Diffusion control of an ion by another in LiNbO3 and LiTaO3 crystals.

Diffusion-doping is an effective, practical method to improve material properties and widen material application. Here, we demonstrate a new physical phenomenon: diffusion control of an ion by another in LiNbO3 and LiTaO3 crystals. We exemplify Ti(4+)/X(n+) (X(n+) = Sc(3+), Zr(4+), Er(3+)) co-diffusion in the widely studied LiNbO3 and LiTaO3 crystals. Some Ti(4+)/X(n+)-co-doped LiNbO3 and LiTaO3 plates were prepared by co-diffusion of stacked Ti-metal and Er-metal (Sc2O3 or ZrO2) films coated onto LiNbO3 or LiTaO3 substrates. The Ti(4+)/X(n+)-co-diffusion characteristics were studied by secondary ion mass spectrometry. In the X(n+)-only diffusion case, the X(n+) diffuses considerably slower than the Ti(4+). In the Ti(4+)/X(n+) co-diffusion case, the faster Ti(4+) controls the diffusion of the slower X(n+). The X(n+) diffusivity increases linearly with the initial Ti-metal thickness and the increase depends on the X(n+) species. The phenomenon is ascribed to the generation of additional defects induced by the diffusion of faster Ti(4+) ions, which favors and assists the subsequent diffusion of slower X(n+) ion. For the diffusion system studied here, it can be utilized to substantially shorten device fabrication period, improve device performance and produce new materials.

Doping by thermal diffusion is an effective and practical method for improving material properties and widening material application. Here, we exemplify Ti4+/Xn+ (Xn+ = Sc3+, Zr4+, Er3+) co-diffusion in LiNbO3 (LN) and LiTaO3 (LT) crystals to demonstrate an interesting phenomenon that a faster ion controls diffusion of another slower ion in the two crystals.

Er3+-doped LN crystal is a promising material for integrated optics as it combines excellent electro-optic, acousto-optic and nonlinear optical properties of LN with good laser property of Er3+. Such an effective combination, together with the possibility of producing a high-quality waveguide, enables broadband amplification and lasing in the telecom wavelength region. Over the past years, a family of Ti (or vapor ZnO)-diffused Er:LN waveguide lasers (amplifiers) and integrated devices have been demonstrated1−3. For any Ti:Er:LN device, selective Er3+ doping is a prerequisite for monolithic integration of active (optically pumped, Er3+-doped) and passive (unpumped) devices on a same substrate, to avoid re-absorption in unpumped Er3+-doped waveguide. The doping is realized by in-diffusion of Er metal or its oxide at a temperature close to the Curie point of crystal. Previous study shows that Er3+ solubility in LN is limited and the diffusivity is rather low45. Very low diffusivity results in very long diffusion time of >100 h. Moreover, the serious photorefractive effect in the LN not only affects the device performance, but also limits both the pumping and operating wavelengths and hence hinders further development of novel devices. It is well known that doping with >4.9 mol% MgO can effectively suppress the effect6. However, as the crystal is heavily MgO-doped, both the diffusivity and solubility degrade further7. This is undesired as the optical gain of a laser or an amplifier increases with the active ion concentration and the low diffusivity results in quite long device fabrication period and hence increased cost. It is imperative to seek other dopants that have a low threshold concentration of photorefractive damage. In addition to the much studied Mg2+ 4, other dopants can also effectively suppress the photorefractive effect. These include divalent Zn2+ 8, trivalent Sc3+ 910, In3+ 11 and Tm3+ 12, and tetravalent Hf4+ 13, Zr4+ 14, and Sn4+ 15. Among them, the Sc3+ and Zr4+ show the lower concentration threshold of photorefractive damage, only 2 mol%. The low Sc3+ or Zr4+ doping concentration enables to increase the Er3+ solubility and diffusivity and improve the material homogeneity for nonlinear use as well. Thus, an LN doped with >2 mol% Sc3+ or Zr4+ would be a more promising material than the Mg-doped one for developing an optical-damage-resistant device.

