1. Introduction

The fabrication of waveguides in nonlinear optical materials such as lithium niobate plays a major technological role in the field of quantum optics and integrated optics [1,2]. Waveguides do not only allow to confine and to guide light in optical integrated circuits (OIC) but also permit to fully utilize the outstanding nonlinear properties of the substrate material [3]. LiNbO₃ (LN) for example shows a strong piezo-electricity, high nonlinear optical coefficients and it is also a ferroelectric [2]. These properties, especially the possibility to achieve quasi-phase-matching (QPM) via domain inversion [4], can be used in OIC for the implementation of novel and more efficient devices.

Concerning the waveguide fabrication in lithium niobate, some well-established methods are titanium in-diffusion (Ti:LN), reverse proton exchange (RPE:LN) [5] and etched ridge waveguides [6]. Moreover, ion implantation provides an easy-to-use and flexible method to fabricate waveguides [7]. In ion-implanted waveguides, the refractive index difference is induced by structural damage at the end of the ion tracks, where nuclear collisions dominate the stopping process. The structural damage modifies the refractive index in the corresponding layer creating a waveguide. Changes in the refractive index of several percent can be achieved with this method, leading to a strong confinement of the light [8].

However, ion implantation is often carried out using low-energy, light ions (H and He) at high fluences which has several limitations concerning waveguide fabrication. First, it severely reduces the nonlinear optical properties of the crystal in the waveguide region due to the lattice damage. Secondly, post-implantation annealing processes can partially remove the refractive index barrier [7], as He easily diffuses out of the sample and does not stabilize the defect structure. As a way to overcome such limitations, the use of heaver ions (atomic mass number A > 12) and higher energies (4-100 MeV) with lower fluences has increased in the last decade [7]. Here, the damage in the waveguide region is mainly induced by electronic interaction, which can be eliminated by low temperature annealing and the refraction index barrier is more stable regarding the annealing process. With this method, the results and possibilities in waveguide fabrication change significantly. Olivares et al. (2005) have shown that amorphization of the lattice only comes into play when the electronic stopping power reaches a certain threshold. The damage in the waveguide region can be limited by low fluences and the refractive index profile necessary for light confinement is achieved due to both the positioning of the implanted ions in the lattice, and by the irreversible and strong structural damage at the end of the implanted-ion trajectories. For example, by irradiating LiNbO₃ with F-ions at fluences of 2x10¹⁴/cm², Bentini et al. (2004) were able to achieve high confinement profiles and losses of around 1 dB/cm [7]. Al-Chalabi even achieved losses as low as 0.2 dB/cm by He-ion implanted waveguides [5]. Thus, the damping lies almost in the same order of magnitude as for other methods such as (RPE:LN), with which Li et al. (1987) [5] were able to produce planar waveguides with optical losses of 0.4 dB/cm, or such as (Ti:LN), with which Luo et al. produced waveguides with losses of 0.022 dB/cm [9]. Furthermore by using (Ti:LN) as well as ridge structures Hu et al. were able to fabricate waveguides with a low damping of 0.05 dB/cm [10].

Especially for nonlinear optical devices, the effect of the mechanism of waveguide formation on the nonlinear properties is crucial. In this context, the effect of a successive annealing process on the position of the implanted ions, the highly-damaged end region and the nonlinear susceptibility presents an interesting topic. Indeed, the annealing can heal lattice defects and therefore helps to recover the nonlinear properties [7]. Although some examinations of the impact on the nonlinear properties concerning light ions (He) implanted into KNbO₃ have been carried out by P. Günter et al. (1995) [11] the influence of heavier ions on the nonlinear properties of most ferroelectric materials remains poorly studied. Since the diffusion rate of heavier ions such as carbon is much lower than for light ones like He, the annealing process may not significantly change the position of the deposited species, so that the refractive index profile is still present after annealing. Furthermore, a much lower fluence is necessary to achieve the same effect in the deposition region.

In order to investigate the suitability of heavy ion implantation for the fabrication of nonlinear optical devices, we examine the impact of carbon implantation on the nonlinear properties of lithium niobate using second-harmonic microscopy and theoretical models. We show that carbon implantation leads to a stable refractive index profile and lower damage due to lower implantation fluence. The post-implantation annealing process leads to a recovery of the nonlinear optical properties of the material, without significantly modifying the doping profile.

2. Sample preparation and experimental instrumentation

Planar waveguides in congruent x-cut MgO:LiNbO₃ were fabricated by carbon-ion implantation using kinetic energies ranging from 3 to 7 MeV with resulting index profiles up to a depth of 4 microns and an irradiation fluence in the regime of 10¹⁴ cm⁻² had been used. To get access to the depth profile of the d₃₃ nonlinear coefficient the samples are polished in a wedge-shape with typical angles of ~1° (Fig. 1). Each sample was cut in two pieces. One half was annealed at 260 °C for 30 minutes, while the second half was kept for reference.

