The quality control of quartz growth: A chinese perspective

Prog, C/ystalGrowth andCharact. Vol. 30, pp. 283-294, 1995

Pergamon

Copydgl'd © 1995 Ebevler Sdence Ltd Printed in Greal Britain. All dghls reserved 0960-8974/95 $29.00

0960-8974(95)00014-3

THE QUALITY CONTROL OF QUAR'I7 GROWTH: A CHINESE PERSPECTIVE Chen Furong P. O. Box 733, Beijing 100018, P. R. China

ABSTRACT The quality of synthetic quartz crystals grown hydrothermally m a i n l y depends on the average growth rate.A mathematical model of the growth rate based on a very large number of experiments has been established. This model is highly suitable for estimating the growth rate, the period and the output of each type of quartz crystal according to the technical design parameters, and plays an important role in the a d m i n i s t r a t i o n of product and the quality control in quartz crystal growth. i. INTRODUCTION Quartz crystal is an important material which is now very w i d e l y used in a whole range of a p p l i c a t i o n s . Q u a r t z is utilized in optical components, due to its special c h a r a c t e r i z a t i o n of double refraction,optical rotatory power and transparency from ultraviolet to the infrared region. M o r e o v e r quartz crystals are widely used as time and frequency control devices in a vast range of electronic devices. Crystals of quartz with variant quality are required for different applications. It is important to dominate the quality of quartz in the process of its g r o w t h , e s p e c i a l l y for crystals u t i l i z e d as frequency control devices at higher frequencies and for surface acoustic wave devices.The quality of single crystal quartz is dependent on the growth technology since many parameters showing the quality level of single crystal quartz are directly related to the technical conditions adopted in quartz growth. It is necessary to establish their relationship in order to find out the main effect on the quality of quartz. 2. PARAMETERS C H A R A C T E R I Z A T I O N Several parameters show the quality level of single crystal quartz, such as mechanical Q, a l u m i n u m content and etch channel density. 283

284

ChenFurong

M e c h a n i c a l Q is a m e a s u r e v a l u e of the a c o u s t i c loss of a q u a r t z c r y s t a l unit. It is d e t e r m i n e d b y i n f r a r e d measurement of the a b s o r p t i o n of q u a r t z at the w a v e n u m b e r of 3500-icm or 3585-icm. V a r i a n t Q v a l u e is r e q u i r e d for q u a r t z c r y s t a l s in d i f f e r e n t a p p l i c a t i o n s , for h i g h q u a l i t y q u a r t z the Q v a l u e is r e q u i r e d to be m o r e than 2.0 m i l l i o n . Some a r t i c l e s h a d r e p o r t e d that the Q v a l u e d e p e n d s on the average g r o w t h rate of s i n g l e c r y s t a l q u a r t z [1][2][3][4]. We also o b t a i n e d the curve ( fig.l ) of m e c h a n i c a l Q v e r s u s the average rate of q u a r t z g r o w t h in N a O H s o l v e n t by the experim e n t s of Y - b a r q u a r t z growth.

\

\

~26(

\

~240

'~22G 200

Z0

30

~0

5o

60

7('

