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Dopant incorporation in single-crystal fibre growth by the laser-heated miniature pedestal growth technique
Journal of Crystal Growth 131 (1993) 457—464
iou ~
North-Holland
CRYSTAL GROWTH
Dopant incorporation in single-crystal fibre growth by the laser-heated miniature pedestal growth technique J.H. Sharp
~,
T.P.J. Han, B. Henderson, R. Illingworth and I.S. Ruddock
Department of Physics and Applied Physics, Unicersity of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, UK Received 23 October 1992; manuscript received in final form 7 March 1993
A theoretical model of single-crystal fibre growth by laser-heated miniature pedestal growth has been developed to account for the transfer of dopant from the source rod to the growing fibre. This model predicts the time evolution of the melt dopant concentration when the source rod dopant concentration is axially non-uniform. From this the axial distribution of dopant in the final grown fibre may be predicted. This model has been experimentally confirmed and an estimate of the evaporation time constant of Ti in the growth of Ti:Al,0 3 fibres made.
1. Introduction
in particular, laser materials. SCFs of ruby,
The laser-heated miniature pedestal growth (LHMPG) method, as developed by Byer et al. [11, is now a well established technique for the growth of single-crystal fibres (SCFs). As can be seen from fig. la, the technique involves the tip of a rod of source material, typically 0.5 mm in diameter, being heated by laser to melting point. A seed crystal, once dipped into the molten zone, is withdrawn at some rate faster than the source material is fed in. By conservation of melt volume, this leads to the crystalline fibre growing at some constant fraction of the source rod diameter. As in float zone growth, this is a crucible free growth method and can therefore produce highpurity, low-defect density single crystals [2]. The flexibility and advantages of the technique as a materials research tool have been amply demonstrated by Feigelson [31and are now recognized by research groups worldwide [4,5]. The main current application of miniature pedestal growth is in the development of novel optical and,
Nd : YAG, Tm : YLF and Ti sapphire with diameters ranging from 3 to 1000 ~m have been grown [6—91with laser action being demonstrated in all of these. These fibres have potential use in the development of miniature, possibly tunable, all solid-state lasers. For laser active crystals, a relatively large dopant concentration is required. This can present two problems when using LHMPG, both related to the transfer of dopant from the source material to the growing crystal. First of all, dopants with low segregation coefficients tend to accumulate in the melt (as in zone refining) and secondly, dopant may also be lost from the melt during growth as a result of evaporation. The ideal dopant, therefore, would have a near unity segregation coefficient and a relatively low vapour pressure. In real materials this is seldom the case and some method whereby we may predict how dopant properties will affect its distribution in the final fibre would indeed be useful. In this paper we discuss two materials which have many desirable properties which suggest them as candidates3~ forGa miniature tunable fibre laser sources, Cr 3Sc1A13O12 (GSAG),
Present address: School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BNI 9QH, UK. 0022-0248/93/$06.OO © 1993
—
Elsevier Science Publishers B.V. All rights reserved
458
J. H. Sharp
et a!.
/ Dopant
Incorporation Ifl .stngle-crcvtalfibn’ growth
where the Cr has a near unity segregation coeffi3~:A1 cient, and Ti 203, in which the Ti has a relatively low segregation coefficient. We examinc how the dopant concentration in the melt evolves over time and hence the spatial distribution in the growing crystal, taking into consideration evaporation from the melt. This allows us to identify the correct conditions for the growth of laser quality crystals. First, we present a simple model of SCF growth by LHMPG and then discuss experimental results in light of this model,
2. Theoretical model In the following derivation the molten zone shape is approximated by a truncated cone of height, h, as indicated in fig. lb. Other parameters used are also indicated in this figure with C1 indicating the of dopant 3) concentration in region i, where I s, ions f, m(in units of cm representing the source rod, the growing fibre and the melt, respectively. The segregation coeffi=
—
hc !,HMPG
cient, k, is defined as C1/C~,where it is assumed that there is sufficient mixing by rapid diffusion and strong convection to give an homogeneous melt thereby allowing us to take k as constant. The diameter reduction ratio is defined as R/r and the melt volume as V. It is assumed that dopant is supplied to the melt solely from the incoming source rod and dopant loss is a result of evaporation from the surface of the melt and also as a result of dopants being taken up by the growing fibre. The evaporation may he characterized by an evaporation time constant, i-, defined as the time taken for C~,to decrease by a factor of e when the fibre and source rod are held stationary. i.e. at zero growth rate. If, in a time interval dt, the fibre grows by an amount dz and the source rod is fed into the melt by an amount dz(), there is a corresponding change, of dopant ions the melt VdC~1,in caused bythe (a) number the number. 71-RC~ dz,in supplied to the melt from the source rod. (h) the number, 7,-r2kC~d:, taken up by the growing
PULl, 1113FF
-~~~-~—-
—‘~-_
CO
~..J
(I~O~,
0-
.
MFI:I
H
~
~....
FEED~
C
(a)
~
SOUI3CE P01
.......,
0-
V
(C\ ..I/~,
(b)
Fig. I. (a) Laser-heated miniature pedestal growth. (h) Model of growth used in theoretical
deri~ation.
