Characterizations of two-photon absorption process induced by defects in aluminum nitride using Z-scan method

In this work, we reported two-photon absorption (TPA) measurements for aluminum vacancies in Aluminum nitride single crystals. We measured the linear transmission and identified the defect levels. Using the Z-scan method, we measured the TPA coefficients of the transitions between defect levels from 380 nm to 735 nm. The transition occurs between the aluminum vacancies defect levels. Furthermore, the power dependence shows good linear fitting, confirming the TPA mechanism. These results will be helpful for the design and fabrication of ultra-low loss waveguides and integrated photonics in the ultraviolet spectral range.


Introduction
Aluminum nitride (AlN) has become a focal point in the realms of photonics and optoelectronics.Traditionally employed in ultraviolet (UV) light-emitting diodes (LEDs) Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.[1,2], high-power laser diodes [3], and photovoltaic devices [4,5], AlN's allure lies in its ultra-wide bandgap (6.2 eV) and high thermal conductivity [6].In the last decade, AlN has emerged as a promising material for integrated photonic applications in the UV-visible spectrum [7].Its intrinsic ultrawide bandgap establishes a transparent window spanning UV to visible wavelengths.Additionally, AlN exhibits exceptional nonlinear optical properties, enabling the development of diverse nonlinear photonic devices and high-performance on-chip electro-optical modulators [8][9][10].Further enhancing its appeal, AlN's compatibility with both traditional CMOS techniques and other III-N material platforms like gallium nitride (GaN) facilitates the heterogeneous integration of light sources, waveguides, modulators, and detectors onto a single photonic chip [11].Moreover, emerging research has been revealing novel structural phases of AlN with intriguing mechanical, thermodynamic, and electronic properties [12,13].As a result, AlN holds significant potential for integrated photonic circuits operating in the UV-visible regime.
Despite its significance, defects arising from hightemperature growth conditions are common in AlN single crystals [14][15][16], leading to increased absorption lossparticularly under high optical power density.Integrated photonic waveguides and resonators often experience performance degradation due to the two-photon absorption (TPA) process [17,18].To comprehend and enhance the performance of AlN-based integrated photonic devices, it is crucial to scrutinize material absorption, particularly TPA, under high optical power density conditions.This study undertakes comprehensive investigations into the TPA of AlN under the high optical power density regime by employing the Z-scan method.The Z-scan method has been widely used in nonlinear research in the last few decades.By focusing a laser through a lens, only the extreme optical intensity at the focal point can trigger various nonlinear optical processes including TPA [19][20][21], three-photon absorption [22], saturation absorption [23], Kerr effect [24], and photoluminescent [25].Therefore, by moving the material in and out of the focal point along the propagation direction of the laser beam (designated as the Z-axis), we can observe transitions between the regime of linear optics (low-power, out-of-focus) and nonlinear optics (high-power, in-focus), which help reveal the nonlinear optical properties of materials under tests.Here, utilizing the Z-scan method, we extracted the TPA coefficient of AlN and explored the wavelength and power dependence of TPA.The findings of our work can be beneficial for optimizing AlN growth conditions thereby contributing to the enhancement of performance in AlN-based integrated photonic devices and circuits.