 

Fig. 1 Scheme of the second-harmonic microscopy setup and the sample geometry; note that the wedge angle is exaggerated for better visibility.

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Preceding the nonlinear measurements, the samples were pre-characterized with confocal linear optical microscopy (LEXT OLS4000) and optical widefield microscopy to verify the wedge angles and check the surface quality. The examinations confirm the targeted angles and show good surface quality. In detail, there are no significant differences in roughness in the implanted part of the wedge and the virgin part, which could affect the optical scans.

We apply second-harmonic (SH) microscopy in the confocal regime for measuring the d₃₃ nonlinear coefficient (cf. Fig. 1). Our setup permits a nonlinear analysis with high spatial resolution in three dimensions [4].

For this, the setup uses a femtosecond pulsed laser with a fundamental wavelength of 800 nm. Due to our confocal arrangement [4] (NA = 0.95; pinhole diameter of 500 nm) the detectable SH-signal (400 nm) originates from a very thin layer of the lithium niobate surface (cf. Fig. 2). In combination with the wedge shape (small angle) the lateral movement permits us to scan a depth-profile of the sample. On the other hand, the excitation pulse has a duration of about 100 fs with a repetition rate of 80 MHz and an average power of about 200 mW, which provides sufficient SH signal for the detector and simultaneously does not have any effect on the crystal structure. This has been verified by successive emission power measurements on the same area of the crystal and permits a non-invasive scan.

 

Fig. 2 Result of a cross-section scan orthogonal to the z-axis of the crystal. One sees the colour-coded intensity of the second-harmonic (SH) signal at the surface of the wedge. Note the different scale of the x- and y-axes.

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3. Results

We have obtained the second-order susceptibility depth-profile in the untreated and annealed samples via several cross-section scans (see Fig. 1) orthogonal to the z-axis. An example of the raw data can be seen in Fig. 2.

One can observe the edge of the wedged sample and the surface sensitivity of the setup which collects a signal in a surface-near region with a width of about 700 nm. Using the line of peak intensity and calculating the depth using trigonometric functions as indicated in Fig. 2, the cross-section scans were converted into second-harmonic power depth-profiles, as shown in Fig. 3. Therefore, we normalize the intensity to the intensity of the pristine bulk material below the implanted layer. As far as the untreated samples are concerned, we were able to demonstrate a characteristic trend for all energies (Figs. 3(a) and 3(b)). In the upper part of the sample (waveguide part) we have acquired a slowly decreasing level below the maximal SH intensity. In a second part (index barrier) we get a sharp asymmetric dip quickly increasing to the maximum intensity. This trend has been previously observed in similar investigations [11]. Furthermore, the analysis of the samples with varying energy (Fig. 3(a)) and varying fluences (Fig. 3(b)) shows the expected properties generated by the ion implantation: The implantation depth (intensity minimum) depends on the energy, but the value of the minimum only on the fluence.

 

Fig. 3 Experimentally acquired nonlinear susceptibility profiles (untreated) for a series of samples with a) same fluences but different implantation energies and b) same implantation energy but different fluences.

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In order to better understand the origin of the drop in the nonlinear susceptibility we also simulated the ion implantation with the SRIM software by J. F. Ziegler [12] for implantation energies from 1 to 10 MeV. The SRIM software and underlying code has been widely used and simulations show a wide agreement with experimental results in the past [7, 12]. The simulations describe on the one hand the range of the implanted carbon ions and on the other hand the vacancies and interstitials caused by collisions of the ion beam with the material nuclei. However the simulation does not take into account damage induced via electronic excitations.

To obtain precise results, which include more information beside the mere stoichiometry, the atomic masses and the information that is already integrated into the SRIM code, it was necessary to feed in the characteristic lattice and displacement energies (E_disp and E_latt, respectively) of the lithium niobate crystal [12].

As these two parameters (cf. Fig. 4) have not been determined for LN so far, we have estimated the corresponding values within the density functional theory. Thereby we perform total energy calculations with the Vienna ab initio simulation package (VASP) implementation [13,14] of the projector-augmented-wave method [15] potentials, with projectors up to l = 3 for Nb and l = 2 for Li, C and O. The wave functions are expanded into plane waves up to a cutoff energy of 400 eV, while the mean-field effects of exchange and correlation are modeled by the PW91 functional [16]. As an approximation, we calculate E_disp and E_latt for ideal, stoichiometric lithium niobate. The presence of intrinsic defects as occurring in congruent LN [17,18] is neglected. Thus, the calculations are performed with rhombohedral 80 atom supercells representing a 2 × 2 × 2 repetition of the LN primitive cell, and a 4 × 4 × 4 Monkhorst-Pack k-point mesh [19] is used to sample the Brillouin zone.