J.H. Sharp et al. / Dopant incorporation in single-crystal fibre growth by LHMPG
459
fibre and (c) the number, VCmT~ dt, lost from the melt by evaporation. Hence,
Substituting this expression for C, into eq. (2) we arrive at the following expression for the dopant
dztj—~r2kCmdz V dC~=~rR2C~
concentration in theaC melt ~ during growth: Cm(t) Ca e~t+ —~---(1 e_$t)
—
~Cm dt. T (1)
Noting that, by conservation of mass in the melt for steady state growth, ~R2 dz 2dz, and 0 pull i~rr rate, we that dz dt, where r’ is the fibre may define the following parameters: =
a
=
1~
irr2r’/V,
=
ak
+
1/i-,
=
(2)
—
Ideally, the dopant concentration in the source rod should be uniform. However, some time is required to align the focus of the CO2 laser and the ends of the source rod and seed crystal. Optimizing the laser power and other growth parameters before commencing growth results in the end of the source rod being at, or near, melting point for a number of minutes. This allows loss of the dopant from the source rod to occur by evaporation from the surface. This may be represented as a spatial dependence of the dopant concentration along the source rod length, with the initial concentration being C~1 when growth commences at time, t 0 and the equilibrium value of the concentration being C50, as =
—
a(C~ t e~~) f3 1 C~0)(e~’
+
(5)
—
— —
=
~‘
and recast eq. (1) as: dCm/dt aC~ 13Cm.
-*
=
.
.
Recasting this equation in terms of the fractional concentratton in the fibre with respect to the asymptotic source concentration and expressing in terms of v and z, we obtain Cf(z) C. 0
=
k C’ e~~”+ ~(1
—
13 a(C’ +
~
—
—
1)
-
(e
~,
-
yz/o
e
—
13z/o)
(6)
,
where C’ is the fractional loss of dopant from the source rod at z 0 due to evaporation and is given by C’ C ./C (7 =
=
Si
sO~
Taking z to obtain the equilibrium concentration in the growing fibre, we have: —~
k a/13. (8) Substituting our definitions of a and 13 we arrive at C~(~)/Cs0 =
00~
We can represent the concentration in the source rod as C5(z)
C~0+ (C~1 C~0)e_2/L,
C~0
(3)
where
where L is some characteristic length not usually susceptible to measurement. Assuming that once growth commences, the source rod is fed continuously into the laser focus and that evaporation from the rod is negligible compared to that from the melt, we define the constant y as,
1= ~
=
=
—
/
‘
and so express C5(t) during growth as: t. C5(t) C~0+ (C~1 C~0)e~’ =
—
(4)
F 1
Cf(c~) —i =
1
+
(9)
~,
(10)
Thus, by plotting [Ct(x)/C~0]~ against i.’~ we have a straight line whose gradient is given by F/i-. Since F can be calculated from the known quantities in (10) the characteristic evaporation time constant can be found. From the above we can now predict the general features to be expected during fibre growth. ~,
Figs. 2 and 3 show the ratio [C~(z)/C~0], as length of fibre when z as 0a atfunction t 0 for expressed in eq.grown (6), plotted of =
=
46(1
i.H. Sharp ci a!.
/ Dopant
incorporation in single-crystal fibre growl/I hr /.HMPG
L
-
fig
=
// /
/
_____________________________
--.
(-HA TON AL ~\( Fig. 2. Predicted fraction of dopani transferred troni the source rod io the fibre with 4 = 0.21. Solid curves U. = (1.1 mm): dashed curves (I. = 5.0 mm) with fibre growih rate: (A) 2.5 mm/mm and (B) 0.5 mm/mm.
•
.
.
various values ot growth rate r’ and different segregation coefficients, k. The other parameters (such as fibre radius and reduction ratio) used in eq. (6) have been chosen to accurately model the actual growth conditions of the fibres used in the later experimental investigations. The parameter C has been chosen to be 0.1 and the evaporation time constant to be T 2.3 mm. For each curve there is an initial sharp rise which, as one can see from the figures, is strongly dependent on the depletion length. L. The final =
and . ____________________
/
- .
// - 1~
_________
________
/ .v~
-
equilibrium level is principally dependent on the fibre pull rate, v; a faster pull rate implies that the loss from the melt due to incorporation into the fibre compared to loss by evaporation is much higher hence giving dopant atoms less time in the melt to he lost from the surface. We notice from ~ that when k is of thc ordcr of unity thc equilibrium concentration is higher in each case when compared to fig. 2 where k 0.21. This results from there being less accumulation of dopant in the melt for the case of higher k and so the evaporation, which is proportional to is reduced. It is also true that as k increases so the transient rise to equilibrium becomes shorter. For laser applications, a uniform gain medium is desirable and so one would cut off and discard this transient. This is in contrast to zone refining,
-
-~ -
-
-
-ONAL~:H.-~ I HH.~--i-~ Fig. 3. Predicted fraction of dopant transferred from the -. . . . source rod to the fibre with k = 0.90. Solid curves (L = 0.1 mm): dashed curves (L = 5.0 mm) with fibre growth rate- (A) 2.5 mm/mm and (B) 0.5 mm/mm.
which also relies on localized melting, where only the “purified” section of crystal is wanted.
3. Experimental techniques In order to confirm the above theory, some method is needed by which the dopant concentration can be measured along the fibre length. A variety of sophisticated techniques are available, however, we have used a relatively simple optical method whereby it is assumed that the fluorescence intensity from a particular section of sample is proportional to the pump light intensity the dopant concentration only. For this to he true, we also have to assume that the pump intensity is not so high as to give rise to saturation and other non-linear effects. Taking the case of a sample which is uniformly excited by some pump source, the above assumptions indicate that the spatial distribution of the fluorescence intensity across the sample gives a direct indication of the dopant distribution. When we wish to make direct comparisons between samples, where we have to measure the absolute fluorescence intensity to give some measure of the dopant concentration in each, then we have to guarantee (1) reproducibly identical illumination of each sample and (2) no change in the collection optics between measurements. This can be readily done if the samples consist of large ,
.