A Ti-diffused LN (Ti:LN) waveguide is a basic component of an LN-based waveguide device. As an alternative, a Ti:LN waveguide co-doped with Zr4+ or Sc3+ can be fabricated by Ti4+ diffusion following Zr4+ or Sc3+-doping. And a Ti:Er:LN co-doped with Zr4+ or Sc3+ can be fabricated by successive diffusion of Er3+, Zr4+ (or Sc3+) and Ti4+. For these two kinds of waveguides, either Ti4+/Er3+, Ti4+/Zr4+ or Ti4+/Sc3+ co-diffusion is concerned in the Ti4+ diffusion procedure. Here we show that the Ti4+ diffuses considerably faster than the Xn+ ( = Er3+, Zr4+or Sc3+) and can control the Xn+ diffusion, enabling to shorten the device fabrication period, lower the cost, promote the Er3+ concentration and improve the device performance.

In comparison with LN, the LT crystal has similar crystal and defect structures, and similar electro-optic and nonlinear properties. Moreover, the LT shows two orders of magnitude higher resistance to the photorefractive damage and has the higher melting temperature of 1650 °C favorable for impurity doping by diffusion method. The LT may find applications similar to the LN. The co-diffusion study is also carried out on the LT crystal.

Fig. 1 shows the measured depth profiles of 6Li, 93Nb, 16O, 45Sc and/or 48Ti SIMS signals detected from the LN plates coated with (a) 160 nm Ti or 50 nm Sc2O3, (b) 50 nm Sc2O3 + 50 nm Ti, (c) 70 nm Sc2O3 + 115 nm Ti, and (d) 160 nm Ti + 118 nm Sc2O3 films after annealing at 1060 oC for 10 h in wet O2. On each panel, the red ball curve represents the measured Sc3+ profile and the magenta ball curve denotes the measured Ti4+ profile. In order to save space, Fig. 1(a) simultaneously shows the two cases of Sc3+- and Ti4+-only diffusion. Because the substrate signal profiles are similar for the two cases of Sc3+- and Ti4+-only diffusion, here only the substrate signals detected from the Sc3+-only diffused sample are shown in Fig. 1(a). We note that all of the substrate signals 6Li, 93Nb and 16O show constancy with depth during the analysis. This is expected because the concentration profiles of these substrate constituents should be homogeneous over the crystal plates. It is found that all of the measured Sc3+ and Ti4+ profiles shown in Fig. 1 can be well fitted by a Gaussian function, whether it is the single diffusion or co-diffusion,

Figure 1

Depth profiles of 6Li, 93Nb, 16O, 45Sc and/or 48Ti SIMS signals detected from five LN plates coated with Ti and/or Sc2O3 film.

where I(z) (i = Sc or Ti) represents the yield of secondary Sc3+ or Ti4+ ions, d denotes the 1/e Sc3+ or Ti4+ diffusion depth. The fitting results are plotted by the green line for Sc3+ and blue for Ti4+. The fitting expression is indicated for each case. One can see that there is an excellent agreement between the fitting and measured curves for each sample, showing that the diffusion reservoir has been exhausted for all of the studied Ti/Sc2O3 samples. In the single diffusion case, dSc (dTi) = 3.8 (7.0) ± 0.2 μm, yielding a diffusivity of (0.26 ± 0.03) [1.23 ± 0.07] μm2/h for Sc3+[Ti4+]. In the co-diffusion case, the dSc (dTi) value is 4.4 (6.3), 5.3 (6.4), 5.5 (6.5), 5.8 (6.4) and 6.4 (6.6) ± 0.2 μm for the Ti/Sc2O3 samples 3–7, respectively. The diffusivity DSc [DTi] is 0.48 ± 0.04 [0.99 ± 0.06], 0.70 ± 0.05 [1.02 ± 0.06] 0.75 ± 0.06 [1.06 ± 0.07], (0.84 ± 0.06) [1.02 ± 0.06] and 1.02 ± 0.06 [1.09 ± 0.07] μm2/h, respectively.