 

Fig. 4 Ball-and-stick illustration of atoms leaving their lattice sites and the calculated energy parameters for the SRIM simulation. Note that red balls are oxygen, light gray balls are niobium and dark gray balls are lithium ions.

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The displacement energy E_disp represents the energy needed to move a target atom more than one atomic spacing away from its original site. It is assumed that when it does not move more than one lattice spacing the atom hops back giving up its recoil energy into phonons. The most fundamental type of damage generated by the displacement is a “Frenkel-Pair”: a single vacancy and a nearby interstitial atom. These defects have been previously investigated by DFT [20–22]. The values were calculated by moving the atom in a simulation in steps of 0.25 Å into an interstitial position and letting the system relax. The minimum energy for which the atom does not hop back to its original place is then the displacement energy. The calculated values as well as the displacement directions are illustrated in Fig. 4.

The lattice binding energy E_latt is the energy a recoiling atom loses when it leaves its lattice site and recoils in the target. The energy invested in breaking electronic bonds and displace the atom off its lattice site is assumed to be transferred into phonons. This part of the energy transferred to a recoiling atom is lost into the surrounding lattice and does not add to the kinetic energy of the recoiled atom. As it is always necessary for a leaving atom to break the bond, the lattice binding energy is always lower than the displacement energy. It is calculated as the difference of the total energy of the system with the atom in the original position and in the interstitial position. Again, the calculated values are reported in Fig. 4. The values of E_disp and E_latt estimated in this work are of similar magnitude of available data for polar oxides [12].

Using the values calculated with the DFT, we obtain the results concerning the ion ranges and the interstitial density distributions illustrated in Fig. 5(a) for an implantation energy of 3 MeV. The graph suggests that the density of the carbon ions is 2-3 orders of magnitude lower than the defect density which supports the fact that the chemical species of the implanted ions should not have crucial influence on the optical properties [6]. Furthermore an interesting fact is the dominance of oxygen interstitials which do not occur in equilibrium as-grown LN. This can be explained in the framework of the used model. Firstly, the energy transfer is very efficient due to almost identical masses with the carbon implanted ions. Second, the probability of scattering is higher due to the high number of oxygen per unit cell. Whether these defects however are also long time stable in the actual samples, still needs to be determined in the future. To get a better comparison of the trends of these curves (including also the generated vacancies) they are plotted normalized to their maxima (Fig. 5(b)).

 

Fig. 5 Simulation results for 3 MeV implantation energy. The graph shows a) the density distributions of carbon and the different interstitials (note that the carbon distribution was multiplied by 100 for better visibility) and b) the normalized density distributions of carbon and the different defects.

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The data of the different defect densities in Fig. 5 show an almost identical trend for all defects, whereas the distribution of the carbon ions is much more localized. Note that due to conservation of momentum the vacancies and interstitial curve show a shift of several lattice constants which is not visible at the scale of the diagram.

In addition, we compare the defect density generated by nuclear scattering with the second-harmonic power profiles. However, it is necessary to have an estimation on the impact of the electronically induced damage. Therefore, we plot the calculated electronic and nuclear stopping forces for the 3 MeV sample in Fig. 6.

 

Fig. 6 Simulation results for 3 MeV implantation energy. The graph shows the stopping forces for the electronic and the nuclear interaction.

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Although we can recognize the similarities between the nuclear stopping force and the defect densities due to nuclear scattering calculated by the SRIM software (cf. Fig. 5), a direct comparison of the electronic stopping force with a corresponding defect density is not possible because the transfer of energy loss to the electronic damage is a nonlinear function. However, the graph shows some fundamental relations, which are important for later interpretations. It expresses that the electronic stopping (and therefore damage via electronic interaction) is most efficient when the ions are fastest whereas the nuclear scattering behaves in an opposite way [12]. Therefore we expect more impact of the electronic interaction in the surface-near region and less in the region of the dip of the second-harmonic power. Furthermore, the absolute values of the electronic stopping are dominant over the nuclear stopping, which is common in this energy regime [7].

In a following step we compare the carbon distribution and the defect density distribution to our measured SH profile. Since the carbon-ion distribution is localized in a certain depth below the main part of the lattice damage one can suggest that the impurity atoms do not significantly change the emission intensity. But instead, the change is caused by the lattice defects.