.
.
J.H. Sharp et al.
/ Dopant
incorporation in single-crystal fibre growth by LHMPG
slabs of material. However, as we shall see, the fibre geometry brings its own difficulties. We have overcome the first of these problems not, as one might initially expect, by using side pumping but by end coupling the pump light into the fibre. End pumping is preferable for two reasons; the coupling efficiency is independent of any variations in the fibre diameter, and the samples to be measured can be end-polished simultaneously to ensure the same optical quality, However, end pumping has its own difficulties since pump intensity is lost as it passes along the fibre due to material absorption and scatter from the fibre sidewalls. Hence the condition that all sections of the fibre receive equal illumination is not held. This can be compensated for if a measure is made of the pump intensity along the fibre length. Assuming that the loss per unit length (both absorption and scatter) is evenly distributed along the fibre, and the intensity of the scattered pump light is proportional only to the pump intensity in the fibre, we can measure the scattered pump intensity along the fibre length and infer from this the internal pump intensity. This will give some function, P(z), which indicates how the intensity of the pump varies along the sample. The fluorescence intensity, F(z), is then
also measured. The required concentration ratio, C~(~)/C50, in eq. (9) can then be calculated from: Cf(~)/C5()=A F(z)/P(z),
~
(11)
where A is a normalizing constant which has been chosen to make Cf(cc)/C50 tend to unity as the pullrate becomes very large. The experimental arrangement used to perform this measurement is shown in fig. 4. Each sample receives identical illumination by means of a 40 x microscope objective. This gives a spot size of approximately 5 ~m; comparing this to a mean sample diameter of 315 ±25 ~m, this implies that the experiment will be relatively insensitive to fibre positioning errors. Samples are placed in a glass capillary tube with an internal diameter of 500 j.~mwhich has been polished to give a half-section to facilitate reproducible positioning. This capillary is mounted on a 5-axis Photon Control micro-positioner which allows the initial alignment of a sample with the focusing optics to a high degree of accuracy. The light from the side of the fibre is collected by a polymer fibre optic cable which has a core diameter of approximately 500 ~m. The end of this cable is accurately positioned above the sample and
Ar LASER
~HECTEOME~
461
~ROS~PE
U~RcOIPUTERL
Fig. 4. Experimental arrangement to measure axial fluorescence and scattered pump light.
462
ii!. Sharp ci il. / Dopant incorporation
aligned to scan in a parallel fashion along the sample length at a constant distance from tiic sample. The other end of this cable is butted against the entrance slit of the Hilger-Watts D285 prism monochromator used to separate the pump and fluorescence signals. The signal was detected using a Hamamatsu R928 photomultiplier tube, the output of which was sent to a Bentham 223 lock-in amplifier. The output from the lock-in was sent, via a buffer, to the on board 8-hit analogue to digital converter of an Acorn Archimedes A310 computer. The computer was used to control the scan rate, step size and integration time for each reading.
4. Experimental results and discussion The single-crystal fibres grown for this investigation were prepared from initially undoped sapphire source rods cut to a length of 3 cm and ground into cylinders with diameters of 550 ~sm. These cylinders were coated with Ti metal using an evaporation technique. They were then heated to a temperature of 1350 K for a period of 24 h in order to oxidize the Ti coating to Ti 2O3. These source rods, with the dopant applied to the surface, were thought to he more susceptible to loss of dopant by “burn off” when the growth is being initiated. Since this method of preparation is quick and simple and can give long source rods it was felt important to study fibre growth from sources of this type. All samples were coated at the same time, four coats of Ti metal being applied to each rod. Fibres were grown under identical conditions with only the pull rate being varied. Table I lists the fibres grown and the growth rates. The fibre diameters varied slightly from sample to sample with a variance of slightly less than 8~% These fibres were grown with i reduction ratio (R : r) of 1.7: 1. in air with a melt aspect ratio of approximately one, giving the height of the melt in each case as 0.6 mm. Other conditions of growth were kept as stable as possible. In fig. 5, the axial fluorescence and pump scatter are shown for fibre E-28. As one might expect this shows an exponential drop in the
in single-crystal fibre growl/I hr LIIMPG
Table I Fibers grown and growth rates
Fibre name
Fibre growth rate (mm/nun) 0.5
[-29 [-25
.1) -
E28
25
_____________________________
—
scattered pump intensity and the corresponding tail off in the fluorescence scan towards the end of the fibre. One problem in analysing these data is that the z I) position is not well defined. =
Since the seed crystal and the grown fibre have similar diameters and polishing the fibre end removes some of the material, it is difficult to say exactly where the fibre began to grow. The error here is around ±1 mm in the worst possible case. Taking the data for each sample and dividing the fluorescence scans by the normalized pump scans, fig. 6 is obtained which shows the axial distribution of the Ti3~ions in the crystal fibre. It is assumed in all these that fluorescence is only due to the Ti3° ion and no other mechanism contributes to the detected signal. From figs. 2 and 6 it can he seen that there is good agreement between the theoretical and experimental results. This compares favourably to the results of Nightingale [10] where the model developed in that case was derived from simpler assumptions ---
—
—
--
/ \ (
-
/.~
~--
~
-
H -
-
( ~
L
L
.
