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Electro-optic coefficients in H+-ion implanted LiNbO3 planar waveguide
Nuclear Instruments and Methods in Physics Research B 147 (1999) 393±398
Electro-optic coecients in H-ion implanted LiNbO3 planar waveguide A. Boudrioua a
a,* ,
S. Ould Salem b, P. Moretti b, R. Kremer
a
, J.C. Loulergue
a
MOPS-Centre Lorrain dÕOptique et dÕElectronique des Solides, Universit e de Metz et Sup elec , Technopole 2000, 2 Rue E Belin, 57078 Metz Cedex 3, France b LPCML, UMR 5620 CNRS, Universit e Claude Bernard Lyon I, 69622 Villeurbanne, France
Abstract The electro-optic properties of proton implanted LiNbO3 waveguides are investigated by measuring the guided mode angular shift when an electric ®eld is applied. It is shown that the values of the r13 and r33 electro-optic coecients are rather well preserved in the waveguides, being independent of the implanted-proton dose in the investigated range (1± 10 ´ 1016 ions/cm2 ). Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: LiNbO3 ; Waveguides; Electro-optical properties; Protons
1. Introduction Materials with high electro-optic performances are needed to elaborate modulators and derivative devices for integrated optic systems. Lithium niobate (LiNbO3 ) is very likely the most extensively studied oxide crystal owing to its large electrooptic coecients (rij ) values and because waveguides can be tailored by dierent ways. Integrated devices, as modulators, elaborated either by Tiindiusion or proton exchange techniques are now commercially available [1]. However, it is known that both these latter processes partly degrade the rij coecients values comparatively to the bulk
* Corresponding author. Tel.: 33 3 87 75 96 08; fax: +33 3 87 75 96 01; e-mail: [email protected]
An alternative route to fabricate waveguides in crystals is to use ion implantation (He or H ) performed at energy in the MeV range. This technique has been successfully applied to a wide range of materials including LiNbO3 [2±6]. A decrease, by up 70%, of the electro-optic eect was also observed in He implanted LiNbO3 planar waveguides [7] and it was suggested that this degradation could be due to strong crystal lattice distortions related to the damage produced by the fabrication process. Reed et al. [8] claimed however that the electro-optic coecient r13 of He -implanted LiNbO3 stripe optical waveguides is only reduced by 20%. In contrast, preliminary measurements showed recently that the electrooptic coecients seems to be rather well preserved in proton implanted LiNbO3 waveguides [9].
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 6 0 2 - 8
394
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
Implantation eects induce an optical barrier with a signi®cant refractive index fall at a few micrometer beneath the surface of the material. At the origin of this phenomenon there is the deposition of energy by collision processes at the end of the ions path, producing nuclear damages. However, the region crossed by the ions, which will be actually used as guiding layer, undergoes itself electronic damages, and at a less extend also some nuclear damages, that may result in some change of the refractive indices [2±6], and generally speaking of modi®cation of the intrinsic optical properties of the bulk. The eect of the implanted ions dose is therefore preponderant in possible degradation of the optical properties, as the electro-optic eect, while the ion beam energy mainly governs the thickness of the obtained guiding layer. In this paper we report on a detailed investigation of the electro-optic properties of H -implanted LiNbO3 planar waveguides, especially on the eect of the implantation dose. These measurements are performed by a simple experimental setup based on the direct use of the prism-coupling technique [9,10].
1(a). First, we measure the guided modes spectrum without electric ®eld, given by the re¯ected intensity versus the angle of incidence. This spectrum is taken as a reference and permits also to characterize the guiding layer, i.e. the determination of the refractive index pro®le. Secondly, similar measurement are performed when an electric ®eld is applied through two co-planar electrodes of gold (Au) beforehand deposited on the surface of the samples (Fig. 1(b)). In this case the guided modes spectrum undergoes an angular shift Da due to the refractive index variation induced by the electrooptic eect. An automated setup enables to maintain the initial experimental conditions, particularly the same coupling eciency. Indeed, displacement of the angular position of modes could also be induced by a change of the coupling eciency. By varying the applied voltage, we were able to determine the variation of guided mode spectrum shift, Da, with respect to the reference one, as a function of applied voltage. According to the used crystal cut, for X propagating waves the r33 and r13 electro-optic coecients are obtained by TE and TM modes excitation, respectively.
