A diffusion technique for producing an inside-maximum distribution of refractive index in glass plates

Volume 52, number 1

OPTICS COMMUNICATIONS

1 November 1984

A DIFFUSION TECHNIQUE FOR PRODUCING AN INSIDE-MAXIMUM DISTRIBUTION OF REFRACTIVE INDEX IN GLASS PLATES T. KANEKO Research Laboratory, Nippon Kogaku K.K., Tokyo 140, Japan Received 10 April 1984

A field-assisted diffusion technique is described for making inside-maximumindex distributions in Na+-containing glass plates. The glass after treatment consists of three different compositions: ion-depleted layer (low index) in the vicinity of the surface, Ag+-penetrated region (high index) and normal region (low index). Some comments on the control of the process axe also included.

1. Introduction

2.2. Diffusion source

In recent years ionic diffusion has been extensively studied for making optical waveguides in glass plates [ 1-25 ]. In particular, two-step diffusion of high- and low-index cations (e.g. Ag+ , Na+) under electric control has been successful in the fabrication of buried waveguides which have inside-maximum index distributions [2,12,15,21,25 ]. However, the technique is limited in usefulness, since diffusing cations are supplied from molten salts (e.g. AgNO 3 , NaNO3); for instance, the withdrawal and cleaning of the substrate from the melt supplying high-index cations will intermit the process and cause rather uncontrolled cooling of the substrate. Here, a simpler, solid-state method based on one-step field-assisted diffusion is proposed.

Diffusion source is a solid silver film deposited chemically or physically (vacuum evaporation) on the glass surface. Ag+ ions are to be dissociated from the film and diffuse-in to increase the refractive index o f the glass.

2.3. Electrodes [26-28] Graphite (Aquadag, Acheson Colloids Co.) is coated as non-reacting electrodes on both surfaces of the Ag-coated glass and dried at a temperature below 50°C. Other materials such as Ag, Cu, T1, Au, AI are unsuitable, mainly because they are liable to react with glass or electromigrate along the glass surface. Graphite electrodes can be very easily removed with hand or with hot water after diffusion treatment.

2. Description of experimental procedure

2.4. Diffusion conditions

2.1. Glass sample

Temperature: 180-240°C. Applied voltage: <~200 V. Preheating time: >~ 10 minutes. Atmosphere: in air. When treated at temperatures above 240°C, glass samples are liable to be tinted yellowish owing to thermal reduction of Ag+. When a de voltage more than 200 V is applied, the graphite anode tends to slightly react with the glass.

Composition (wt%): SiO 2 71, Na20 15, ZnO 5, PbO 3, A1203 2, others 4. Refractive index: 1.5141.515. Glass transition temperature: 474°C. Density: 2.59 g/cm 3 . Dimensions: 33 mm in diameter, 1.2 mm in thickness.

0 030-4018/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

17

Volume 52, number 1

OPTICS COMMUNICATIONS

I I

g ~ [ recorder~

[.//.~/.//////'y/~-------4~ ~

I

~

I ~~-----~ I. |l

- ~

1 November 1984

electric source ~

graphite silverfilm [ glass volt-meter graphite electricfurnace

® Fig. 1. ExperirnentM setup ~ r making an inside-maximum index di~ribution m a Na+¢ontainmg #ass plate ~: current).

2.5. Principle of the diffusion process [29] An inside-maximum index distribution is formed in glass according to the set-up shown in fig. 1 [26]. Fig. 2 shows a time characteristic o f current. The decrease o f current after the time t o results from the depletion o f A g + and Na + ions in the vicinity o f the anode surface. The ion-depleted region has a vitreous silica-like structure and therefore displays a lower index compared to untreated glass [28]. After

the silver film has become depleted, the graphite anode film is almost only electrostatically attracted (though the attracting force appears to be pretty large) to the glass surface. Therefore, the sample should be pressed under a load o f 100 to 400 grams during the treatment. I (arbitrary

units)

z (t.m) 5

10

15

surface(?) 0

to

Fig. 2. Current-time characteristic during the field-assisted Ag+ diffusion process (to: time when a silver film becomes depleted from the anode). 18

Fig. 3. Depth distribution of silver from electron-microprobing (I: silver concentration, z: depth, diffusion source: silver film deposited chemically, diffusion conditions: temperature 230°C, applied voltage 45 V, t o 2418 s, total time 4203 s, current (0 < t < t o) 2.1 mA, totally transported charge 6.40 C).

