Experimental study of
Cu1–Na1 exchanged glass waveguides
H. Marquez, D. Salazar, A. Villalobos, G. Paez, and J. Ma. Rincon
Optical waveguides have been obtained by ﬁeld-assisted Cu1–Na1 exchanged on glass. The refractive
index proﬁles of the waveguides are determined by means of the prism-coupling technique and Chiang’s
method 3J. Lightwave Technol. LT-3, 385 1198524, and they correlate with the index proﬁle calculated as a
function of the glass composition. The composition proﬁle is examined with the aid of a scanning
electron microscopy with energy-dispersive x-ray analysis, and the diffusion process is explained by the
one-dimensional diffusion equation.
1. Introduction to ensure good electrical contact and to prevent
The ion-exchange technique has been considered as oxidation and ﬂaking of the copper during the diffu-
an important method for producing high-quality sion process, a 0.5-µm gold ﬁlm was deposited on top
graded refractive index optical waveguides in glass of the copper ﬁlms, and similarly on the backsurface
substrates. Passive integrated optical devices pro- of the substrate. This structure served as the anode
duced by this technique show potential for low produc- and cathode. An Edwards evaporator with a work-
tion cost, immunity to optical damage, and low losses ing pressure of 1025 Torr was used, and ultrapure
for propagation and coupling with commercial ﬁber 199.99% Alfa-Aesar2 Au and Cu starting materials
interfacing.1–3 Ion-exchange glass waveguides are were evaporated from tungsten boats. The ﬁlm thick-
typically fabricated with molten salts as ion sources. nesses were measured by the method of multiple-
In the case of electric-ﬁeld-assisted diffusion, silver beam interference.
ﬁlms are used extensively as ion sources. This solid- The diffusion was carried out at 350 °C in a Ther-
state ion exchange technique has been used by sev- molyne furnace. The electric current ﬂow was moni-
eral groups.4 In contrast, in the case of diffusion of tored during the diffusion process by the use of a
copper ions in glass substrates, only a limited amount digital multimeter in series with the voltage source.
of information has been published.5–9 We present A scanning electron microscope with energy-disper-
experimental results concerning the refractive index sive x-ray analysis 1SEM@EDX2 was used for microana-
proﬁle and diffusion process of planar waveguides lytical characterization. Specimens coated by a thin
obtained by copper ﬁlm diffusion. sputtered Au layer were prepared for SEM@EDX
measurements by the use of a Zeiss Model DSM-
2. Experimental 950@Tracor-Northern Series II instrument with a
Initially, a copper ﬁlm of approximately 1-µm thick- conﬁguration working at 20 kV. An automatic prism-
ness was deposited on a soda-lime glass substrate by coupling system, Metricon Model 2010, was used for
the use of a thermal evaporation system. As a way the optical characterization of the waveguides.
3. Results and Discussion
H. Marquez, D. Salazar, A. Villalobos, and G. Paez are with the
Departamento de Optica, Centro de Investigacion Cientiﬁca y de A. Refractive Index Change by Ion Substitution
Educacion Superior de Ensenada, Km. 107, Tijuana-Ensenada, In the binary ion-exchange process Cu1 = Na1, both
Apartado Postal 2732, Ensenada Baja California, Mexico. J. Ma. cations that exchange with each other are network