Fig. 2 shows the depth profiles of 7Li, 109NbO, 32O2, 123ZrO2 and/or 64TiO negative-ion SIMS signals detected from five representative LN samples that were initially coated with (a) 160 nm Ti or 80 nm Zr2O2, (b) 60 nm ZrO2 + 65 nm Ti, (c) 60 nm ZrO2 + 135 nm Ti, and (d) 60 nm ZrO2 + 185 nm Ti films. Fig. 2(a) shows the Zr4+-only diffusion case. For convenience, the Ti4+-only diffusion profile is again included in Fig. 2(a). Similar to the Ti4+/Sc3+ co-diffusion case, both the Ti4+ and Zr4+ profiles follow well the Gaussian function too. The fitting expression is indicated for each case. In the single diffusion case, dZr = 3.4 ± 0.2 μm, yielding a diffusivity of (0.29 ± 0.04) μm2/h. In the co-diffusion case the dZr (dTi) is 4.0 (6.8), 4.4 (6.9), 4.7 (7.1) and 5.0 (7.0) ± 0.2 μm for the Ti/ZrO2 samples 3, 4, 5 and 6, respectively. The resultant diffusivity DZr [DTi] is 0.40 ± 0.04 [1.16 ± 0.07], 0.48 ± 0.04 [1.19 ± 0.07], 0.55 ± 0.05 [1.26 ± 0.07] and (0.63 ± 0.05) [1.23 ± 0.07] μm2/h, respectively.

Figure 2

Depth profiles of 7Li, 109NbO, 32O2, 123ZrO2 and 64TiO (48Ti) SIMS signals detected from five LN plates coated with Ti and/or ZrO2 films.

For the Ti/Er LN samples, for which the SIMS results are not shown for save space, under the diffusion condition adopted, 1130 oC/50 h, the Ti4+ ion penetrates too deep to attain its entire profile using the SIMS technique. But the entire Er3+ profile, which we are more interested in, can be obtained. Analysis shows that the measured Er3+ profile follows also the Gaussian function for all of the studied Ti/Er LN samples. The fit yields a dEr value of 3.6, 4.4, 4.8, 5.0, 5.6, 6.2 and 4.7 ± 0.2 μm for the Ti/Er LN samples 1–7, respectively. The resulting diffusivity DEr is 6.5 ± 0.06, 9.7 ± 0.09, 11.8 ± 1.1, 12.6 ± 1.2, 15.7 ± 1.4, 19.2 ± 1.5 and (11.1 ± 1.0) × 10−2 μm2/h, respectively.

In the following we discuss the Ti4+/Xn+ co-diffusion features and the mutual influence issue of Ti4+ and Xn+ diffusion in the LN. First, we compare the diffusivities of the related four ions in the single diffusion case. The Ti4+ diffusion in the LN crystal has been studied since the 1980’s 16171819, and the diffusivity data reported show a large diversity perhaps due to different extents of suppression for Li2O out diffusion. The Ti4+-only diffusivity here, ~1.23 μm2/h @ 1060 oC, is closer to the value reported by Fukuma and Noda, ~0.98 μm2/h17. A comparison shows that in the single diffusion case the Zr4+, Sc3+ and Er3+ ions diffuse respectively four-, five-fold and one order of magnitude slower than the Ti4+. The ion for the diffusivity from high to low is Ti4+, Zr4+, Sc3+ and Er3+ in order. This is associated with their differences in atomic mass, ionic radius and chemical valence as well.

Next, we focus on the Ti4+/Xn+ co-diffusion features in the LN. We note from the diffusivity data given above that the Ti4+ ion assists and controls the diffusion of all the Xn+ ions. The co-diffusion of Ti4+ leads to considerable increase in Xn+ diffusivity and the Xn+ diffusivity increases with the initial thickness of Ti-metal film coated. As the Ti thickness is increased from zero to ~200 nm, the Xn+ diffusivity increases from 0.26 to 1.02 μm2/h for Sc3+, from 0.30 to 0.62 μm2/h for Zr4+, and from 6.5 × 10−2 to 19.2 × 10−2 μm2/h for Er3+. The increase is more than four-, two- and three-fold, respectively. To quantify the relation of Xn+ diffusivity to Ti thickness, in Fig. 3 we plot the Xn+ diffusivity against the initial Ti thickness (red balls for Sc3+, green balls for Zr4+ and magenta balls for Er3+). The error bar is indicated for each data. One can see that the diffusivity and the initial Ti thickness follow a linear relationship for all the Xn+ ions. The red, green and magenta lines in Fig. 3 represent the linear fits to the respective experimental data. The fitting expression is DSc [μm2/h] = 0.276 + 3.72 × 10−3 × (Ti thickness) for Sc3+, DZr [μm2/h] = 0.295 + 1.62 × 10–3 × (Ti thickness) for Zr4+, and DEr [μm2/h] = 0.0659 + 6.405 × 10–4 × (Ti thickness) for Er3+. The fitting error is within 10%.