~
-
-
-
-
-
-
- -
Fig. 5. Axial fluorescence (dashed line) and scattered pump light (solid line) from fibre [-28.
J.H. Sharp et al.
/
Dopant incorporation in single-crystalfibre growth by LHMPG
of the starting conditions and consequently failed to predict the rising tail of the dopant concentration at the start of growth seen in both the experimental results above and those of Nightingale. In fig. 6 the anticipated asymptotes of the curves are indicated at the right-hand side of the graph. These extrapolated values have an estimated error of ±5%.Since the total length of fibre which could be grown was limited by experimental constraints to 40 mm, it is seen in fig. 6 that the dopant concentration in the fibre has not quite reached equilibrium for the samples grown at rates greater than 1.5 mm/mm. An obvious improvement to this would be to extend the length of fibre which can be grown and make the asymptotic values of concentration easier to measure. The LHMPG growth system used for these studies is currently being modified to increase the possible fibre length to some tens of inches. Fig. 7 shows the ratio C~(cc)/C50 calculated from eq. (11) and plotted against the reciprocal of the growth rate. For this set of experimental conditions the normalizing constant, A, was set to 0.341 to give a concentration ratio of unity at 0. A straight line can be drawn through the points as predicted by eq. (9). The gradient of the line (least squares fit) is 2.34 (mm/minY’.2 With estik 0.21tofor [11], and V/rrr of 2.31 mated be Ti:sapphire 1.0 mm, we obtain a value mm for the evaporation time constant, i-, under =
=
20
C000OB
15
,,.
-O
-
‘1/
LL
463
-
4 2
--
pJ~ra~ Fig. 7. Reciprocal asymptotic values from fig. 6 versus reciprocal of growth rate.
these conditions. The good fit of the data to a straight line as shown in fig. 7 confirms the assumption that the segregation coefficient, k =
Cf/Cm, can be taken as constant. The only van-
able in this calculation which has to be estimated in any way is the melt volume. The actual shape of the melt can be calculated from the work of Fejer [12] with accuracy; however, the simplified melt shape used here is expected to give an error in the melt volume of approximately 5%. thecalculate, rate of evaporation of thebegins, melt, oneKnowing can now before growth what the equilibrium fractional concentration transferred to the fibre from the source rod in the growth of Ti : sapphire SCFs will be by the use of eq. (8). This implies that we can now determine the required doping level of the source rod to achieve the desired Ti3~concentration for laser applications. This information is also of great use since high levels of Ti in the melt can act to destabilize the molten zone shape and lead to pronounced growth instability [13]. Estimating the Ti concentration in the melt allows one to control growth conditions to ensure that doping levels are not so high as to lead to instability.
0000-26
1-—~ -2
~
20
30
6200-25 E511P-29 40
50
ROSflON/mm Fig. 6. Axial distribution of Ti3~ ions in fibres listed in table 1.
5. Conclusions The theoretical model of how dopant is incorporated into growing SCFs has been experimen-
464
J.H. Sharp ci a!.
/ Dopant
incorporation in single-crystal fibre growl/I by LHMPG
tally confirmed and has allowed the evaporation time constant of Ti from a sapphire melt to he estimated. Knowledge of this time constant gives the crystal grower much predictive power over the final concentration of dopant in the grown fibre and information on the axial distribution of this dopant
Acknowledgements We would like to acknowledge the support (.)f the SERC through the NLO initiative programme and also Barr & Stroud Ltd., UK, for additional financial support.
References [I] MM. Fejer, iL. Nightingale. GA. Magel and R.L. Byer, Rev. Sci. lnstr. 55 (1984)1791.
[21R.S.
Feigelsen. W.L. Kway and R.K. Route. Opt. Lng. 24 (1985) 1102. [31R.S. Feigelson, Mater. Sci. Eng. B 1(1988) 67. [41Ji- Yangyang, Zhao Shuqing, Huo Yujing, Zhang }longwu. Li Ming and Huang Chaoen. J. Crystal Growth 112 (1991) 283.
[51W.
Jia. L. Lu. B.M. Tissue and W.M. Yen. J. Crystal Growth 109 (1991) 329. [6] CA. Burrus and J. Stone. AppI. Phys. Letters 26 (1975) 318. [7] J. Stone and CA. Burrus. Fiber lntcgr. Opi. 2 (1979)19. [8] R.S.F. Chang, H. Hara, S. Chaddha, S. Sengupta and N. Djeu, IEEE Photon. Technol. Letters PTL-2 (1990) 695. [9] L.G. DcShazer, K.W. Kangas. R. Route and R.S. Feigelson, in: Infrared Optical Materials and Fibers V. SPIE Proc.. Vol. 843 (1987) p. 118. [10] J.L. Nightingale. The growth and optical applications of single-crystal fibres. PhD Thesis, Stanford University (1986) [11] A. Sanchez. A.J. Strauss. R.L. Aggarwal and RE. Fahey. IEEE J. Quantum Electron. QE-24 (1988) 995. [12] MM. Fejer, Single-crystal fibers: growth dynamics and . . . . non-linear optical interactions. PhD Thesis. Siantord University (1986). [13] J.H. Sharp, T.P.J. Han, B. 1-lenderson and R. lllingworth. to he published.