2. Experimental methods
3. Theoretical considerations
We used Y-cut single crystals of LiNbO3 commercialized by Crystal-Tech (USA). The implantation is performed onto samples of dimensions 20 ´ 10 ´ 1 mm3 cut from the same wafer by using a Van de Graa accelerator with an energy of 800 keV. The dose was varied from 1 ´ 1016 H /cm2 to 10 ´ 1016 H /cm2 . Particular attention was paid to maintain the same implantation conditions by carefully controlling the beam ¯ux and the temperature of the sample. The latter was kept close to 25°C by mean of a combined heating and cooling system. A beam scan over an area of about 10 cm2 was used to guarantee an homogeneous irradiation and prevent excessive space charge eects which could locally modify the polarization into the material. For the electro-optic measurements, we used the angular shift method [9,10] which consists of a prism-in coupling technique, as depicted on Fig.
For two coplanar electrodes, the real electric ®eld distribution into the guiding layer is obtained using the conformal transformation method [11,12]. In our experimental con®guration, since we used two electrodes separated by a gap g 150 lm, the electric ®eld which is applied over a thickness of less than 10 lm only, can be considered as uniform. Moreover, in the center between the two electrodes, only the Zcomponent of the electric ®eld is non-zero. Therefore, the overlap integral calculation between the optical and the applied electric ®elds can be avoided. Since the propagation constants of the modes (thus, the eective indices) in the structure strongly depend on the refractive index of the core, the synchronous angle (a) changes when an electric ®eld is applied. The resulting shift Da, can be written as [9]
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
395
Fig. 1. (a) Ôm-linesÕ setup for characterizing planar optical waveguides and electro-optic measurements. (b) Schema of the electrode geometry used for the EO coecients measurement. Two planar electrodes of gold are deposited on the large surface of the waveguide.
Da
da da dNm Dn Dn dn dNm dn
r13
2Ko Cno n3o C
and
r33
2Ke Cne n3e C
where Dn is given by
for TM and TE polarisations, respectively, where:
1 Dn n3 rij E; 2
C
n is the refractive index of the guide and Nm the eective index of the guided mode m. Then, from geometrical analysis involving the prism, the airgap, the guiding region and the substrate, we obtain
no is the ordinary refractive index, ne the extraordinary refractive index, Ko and Ke : are constants depending on the polarization used. Cno and Cne are the linear coecients of the curves Da f(V) and V the applied voltage. The measurement of the
1 pg
396
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
two main parameters Cno and Cne yields, therefore the electro-optic coecients under consideration. 4. Results and discussion The determination of eective mode indices from the guided modes spectrum allows us to reconstruct the refractive index pro®les using an improved inverse WKB method [13]. This method is the commonly used approximation to characterize planar optical waveguides. Typical results are showed on Fig. 2. It is worth to note that: (1) both no and ne refractive indices follow nearly a step-like variation, (2) both index falls coincide and correspond to a common optical barrier (3) comparatively to the bulk values, only a slight index change, which variation sense is in dependence of the index (ordinary or extraordinary), occurs in the guiding layer. In any case, these changes are far less weaker than those reported for He implanted LiNbO3 [2,3]. It can be therefore speculated that the intrinsic optical properties of the material have not been modi®ed by the elaboration process. Moreover, the variation of the square of eective mode indices as a function of (m+1)2 , where m
Fig. 2. Ordinary and extraordinary refractive index pro®les of H -LiNbO3 waveguide implanted at 800 keV with a dose of 6 ´ 1016 ions cmÿ2 (left and bottom scales). Also reported are the measured data points and theoretical ®tted data curves of the square of eective mode indices variation as a function of (m + 1)2 (right and top scales).
Fig. 3. Angular shift (Da) versus applied voltage (V) in an H LiNbO3 waveguide implanted with 6 ´ 1016 ions cmÿ2 (at 800 keV), of several TM (a) and TE (b) modes.
Fig. 4. EO coecient r13 values versus the mode number in a sample implanted with a dose of 4 ´ 1016 H cmÿ2 .