Figure 3

Diffusivity in LN of (a) Sc3+, Zr4+, Ti4+ at 1060 oC and (b) Er3+ at 1130 °C versus initial Ti metal film thickness in the Ti4+/Xn+ co-diffusion case.

In contrast, the Ti4+ diffusivity in the co-diffusion case changes little. For straightforwardness, the Ti4+ diffusivity is also plotted in Fig. 3(a). The red (green) squares represent the Ti4+ diffusivity in the case of co-diffusion with the Sc3+(Zr4+). The line is drawn to guide the eyes only. In the Ti4+/Er3+ co-diffusion case, the Ti4+ diffusivity is not available as we cannot obtain the entire Ti4+ profile. One can see that the co-diffusion of Sc3+ only induces slight decrease of Ti4+ diffusivity from ~1.2 to ~1 μm2/h and the decrease is no more than 20%. In the Ti4+/Zr4+ co-diffusion case, the Ti4+ diffusivity is hardly influenced by the Zr4+ co-diffusion. It remains unchanged within the error no matter how the initial Ti or ZrO2 film thickness changes, i. e., in the co-diffusion case the Ti4+ diffusion is actually in the scenario of single diffusion. Moreover, the Ti4+ diffusivity is independent of the Ti thickness (i. e. independent of the Ti4+ concentration), consistent with the single-diffusion case. In addition, the Ti4+ diffusivity is also independent of the initial Sc2O3 or ZrO2 film thickness.

Subsequently, we pay attention to the effect of coating sequence on the diffusion. As described above, the samples have different coating sequences of Xn+ and Ti films (see Table 1 for details). We note from Fig. 3 that both Xn+ and Ti4+ diffusivities appear not to be influenced by the coating sequence. Here we exemplify the Ti4+/Er3+ samples 3 and 7 to demonstrate it. One can see from Table 1 that the two samples were coated with the same thickness of Er (22 nm) and Ti (76 nm). Their only difference is in the coating sequence. We note that the Er3+ in the two samples has the similar diffusivities, (11.8 ± 1.1) × 10–2 μm2/h in sample 3 and (11.1 ± 1.0) × 10–2 μm2/h in sample 7. We may conclude that the coating sequence does not affect the Er3+ diffusivity. This should be also true for the Ti4+ diffusivity.

Table 1

Summary of initial Sc2O3/Ti, ZrO2/Ti and Er/Ti film thicknesses coated onto LNs.

Sample No.	1	2	3	4	5	6	7
Sc2O3/Ti film thickness (nm)	0/160	50/0	50*/50	70*/115	50*/120	118/160*	50*/195
ZrO2/Ti film thickness (nm)	—	80/0	60*/65	60*/135	140/160*	60*/185	—
Er/Ti film thickness (nm)	17/0	17*/45	22*/76	22*/94	21*/146	21*/197	22/76*

*The oxide or metal film was coated at first.