iou ~
North-Holland
CRYSTAL GROWTH
Dopant incorporation in single-crystal fibre growth by the laser-heated miniature pedestal growth technique J.H. Sharp
~,
T.P.J. Han, B. Henderson, R. Illingworth and I.S. Ruddock
Department of Physics and Applied Physics, Unicersity of Strathclyde, 107 Rottenrow, Glasgow G4 0NG, UK Received 23 October 1992; manuscript received in final form 7 March 1993
A theoretical model of single-crystal fibre growth by laser-heated miniature pedestal growth has been developed to account for the transfer of dopant from the source rod to the growing fibre. This model predicts the time evolution of the melt dopant concentration when the source rod dopant concentration is axially non-uniform. From this the axial distribution of dopant in the final grown fibre may be predicted. This model has been experimentally confirmed and an estimate of the evaporation time constant of Ti in the growth of Ti:Al,0 3 fibres made.
1. Introduction
in particular, laser materials. SCFs of ruby,
The laser-heated miniature pedestal growth (LHMPG) method, as developed by Byer et al. [11, is now a well established technique for the growth of single-crystal fibres (SCFs). As can be seen from fig. la, the technique involves the tip of a rod of source material, typically 0.5 mm in diameter, being heated by laser to melting point. A seed crystal, once dipped into the molten zone, is withdrawn at some rate faster than the source material is fed in. By conservation of melt volume, this leads to the crystalline fibre growing at some constant fraction of the source rod diameter. As in float zone growth, this is a crucible free growth method and can therefore produce highpurity, low-defect density single crystals [2]. The flexibility and advantages of the technique as a materials research tool have been amply demonstrated by Feigelson [31and are now recognized by research groups worldwide [4,5]. The main current application of miniature pedestal growth is in the development of novel optical and,
Nd : YAG, Tm : YLF and Ti sapphire with diameters ranging from 3 to 1000 ~m have been grown [6—91with laser action being demonstrated in all of these. These fibres have potential use in the development of miniature, possibly tunable, all solid-state lasers. For laser active crystals, a relatively large dopant concentration is required. This can present two problems when using LHMPG, both related to the transfer of dopant from the source material to the growing crystal. First of all, dopants with low segregation coefficients tend to accumulate in the melt (as in zone refining) and secondly, dopant may also be lost from the melt during growth as a result of evaporation. The ideal dopant, therefore, would have a near unity segregation coefficient and a relatively low vapour pressure. In real materials this is seldom the case and some method whereby we may predict how dopant properties will affect its distribution in the final fibre would indeed be useful. In this paper we discuss two materials which have many desirable properties which suggest them as candidates3~ forGa miniature tunable fibre laser sources, Cr 3Sc1A13O12 (GSAG),
Present address: School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, BNI 9QH, UK. 0022-0248/93/$06.OO © 1993
—
Elsevier Science Publishers B.V. All rights reserved
458
J. H. Sharp
et a!.
/ Dopant
Incorporation Ifl .stngle-crcvtalfibn’ growth
where the Cr has a near unity segregation coeffi3~:A1 cient, and Ti 203, in which the Ti has a relatively low segregation coefficient. We examinc how the dopant concentration in the melt evolves over time and hence the spatial distribution in the growing crystal, taking into consideration evaporation from the melt. This allows us to identify the correct conditions for the growth of laser quality crystals. First, we present a simple model of SCF growth by LHMPG and then discuss experimental results in light of this model,
2. Theoretical model In the following derivation the molten zone shape is approximated by a truncated cone of height, h, as indicated in fig. lb. Other parameters used are also indicated in this figure with C1 indicating the of dopant 3) concentration in region i, where I s, ions f, m(in units of cm representing the source rod, the growing fibre and the melt, respectively. The segregation coeffi=
—
hc !,HMPG
cient, k, is defined as C1/C~,where it is assumed that there is sufficient mixing by rapid diffusion and strong convection to give an homogeneous melt thereby allowing us to take k as constant. The diameter reduction ratio is defined as R/r and the melt volume as V. It is assumed that dopant is supplied to the melt solely from the incoming source rod and dopant loss is a result of evaporation from the surface of the melt and also as a result of dopants being taken up by the growing fibre. The evaporation may he characterized by an evaporation time constant, i-, defined as the time taken for C~,to decrease by a factor of e when the fibre and source rod are held stationary. i.e. at zero growth rate. If, in a time interval dt, the fibre grows by an amount dz and the source rod is fed into the melt by an amount dz(), there is a corresponding change, of dopant ions the melt VdC~1,in caused bythe (a) number the number. 71-RC~ dz,in supplied to the melt from the source rod. (h) the number, 7,-r2kC~d:, taken up by the growing
PULl, 1113FF
-~~~-~—-
—‘~-_
CO
~..J
(I~O~,
0-
.
MFI:I
H
~
~....
FEED~
C
(a)
~
SOUI3CE P01
.......,
0-
V
(C\ ..I/~,
(b)
Fig. I. (a) Laser-heated miniature pedestal growth. (h) Model of growth used in theoretical
deri~ation.