fig.1. R e l a t i o n s h i p b e t w e e n m e c h a n i c a l Q and the a v e r a g e rate in Y - b a r q u a r t z g r o w t h The curve shows that the Q v a l u e a n d the a v e r a g e rate are i n v e r s e l y p r o p o r t i o n a l , i n o t h e r w o r d s , a l o w e r a v e r a g e rate m u s t be d o m i n a t e d in o r d e r to get s i n g l e quartz with a higher Q value. In our e x p e r i m e n t s c o n t r o l l i n g the a v e r a g e g r o w t h rate to less than 35 m l s / d a y r e s u l t s in o b t a i n i n g q u a r t z w i t h the Q v a l u e of m o r e t h a n 2.5 m i l l i o n in 1.2M N a 0 H s o l v e n t w i t h Li salt impurity. A l u m i n u m c o n t e n t is an i m p o r t a n t p u r i t y factor. If in the l a t t i c e an a l u m i n u m a t o m s u b s t i t u t e s for a s i l i c o n atom, an a l u m i n u m - m e t a l c e n t e r A I - M ÷ is formed, this c e n t e r is d i s s o c i a t e d in a r a d i a t i o n e n v i r o n m e n t and forms an AI-OH- or A l - h o l e pair; it can i n d u c e f r e q u e n c y o f f s e t s in the s t e a d y s t a t e and w i t h t r a n s i e n t r a d i a t i o n [ 5 ] [6] . M a r t i n and A r m i n g t o n [ 7 ] have f o u n d a direct proportional relationship between aluminum content and the a v e r a g e g r o w t h rate ( fig.2 ). The d a t a shows that the a l u m i n u m c o n t e n t b e c o m e s l o w e r w h e n the g r o w t h rate d e c r e a s e s . O t h e r e x p e r i m e n t s a l s o p r o v e that the a l u m i n u m c o n t e n t of s y n t h e t i c q u a r t z d e p e n d s d i r e c t l y on the a l u m i n u m c o n t e n t of the n u t r i e n t used. High purity quartz w i t h an a l u m i n u m concentration below 0.2 p p m are o b t a i n e d by the w a y of e m p l o y i n g the n u t r i e n t w i t h a l o w e r a l u m i n u m c o n t e n t and k e e p i n g the g r o w t h rate b e l o w 45 m l s / d a y .

The Quality Control of Quartz Growth

285

e

v

~_,

Q5

r

o.,

0.4-

g E 02 c

ic

6 0.I ~

0 Gr.,:,:.,..=tt-4


Rate

fig.2. R e l a t i o n b e t w e e n a l u m i n u m and the a v e r a g e g r o w t h rate [7]

s/"da>")

content

The d i s l o c a t i o n d e n s i t y and the l a t t i c e d i s t o r t i o n h a v e a s e r i o u s e f f e c t on the q u a l i t y of q u a r t z c r y s t a l p l a t e s . Disloc a t i o n s c o n t a i n m a n y a c t i v e ions e t c h e d e a s i l y b y a c i d in the p r o c e s s of c r y s t a l p l a t e f a b r i c a t i o n , it r e s u l t s in the format i o n of e t c h c h a n n e l s into w h i c h i m p u r i t i e s m a y s i n k f r o m the s u r f a c e of the c r y s t a l plate. The l a t t i c e d i s t o r t i o n m a y c a u s e strain a n d i n c r e a s e the p o s s i b i l i t y of b r e a k a g e d u r i n g fabrication. S.Taki[8] has r e p o r t e d on s i n g l e q u a r t z c r y s t a l s g r o w n with different Q value and their dislocations and their measured d i s t o r t i o n (Table l). T a b l e I. Dislocation density and lattice d i s t o r t i o n c o r r e s p o n d i n g to the Q value[8] Sample NO.

Q value (106 )

1 2 3 4 5 6 7 8 9

0.3 0.6 1.2 i. 5 1.9 2.1 2.3 2.4 2.5

dislocation density (cm -3)

103 10 i0

~ > > ~ ~

103 105 105 104 102 I0 I0 i0 I0

lattice distortion *i0-6 (~d/d) >25 20 ~ 25 I0 ~ 14 3 - 6 0.51 0.3 - 0.8 0.2 - 0.6 0.i ~ 0.5 0.i ~ 0.5

The d a t a in T a b l e 1 i n d i c a t e that t h e r e is an i n v e r s e relationship between mechanical Q and the d i s l o c a t i o n density and the l a t t i c e d i s t o r t i o n . S i n c e m e c h a n i c a l Q is d e p e n d e n t on the a v e r a g e g r o w t h rate, the d i s l o c a t i o n density and lattice d i s t o r t i o n are d i r e c t l y p r o p o r t i o n a l ~to the a v e r a g e g r o w t h rate. The e t c h c h a n n e l d e n s i t y w h i c h is a m e a s u r e of the v a l u e of the dislocation density decreases rapidly with reducing average

286

ChenFumng

growth rate. The etch channel density is also dependent on the quality of seeds used, because the dislocations on the surface of the seed m a y extend along the direction of quartz growth. R e c e n t l y experiments using higher quality seeds and nutrient were carried out by us and synthetic quartz crystals were grown in the pure-z region in N a O H solution were obtained w i t h the Q value of m o r e than 2.5 m i l l i o n w i t h an etch channel d e n s i t y about 2 - 1 0 / c m 3.