Volume 52, number 1

OPTICS COMMUNICATIONS

1 November 1984

tinct interference curves in visible reflection spectra. Fig. 4 shows a relation between optical path lengths fd(t) n dz and total charges q(t) transported through the samples. Here n is the refractive index of a reflecthag layer, d(t) the thickness of the layer and z depth from the anode-side surface of glass. We can confLrm from the figure the existence of two optical interfaces in glass the surface of which Ag+ is depleted from. On the other hand, no interference curve was obtained from cathode-side surfaces of treated samples. This suggests that Na+ ions are not piled up in the vicinity of the cathode-side surface.

3. Results and discussion

3.1. Visible reflection spectra Fig. 3 shows an electron microprobe profile of silver beneath the anode-side surface of a treated sample (Hitachi SEM X 560-Kevex 5100). An absence of silver and sodium at the anode-side surface was confirmed, respectively, by an ESCA spectrometer (YHP 5950A) and by an XRF spectrometer (Rigaku 3063). Both interfaces of Ag+-containing region/Na + only-containing region and ion-depleted layer/Ag+-containing region have steep changes in Ag+ concentration. These steep changes display dis-

® J

10

m._ v

%.

×

0

i

i

i

I

i

I

1

2

3

4

5

6

q(t)

(c)

Fig. 4. Relation between Sdo(t)n dz and q (t) (at 230°C), • silver film is undepleted (45 V), o silver f'fimis undepleted (90 V), × silver film is depleted (45 V), ~ silver f'dmwas not coated (45 V). 19

Volume 52, number 1

OPTICS COMMUNICATIONS

1 November 1984

3.2. Infrared reflection spectra

3.3. Control o f the process

The similarity between the ion-depleted region of a treated glass and vitreous silica is substantiated by the ir reflection spectra shown in fig. 5 (Hitachi Infrared Spectrometer 285). The spectrum for the depleted surface shows a shift in the S i - O - S i vibrational mode toward the value observed for fused silica (X ~ 9 tzrn). On the other hand, the spectrum for the cathode-side surface shows the same spectrum as untreated glass.

3.3.1. Current-voltage characteristics for 0 < t < t o All the current-time characteristics observed took the same profdes as that depicted in fig. 2. For every sample, current became constant (= i0) within several seconds. Fig. 6 shows a current (i0)-applied voltage (V) characteristic for a sample. The linearity of i 0 - V seen in the figure can be interpreted as follows. The total charge q transported through a sample from t = 0 to t = t ( < t o ) is connected with the total amount M of

9O

fused silica

80

70

6O

5O [-~ H

>

40

surface

•••,depleted

E~ 0

~

cathode-side surface normal glass

30

20

//

10

tt

ft

0

' undepleted s u r f a c e

i

!

I

I

i

7

8

9

10

11

I

I

I

I

12 13 1415

l

I

20

25

(rm) Fig. 5. Infrared reflection spectra for fused silica and depleted (anode-side), cathode-side, and normal surfaces of sample glass (a spectrum of Ag+-undepleted surface is included for comparison). 20

Volume 52, number 1

OPTICS COMMUNICATIONS

1 November 1984

scattering in temperature, sample thickness, penetration area of Ag+ and electrode resistivity; the higher the temperature, the larger the scattering. Let us estimate a variation in i 0 due to a variation AT in temperature T. According to the diffusion theory,

i,(mA)

D =D O exp(-E/RT), at

200"C

1 e

f3=eD/fkT.

Here D is diffusion constant (cm 2 s - l ) , D O preexponential factor (cm 2 s - l ) , E activation energy (kcal m o l e - l ) , R gas constant (=1.986 X 10 -3 kcal mole -1 K -1), f correlation factor (1), k Boltzmann constant (= 1.38 × 10 -23 joule K - 1 ) and T absolute temperature (K). From eqs. (3) and (4) we have

io(T + AT) = i o ( T ) [1 + ( A T / T ) ( E / R T -

0

,,

0

,,

I,

,

,

50

~PmED

,

l,

,,

IO0

VOLTA6E

,I

1)].