The comparison of the peak of defect density distribution and the dip in the nonlinear susceptibility however yields only small differences of about 100 nm which are due to the polishing process after the implantation and limitations of the theoretical model. Thus, we deliberately set the peak and dip to the same depth and project the defect density into the SH depth-profile and normalize it to the value of the dip. The result is shown in Fig. 7 and demonstrates how well the shapes of the two curves correspond. At least in the area of the index barrier (carbon distribution peak) the curves show very good correspondence which gets worse in surface-near regions. However, this might be due to the simulation which cannot simulate the damage caused by the electronic energy deposition [12]. This damage is able to explain the offset in the upper region [23] where the energy loss has to be mostly induced by phenomena of the electronic interaction of the impinging ions and the material and grows with increasing implantation energy.

 

Fig. 7 Comparison of the defect distribution with the second-harmonic depth-profiles (for 3 MeV (left) and 6 MeV (right)).

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The observed change induced via the electronic interaction in the nonlinear susceptibility is however small in relation to the nuclear interaction, although stopping forces are much higher (cf. Fig. 6). In fact, a relative low transfer of deposited energy into permanent structural damage is often observed when the stopping force is below a certain threshold. For LiNbO₃ literature suggests that amorphous track forming starts with stopping forces of more than 5keV/nm [7], which are not reached in this case. Hence, we can exclude track formation in the sample. In contrast, the relative low transfer of deposited energy into lattice defects can also be linked to the low change of the nonlinear susceptibility in our case. Thus, we can suppose that the energy deposited in the electronic system is often not large or concentrated enough to break bonds when thermalizing, since opposed to a direct nuclear collision, the energy is more distributed. Moreover, we see a strong correlation between the lattice defects and the optical susceptibility of second-order, which proves to be very sensitive to structural changes.

On the other hand, the annealed samples show similar behavior compared to the as-implanted samples with some specific differences, namely the dips as well as the levels went up by about 10-25% of the maximum value (cf. Figs. 8(a) and (b)).

 

Fig. 8 Second-harmonic depth-profiles for a) a single implanted and b) a doubly implanted sample for the annealed (red) and as implanted (black) case. For the annealing process we used a temperature of 300 °C and an exposure time of 30 min.

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Figure 8 shows the SH depth-profile for a single and doubly implanted sample in the untreated and annealed case. Therefore, in Fig. 8(b) the implantation profile is modified to a superposition of two profiles for different energies. Note for example, that the highlighted signal dip ΔI corresponding to 4 MeV is below the signal intensity for the 7 MeV dip, although both ions are implanted with the same fluence. In fact, the 7 MeV ions, which penetrate deeper into the material, leave an additional amount of damage to the profile of the 4 MeV ions. This damage corresponds to the lowered level which is observed as a typical characteristic of all the depth profiles.

Thus the annealing process has partially recovered the damage in the lattice structure. A re-increase of the nonlinear properties which is proportional to the induced damage appears for almost every sample of the series (Fig. 9), which shows the stochastic nature of the healing-process. Therefore, it remains an interesting aspect to tune the annealing parameters and to test how much re-crystallization can be achieved, when simultaneously further re-crystallization decreases the optical barrier of the waveguide, which has to be avoided for devices [24].

 

Fig. 9 Overview of the re-enhancement of the second-harmonic power emission after annealing for different implantation fluences. Note that ΔI corresponds to the highest signal drop illustrated in Fig. 8(a).

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4. Conclusion

The second-harmonic properties of waveguides fabricated by ion implantation in congruent MgO:LiNbO₃ were examined by spatially resolved and surface-sensitive SH-microscopy. In detail, we use x-cut samples which are polished in a wedge shape geometry to obtain information in depth via cross-section scans. The emerging depth-profiles of the SH power provide us with maps of the magnitude of the effective nonlinear coefficient. All obtained data show a specific behavior which can be subdivided in three regions. In the most surface-near region we observe a slowly decreasing level. The second region is characterized by a characteristic dip, which can be linked to the nuclear interaction damage. In the third region (bulk) the SH response corresponds to the virgin material again.

For a microscopic insight, we simulate the ion implantation using the “SRIM” software package. The simulation data primarily states that the ion irradiation induced defect density surpasses the density of the incorporated carbon ions distribution by 2-3 orders of magnitude and therefore the defects dominate the changes in the crystal properties. Secondly, the data also suggest that a considerable amount of energy was put into electronic interactions and corresponding electronic defects.

With this knowledge, we compare the typical defect distribution curve with the obtained SH intensity depth-profiles and obtain good agreement in the dip region caused by nuclear induced damage. An additional decrease of the intensity in the surface-near region is traced back to the damage introduced via electronic excitations by the impinging ions.

In this context, the examination of the annealed samples delivers an expected result: The SH-emission increases for the entire depth range in dependence of the formerly induced damage. In combination with the usage of even heavier ions, where the electronic stopping force becomes dominant, this opens up interesting possibilities for the optimization of the waveguide formation mechanism including the post-implantation process.