3. INCLUSIONS

Inclusion density is another major quality factor in the assessment of crystals of quartz. Inclusions can be in the form of solid inclusions or liquid-gas inclusions. Few liquid-gas inclusions are found in synthetic quartz under conditions of growth of a large percent of fill or by increasing the temp e r a t u r e of the growth region. The inclusions found u s u a l l y in quartz are solid inclusions. The existence of acmite(NaFeSi206) on the inner wall of autoclaves is g e n e r a l l y the m a i n resource of solid inclusions in single quartz. Otherwise if the s u p e r s a t u r a t i o n of SiO in the liquid is too great to crystallize in time, m a n y reaction products, such as m i c r o p a r t i c l e s of acmite are formed in the solution and later enter the crystal of quartz being grown. It is the reason why m a n y inclusions appear in synthetic quartz grown in NaOH or Na2CO 3 solution where quantities of spontaneously n u c l e a t e d tiny crystals of quartz grow in the a u t o c l a v e due to u n d u l a t i n g temperatures in the growth region. Table 2 shows the effect of the growth conditions on inclusion formation. Table 2. The inclusion conditions

relative

to the technical

solvent

dT (°C)

pressure (MPa)

spontaneous nucleation

inclusion

1.2N N a O H

45

145

a few

a few

1.2N N a O H

35

145

few

few

1.2N N a O H

30

141

few

few

1.2N N a O H

35

127

few

a few

1.2N N a O H 35 +0.5N Na2CO 3

145

many

many

eliminate the For these reasons it is not enough to only acmite on the inner wall of the autoclave, more w o r k must be done to decrease solid inclusions,by reducing the fluctuations in the growth temperature and by suitable d e s i g n choosing

The Quali~ Control~ Q u a ~ z G ~ h

287

t e c h n i c a l p a r a m e t e r s that control the s u p e r s a t u r a t i o n of SiO 2 in solution. A large capacity a u t o c l a v e can p l a y a role in r e d u c i n g the effects of solid inclusions. In J a p a n a large a u t o c l a v e w i t h a 650mm inner d i a m e t e r was u t i l i z e d for single quartz growth. In C h i n a , w e also s u c c e e d e d in the b a t c h p r o c e s s for the p r o d u c t i o n of l a r g e ' o p t i c a l q u a r t z ( w e i g h t : 5 - 10kg) by the way of the choice of the strict control of the t e c h n i c a l c o n d i t i o n s in a u t o c l a v e s w i t h a 2 5 0 m m inner diameter.

The p h o t o g r a p h

of large

4. G R O W T H

RATE

optical

quartz

FUNCTION

Since there is a great effect of the q r o w t h rate on the q u a l i t y of single quartz g r o w n in the h y d r o t h e r m a l method, the c o n s e q u e n c e how to d e t e r m i n e the a v e r a g e rate is an i m p o r t a n t p r o b l e m for us. M a n y e x p e r i m e n t s prove the rate of g r o w t h is i n f l u e n c e d by a n u m b e r of technical conditions; they are found to be: l . s u r f a c e area of the seed; 2 . t e m p e r a t u r e d i f f e r e n c e b e t w e e n d i s s o l v i n g and g r o w t h zones; 3 . p e r c e n t of b a f f l e left open; 4 . c o n c e n t r a t i o n of solvent; 5 . p e r c e n t of fill; 6 . g r o w t h temperature; 7 . s u r f a c e area of nutrient; 8 . o r i e n t a t i o n of seed; In the technical c o n d i t i o n s a b o v e , t e m p e r a t u r e d i f f e r e n c e has a v e r y r e m a r k a b l e effect on the rate. R . A . L a u d i s e [9] had demon-