,

150

(V)

3.3.2. q - M relation Eq. (1) can be rewritten as q - 0 . 8 9 2 ( A g ÷)

fort
(6)

where (Ag +) is the total weight (mg) o f Ag+ ions contained in a treated sample. Eq. (6) is substantiated from the data shown in table 1 (see fig. 7). Fig. 4 also suggests the linearity o f q - M .

Ag+ penetrated per unit cross-sectional area by the relation t

(1)

Here e is unit charge (=1.60 X 10 -19 C) andA the penetration area o f Ag÷. According tO the diffusion theory,M is given by

3.3.3. Relation between film thickness (dr) and equivalent diffusion thickness {dD) The number n o f Ag+ ions contained in a silver film per unit cross-sectional area is given by

M - C O~Ft = C O(3Vt/d 0 ,

n = oclfN] 108,

(2)

where C O is the surface concentration of Ag+, 13the mobility of Ag+, F a dc electric field (= V/do) and d O the sample thickness. From eqs. (1) and (2) we have i 0 = dq/dt - eACo~JV[d 0 c~ V .

(5)

I f E = 20 kcal mole -1 , T = 473 K and AT = 1 K, then i 0 (T + AT) -- 1.043i 0 (T). Thus, a small variation in T causes a pretty large variation in i 0 . Therefore, the diffusion process should be controlled on the basis of a constant applied current (t0) rather than a constant applied voltage (I1).

Fig. 6. Current-applied voltage characteristic (t < t 0) observed for a sample.

q - f i0 d t - e A M . 0

(4)

(3)

From this and fig. 6 we get ~3= 1.13 X 10 -2/~m2/s V (at 200°C), where the values o f A = 8.03 cm 2 and C O = 7.34 X 1021 cm -3 are taken. However, some scattering in i 0 values was seen among treated 167 samples, probably due to some

(7)

Table 1 Data for checking eq. (1) (T: 230°C) Sample

V(V)

i 0 (mA)

q ((2)

Ag÷(mg) a)

1 2

23 45

0.74 1.725

3.33 6.21

4.0 7.2

3

45

1.725

7.24

8.1

a) From a chemical analysis. 21 ¸

Volume 52, number 1

OPTICS COMMUNICATIONS

1 November 1984 a

q (c)

c ~

silver fi!m~ 0.16

rm

0.32

fm

glass

(A) before treated c

a

b

i

i

t

i

, , l

0

•

I

0

I

1

I

2

&

I

I

I

6

I

glass

l

I

8

(Ag+) (mg) (B) after treated

Fig. 7. q (t < to)-M relation, solid line: calculated from eq. (6).

where p is f'flm density and N Avogadro's number (=6.023 X 1023 m o l e - I ) . If we approximate that the Ag + concentration profile in a treated sample takes a step function-like shape with width dD, then M = C0 dD

(C0 : concentration o f Ag +) ,

(8)

which equals n after the film has become depleted. From eqs. (7) and (8) we have

dD= (oN/108) d f / C 0

.

(9)

F o r instance, i f d f = 1.25pro, G 0 = 7.34 X 1021 cm - 3 and O = 10.5 g cm - 3 (density o f bulk silver), then we have d D = 1 0 / a n . Silver film was step-wise deposited on a glass sample, as shown in fig. 8A. Then, the sample was diffusion-treated under the conditions o f 240°C, 90 V and 1 hr. ( i 0 : 5 . 0 mA, final current: 0.1 mA.) Optical path differences produced between Ag+-penetrated regions (a, b) and Ag+-not penetrated region (c) were +0.30 tan ( a - c ) and +0.I 5/am ( b - c ) . I f d D ( a ) and dD(b ) are estimated to be, respectively, 2.6/am and 1.3/am on the basis o f eq. (9), then the index increase o f the glass produced by the Ag + penetration is about 0.11. This value is in good agreement with the value 0.10 reported in [19]. 22

Fig. 8. Film-glass sample for measuring optical path Increases due to Ag+ penetration.