Similar feature that the Ti4+ ion assists and controls Er3+ diffusion is also observed for the Ti4+ /Er3+ co-diffusion system in the LT crystal. From the measured Er3+ profiles, which follow either a Gaussian function or an error function of complement (erfc), the Er3+ diffusivities at different diffusion temperatures of 1200, 1300, 1400, 1450 and 1500 °C are obtained and given in Table 2. For straightforwardness, the diffusivities are plotted against the inverse of temperature 1/T (in unit of 1/K) in Fig. 4 for both cases of Er3+/Ti4+ co-diffusion and respective single diffusion. For reader’s convenience, the temperature is indicated for each data point. The red balls represent the Er3+ diffusivities in the case of Er3+-only diffusion. The red line represents the linear fit to the red balls on the semi-logarithmic scale and the fitting expression is indicated. The blue balls denote the Er3+ diffusivities in the Ti4+/Er3+ co-diffusion case. The blue data indicated near the blue balls denote the initial thicknesses of Ti-metal film coated. Indeed, one can see that for a given temperature the Ti4+ co-diffusion leads to definite increase in Er3+ diffusivity. The Er3+ diffusivity increases with the increased initial Ti-metal film and the increase ranges from 1.6 to 6-folds, depending on the initial thickness of the Ti-metal film coated.

Table 2

Summary of initial Er/Ti film thicknesses coated onto LTs. Also included are the diffusion condition adopted and the Er3 + diffusivity deduced.

Sample No.	1	2		3		4	5
Er/Ti film thickness (nm)	16/0	16/0		12/0		30/0	12/0
Diffusion temperature	1200 °C	1300 °C		1400 °C		1450 °C	1500 °C
Diffusion time	30 h	25 h		17 h		17 h	10 h
Er3+ diffusivity (×10−4 μm2/h)	2.40	25.0		376.5		276.9	1322.5
Sample No.	6	7	8	9	10	11	12
Er/Ti film thickness (nm)	16*/44	25*/65	25*/104	16*/162	16*/200	23/100*	23/160*
Diffusion temperature	1200 °C	1300 °C	1300 °C	1400 °C	1400 °C	1450 °C	1500 °C
Diffusion time	30 h	25 h	25 h	17 h	17 h	13 h	10 h
Er3+ diffusivity (×10−4 μm2/h)	12.1	40.3	130.6	588.2	874.1	1730.8	3240.0

*The metal film was coated at first.

Figure 4

Temperature dependences of Er3+ and Ti4+ diffusivities in LT. Red balls: Er3+ diffusivity in the Er3+-only diffusion case; blue balls: Er3+ diffusivity in the Ti4+/Er3+ co-diffusion case; magenta balls: Ti4+ diffusivity in the Ti4+/Er3+ co-diffusion case; magenta line: Ti4+ diffusivity in the Ti4+-only diffusion case reported in [20]. The red line represents the linear fit to the red balls on the semi-logarithmic scale and the fitting expression is indicated. The blue data indicated near the blue balls denote the initial thicknesses of Ti-metal film coated.

Like in the co-diffusion case in LN, the Ti4+ diffusivity in the co-diffusion case in LT changes little too. In Fig. 4 the magenta balls represent the Ti4+ diffusivities in the Ti4+/Er3+ co-diffusion case (For some LT samples, an entire Ti4+ profile can be obtained, enabling to obtain the Ti4+ diffusivity. This is distinguished from the LN case). The magenta line represents the temperature dependence of Ti4+ diffusivity in the Ti4+-only diffusion case. The line is drawn from the data calculated using the diffusion constant and activation energy values reported for Ti4+ single diffusion in LT20. We note that in the single diffusion case in LT the Ti4+ diffusivity is at least two orders of magnitude larger than the Er3+ diffusivity. In the co-diffusion case in LT the Ti4+ diffusivity does not reveal a remarkable difference from that in the Ti4+-only diffusion case, consistent with the case in LN. In addition, the Er3+ and Ti4+ diffusivities in the co-diffusion case in LT are also not affected by either the initial thickness of Er-metal film coated or the coating sequence of the two metal films.