J.H. Sharp et al. / Dopant incorporation in single-crystal fibre growth by LHMPG
459
fibre and (c) the number, VCmT~ dt, lost from the melt by evaporation. Hence,
Substituting this expression for C, into eq. (2) we arrive at the following expression for the dopant
dztj—~r2kCmdz V dC~=~rR2C~
concentration in theaC melt ~ during growth: Cm(t) Ca e~t+ —~---(1 e_$t)
—
~Cm dt. T (1)
Noting that, by conservation of mass in the melt for steady state growth, ~R2 dz 2dz, and 0 pull i~rr rate, we that dz dt, where r’ is the fibre may define the following parameters: =
a
=
1~
irr2r’/V,
=
ak
+
1/i-,
=
(2)
—
Ideally, the dopant concentration in the source rod should be uniform. However, some time is required to align the focus of the CO2 laser and the ends of the source rod and seed crystal. Optimizing the laser power and other growth parameters before commencing growth results in the end of the source rod being at, or near, melting point for a number of minutes. This allows loss of the dopant from the source rod to occur by evaporation from the surface. This may be represented as a spatial dependence of the dopant concentration along the source rod length, with the initial concentration being C~1 when growth commences at time, t 0 and the equilibrium value of the concentration being C50, as =
—
a(C~ t e~~) f3 1 C~0)(e~’
+
(5)
—
— —
=
~‘
and recast eq. (1) as: dCm/dt aC~ 13Cm.
-*
=
.
.
Recasting this equation in terms of the fractional concentratton in the fibre with respect to the asymptotic source concentration and expressing in terms of v and z, we obtain Cf(z) C. 0
=
k C’ e~~”+ ~(1
—
13 a(C’ +
~
—
—
1)
-
(e
~,
-
yz/o
e
—
13z/o)
(6)
,
where C’ is the fractional loss of dopant from the source rod at z 0 due to evaporation and is given by C’ C ./C (7 =
=
Si
sO~
Taking z to obtain the equilibrium concentration in the growing fibre, we have: —~
k a/13. (8) Substituting our definitions of a and 13 we arrive at C~(~)/Cs0 =
00~
We can represent the concentration in the source rod as C5(z)
C~0+ (C~1 C~0)e_2/L,
C~0
(3)
where
where L is some characteristic length not usually susceptible to measurement. Assuming that once growth commences, the source rod is fed continuously into the laser focus and that evaporation from the rod is negligible compared to that from the melt, we define the constant y as,
1= ~
=
=
—
/
‘
and so express C5(t) during growth as: t. C5(t) C~0+ (C~1 C~0)e~’ =
—
(4)
F 1
Cf(c~) —i =
1
+
(9)
~,
(10)
Thus, by plotting [Ct(x)/C~0]~ against i.’~ we have a straight line whose gradient is given by F/i-. Since F can be calculated from the known quantities in (10) the characteristic evaporation time constant can be found. From the above we can now predict the general features to be expected during fibre growth. ~,
Figs. 2 and 3 show the ratio [C~(z)/C~0], as length of fibre when z as 0a atfunction t 0 for expressed in eq.grown (6), plotted of =
=
46(1
i.H. Sharp ci a!.
/ Dopant
incorporation in single-crystal fibre growl/I hr /.HMPG
L
-
fig
=
// /
/
_____________________________
--.
(-HA TON AL ~\( Fig. 2. Predicted fraction of dopani transferred troni the source rod io the fibre with 4 = 0.21. Solid curves U. = (1.1 mm): dashed curves (I. = 5.0 mm) with fibre growih rate: (A) 2.5 mm/mm and (B) 0.5 mm/mm.
•
.
.
various values ot growth rate r’ and different segregation coefficients, k. The other parameters (such as fibre radius and reduction ratio) used in eq. (6) have been chosen to accurately model the actual growth conditions of the fibres used in the later experimental investigations. The parameter C has been chosen to be 0.1 and the evaporation time constant to be T 2.3 mm. For each curve there is an initial sharp rise which, as one can see from the figures, is strongly dependent on the depletion length. L. The final =
and . ____________________
/
- .
// - 1~
_________
________
/ .v~
-
equilibrium level is principally dependent on the fibre pull rate, v; a faster pull rate implies that the loss from the melt due to incorporation into the fibre compared to loss by evaporation is much higher hence giving dopant atoms less time in the melt to he lost from the surface. We notice from ~ that when k is of thc ordcr of unity thc equilibrium concentration is higher in each case when compared to fig. 2 where k 0.21. This results from there being less accumulation of dopant in the melt for the case of higher k and so the evaporation, which is proportional to is reduced. It is also true that as k increases so the transient rise to equilibrium becomes shorter. For laser applications, a uniform gain medium is desirable and so one would cut off and discard this transient. This is in contrast to zone refining,
-
-~ -
-
-
-ONAL~:H.-~ I HH.~--i-~ Fig. 3. Predicted fraction of dopant transferred from the -. . . . source rod to the fibre with k = 0.90. Solid curves (L = 0.1 mm): dashed curves (L = 5.0 mm) with fibre growth rate- (A) 2.5 mm/mm and (B) 0.5 mm/mm.
which also relies on localized melting, where only the “purified” section of crystal is wanted.
3. Experimental techniques In order to confirm the above theory, some method is needed by which the dopant concentration can be measured along the fibre length. A variety of sophisticated techniques are available, however, we have used a relatively simple optical method whereby it is assumed that the fluorescence intensity from a particular section of sample is proportional to the pump light intensity the dopant concentration only. For this to he true, we also have to assume that the pump intensity is not so high as to give rise to saturation and other non-linear effects. Taking the case of a sample which is uniformly excited by some pump source, the above assumptions indicate that the spatial distribution of the fluorescence intensity across the sample gives a direct indication of the dopant distribution. When we wish to make direct comparisons between samples, where we have to measure the absolute fluorescence intensity to give some measure of the dopant concentration in each, then we have to guarantee (1) reproducibly identical illumination of each sample and (2) no change in the collection optics between measurements. This can be readily done if the samples consist of large ,
.
