electrochem. Soc., Pennington, NJ, 1981) p. 113. [9] P.H.O. Rappl, L.F. Matteo Ferraz, H.J. Scheel, M.R.X. Barros and D. Schiel, J. Crystal Growth 70 (1984) 49. [11] [10] J.R. R.R. Abernathey Dils, J. Eng.and Power, F. Rosenberger, Trans. ASME J. Fluid 95A (1973) Mech. 265. 160 (1985) 137. [121 R.R. Dils, Corrosion 33 No. 11 (1977) 385.