Polarization dependent multiphoton absorption in ZnO thin films

Studying the polarization dependent nonlinear absorption of intense femtosecond laser pulses in solids is of major interest for fundamental physics as well as for many technological applications, such as the polarization dependent damage threshold of materials. Conventionally, either laser induced material modifications [1–3] or photoconductivity measurements [4–7] have been conducted to clarify the role of the laser pulse polarization for the carrier excitation. In this work, we report on the pump laser polarization dependence of the near ultraviolet (NUV) emission from intrinsic and Al-doped ZnO polycrystalline thin films to study the role of the laser ellipticity in the electron excitation process. In contrast to earlier works [4–7], our method allows to precisely determine the amount of nonlinearly excited carriers with a straightforward and non-destructive approach.

The thin films were optically excited with 50 fs long laser pulses at a central wavelength of 810 nm and 1 kHz repetition rate, delivered from an amplified Ti:sapphire laser system. A λ/2-plate in combination with a thin film polarizer was used to adjust the pulse energy in the experiment (see supplementary information, figure S1 (stacks.iop.org/JPhysD/53/055102/mmedia)). The polarization was controlled with a broadband λ/4-plate. The laser pulses were loosely focused with a spherical lens (f   =  50 cm) onto the sample at normal incidence. The sample was placed out of focus where the beam diameter was ~0.6 mm in order to further reduce the intensity below the damage threshold. The emitted NUV light was collected in transmission geometry using a 36  ×  magnification reflective objective (Newport 50102) and detected with a spectrometer (Ocean Optics USB 4000). All experiments were carried out at room temperature and ambient atmosphere.

Intrinsic, about 300 nm thick, polycrystalline ZnO thin films were grown by magnetron rf-sputtering (rf-power about 150 W) on 0.5 mm thick c-plane sapphire substrates at a pressure of about 2.95 · 10⁻³ mbar in an argon atmosphere with a small amount (2 vol%) of oxygen. The Al-doped ZnO thin films were fabricated by subsequent ion implantation of aluminium into the as-grown intrinsic ZnO thin films. We used a combination of several ion energies ranging from 40 to 300 keV in order to ensure a homogeneous doping profile from 50 nm to 200 nm (see supplementary information, figure S2). The ion ranges were simulated with the Monte-Carlo program package SRIM [8]. We used ion fluences ranging from 5 · 10¹⁴ ions cm⁻² at 40 keV to 5.7 · 10¹⁵ ions cm⁻² at 180 keV, yielding an Al-concentration roughly being 0.5 at.%. Finally, both samples were thermally annealed in air at 900 °C for 60 min for removing the implantation damage. The structural properties of the films were analysed with scanning electron microscopy (SEM) and x-ray diffraction (XRD). The XRD data reveal a preferred c-plane crystalline orientation of the grains perpendicular to the surface normal of both the intrinsic and Al-doped ZnO thin films. Using the Scherrer equation [9], a comparable grain size of ~200 nm for both, the intrinsic and the Al-doped thin film, was determined. The SEM images, see supplementary information figure S3, were used to confirm the column like growth of the thin film grains and the film thickness.

Polycrystalline ZnO thin films are well known sources of stimulated NUV emission when they are pumped by single photon absorption in the UV [10–19]. Instead, we used ~50 fs long pump pulses at 810 nm central wavelength in our experiment. According to the ratio of the intrinsic ZnO band gap (3.37 eV) and our pump-photon energy (1.53 eV), carrier excitation requires a three photon absorption process to excite one electron from the valence (VB) to the conduction band (CB) [20, 21]. The resulting emission of intrinsic and Al-doped ZnO thin films were measured and are shown in figures 1(a) and (b) for pump intensities below, close to, and above the threshold for stimulated emission using linear polarized laser pulses. Two dominant emission bands/lines, at 378 nm and 405 nm, are observed in the emission spectra for the lowest excitation intensity. These lines originate from the recombination of free excitions in ZnO at room temperature [10–12] and second harmonic generation (SHG) in ZnO of the pumping laser pulse [22], respectively. Increasing the pump intensity, a third distinct line emerges between the emission lines from the excitons and SHG. With increasing pump intensity, this additional emission line shows a strong red-shift and a super-linear increase. Therefore, this third emission band is attributed to stimulated emission originating from the electron hole plasma (EHP) at high excitation densities [10–15]. All intensities given in the text are corrected for the reflection losses at the interfaces air-substrate and substrate-thin film.