Rincon is with the Departamento de Ciencias de los Materiales,
modiﬁers. The ionic radius of the Cu1 is 0.96 Å,
Instituto de Ciencias-Eduardo Torroja, Serrano Galvache s@n,
28033 Madrid, Spain.
which is similar to the ionic radius of the Na1 of
Received 16 September 1994; revised manuscript received 17 0.95 Å.10,11 As a result, the basic structure of the
March 1995. glass is left unchanged and only the refractive index
0003-6935@95@255817-06$06.00@0. of the glass is modiﬁed. The change in refractive
r 1995 Optical Society of America. index is taken to be proportional to the concentration
1 September 1995 @ Vol. 34, No. 25 @ APPLIED OPTICS 5817
of dopant ions introduced in the glass. The net Table 1. Compositional Data for a Glass Substrate
refractive index variation depends on three major Material wt. % mol. wt. nM mM NM
physical changes: ionic polarizability, molar volume
1related to ionic size2, and the stress state created by SiO2 72.08 60.08 2 1 0.41248
the ionic substitution. Besides these three factors, a CaO 6.52 56.08 1 1 0.0399
Al2O3 1.26 101.96 3 2 0.0085
secondary inﬂuence on the index is caused by the
MgO 3.86 40.31 1 1 0.0329
accompanying effect of the electronic polarizability of Na2O 15.32 61.98 1 2 0.1699
the neighboring oxygen ions.1,4 K2O 0.796 94.20 1 2 0.0058
The usual explanation for the index change result- TiO2 0.03 79.90 2 1 0.000129
ing from ion exchange is based on the fact that the BaO 0.013 153.34 1 1 0.000029
ions participating in the exchange have different B2O3 0.07 69.62 3 2 0.000691
electronic polarizabilities and that they occupy a Traces 0.05
different volume of the glass. Quantitatively, an
accurate empirical model exists to predict the value of
the index change that results from the replacement of calculated from the chemical composition of the glass
one ion by another in the bulk composition of the substrate is nd 5 1.5139, which is in agreement with
glass.12 The basic model predicts that the value of the experimental refractive index measured by a
the index, nd 1x2, resulting from the ionic substitution, refractometer with a value of 1.514 1 0.0003.
is given by Using relation 122 and the calculated values for V0 5
13.866, DV 5 0.06456, R0 5 7.1259, and DR 5 2.4312,
nd 1x2 5 1 1
oa M NM 1x2
we ﬁnd it clear that the contribution to Dn from the
ionic polarizability, DR, induced by Cu ions is higher
V1x2 k 1 bSi 1 o CM NM 1x2
than the contribution from the change in the molar
where x is the fraction of the cations replaced by the volume, R0DV@V0, caused by the difference in the ionic
income ion, NM is the number of moles of ion I radius of the two ions in the glass network. From
contributed by the molecular component, M, of chemi- relation 122 it is possible to estimate that the maxi-
cal composition Im On per mole of oxygen ions contrib- mum gradient index expected from a complete ion
uted by all the components of the glass; aM and cM are exchange, Cu1 = Na1, is Dn < 0.17.
the refraction and volume constants, and k and bSi are A conventional electron-beam scanning method
constants. The values for the volume, refraction, was used for determining the concentration proﬁle of
and bSi constants are given in Refs. 12–14. Besides Cu in glass. A SEM@EDX microanalysis of the pla-
nar waveguides indicates a different composition for
Eq. 112, a useful approximation of the index change
the analysis of the waveguide compared with that of
resulting from the ionic substitution, Dn, is given by
bulk glass. It is possible to appreciate from Fig. 1
R0DV that the diffusion process leaves the basic structure of
V 1 2,
Dn < DR 2 122 the glass almost unchanged and changes only the
where V0 is the volume of the base glass per gram
atom of oxygen, R0 is the refraction of the glass base
per gram atom of oxygen, and DV 5 1aCu 2 aNa2NNa
and DR 5 1nd 2 12V0 are the changes of volume and
refraction if a complete ion exchange 1Cu1 = Na12
occurs. From relation 122 we see that a linear relation-
ship exists between the fraction of the Cu ions in the
glass and the index change. In this simple model the
index change represented by relation 122 is caused by
two factors: the ﬁrst term arises as a result of the
difference in the ionic polarizability of the exchanging
ions, and the second term represents the contribution
from the change in the molar volume of the glass
caused by the difference in the ionic radius of the two
Table 1 lists compositional data for the glass matrix
used as the substrate. From these data we obtain
V0 5 k 1 13.83545. Considering that the substrate
glass density is r 5 2.475 g@cm3 and using the
equation V0 5 1rA221, where A is the number of moles
of oxygen per gram of glass, we ﬁnd that the value
obtained for constant k is 0.0309. The values for the
volume and refraction compositional data for the Fig. 1. Composition proﬁle of a Cu ion-exchanged planar wave-
glass are given in Refs. 12–14. The refractive index guide by SEM@EDX.