OhenFumng

288

strated that the rate R is a linear function of the temperature difference dT and extrapolates to zero rate at zero dT. Thus: R

~

dT

A . A . S h t e r n b e r g had reported the growth rate and the surface area S of seed are inversely proportional [i0], the relation can be w r i t t e n as: R

~

I/S

This rate R m e a s u r e d by experiments is an average value, but the rate in practice varies from day to day in a growth run. If we find the rule for the functional rate change, not only the average rate can be d e t e r m i n e d to control the quality of quartz, but also the p e r i o d and the output of quartz growth can be estimated. The author has worked on e s t a b l i s h i n g a suitable computational model of quartz growth for several years which can be used a n a l y t i c a l l y to calculate the growth rate every day. There are limits to the assurance of the q u a l i t y of quartz a s s o c i a t e d with the metal material of the autoclave and w i t h the pressure and temperature used, but here we only consider the influence of the surface area of seed and the temperature d i f f e r e n c e , t h e other conditions remaining constant at their best values. In NaOH solution, these are: --percent of fill: 82%; --the c o n c e n t r a t i o n of solution: 1.2N; --percent of baffle left open: 6%; --growth temperature: 340°C; --orientation of seed: (0001); --seed was chemically etched in 48% HF for 60min. In order to establish the function for growth rate, define again S as the surface area of quartz being grown. So the rate equation is written as: R=G*dT/S where:

R is the growth rate on one day; dT is the temperature difference; S is total surface area of quartz being grown; G is variable coefficient related to the crystallizable probability.

It is v e r y difficult to determine the G value because the rule of crystallizable p r o b a b i l i t y changes during a growth run and is different for each type of quartz. Several parameters m a y be cited to simulate the changing value of G and can be used to a p p r o x i m a t e l y calculate by computer to determine their relationships. The data selected for simulant calculation come from the following experiments, they were: -- Y-bar quartz growth; -- Z-plate quartz(thickness: 2 0 - 145 mm) growth; -- Z-block quartz(thickness: 20 - 85 mm) growth. The above experiments were done under different conditions

TheQuali~ Contml~ Q u a ~ Gro~h

2~

of surface area of seed, temperature d i f f e r e n c e , p e r i o d and output. Employing the data p r e s e n t e d ' a n analogical calculation results in e s t a b l i s h i n g a m a t h e m a t i c model, which is suitable for the growth of single quartz' crystals of v a r i a b l e size.

5. EXPERIMENTAL

EQUIPMENT

The data were adopted from experiments involving four type of autoclave. The autoclaves's specifications are arranged in Table 3. Table 3. Size of autoclaves type inside length (mm) inside diameter (mm) volume

i#

2#

3#

4#

4500

3710

4740

2600

250

250

270

150

221

182

271

46

(I) All of these autoclaves were closed using a m o d i f i e d Bridg m a n seal. In this article, all the data shown are adopted from the first type of autoclave used. There are a several hundred of this type of equipment in China. They are made from PCrNi3Mo V A steel, and made by The Second Mechanical Factory. This type of autoclave as used in a growth run is shown in figure 3. The temperature is controlled with a DWK-702 c o n t r o l l e r , t h e toler-

P'F~E :~.i:::i_Ii~.:E;

/.--

.............

TESTER

SEAL RING

....................... ~.+ ..... ,,._

iFID i = ..,,// BOTTOM MEASURE T . C .

~

F

B~FFLE NUTRIENT

Im~' <~"

fig.3.

TOP CONTROL T . C .

.

