Experimental study of Cu 1-Na 1 exchanged glass waveguides

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					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
                  R1x2
                         511
                                   oa      M NM 1x2
                                                            ,   112
                                                                      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,
                          x
                  Dn <      DR 2                                122   the glass almost unchanged and changes only the
                          0          V0

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
ions.1
  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
of separation.
   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
                                                                  form

                                                                              c0       x 2 µEt            µEx       x 1 µEt
                                                                               23
                                                                        C5       erfc1          2 1 exp1 D 2erfc1           24 ,    132
                                                                                          w0                          W0

                                                                  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.
                                                                                                               `
                                                                                                              z
                                                                  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,

                                                                                                          Ea
                                                                                         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
                                                                  21.34 kcal@mol.
Fig. 2. Refractive index profile calculated from the composition     Figure 5 is a plot of the effective depth versus Πt,
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
                                                                          microanalysis.
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 ,
                                            um
               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
                                                                           4.   Conclusions
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,
                                                 Effective Index
  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
      75              4            0          1.5790          1.5787
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5822        APPLIED OPTICS @ Vol. 34, No. 25 @ 1 September 1995