.
.
J.H. Sharp et al.
/ Dopant
incorporation in single-crystal fibre growth by LHMPG
slabs of material. However, as we shall see, the fibre geometry brings its own difficulties. We have overcome the first of these problems not, as one might initially expect, by using side pumping but by end coupling the pump light into the fibre. End pumping is preferable for two reasons; the coupling efficiency is independent of any variations in the fibre diameter, and the samples to be measured can be end-polished simultaneously to ensure the same optical quality, However, end pumping has its own difficulties since pump intensity is lost as it passes along the fibre due to material absorption and scatter from the fibre sidewalls. Hence the condition that all sections of the fibre receive equal illumination is not held. This can be compensated for if a measure is made of the pump intensity along the fibre length. Assuming that the loss per unit length (both absorption and scatter) is evenly distributed along the fibre, and the intensity of the scattered pump light is proportional only to the pump intensity in the fibre, we can measure the scattered pump intensity along the fibre length and infer from this the internal pump intensity. This will give some function, P(z), which indicates how the intensity of the pump varies along the sample. The fluorescence intensity, F(z), is then
also measured. The required concentration ratio, C~(~)/C50, in eq. (9) can then be calculated from: Cf(~)/C5()=A F(z)/P(z),
~
(11)
where A is a normalizing constant which has been chosen to make Cf(cc)/C50 tend to unity as the pullrate becomes very large. The experimental arrangement used to perform this measurement is shown in fig. 4. Each sample receives identical illumination by means of a 40 x microscope objective. This gives a spot size of approximately 5 ~m; comparing this to a mean sample diameter of 315 ±25 ~m, this implies that the experiment will be relatively insensitive to fibre positioning errors. Samples are placed in a glass capillary tube with an internal diameter of 500 j.~mwhich has been polished to give a half-section to facilitate reproducible positioning. This capillary is mounted on a 5-axis Photon Control micro-positioner which allows the initial alignment of a sample with the focusing optics to a high degree of accuracy. The light from the side of the fibre is collected by a polymer fibre optic cable which has a core diameter of approximately 500 ~m. The end of this cable is accurately positioned above the sample and
Ar LASER
~HECTEOME~
461
~ROS~PE
U~RcOIPUTERL
Fig. 4. Experimental arrangement to measure axial fluorescence and scattered pump light.
462
ii!. Sharp ci il. / Dopant incorporation
aligned to scan in a parallel fashion along the sample length at a constant distance from tiic sample. The other end of this cable is butted against the entrance slit of the Hilger-Watts D285 prism monochromator used to separate the pump and fluorescence signals. The signal was detected using a Hamamatsu R928 photomultiplier tube, the output of which was sent to a Bentham 223 lock-in amplifier. The output from the lock-in was sent, via a buffer, to the on board 8-hit analogue to digital converter of an Acorn Archimedes A310 computer. The computer was used to control the scan rate, step size and integration time for each reading.
4. Experimental results and discussion The single-crystal fibres grown for this investigation were prepared from initially undoped sapphire source rods cut to a length of 3 cm and ground into cylinders with diameters of 550 ~sm. These cylinders were coated with Ti metal using an evaporation technique. They were then heated to a temperature of 1350 K for a period of 24 h in order to oxidize the Ti coating to Ti 2O3. These source rods, with the dopant applied to the surface, were thought to he more susceptible to loss of dopant by “burn off” when the growth is being initiated. Since this method of preparation is quick and simple and can give long source rods it was felt important to study fibre growth from sources of this type. All samples were coated at the same time, four coats of Ti metal being applied to each rod. Fibres were grown under identical conditions with only the pull rate being varied. Table I lists the fibres grown and the growth rates. The fibre diameters varied slightly from sample to sample with a variance of slightly less than 8~% These fibres were grown with i reduction ratio (R : r) of 1.7: 1. in air with a melt aspect ratio of approximately one, giving the height of the melt in each case as 0.6 mm. Other conditions of growth were kept as stable as possible. In fig. 5, the axial fluorescence and pump scatter are shown for fibre E-28. As one might expect this shows an exponential drop in the
in single-crystal fibre growl/I hr LIIMPG
Table I Fibers grown and growth rates
Fibre name
Fibre growth rate (mm/nun) 0.5
[-29 [-25
.1) -
E28
25
_____________________________
—
scattered pump intensity and the corresponding tail off in the fluorescence scan towards the end of the fibre. One problem in analysing these data is that the z I) position is not well defined. =
Since the seed crystal and the grown fibre have similar diameters and polishing the fibre end removes some of the material, it is difficult to say exactly where the fibre began to grow. The error here is around ±1 mm in the worst possible case. Taking the data for each sample and dividing the fluorescence scans by the normalized pump scans, fig. 6 is obtained which shows the axial distribution of the Ti3~ions in the crystal fibre. It is assumed in all these that fluorescence is only due to the Ti3° ion and no other mechanism contributes to the detected signal. From figs. 2 and 6 it can he seen that there is good agreement between the theoretical and experimental results. This compares favourably to the results of Nightingale [10] where the model developed in that case was derived from simpler assumptions ---
—
—
--
/ \ (
-
/.~
~--
~
-
H -
-
( ~
L
L
.