.................

i

SEED

The specification

E:OTTOH CONTROL T . C .

of the autoclaves

used

290

C~wmF.~

ance of temperature tested is about ±0.5°C. The pressure is tested with the pressure-tester at the top of the autoclave. 6. THE RATE CURVE The rate model had been examined in practice. The values simulated with this model very closely approach to the practi-

~: 0 i+

•

+

Cla>'

fig.4. The rate curve off Y-bar quartz

"o

f_

0 f_

day

fi9.5. The rate curve of Z-plate quartz ">',

"o8C

+

.

•

~40 IL

c-

.~,20 c, C.,

'~-' 0

Io

zo

~

4o

so

Oo

~o

~o ~ d@.>"

fig.6. The rate curve of Z-block quartz

TheQuali~ Co~rol~ Qua~ Gro~h

291

cal result, s u c h as the a v e r a g e g r o w t h rate, the p e r i o d of the run, and the total o u t p u t of q u a r t z in an a u t o c l a v e . Several t y p i c a l c u r v e s of the rate are p l o t t e d u s i n g the mathematical m o d e l in fig.4, fig.5 a n d fig.6. The t e c h n i c a l c o n d i t i o n s corr e s p o n d i n g are a r r a n g e d in T a b l e 4 and T a b l e 5.

T a b l e 4. The d a t a for d i f f e r e n t quartz crystal growth type

Y-bar

seed (g) period (day) a v e r a g e rate (mls/day) dT (°C) output (kg) seeds n u m b e r

z-plate

types

of

z-block

1063

2783

4260

66

82

74

32

45

49

35

35

35

84

86

86

440

55

60

* s u r f a c e a r e a of seed can be c a l c u l a t e d w i t h the w e i g h t of q u a r t z

Table type

5. The size of q u a r t z

crystals

Y-bar

z-plate

z-block

15.5 - 16

86.5 - 87

167 - 172

X

(mm)

Y

(mm)

2 2 5 - 226

Z

(mm)

2 2 - 23.5

190 36.5 ~ 39

95 36 - 3 9

All the c u r v e s a b o v e s h o w the rate g r a d u a l l y r e d u c i n g w i t h the lapse of time in a g r o w t h run. The rate c u r v e for Y-bar quartz growth assumes apparently a parabolic shape. In fig. 5 the rate curve p a r a b o l i c a l l y approaches linearity. Figure 6 shows the rate curve is l i n e a r in Z - b l o c k growth. C h a n g i n g the t e c h n i c a l p a r a m e t e r c a u s e s a v a r i a t i o n of rate and p e r i o d of growth. In fig.4, if the t e m p e r a t u r e difference dT= 40°C, a n e w curve is p l o t t e d in fig.7, it shows that the p e r i o d and the a v e r a g e rate turn into 58 day a n d 37 m l s / d a y , w h e n the d i f f e r e n c e of t e m p e r a t u r e c h a n g e s f r o m 35°C to 40°C.

292

Chen Furong

13

5# E &l 4-,

c~ f.-

~: 20 6

f_ CI

10

fig.7.

Z

1

~:;. L 20

4'0

The rate c u r v e s i. dT=40°C;

~

:

go

7b

_2:

80 da>

for the c o n d i t i o n s 2. dT=35°C

Photograph of q u a r t z c r y s t a l s : t h e y are z - b l o c k , Y - b a r a n d z - p l a t e q u a r t z f r o m left to right in the front row. In the b a c k row it is an o p t i c a l q u a r t z crystal.

7. Q U A L I T Y

CONTROL

S i n c e the rate curve can be o b t a i n e d in a d v a n c e by anal y t i c a l c a l c u l a t i o n , it is e a s y to d e t e r m i n e the a v e r a g e g r o w t h rate a n d c o n t r o l the s u p e r s a t u r a t i o n of SiO 2 in s o l u t i o n a c c o r d