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
is the mode number, as reported in Fig. 2, are in a well agreement with linear theoretical ®tted curves, which are actually speci®c of real step-index waveguides [11]. Therefore, refractive index values can be determined using the modes dispersion equation, as described in Ref. [5]. These features are of great interest because they allow us to utilize for our study the simple step-index waveguide model. Fig. 3 show typical results of the synchronous angle changes (Da) observed for TM (Fig. 3(a)) and TE (Fig. 3(b)) modes as a function of the applied voltage. Note that the angular shifts reported concern dierent guided mode numbers. They all behave linearly and their variations can be represented by the same straight line. This result is in agreement with the theoretical analysis given above: a uniform electric ®eld induces a uniform angular shift whatever the guided mode to be considered, as expected for a linear electro-optic eect (i.e. the Pockels eect). In Fig. 4 we have reported the values of the r13 electro-optic coecient, deduced from TM excitation measurements, as a function of the mode number. In addition to the fact that the r13 value is in a good agreement with the known bulk one [14], no evident evolution can be noticed, con®rming therefore our assumption on the uniformity of the applied ®eld in the waveguides. Finally, the electro-optic coecients r13 and r33 measured for various implanted doses are reported in Table 1. We must emphasize that, as discussed elsewhere [6], the m-lines spectra of extraordinary index are generally smooth, with dips less pronounced than those observed for ordinary one, speci®cally for low dose implantation, leading
397
therefore to some diculties for measuring the r33 coecient. Measurements on samples S1 and S2 for instance were not successful. On the contrary, a better accuracy is obtained with the TM modes (no index excitation) for the r13 measurements. However, note that in the whole the obtained values are very close to those of the bulk, i.e. r13 9.6 pm.Vÿ1 and r33 30.9 pm.Vÿ1 [14]. Moreover, taking into account the above mentioned diculties, we can reasonably assume that the electro-optic coecients r13 and r33 do not present any clear dependence, in the investigated range, on the proton implantation dose. We can therefore expect that optimum electro-optic performances should be achieved in electromodulators elaborated by this method. 5. Conclusion The electro-optic coecients have been investigated in H -implanted LiNbO3 planar optical waveguides by using a technique based on prismcoupling. Our measurements are in good agreement with a model assuming a linear shift of guided modes under an applied electric ®eld, as expected for Pokels eects. The values of the r13 and r33 coecients are found close to the bulk and any clear evolution as a function of the implantation dose (from 1 ´ 1016 to 10 ´ 1016 H /cm2 ) has been evidenced This study shows therefore that protons implantation preserves the electro-optic properties of LiNbO3 . It also demonstrates the interest of ion implantation to produce planar waveguides in active optical materials towards practical use in optical integrated systems.
Table 1 EO coecients r13 and r33 values for various implantation doses Sample
Dose (H /cm2 )
r13 (0.7) (pm.Vÿ1 )
r33 (1.2) (pm.Vÿ1 )
S1 S2 S3 S4 S5
2 ´ 1016 4 ´ 1016 6 ´ 1016 8 ´ 1016 10 ´ 1016
10.0 11.8 9.3 ) 11.2
) ) 28.6 32.4 24.4
398
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
References [1] F.J. Leonberger, S.W. Meritt, Proc ECIOÕ95, Delft, The Netherlands, 1995, p. 475. [2] P.D. Townsend, Nucl. Instr. and Meth. B 46 (1990) 18. [3] P.J. Chandler, P.D. Townsend, Nucl. Instr. and Meth. B 19/20 (1987) 921. [4] P. Moretti, P. Thevenard, K. Wirl, P. Hertel, H. Hesse, E. Kratzig, G. Godefroy, Ferroelectrics 128 (1992) 13. [5] A. Boudrioua, P. Moretti, J.C. Loulergue, K. Polgar, Phys. Stat. Sol. (a) 153 (1996) 553. [6] P. Bindner, A. Boudrioua, P. Moretti, J.C. Loulergue, Nucl. Instr. and Meth. B 142 (1998) 329.
[7] G.L. Destefanis, J.P. Gaillard, E.L. Ligeon, S. Valette, J. Appl. Phys. 50 (12) (1979) 596. [8] G.T. Reed, B.L. Weiss, Elect. Lett. 23 (8) (1987) 424. [9] A. Boudrioua, P. Moretti, J.C. Loulergue, J. Non-Cryst. Solid 187 (1995) 443. [10] A. Boudrioua, J.C. Loulergue, Phys. Stat. Sol. (a) 153 (1996) 553. [11] D. Marcuse, IEEE J. Quant. Elect. QE-18 (3) (1982) 393. [12] P. Vandenblucke, P.E. Lagasse, W. Elect. 1 (76) (1974) 295. [13] K.S. Chiang, J. Lightwave Tech. LT (1985) 385. [14] P. G unter (Ed.), Electro-Optic and Photorefractive Materials, Springer, Berlin 1987.