~
-
-
-
-
-
-
- -
Fig. 5. Axial fluorescence (dashed line) and scattered pump light (solid line) from fibre [-28.
J.H. Sharp et al.
/
Dopant incorporation in single-crystalfibre growth by LHMPG
of the starting conditions and consequently failed to predict the rising tail of the dopant concentration at the start of growth seen in both the experimental results above and those of Nightingale. In fig. 6 the anticipated asymptotes of the curves are indicated at the right-hand side of the graph. These extrapolated values have an estimated error of ±5%.Since the total length of fibre which could be grown was limited by experimental constraints to 40 mm, it is seen in fig. 6 that the dopant concentration in the fibre has not quite reached equilibrium for the samples grown at rates greater than 1.5 mm/mm. An obvious improvement to this would be to extend the length of fibre which can be grown and make the asymptotic values of concentration easier to measure. The LHMPG growth system used for these studies is currently being modified to increase the possible fibre length to some tens of inches. Fig. 7 shows the ratio C~(cc)/C50 calculated from eq. (11) and plotted against the reciprocal of the growth rate. For this set of experimental conditions the normalizing constant, A, was set to 0.341 to give a concentration ratio of unity at 0. A straight line can be drawn through the points as predicted by eq. (9). The gradient of the line (least squares fit) is 2.34 (mm/minY’.2 With estik 0.21tofor [11], and V/rrr of 2.31 mated be Ti:sapphire 1.0 mm, we obtain a value mm for the evaporation time constant, i-, under =
=
20
C000OB
15
,,.
-O
-
‘1/
LL
463
-
4 2
--
pJ~ra~ Fig. 7. Reciprocal asymptotic values from fig. 6 versus reciprocal of growth rate.
these conditions. The good fit of the data to a straight line as shown in fig. 7 confirms the assumption that the segregation coefficient, k =
Cf/Cm, can be taken as constant. The only van-
able in this calculation which has to be estimated in any way is the melt volume. The actual shape of the melt can be calculated from the work of Fejer [12] with accuracy; however, the simplified melt shape used here is expected to give an error in the melt volume of approximately 5%. thecalculate, rate of evaporation of thebegins, melt, oneKnowing can now before growth what the equilibrium fractional concentration transferred to the fibre from the source rod in the growth of Ti : sapphire SCFs will be by the use of eq. (8). This implies that we can now determine the required doping level of the source rod to achieve the desired Ti3~concentration for laser applications. This information is also of great use since high levels of Ti in the melt can act to destabilize the molten zone shape and lead to pronounced growth instability [13]. Estimating the Ti concentration in the melt allows one to control growth conditions to ensure that doping levels are not so high as to lead to instability.
0000-26
1-—~ -2
~
20
30
6200-25 E511P-29 40
50
ROSflON/mm Fig. 6. Axial distribution of Ti3~ ions in fibres listed in table 1.
5. Conclusions The theoretical model of how dopant is incorporated into growing SCFs has been experimen-
464
J.H. Sharp ci a!.
/ Dopant
incorporation in single-crystal fibre growl/I by LHMPG
tally confirmed and has allowed the evaporation time constant of Ti from a sapphire melt to he estimated. Knowledge of this time constant gives the crystal grower much predictive power over the final concentration of dopant in the grown fibre and information on the axial distribution of this dopant
Acknowledgements We would like to acknowledge the support (.)f the SERC through the NLO initiative programme and also Barr & Stroud Ltd., UK, for additional financial support.
References [I] MM. Fejer, iL. Nightingale. GA. Magel and R.L. Byer, Rev. Sci. lnstr. 55 (1984)1791.
[21R.S.
Feigelsen. W.L. Kway and R.K. Route. Opt. Lng. 24 (1985) 1102. [31R.S. Feigelson, Mater. Sci. Eng. B 1(1988) 67. [41Ji- Yangyang, Zhao Shuqing, Huo Yujing, Zhang }longwu. Li Ming and Huang Chaoen. J. Crystal Growth 112 (1991) 283.
[51W.
Jia. L. Lu. B.M. Tissue and W.M. Yen. J. Crystal Growth 109 (1991) 329. [6] CA. Burrus and J. Stone. AppI. Phys. Letters 26 (1975) 318. [7] J. Stone and CA. Burrus. Fiber lntcgr. Opi. 2 (1979)19. [8] R.S.F. Chang, H. Hara, S. Chaddha, S. Sengupta and N. Djeu, IEEE Photon. Technol. Letters PTL-2 (1990) 695. [9] L.G. DcShazer, K.W. Kangas. R. Route and R.S. Feigelson, in: Infrared Optical Materials and Fibers V. SPIE Proc.. Vol. 843 (1987) p. 118. [10] J.L. Nightingale. The growth and optical applications of single-crystal fibres. PhD Thesis, Stanford University (1986) [11] A. Sanchez. A.J. Strauss. R.L. Aggarwal and RE. Fahey. IEEE J. Quantum Electron. QE-24 (1988) 995. [12] MM. Fejer, Single-crystal fibers: growth dynamics and . . . . non-linear optical interactions. PhD Thesis. Siantord University (1986). [13] J.H. Sharp, T.P.J. Han, B. 1-lenderson and R. lllingworth. to he published.