The phenomenon that Ti4+ assists and controls Xn+ diffusion is explained as follows. Ti4+ enters into the bulk prior to Xn+ because of its high mobility. The diffusion of Ti4+ into the crystal results in generation of a large number of additional defects, which favors and assists subsequent diffusion of the slower Xn+ ion. In a sense, Ti4+ functions as the path-breaker for Xn+. One can anticipate that Ti4+ can also assist and control the diffusion of other ions that diffuse slower than Ti4+. As Ti4+ diffuses much faster than Xn+ and Ti4+ diffusion in co-diffusion case is actually in the scenario of single diffusion, it is thus comprehensible that Xn+ affects Ti4+ diffusion little and the Ti4+ diffusivity is independent of the thickness of either Xn+ or the Ti film. The small effect of coating sequence may be explained as follows. Both Xn+ and Ti4+ share the same diffusion reservoir, which is quickly formed in the early stage (t < 1 h) of the diffusion procedure2145. The reservoir formed by stacked layers with the Ti film directly in contact with the substrate should have no difference from that with the Xn+ film directly in contact with the substrate. Thus, the Xn+ diffusion shows small effect of coating sequence. As for the behavior that different Xn+ ions gain different extents of diffusion assistance by Ti4+, we consider this is associated with the differences in atomic mass, ionic radius and chemical valence as well.

The Ti4+/Xn+ co-diffusion in LN or LT crystal can be modeled by two independent Fick-type equations: where Ci(z, t) (i = Ti4+ or Xn+) denotes the Ti4+ or Xn+ concentration at depth z after diffusion time t, and Di is the diffusivity of Ti4+ or Xn+. The preceding results and discussion show that the Xn+ diffusivity is dependent of Ti4+-concentration while the Ti4+ diffusivity is independent of either the Xn+- or Ti4+-concentration. In addition, Di may also depend on the crystal composition. The lower the crystal composition is, the higher the diffusivity of an ion is19. Li2O out-diffusion phenomenon usually accompanies ion diffusion into the crystal. Regarding the LN and LT samples studied here, it is essential to examine if the phenomenon has taken place in the diffusion procedure. Here, the optical method of refractive index measurement was used to estimate the Li2O-content at the doped part of LN or LT sample surface2223. A comparison with the initial composition allows us to estimate the extent of Li2O out-diffusion. In addition, from the viewpoint of waveguide formation, which is induced mainly by the Ti4+ dopants, it is also crucial to know if the Xn+ diffusion-doping contributes to the refractive index of the LN or LT substrate.

The Xn+ doping effect on the substrate refractive index can be determined by measuring and comparing the index values at the doped and undoped sample surface parts in the Xn+-only diffusion case. For the Sc3+-, Zr4+- and Er3+-only diffusion case, the refractive index measurements at the doped and undoped parts of surface show that each dopant has little contribution to the substrate index. This is for both cases of LN and LT. From the measured indices, the Li2O-contents at the doped and undoped surface parts of the Xn+-only doped samples were evaluated on the basis of the Li2O-content-dependent Sellmeier equation2223. The results show that for the Sc3+- and Zr4+-only diffusion cases in LN the Li2O-content at doped surface equals that at undoped surface and can be thought as identical to that of the as-grown congruent crystal within the experimental error of ±0.1 mol%. This means that Li2O out-diffusion is not measurable for the Sc3+- or Zr4+-only doped LN samples. In the case of Er3+-only diffusion in LN, because of the higher diffusion temperature 1130 oC, the 50 h diffusion time resulted in 0.2–0.3 mol% minor Li2O content loss due to slight Li2O out-diffusion. For the Er3+-only diffusion in LT, as the diffusion temperature is below 1400 oC, the Li2O out-diffusion resulted in slight Li2O content loss of <0.3 mol%. Higher than 1400 oC, Li2O out-diffusion caused moderate Li2O content loss of <0.6 mol%.

For the case of Ti4+/Xn+ co-diffusion, it is impossible to evaluate the Li2O-content accurately at the doped surface because of Ti4+ presence, which induces a local index increase. But it is possible to evaluate it indirectly by referencing the situation at the undoped part of the crystal surface. The results show that the Li2O-content at the undoped surface part does not reveal a noticeable change from the single diffusion case to the co-diffusion case, and this is the case for all of the co-diffused LN and LT samples under study. Although the situation in the co-diffused layer is sophisticated because of Ti4+ presence, the composition at the co-doped surface part should not have a large difference from that at the undoped part.