Electro-optic coecients in H-ion implanted LiNbO3 planar waveguide A. Boudrioua a
a,* ,
S. Ould Salem b, P. Moretti b, R. Kremer
a
, J.C. Loulergue
a
MOPS-Centre Lorrain dÕOptique et dÕElectronique des Solides, Universit e de Metz et Sup elec , Technopole 2000, 2 Rue E Belin, 57078 Metz Cedex 3, France b LPCML, UMR 5620 CNRS, Universit e Claude Bernard Lyon I, 69622 Villeurbanne, France
Abstract The electro-optic properties of proton implanted LiNbO3 waveguides are investigated by measuring the guided mode angular shift when an electric ®eld is applied. It is shown that the values of the r13 and r33 electro-optic coecients are rather well preserved in the waveguides, being independent of the implanted-proton dose in the investigated range (1± 10 ´ 1016 ions/cm2 ). Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: LiNbO3 ; Waveguides; Electro-optical properties; Protons
1. Introduction Materials with high electro-optic performances are needed to elaborate modulators and derivative devices for integrated optic systems. Lithium niobate (LiNbO3 ) is very likely the most extensively studied oxide crystal owing to its large electrooptic coecients (rij ) values and because waveguides can be tailored by dierent ways. Integrated devices, as modulators, elaborated either by Tiindiusion or proton exchange techniques are now commercially available [1]. However, it is known that both these latter processes partly degrade the rij coecients values comparatively to the bulk
* Corresponding author. Tel.: 33 3 87 75 96 08; fax: +33 3 87 75 96 01; e-mail: [email protected]
An alternative route to fabricate waveguides in crystals is to use ion implantation (He or H ) performed at energy in the MeV range. This technique has been successfully applied to a wide range of materials including LiNbO3 [2±6]. A decrease, by up 70%, of the electro-optic eect was also observed in He implanted LiNbO3 planar waveguides [7] and it was suggested that this degradation could be due to strong crystal lattice distortions related to the damage produced by the fabrication process. Reed et al. [8] claimed however that the electro-optic coecient r13 of He -implanted LiNbO3 stripe optical waveguides is only reduced by 20%. In contrast, preliminary measurements showed recently that the electrooptic coecients seems to be rather well preserved in proton implanted LiNbO3 waveguides [9].
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 6 0 2 - 8
394
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
Implantation eects induce an optical barrier with a signi®cant refractive index fall at a few micrometer beneath the surface of the material. At the origin of this phenomenon there is the deposition of energy by collision processes at the end of the ions path, producing nuclear damages. However, the region crossed by the ions, which will be actually used as guiding layer, undergoes itself electronic damages, and at a less extend also some nuclear damages, that may result in some change of the refractive indices [2±6], and generally speaking of modi®cation of the intrinsic optical properties of the bulk. The eect of the implanted ions dose is therefore preponderant in possible degradation of the optical properties, as the electro-optic eect, while the ion beam energy mainly governs the thickness of the obtained guiding layer. In this paper we report on a detailed investigation of the electro-optic properties of H -implanted LiNbO3 planar waveguides, especially on the eect of the implantation dose. These measurements are performed by a simple experimental setup based on the direct use of the prism-coupling technique [9,10].
1(a). First, we measure the guided modes spectrum without electric ®eld, given by the re¯ected intensity versus the angle of incidence. This spectrum is taken as a reference and permits also to characterize the guiding layer, i.e. the determination of the refractive index pro®le. Secondly, similar measurement are performed when an electric ®eld is applied through two co-planar electrodes of gold (Au) beforehand deposited on the surface of the samples (Fig. 1(b)). In this case the guided modes spectrum undergoes an angular shift Da due to the refractive index variation induced by the electrooptic eect. An automated setup enables to maintain the initial experimental conditions, particularly the same coupling eciency. Indeed, displacement of the angular position of modes could also be induced by a change of the coupling eciency. By varying the applied voltage, we were able to determine the variation of guided mode spectrum shift, Da, with respect to the reference one, as a function of applied voltage. According to the used crystal cut, for X propagating waves the r33 and r13 electro-optic coecients are obtained by TE and TM modes excitation, respectively.