5818 APPLIED OPTICS @ Vol. 34, No. 25 @ 1 September 1995
proportion of Cu and Na in the waveguide. The
electron-beam scanning direction was perpendicular
to the surface, and every scanning position had 1 µm
The maximum value of the change in the refractive
index obtained from the optical analysis of the
Cu–glass waveguides is Dn < 0.075 1see Subsection
3.C2. This value is lower than the maximum value,
Dn < 0.17, calculated with relation 122. We note that
the difference between these two values is the small
variations of each Nm caused by the variation of x,
which are considered in Eq. 112 but not in relation 122.
These small contributions are critical for the correct
simulation of the index proﬁles of Cu–glass wave-
guides as a function of the chemical composition
proﬁle. Therefore, the refractive index proﬁle was
calculated by the use of Eq. 112 instead of relation 122.
Figure 2 shows the refractive index proﬁle for the
Cu–glass waveguide obtained by Eq. 112.
B. Diffusion Process Fig. 3. Current density versus time for Cu–glass waveguides.
We followed the evaporation step by placing the
substrates into a furnace and heating them to the
exchange temperature. Thermal equilibrium was The evolution of the ionic concentration distribu-
reached before the exchange process was started by tion in the glass during the ion-exchange process has
the applied voltage. Diffusion was carried out at been interpreted by the use of diffusion theories.
350 °C, with an electric ﬁeld of 30 V@mm, for periods Mass transport in an isotropic, homogeneous medium
ranging from 15 to 100 min, after which the sample such as glass in the presence of an externally applied
was removed from the furnance and allowed to cool to electric ﬁeld can be considered as the diffusion of
room temperature in the laboratory environment. mobile ions in a semi-inﬁnite medium with nonblock-
In Fig. 3 we present a typical plot of current versus ing electrodes under a dc ﬁeld, and it can be described
time for waveguides fabricated with Cu ﬁlms approxi- by a modiﬁed Fick equation. Therefore, the ionic
mately 1 µm in thickness. The current is almost concentration distribution in the glass can be de-
constant after the ﬁrst few minutes; much later the scribed by the analytical solution of the diffusion
current decreases and approaches zero. This behav- equation. In this case the solution is subject to
ior is similar to that reported by other authors for boundary conditions C10, t2 5 C0 for t $ 0, i.e., the
silver ﬁlm diffusion.15 surface concentration remains constant. Using these
conditions, we see that the analytical solution has a
c0 x 2 µEt µEx x 1 µEt
C5 erfc1 2 1 exp1 D 2erfc1 24 , 132
where E is the electric ﬁeld, µ is the mobility, D is the
diffusion coefficient, the effective diffusion depth is W0
5 2ŒDt , and erfc1z2 5 2@Œp e exp12a22da.
Here W0 is the effective depth of diffusion and corre-
sponds to C1W0, t2 5 0.157C0.16
Logarithms of diffusion coefficients, ln D, estimated
from data taken over a 100-min period are plotted as a
function of reciprocal temperature, 1@T, in Fig. 4.
We assume that the diffusion coefficient is expressed
by an Arrhenius-type equation,
D 5 D0 exp 2 1 RT 2, 142
where Ea is the activation energy for diffusion. A
curve ﬁtted to the data shown in Fig. 4 gives Ea 5
Fig. 2. Refractive index proﬁle calculated from the composition Figure 5 is a plot of the effective depth versus Œ t,
proﬁle of the waveguide. which shows a linear relationship between both pa-
1 September 1995 @ Vol. 34, No. 25 @ APPLIED OPTICS 5819
Fig. 4. Logarithm of the diffusion coefficient as a function of 1@T.
Fig. 6. Copper proﬁles from the diffusion equation and SEM@EDX
rameters of the exchange system. From the relation
d 5 ŒDt, the diffusion coefficient, D, can be deter-
mined. Taking the slope of the least-squares ﬁt not present.17 SEM observations of the glass matrix
1solid curve2 to the points in Fig. 5 leads to a value of before and after Cu diffusion show high homogeneity,
D 5 5.3 3 10216 m2@s. similar to the typical microstructure of a soda-lime
Through the use of Eq. 132, the Cu concentration glass. The microstructure of the Cu–glass wave-
distribution of ﬁeld-assisted ion-exchanged glass pla- guides does not exhibit metallic Cu droplets. It is
nar waveguides has been obtained and compared with well known that the metallic particles in optical
results obtained from the SEM@EDX microanalysis. waveguides can give rise to additional absorption
The comparison is shown in Fig. 6. bands and scattering losses.