References [1] W.G. French and A.D. Pearson, Ceram. Bull 49 (1970) 974. [2] T. lzawa and H. Nakagome, Appl. Phys. Lett. 21 (1972) 584. [3] T.G. Giallorenzi, E.J. West, R. Kirk, R. Ginther and R.A. Andrews, Appl. Opt. 12 (1973) 1240. [4] A. Gedeon, Appl. Phys. 6 (1975) 223. [5] G. Stewart, C.A. Millar, P.J.R. Laybourn, C.D.W. Wilkinson and R.M. De La Rue, IEEE J. Quantum Electron. QE-13 (1977) 192. [6] G.H. Chartier, P. Jaussaud, A.D. de Oliveira and O. Parriaux, Electron. Lett. 14 (1978) 132. [7] G. Stewart and P.J.R. Laybourn, IEEE J. Quantum Electron. QE-14 (1978) 930. [8] G.L. Tangonan, L.E. Gorre and D.L. Persechini, Optics Comm. 27 (1978) 358. [9] A.A. Zlenko, N.M. Lyndin, V.A. Sychugov, A.V. Tishchenko and G.P. Shipulo, Sov. J. Quantum Electron. 9 (1979) 611. [10] A. Guez, P.C. Jaussaud and G.H. Chartier, Rev. Phys. Appl. 14 (1979) 847. [ 1 I] V. Neuman, O. Parriaux and L.M. Walpita, Electron. Lett. 15 (1979) 704. [12] G. Chartier, P. Collier, A. Guez, P. Jaussaud and Y. Won, Appl. Opt. 19 (1980) 1092.

Volume 52, number 1

OPTICS C O M M U N I C A T I O N S

[ 13 ] V. Neuman, O. Parriaux, C.W. Pitt, A.A. Stride and L.M. Walpita, Proc. Electro-Optics Laser Int. Conf. 1980, Brighton, England 19. [ 14] C.W. Pitt, A.A. Stride and R.I. Trigle, Electron. Lett. 16 (1980) 701. [15 ] H.-J. Lilienhof, K.F. Heidemann, D. Ritter and E. Voges, Optics Comm. 35 (1980) 49. [16] G.T. Petrovskii, K.A. Agafonova, A.V. Mishin and N.V. Nikonorov, Fiz. Khim. Stekla 7 (1981) 98. [ 17] G.T. Petrovskii, K.A. Agafonova and A.V. Mishin, Soy. Tech. Phys. Lett. 7 (1981) 394. [18] G.T. Petrovskii, K.A. Agafonova, A.V. Mishin and N.V. Nikonorov, Soy. I. Quantum Electron. 11 (1981) 1387.

[19] G.H. Chartier, J.L. Coutaz, A. Girod, P. Jaussaud and O. Parrlaux, J. Non-Crystalline Solids 47 (1982) 259. [20] V. Hinkov, Wave Electronics 4 (1982) 147. [21] H.-J. Lilienhof, E. Voges, D. Ritter and B. Pantschew, IEEE ]. Quantum Electron. QE-18 (1982) 1877.

1 November 1984

[22] R.G. Walker and C.D.W. Wilkinson, Appl. Opt. 22 (1983) 1029. [23] R.G. Walker, C.D.W. Wilkinson and J.A.H. Wilkinson, Appl. Opt. 22 (1983) 1923. [24] R.G. Walker and C.D.W. Wilkinson, Appl. Opt. 22 (1983) 1929. [25] G.L. Tangonan and H.-W. Yen, 4th Topical Meeting on Gradient-Index Optical Imaging Systems 1983, Kobe, Japan 148. [26] A.J.C. Hall and J.G. Hayes, Interstitial patterns (Defence Standards Laboratories Technical Note 50), Australian Defence Scientific Service, Victoria, 1958. [27] D.E. Carlson, J. Am. Ceram. Soc. 57 (1974) 291. [28] D.E. Carlson, K.W. Hang and G.F. Stockdale, J. Am. Ceram. Soc. 57 (1974) 295. [29] T. Kaneko and H. Yamamoto, referred to in Proc. 10th Intern. Congr. Glass 1974, Kyoto, Japan 15-84.

23