Material characteristics of AIN
The bulk AlN substrate has a hexagonal Wurtzite structure and crystallizes in the hexagonal P6 3 mc space group (No. 186).Four nitrogen N 3− atoms form a corner-sharing AlN4 tetrahedron to confine an aluminum Al 3+ atom.Each Al atom is coordinated tetrahedrally to form four equivalent bonds with N atoms.Typically, wurtzite AlN crystals show three common growth planes, c-plane (0001), m-plane (11 10), and a-plane (11 20).To identify the orientation of our bulk AlN sample, an x-ray diffraction (XRD) measurement was conducted, and the result is shown in figure 1(a).By comparing with the standard XRD data of AlN crystal, all peaks in the XRD figure are identified.The XRD pattern of the bulk AlN sample shows a strong characteristic diffraction peak (0002), indicating that the crystal possesses single-crystal quality along c-plane orientation.The insets show the diagram of the 2θ scanning method and the different orientations of AlN material, including c-, m-, and a-plane.
To further confirm the single-crystal quality of the bulk AlN sample, we measured the rocking curve (RC) of the (0002) plane as shown in figure 1(b).The inset shows the illustration of the RC scanning method.RC measurement reveals the width of the diffraction peaks.The measured full-width half maximum (FWHM) is 0.0098 • (∼35 arcsecs), which is a stateof-art quality [26][27][28].The increase in the peak widths can be attributed to the misorientation and stain of crystallites.This extremely narrow peak indicates the supreme single-crystal quality.
Ideally, the ultra-wide bandgap of 6.2 eV of AlN corresponds to a cut-off wavelength for lossless light transmission as deep as 200 nm, indicating high transparency from deep ultraviolet to near-infrared (NIR) spectra.However, the hightemperature environment for growing high-quality AlN inevitably introduces defects to the AlN crystals.That's the reason why various defects such as aluminum vacancies (V Al ), nitrogen vacancies (V N ), and oxygen substitutional impurity (O N ) exist inside the AlN crystals [14].Since the required formation energies for various defects are different, the generated defects exist along different crystal orientations.Since N atoms are usually used as end-capping atoms along [0001] orientation, V N defects can be produced on the crystal face along [0001] orientation under a high-temperature growth condition.These defects introduce new defect levels between the valance band and conduct band, resulting in new photon absorption peaks.Thus, the obtained AlN single crystal usually shows a pale yellow color [29], which is the same as the color of our sample.
To measure the absorption, the transmittance from 200 nm (deep UV) to 1000 nm (IR) of the AlN single crystal sample was measured in figure 1(c).In order to reduce the scattering loss and increase the transmittance during the measurements, Allied High Tech MultiPrep™ System was applied to polish the sample.The backside of the AlN substrate sample was polished by a machine-assisted grinding method with a diamond lapping film of 0.1 µm grade.The thickness of the sample was measured by a micrometer to be 207 µm.The polishing process was carefully controlled so that the thickness of different locations on the sample was almost identical.Two measurements were carried out in different locations on this sample.Their results are almost identical as well.The transmittance stays at ∼70% in visible spectra and significantly decreases at short wavelength from 450 nm.The inset shows a cut-off wavelength at around 370 nm, which is longer than the predicted 206 nm.The red-shifting phenomenon of the cut-off wavelength is assumed to be caused by the defect levels.To identify the exact location of the defect level, the linear absorption coefficient α is calculated as well using equation ( 1): In equation (1), ν is the frequency of incident photons, hν is the energy of incident photons, E g is the material intrinsic bandgap, and A is the linear fitting slop.As shown in figure 1(d), a linear fitting was applied at the absorption edge.We can find the bandgap is 3.317 eV (373.8 nm), which is much smaller than the intrinsic bandgap 6.2 eV (200 nm).Similar absorption peaks were observed in previous reports as well.Thus, we can confirm that this absorption is caused by the transition between the defect levels.From the calculation and analysis, this absorption is mainly caused by the aluminum vacancy (V Al ) [30].And it was identified as the transition between the V Al 2− level and V Al 3− level.

TPA characterization of AIN based on Z-scan measurements
To further investigate the absorption properties of this defect level, we built a Z-scan system to test it under high optical power density.Besides the linear absorption under low energy intensity, there are nonlinear absorption needs to be taken into consideration as well.With the increasing light intensity, the multi-photon absorption becomes significant.As shown in figures 2(a) and (b), the measurement setup is based on the Z-scan method [19,24,31].The light source was an ultrafast titanium-sapphire laser with a 100 fs pulse width and 80 MHz repetition rate (Chameleon Discovery NX).The laser was tunable from 680 nm to 1300 nm.A commercial frequency doubler with χ 2 crystal was used to generate a second harmonic wave from 340 nm to 650 nm.Due to the power attenuation from the optics and the linear absorption from the sample in the UV region, the shortest working wavelength was limited to 380 nm in this work.The mainstem laser was then focused by an objective lens (×5, NA = 0.1) and normally coupled onto the AlN sample.The sample was placed on a translation stage to move across the focal point.The transmitted light was then collected by a lens and sent to a power meter.
To test the reliability of the setup, the beam size of the output light was used as an indicator.Based on the equation ( 2), with a Gaussian (beam propagation ratio M 2 = 1) incident beam diameter (D) of 4 mm and a focal length (f ) of 25.4 mm, the waist radius (ω 0 ) of spot size is ∼4 µm (1/e 2 of maximum intensity) at the focal point.λ is the wavelength of incident photons.This value was consistent with the beam diameter we extracted from open-aperture Z-scan measurements.The incident power was controlled under 250 mW, corresponding to the single pulse energy density of 0.0062 J cm −2 .The laserinduced damage threshold measured for femtosecond pulses of AlN material is 1.06 ± 0.26 J cm −2 , which is almost 200 times higher than the operation pulse energy density used in this work [32].Thus, we neglected the laser-induced damage effects.
For time-to-flight measurement, the laser power was sampled 7% by a beam splitter and the branch was sent to a power meter for real-time monitoring.The power meter can monitor the incident power when collecting the transmission light, which excludes the influence of the power fluctuation of the pump laser.
Due to the linear absorption and reflectance, the effective thickness is different from the physical thickness.As shown in figure 2(c), we calculate the effective thickness using the transmittance measurement and reflectance calculations.It is smaller than the physical one and decreases towards a short wavelength due to the high absorption in UV.The effective thickness will be applied to our Z-scan measurements shown below.
The sample translation and data collection were controlled by a homemade script to enable automatic testing.As shown in figure 2(d), the sample was controlled to move precisely step by step by 50 µm.Since the power meter needs response time, the data was collected only after the intensity value became stable.
The TPA coefficient can be obtained from the open aperture scanning using equations ( 3) and (4) [21]: T is the normalized transmittance.α TPA is the TPA coefficient.I 0 is the peak laser intensity at the center of the focal spot.L eff is the effective sample thickness as we discussed before.Z is the translation distance of the AlN sample from the focal position.Z 0 is the Reighley range of the laser beam, which should be larger than the physical thickness of the sample to satisfy the thin film approximation in this Z-scan method.n is the linear refractive index, which is dependent on wavelength.λ is the wavelength in free space.
The wavelength dependence of the TPA coefficient is plotted in figure 3(a).For the data credibility, five positions were randomly chosen on the sample.Each position was tested independently.And finally, the mean value, standard deviation, and standard error (SE) are plotted as well.After the statistical analysis, the curve shows a broad peak at around a wavelength of 600 nm.It decreases slowly towards the UV region, and fast towards the infrared region.The cut-off wavelength is at ∼740 nm, which is exactly twice the cut-off wavelength in our transmittance measurements in figure 1(d).Therefore, we can confirm that the TPA occurs between the V Al 2− and V Al 3− defect levels as we described above.It is the main reason causing the red-shifting of cut-off wavelength from 200 nm to 373 nm.The broad TPA peak may come from the broad defect levels.Additionally, there is no shoulder peak observed, so the transitions between these two defect levels is much stronger than other transitions.Our result concurs well with previous TPA reports on other wide bandgap materials, such as GaN [20] and β-Ga 2 O 3 [21] 1 The power dependence was tested under two wavelengths: 500 nm and 650 nm.Figures 3(b) and (c) show the scanning results under different incident power.The scattered data was fitted with equation (3).It can be clearly observed that the TPA becomes more and more significant with the increasing laser power, which supports our expectations.By finding the valley points, we can extract the maximum transmittance drop (∆T), which occurs at the focal point (z = 0).According to equation ( 5), ∆T should be theoretically proportional to the peak intensity I 0 .We plotted the scattered points ∆T with I 0 in the insets.Both figures 3(b) and (c) show a pretty good linear fitting result.Therefore, we can draw two conclusions: (1) only TPA contributes to the transitions between defect levels.The fitting relationship is the way how to distinguish multiphoton absorptions.The ∆T (z = 0) in one-photon absorption are caused by geometry scattering, which is independent of I 0 .The ∆T (z = 0) in TPA is linearly proportional to I 0 , which is observed in our results.The ∆T (z = 0) in three-photon or four-photon absorption is quadratically or cubically proportional to I 0 .Thus, we can know there was only TPA during the z-scan.(2) Absorption saturation was not observed in the AlN sample.Typically, absorption saturation occurs when there is insufficient time for carriers to decay back to the ground state before the ground state becomes depleted, which results in decreased absorption at high incident light intensity.The insets show good linear fitting even under high laser intensity, implying those defect levels may have a fast response time.