2. Experimental methods
3. Theoretical considerations
We used Y-cut single crystals of LiNbO3 commercialized by Crystal-Tech (USA). The implantation is performed onto samples of dimensions 20 ´ 10 ´ 1 mm3 cut from the same wafer by using a Van de Graa accelerator with an energy of 800 keV. The dose was varied from 1 ´ 1016 H /cm2 to 10 ´ 1016 H /cm2 . Particular attention was paid to maintain the same implantation conditions by carefully controlling the beam ¯ux and the temperature of the sample. The latter was kept close to 25°C by mean of a combined heating and cooling system. A beam scan over an area of about 10 cm2 was used to guarantee an homogeneous irradiation and prevent excessive space charge eects which could locally modify the polarization into the material. For the electro-optic measurements, we used the angular shift method [9,10] which consists of a prism-in coupling technique, as depicted on Fig.
For two coplanar electrodes, the real electric ®eld distribution into the guiding layer is obtained using the conformal transformation method [11,12]. In our experimental con®guration, since we used two electrodes separated by a gap g 150 lm, the electric ®eld which is applied over a thickness of less than 10 lm only, can be considered as uniform. Moreover, in the center between the two electrodes, only the Zcomponent of the electric ®eld is non-zero. Therefore, the overlap integral calculation between the optical and the applied electric ®elds can be avoided. Since the propagation constants of the modes (thus, the eective indices) in the structure strongly depend on the refractive index of the core, the synchronous angle (a) changes when an electric ®eld is applied. The resulting shift Da, can be written as [9]
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
395
Fig. 1. (a) Ôm-linesÕ setup for characterizing planar optical waveguides and electro-optic measurements. (b) Schema of the electrode geometry used for the EO coecients measurement. Two planar electrodes of gold are deposited on the large surface of the waveguide.
Da
da da dNm Dn Dn dn dNm dn
r13
2Ko Cno n3o C
and
r33
2Ke Cne n3e C
where Dn is given by
for TM and TE polarisations, respectively, where:
1 Dn n3 rij E; 2
C
n is the refractive index of the guide and Nm the eective index of the guided mode m. Then, from geometrical analysis involving the prism, the airgap, the guiding region and the substrate, we obtain
no is the ordinary refractive index, ne the extraordinary refractive index, Ko and Ke : are constants depending on the polarization used. Cno and Cne are the linear coecients of the curves Da f(V) and V the applied voltage. The measurement of the
1 pg
396
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
two main parameters Cno and Cne yields, therefore the electro-optic coecients under consideration. 4. Results and discussion The determination of eective mode indices from the guided modes spectrum allows us to reconstruct the refractive index pro®les using an improved inverse WKB method [13]. This method is the commonly used approximation to characterize planar optical waveguides. Typical results are showed on Fig. 2. It is worth to note that: (1) both no and ne refractive indices follow nearly a step-like variation, (2) both index falls coincide and correspond to a common optical barrier (3) comparatively to the bulk values, only a slight index change, which variation sense is in dependence of the index (ordinary or extraordinary), occurs in the guiding layer. In any case, these changes are far less weaker than those reported for He implanted LiNbO3 [2,3]. It can be therefore speculated that the intrinsic optical properties of the material have not been modi®ed by the elaboration process. Moreover, the variation of the square of eective mode indices as a function of (m+1)2 , where m
Fig. 2. Ordinary and extraordinary refractive index pro®les of H -LiNbO3 waveguide implanted at 800 keV with a dose of 6 ´ 1016 ions cmÿ2 (left and bottom scales). Also reported are the measured data points and theoretical ®tted data curves of the square of eective mode indices variation as a function of (m + 1)2 (right and top scales).
Fig. 3. Angular shift (Da) versus applied voltage (V) in an H LiNbO3 waveguide implanted with 6 ´ 1016 ions cmÿ2 (at 800 keV), of several TM (a) and TE (b) modes.
Fig. 4. EO coecient r13 values versus the mode number in a sample implanted with a dose of 4 ´ 1016 H cmÿ2 .