In words, each Xn+ dopant has little contribution to the LN or LT index. The index increase in the Ti4+/Sc3+- or Ti4+/Zr4+-codoped LN layer is contributed mainly from the Ti4+ doping while not from Sc3+ or Zr4+ doping or Li2O out-diffusion. In the Ti4+/Er3+-codoped LN or LT layer, the index increase includes both the dominant contribution from Ti4+ dopants and the slight contribution due to slight Li2O out-diffusion. As Li2O out-diffusion is not serious for the Ti4+/Er3+-codoped samples and is not measurable for the Ti/Sc2O3 and Ti/ZrO2 samples, the diffusivities of both Ti4+ and Xn+ can be regarded as Li2O-content-independent for all of the LN and LT samples under study. Thus, the Ti4+/Xn+ co-diffusion can be described by two independent Fick-type equations with a constant Ti4+ diffusivity and an Xn+ diffusivity independent of Li2O-content but dependent of Ti4+-concentration. Whether the diffusivity is constant or concentration-dependent, Eq. (2) has two possible forms of solution: either the erfc or Gaussian function. When the diffusion time t is shorter than the depletion time of the diffusion reservoir t1, the diffusion reservoir is not exhausted and Eq. (2) has an erfc solution. When t > t1, the reservoir is exhausted, the ions diffuse continuously into the bulk, the surface ion concentration degrades and the profile transforms to a Gaussian type. As stated above, the Xn+ and Ti4+ ions in all the studied samples follow either the Gaussian or the erfc profile. Thus, the model proposed is verified by the experiment.

Finally, we would like to give a brief discussion on the potential application of diffusion-controlled feature. Here we exemplify the Ti4+/Er3+ co-diffusion case in LN. Present study shows that, in the case of co-diffusion with Ti4+, the time required to reach a desired Gaussian Er3+ profile with a typical 1/e depth of 5–6 μm needs only 50 h due to Ti4+-enhanced Er3+ diffusion. While in the Er3+-only diffusion case, this requires at least 100 h. Therefore, by employing the co-diffusion method the time consumed for Er3+ doping and hence the device fabrication period can be shortened substantially. Moreover, as described above, the Ti4+ diffusion results in generation of a large number of additional defects, which favors to promote successively the Er3+ solubility, Er3+ doping concentration and optical gain.

In summary, in the case of single diffusion in LN, Sc3+, Zr4+ and Er3+ ions diffuse respectively five-, four-fold and one order slower than Ti4+. In the case of single diffusion in LT, Er3+ diffuses at least two orders of magnitude slower than Ti4+. In the Ti4+/Xn+ co-diffusion case in LN or LT, the faster Ti4+ assists and controls the diffusion of the slower Xn+ because Ti4+ enters into the bulk prior to the Xn+ due to its higher mobility and the Ti4+ diffusion into the crystal results in generation of a large number of additional defects, which favors and assists the subsequent diffusion of the slower Xn+ ion. The Xn+ diffusivity can be controlled by the initial thickness of Ti-metal film coated and both follow a linear relationship. Different Xn+ ions gains different extents of assistance by Ti4+. This is associated with the differences of Xn+ ions in atomic mass, ionic radius and valence as well. The phenomenon that a faster ion assists and controls diffusion of another slower ion should reflect a generalized physical law. Similar phenomenon should also take place in other solids as long as the diffusion of the faster ion can induce generation of defects. This conclusive anticipation needs to be verified in the future by studying more materials such as semiconductor materials. For the diffusion system studied here, the phenomenon can be utilized to largely shorten the device fabrication period, lower the cost, promote the Er3+ doping concentration and hence improve the device performance. It can be also utilized to develop new materials.