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In the following, we only consider the evolution of the spectral features attributed to excitons and stimulated emission of ZnO not discussing the SHG signal, which has been already widely studied [22]. In order to distinguish between the different contributions of the measured spectra, we fitted a sum of three Gaussian distributions to the measured data. While the full width half maximum (FWHM) and the position of the emission maximum were directly obtained from the fit, the total yield was determined by integrating the contributions from the spontaneous and stimulated emission. Figures 1(c)–(e) show the spectrally integrated emission yield, the spectral FWHM, and the position of the emission maxima as a function of the excitation laser intensity for the intrinsic (blue) and Al-doped ZnO thin film samples (red). The vertical dashed lines indicate the threshold intensity when the stimulated emission from an EHP dominates the emission spectra. We observe a lower threshold and a more pronounced broadening of the emission spectra for the doped sample. This can be explained by the higher intrinsic carrier density in the conduction band (CB) for the highly n-type doped ZnO. Thus, less additional carriers have to be excited to reach the Mott density for EHP formation [23]. Additionally, the activated dopants block the low CB states and hence reduce the loss in the lasing process due to reabsorption. In our case we exclude significant effects caused by a variation of the doping dependent band gap because of the minor difference of only a few tenth of meV for the intrinsic and the 0.5 at.% doped thin film [24, 25].

However, the qualitative evolution of the integrated yield, FWHM and the position of the emission maximum are similar below the threshold for both the intrinsic and Al-doped ZnO thin films. We observe a nearly constant FWHM and position of the emission maximum of free excitons, only the integrated yield increases with the pump intensity. Near the stimulated emission threshold, the yield, FWHM, and emission maximum show a rapid change with the pump intensity, in agreement with previous experiments [10–12, 15]. Near the pump laser threshold, we observed a deviation from the expected slope of 3 for the spontaneous emission expected for a three photon absorption process. This deviation is a signature that stimulated emission already provides a significant contribution to the emission. For a better understanding of the laser performance and especially the role of multiphoton excitation we calculated the photon yield as a function of the pumping intensity. We solved a set of three coupled rate equations considering the temporal evolution of the photon number, density of hot and thermal electrons, respectively. The equations as well as the boundary conditions and parameters used in the model are given in the SI. The calculated integrated photon yield as a function of the excitation intensity is depicted in figure 1(c)) and is in excellent agreement with experimentally measured numbers after a reasonable choice of the model parameters, as explained in the SI. The agreement provides not only confidence for the validity of the model it is also a further proof of lasing in the thin films.

The XRD measurements of our samples show that the c-axes of the micro-crystallites are preferentially oriented perpendicular to the sample surface. Thus, we expect no dependence of the emission when rotating the linear polarization direction under normal incidence. Indeed, our measurements confirmed that the emission spectra are identical for all orientations of the incident linear polarization. Thus, we can exclude any absorption anisotropy for linearly polarized pumping.

The influence of the pump beam ellipticity for three photon absorption in thin ZnO films is presented in figure 2 for a pumping intensity below the threshold for stimulated emission. For this intensity only the broadband emission around 380 nm is observed. Figures 2(b) and c) show a comparison of the ellipticity dependence for the spectrally integrated emission signal of the intrinsic and the Al-doped sample. For both samples, the strongest integrated emission signal is observed for linear polarization and the modulation period is about 90° (rotation angle of the λ/4 plate) with a pronounced minimum for circular polarization. The emission yield for circularly polarized pump pulses is about 0.6 times lower than for linear polarization. Our results indicate that the dependence of emission on the pump laser ellipticity is not affected by doping and resulting enhanced density of free carriers.