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
is the mode number, as reported in Fig. 2, are in a well agreement with linear theoretical ®tted curves, which are actually speci®c of real step-index waveguides [11]. Therefore, refractive index values can be determined using the modes dispersion equation, as described in Ref. [5]. These features are of great interest because they allow us to utilize for our study the simple step-index waveguide model. Fig. 3 show typical results of the synchronous angle changes (Da) observed for TM (Fig. 3(a)) and TE (Fig. 3(b)) modes as a function of the applied voltage. Note that the angular shifts reported concern dierent guided mode numbers. They all behave linearly and their variations can be represented by the same straight line. This result is in agreement with the theoretical analysis given above: a uniform electric ®eld induces a uniform angular shift whatever the guided mode to be considered, as expected for a linear electro-optic eect (i.e. the Pockels eect). In Fig. 4 we have reported the values of the r13 electro-optic coecient, deduced from TM excitation measurements, as a function of the mode number. In addition to the fact that the r13 value is in a good agreement with the known bulk one [14], no evident evolution can be noticed, con®rming therefore our assumption on the uniformity of the applied ®eld in the waveguides. Finally, the electro-optic coecients r13 and r33 measured for various implanted doses are reported in Table 1. We must emphasize that, as discussed elsewhere [6], the m-lines spectra of extraordinary index are generally smooth, with dips less pronounced than those observed for ordinary one, speci®cally for low dose implantation, leading
397
therefore to some diculties for measuring the r33 coecient. Measurements on samples S1 and S2 for instance were not successful. On the contrary, a better accuracy is obtained with the TM modes (no index excitation) for the r13 measurements. However, note that in the whole the obtained values are very close to those of the bulk, i.e. r13 9.6 pm.Vÿ1 and r33 30.9 pm.Vÿ1 [14]. Moreover, taking into account the above mentioned diculties, we can reasonably assume that the electro-optic coecients r13 and r33 do not present any clear dependence, in the investigated range, on the proton implantation dose. We can therefore expect that optimum electro-optic performances should be achieved in electromodulators elaborated by this method. 5. Conclusion The electro-optic coecients have been investigated in H -implanted LiNbO3 planar optical waveguides by using a technique based on prismcoupling. Our measurements are in good agreement with a model assuming a linear shift of guided modes under an applied electric ®eld, as expected for Pokels eects. The values of the r13 and r33 coecients are found close to the bulk and any clear evolution as a function of the implantation dose (from 1 ´ 1016 to 10 ´ 1016 H /cm2 ) has been evidenced This study shows therefore that protons implantation preserves the electro-optic properties of LiNbO3 . It also demonstrates the interest of ion implantation to produce planar waveguides in active optical materials towards practical use in optical integrated systems.
Table 1 EO coecients r13 and r33 values for various implantation doses Sample
Dose (H /cm2 )
r13 (0.7) (pm.Vÿ1 )
r33 (1.2) (pm.Vÿ1 )
S1 S2 S3 S4 S5
2 ´ 1016 4 ´ 1016 6 ´ 1016 8 ´ 1016 10 ´ 1016
10.0 11.8 9.3 ) 11.2
) ) 28.6 32.4 24.4
398
A. Boudrioua et al. / Nucl. Instr. and Meth. in Phys. Res. B 147 (1999) 393±398
References [1] F.J. Leonberger, S.W. Meritt, Proc ECIOÕ95, Delft, The Netherlands, 1995, p. 475. [2] P.D. Townsend, Nucl. Instr. and Meth. B 46 (1990) 18. [3] P.J. Chandler, P.D. Townsend, Nucl. Instr. and Meth. B 19/20 (1987) 921. [4] P. Moretti, P. Thevenard, K. Wirl, P. Hertel, H. Hesse, E. Kratzig, G. Godefroy, Ferroelectrics 128 (1992) 13. [5] A. Boudrioua, P. Moretti, J.C. Loulergue, K. Polgar, Phys. Stat. Sol. (a) 153 (1996) 553. [6] P. Bindner, A. Boudrioua, P. Moretti, J.C. Loulergue, Nucl. Instr. and Meth. B 142 (1998) 329.
[7] G.L. Destefanis, J.P. Gaillard, E.L. Ligeon, S. Valette, J. Appl. Phys. 50 (12) (1979) 596. [8] G.T. Reed, B.L. Weiss, Elect. Lett. 23 (8) (1987) 424. [9] A. Boudrioua, P. Moretti, J.C. Loulergue, J. Non-Cryst. Solid 187 (1995) 443. [10] A. Boudrioua, J.C. Loulergue, Phys. Stat. Sol. (a) 153 (1996) 553. [11] D. Marcuse, IEEE J. Quant. Elect. QE-18 (3) (1982) 393. [12] P. Vandenblucke, P.E. Lagasse, W. Elect. 1 (76) (1974) 295. [13] K.S. Chiang, J. Lightwave Tech. LT (1985) 385. [14] P. G unter (Ed.), Electro-Optic and Photorefractive Materials, Springer, Berlin 1987.