Materials and Methods

Commercial Z-cut congruent LN and LT plates with 0.5 mm thickness and optical grade surfaces were used in the present study. These congruent LN and LT plates have the same Li2O content of 48.6 ± 0.1 mol%. The ordinary and extraordinary refractive indices at the surface of each as-grown plate were first measured. Stacked Ti (99.99%) metal and Sc2O3 (99.999%) [or ZrO2 (99.99%) or Er metal (99.9%)] films with different thicknesses and coating sequences were then coated onto one surface of each plate, and only half of the surface was coated. The uncoated part is for reference. For the reference too, some LN and LT plates were only coated with Ti, Er, Sc2O3 or ZrO2 film. After the film coating, the plates were annealed in an atmosphere of flowing O2 bubbled through room-temperature water at a rate of 1.5 × 10−3 m3/min. Table 1 summarizes the initial metal and oxide film thicknesses coated onto each LN plate. The LN samples studied can be divided into three groups of Ti/Sc2O3, Ti/ZrO2 and Ti/Er. Each group was subjected to a same annealing procedure. The diffusion temperature/duration was chosen as 1130 oC/50 h for the Ti/Er samples and 1060 oC/10 h for the other samples. The 1060 oC/10 h is the standard fabrication condition for a conventional Ti-diffused waveguide on an LN substrate. Table 2 summarizes the Er and Ti film thicknesses coated onto those LT plates. The LT samples studied here can be classified into two groups, i. e., the Er3+-only doped group including samples 1–5 and the Ti4+/Er3+-codoped group with inclusion of samples 6–12. Different from the LN samples, the LT samples were annealed at different temperatures of 1200–1500 oC and for different durations of 10–30 h. Table 2 specifies the diffusion condition adopted for each sample. Note that the samples in Tables 1 have different initial thicknesses and coating sequences of Ti metal and Er metal or oxide films. The asterisk means that the oxide or metal film was coated first.

After diffusion, the ordinary and extraordinary indices at the doped and/or undoped parts of the surface were measured (at 25 ± 0.1 oC). For the Ti4+-only or Ti4+/Xn+-codoped samples, the measurements were carried out only on the undoped surface part because the Ti4+-doping induces an increase of refractive index (and hence formation of an optical waveguide). For the Xn+-only doped samples, the measurements were performed on the Xn+-doped and undoped surface parts. The refractive index was measured at the 1311 and 1553 nm wavelengths using a commercial Metricon 2010 prism coupler (Metricon Corp., Pennington, NJ), which is based on the working principle of measuring the critical angle of total reflection. The refractive index measured by this method is the value at the crystal surface because the total reflection takes place there. For a Z-cut LN or LT plate, one can choose a transverse magnetic/electric polarization scheme to measure the extraordinary/ordinary index.

Secondary ion mass spectrometry (SIMS) was used to analyze the depth profile of diffused Sc, Zr, Er, Ti ions, as well as the substrate constituents Li, Nb, Ta and O. The analysis was accomplished by a time-of-flight second ion mass spectrometry [ToF SIMS V (ION-TOF GmbH, Münster, Germany)]. A Cs+-beam (~45 μm in diameter) with 30–35 nA at 3 keV was used to sputter a crater of either 120 × 120 or 150 × 150 μm2 and a pulsed bismuth ion beam of 1 pA at 25 keV was used to analyze the positive or negative secondary ions. Positive secondary ion detection was adopted for the Ti/Sc2O3 and Ti/Er samples, while negative ion detection was adopted for the Ti/ZrO2 samples to improve Zr sensitivity, which is rather low in the case of positive ion detection. Positive or negative ions from a central area of (18.5 × 18.5) - (25.4 × 25.4) μm2 inside the crater were detected. During the analysis, a low-energy pulsed electron gun was used to neutralize the positive charges and hence degrade the surface charge accumulation. For the same purpose, before the analysis a 30-nm thick silver film was coated on the sample surface to be analyzed. The trace and the depth of each erosion crater were measured by a Tencor Alpha Step 200 profilometer (KLA-Tencor Corp., Milpitas, CA). The depth resolution was mainly determined by the roughness of crater under analysis and is better than 5 nm in our case.

Author Contributions

The experiments were conceived, designed and carried out by D.L.Z., Q.Z. and C.X.Q.; Q.Z. and C.X.Q. prepared the samples and carried out the optical measurements; D.L.Z. and D.Y.Y. analyzed and interpreted the data; The SIMS analysis was performed by W.H.W and E.Y.B.P.; D. L. Z. and E.Y.B.P. wrote the manuscript with the assistance of all other co-authors.

Additional Information

How to cite this article: Zhang, D.-L. et al. Diffusion control of an ion by another in LiNbO3 and LiTaO3 crystals. Sci. Rep. 5, 10018; doi: 10.1038/srep10018 (2015).