The Quali~ C o ~ m l ~ Qua~ Gm~h

293

ing to the conditions m a n a g e d . O t h e r w i s e one must take steps in two aspects : one is to employ regularly the nutrient from a special resource; another is to get the curve of the relationship b e t w e e n the rate and the machanical Q and a l u m i n u m content by practical measurement just as in fig.l and fig.2. On the b a s i s of the results presented, controlling the quality of synthetic quartz becomes entirely feasible. The v a r i a t i o n of the rate results in the irregularity of mechanical Q and impurity content in a synthetic quartz crystal. This affects directly the quality of resonators, the irregularity of impurity content causes the changing of the refraction power in an optical quartz crystal. In fig.4, fig.5 and fig.6 the difference of growth rate between the earlier stage and the last stage is greatest for Y-bar quartz growth,and its u n i f o r m i t y becomes very poor. conversely, the u n i f o r m i t y of zblock quartz is fairly good because smaller changes of the rate occur in a period. Obviously, to improve the u n i f o r m i t y of synthetic quartz, the rate of growth must remain constant throughout a run. The effective m e t h o d is to control the difference of temperature dT gradually by increasing and keeping the temperature of the growth zone fixed. In Japan, the m e t h o d of increasing linearly the b o t t o m temperature was used, but it is considered that the rate is not constant in the situation presented. Their data does not represent the result of fixed q u a n t i t y calculation. Here, the rate model is used to calculate the temperature difference in reverse by choosing a fixed rate.The result of this calculation displays that b o t t o m temperature must increase nonlinearly for a fixed growth rate in a run for m a n u f a c t u r i n g any type of quartz. In fig.8, it is shown dominating the temperature in the dissolving zone increasing gradually in order to m a i n t a i n the growth rate constant at about 40 m l s / d a y in z-block quartz growth as displayed in Table 4. This m e t h o d is suitable for optical quartz growth and convenient for improvement of optical uniformity. 50

jJ

40 .f

2C

I0 JO

20

50

40

50

60

70

80

S0

day fig.8. The curve of dT controlled in Z-block quartz growth with the top temperature fixed

294

ChenFumng 8. CONCLUSION

It makes practical sense to establish a m a t h e m a t i c a l controlling model for the rate of synthetic quartz g r o w t h in order to dominate the quality of crystals. This model also has a great effect on the management of the p r o d u c t i o n of single quartz, but it is not enough to employ the model for controlling solid inclusions. To solve the p r o b l e m of solid inclusion, we must take into c o n s i d e r a t i o n the additional v i e w p o i n t of the formation energy of the reactants. If one could e s t a b l i s h the formula for the formation energy of the solid inclusion,the p r o b l e m presented could be settled easily. From this point of view, there will be more w o r k being done in future.

ACKNOWLEDGEMENTS

I would like to acknowledge Professor Zhong W e i z h u o and Professor Hua Dachen who cooperated w i t h me in the first stage. Also I would like to thank Senior Engineer Wang Ziwen and Wang Xiaogang of RISC for their work of p r o d u c i n g quartz crystals.

REFERENCES i. C.S.

Brown,

Proc.

Soc(

London

) , 75

2. N.S. Lias, E.E. Grudenski, E.D. Crystal Growth 18 (1973) I. 3. D. C h a k r a b o r t y

J. Crystal

5. J.C. King and H.H. (1972) 23.

Sander,

459.

Kolb and R.A.

and P. Saha Indian,

4. D. Chakraborty,

(1960)

Growth

J. Phys. 41

IEEE Trans.

(1977) Nucl.

Laudise,

J.

(1974)

439.

48

177. Sci.

6. F. Euler, P. Ligor, A. Kahan, P. Pellegrini, T.M. and T.F.Wrobel, IEEE Trans. N u c l . S c i . N S - 2 5 (1978) 7. J.J. 203.

M a r t i n and A.F.Armington,

8. S. Taki, 313.

J. Crystal G r o w t h

Prog. Crystal Growth and Charact.Mater.

9. R.L. Barns, E.D, 34 (1976) 189.

Kolb

10.A.A.

Hydrothermal

Shternberg,

and R.A.

Laudise,

Syn.

Crystal

NS-21

Flanagan 1267. 62

(1983)

23

(1991)

J. Crystal G r o w t h

(1971)

25.