Conclusion
In summary, we report TPA measurements for aluminum vacancies in AlN single crystals.Using the Z-scan method, we measured the TPA coefficients from 380 nm to 735 nm.AlN exhibits the maximum TPA coefficient of 1.04 cm GW −1 at the wavelength of 650 nm.The TPA coefficient has a cutoff wavelength at 740 nm, which agrees with the linear transmission cut-off wavelength at 373 nm.The transition occurs between the aluminum vacancies defect levels.Furthermore, the power dependence shows good linear fitting, confirming the TPA mechanism.Absorption saturation was not observed in this sample.These results will be important for the design and fabrication of ultra-low loss waveguides and nonlinear integrated photonics in the UV regime and under high laser intensity.

Figure 1 .
Figure 1.(a) XRD 2θ scanning on the AlN sample.The crystal mainly orientates along the characteristic diffraction peak (0002).The insets show the 2θ scanning setup and different orientations in AlN crystal (c-, m-, a-plane).(b) XRD ω scanning on the (0002) plane.The small FWHM = 0.0098 • (∼35 arcsec) indicates excellent crystal quality.The insets show the ω scanning setup.(c) Linear transmittance measurements on different locations on the AlN sample.The absorption coefficient α is calculated and plotted as well.The inset shows the detail at the absorption edge.(d) According to equation (1), the (αhν) 2 is plotted by the photon energy.A linear fitting was applied at the absorption edge, and the bandgap was found to be 3.317 eV.

Figure 2 .
Figure 2. (a) Illustration of the Z-scan measurement system.(b) Diagram of the Z-scan measurement system.OB is the objective lens to focus the incident beam.L is the lens to collect the transmission light.A is the aperture.PC is the computer to automatically control the stage translation and data collection.(c) The difference between the physical thickness (207 µm) and the effective thickness considering linear absorption and reflectance.(d) Data recording when the stage moves across the focal point.As shown in the inset, the data was recorded only when the intensity value was stable.

Figure 3 .
Figure 3. (a) Wavelength dependence of TPA coefficient from UV to visible spectra.A broad peak was observed at ∼600 nm.A cut-off wavelength was observed at ∼740 nm, which agrees with the linear transmission measurements.(b) Power dependence of Z-scan curves at the wavelength of 500 nm.(c) Power dependence of Z-scan curves at the wavelength of 650 nm.The insets show the linear dependence between the maximum transmission drop and the peak laser intensity.