Cu ion-exchanged waveguides do not show colora-
C. Optical Characterization
tion. They have an absorption band only near 280
nm, and this band can be attributed to Cu1. The The waveguides were analyzed by the use of a Metri-
typical absorption bands caused by Cu21 and colloidal con Model 2010 prism-coupler system; the main com-
Cu0, located near 360 and 560 nm, respectively, are ponents of the equipment are shown in Fig. 7. A
laser beam strikes the base of a prism with a high
refractive index and is reﬂected onto a photodetector.
The waveguide to be analyzed is brought into contact
with the prism base by means of a coupling head.
The angle of incidence, u, of the laser beam can be
varied by means of a rotary stage on which the prism,
waveguide, coupling head, and photodetector are
Fig. 5. Effective depth versus square root of the diffusion time. Fig. 7. Principle of operation of the prism-coupling technique.
5820 APPLIED OPTICS @ Vol. 34, No. 25 @ 1 September 1995
mounted. At certain values of u, called mode angles,
photons violate the total internal reﬂection criterion
and tunnel from the base of the prism into the
waveguide and enter into optical propagation modes,
causing a sharp drop in the intensity of the light
striking the photodetector. In the prism-coupling
method, as shown in Fig. 7, an incident light beam
enters the prism at an angle u. At the prism base,
the light beam forms an angle f to the normal. This
angle, f, determines the phase velocity in the z
direction of the incident beam in the prism and in the
gap between the prism and the waveguide.4,18
Efficient coupling of light into the waveguide occurs
only when we choose the angle such that vi is equal to
the phase velocity, vm , of one of the guided modes of
the waveguide 1m 5 0, 1, 2, . . .2.
The effective refractive index, Nm , of the mth mode
is related to um , by
3 1 2 1 A4 ,
Nm 5 np sin sin21 sin 152
np Fig. 8. Refractive index proﬁles of the waveguide obtained from
optical analysis and from the composition proﬁle.
where A and np are the base angle and refractive
index of the prism, respectively. The effective refrac-
tive indices of the guided modes, shown in Table 2,
were obtained by the measurement of the coupling difference in refractive index proﬁles for the two
mode angles of the prism coupler. The refractive polarizations is also small.
index proﬁles of the waveguides were then calculated
by the use of Chiang’s algorithm,19 which creates a
continuous effective index function from a set of
discrete effective indices, which is then used to con- Copper ion-exchanged glass waveguides have been
struct a refractive index proﬁle by numerically solv- obtained by means of solid-state diffusion from 1-µm-
ing the inverse WKB equation. Figure 8 shows the thick copper ﬁlms at 350 °C, assisted by an electric
calculated refractive index proﬁles for TE and TM ﬁeld of 30 V@mm for periods ranging from 15 to 100
polarizations of the waveguide that has six modes, min. The model used to predict the values of the
together with the index proﬁle calculated from the index change that results from replacing Cu1 by Na1
composition proﬁle. These calculations agree fairly in the composition proﬁle of the glass indicates that
well. The observed modal birefringence was almost Dnmax 5 0.073, which is close to the value of Dnmax 5
negligible, and the TM modes were even slightly 0.075 calculated from the optical analysis of the
higher than the TE modes. As a consequence, the waveguides. Therefore, the change of refractive in-
dex in Cu–glass waveguides can be attributed mainly
to the rise of ionic polarizability in the glass network
by the incoming Cu1 ions. The experimental values
Table 2. Effective Mode Indices of Cu-Diffused Waveguides at 632.8 nm obtained for the activation energy, E, and diffusion
coefficient are 21.34 kcal@mol and 5.39 3 10216 m2@s,
Diffusion No. of Mode respectively.
time 1min2 Modes Order TE TM
The authors were supported by Consejo Nacional de
15 1 0 1.5381 1.5364 Ciencia y Tecnologia under program P.1299-A920 and
30 2 0 1.5698 1.5706 by the Consejo Nacional de Ciencia y Tecnologia–
1 1.5316 1.5317 Consejo Superior de Investigaciones Cientiﬁcas coop-
60 3 0 1.5682 1.5690 eration program E.130.977.
1 1.5491 1.5498
2 1.5268 1.5270 References
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