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Figure 3(a) shows the emission spectra as function of the rotation angle of the λ/4-plate while the pump intensity is fixed to 0.95 times the threshold intensity. The stronger emission for linear polarization pumping is clearly demonstrated in agreement with the results for pure spontaneous emission in figure 2. Figure 3(b) depicts the emission spectra for linear (green) and circular (black) polarized pump pulses. While the broad emission of free excitons is observed for both polarizations, the stimulated emission peak at around 390 nm is only observed for linearly polarized pumping. Therefore, the onset of stimulated emission can be controlled by adjusting the pump beam ellipticity.

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Both the onset of stimulated emission (figure 3) and the intensity of excitonic emission (figure 3) is linked to the number of excited carriers. Our results indicate that the generation of excited carriers i.e. the absorption of the pump pulse energy is strongly influenced by the polarization of the pump laser. For both ZnO samples, we observe an enhanced absorption for linearly polarized light compared to circular polarization. This finding is not in full agreement with previously published results [4] suggesting that for low order N-photon absorption (N  <  5) circularly polarized light is more effective than linearly polarized, and for a N  =  6 photon process linearly polarized light results into a higher excited carrier density. The findings of Temnov et al [4] are confirmed by experiments on laser material processing using linearly and circularly polarized laser pulses [2, 3]. Additionally, Liu et al [1] observed a dependence of the linear and circular laser induced damage threshold on the numerical aperture (NA) of the focusing optics in the experiment. Gawelda et al [26] investigated laser polarization dependent generation of filaments in dielectrics and found a higher critical power to initiate a filament using circularly polarized pulses compared to linearly polarized ones. This contrasts with the measurements of Du et al [27] showing the same threshold intensity for laser induced breakdown in dielectrics using linearly or circularly polarized laser beams. These previous investigations, besides their very different experimental conditions, do not allow distinguishing between the polarization dependence of the nonlinear absorption and the polarization dependence of the subsequent processes such as self-focusing or avalanche ionization. In our experiments, nonlinear propagation effects like self-focusing can be safely excluded due to the small thickness of the ZnO films. Simulations for our experimental parameters reveal that avalanche ionization can be neglected and the carriers are excited via three-photon absorption only. Therefore, our experimental setup provides direct access to the polarization dependent three-photon absorption coefficient. From the results presented in figure 2 we estimate the ratio of the spectrally integrated spontaneous emission signal for linear and circular polarizations of the pump pulse to ~1.8. This ratio is also independent from the pump intensity. To understand the observed ratio, we followed the work of Arifzhanov et al [5]. They investigated the polarization dependence of the three-photon excitation rate in bulk semiconductors theoretically and experimentally. Their study revealed that the three-photon absorption rate for linear and circular polarization varies as a function of the ratio $\frac{3 \hbar \omega }{{{E}_{g}}}$, where ${{E}_{g}}$ is the band gap of the material and $\hbar \omega$ is the pumping photon energy. Using this approach, we estimated the ratio of the three-photon absorption coefficients for linear and circular polarized light to be ~1.5 for our experimental conditions. This ratio is directly related to the measured ratio of the integrated spontaneous emission yield of ~1.8 determined in our experiment (figure 2). The observed higher three photon absorption rate for linearly polarized light can be explained by the higher number of allowed optical transitions for a given band structure including the contributions of higher conduction band states [5, 6]. From the integrated yield of the emission spectra shown in figure 3(b)) we can estimate an integrated yield ratio of 5.1 between linear and circular pumping. Solving the rate equations (given in the SI) for an intensity of 0.95 I_th, we obtain a ratio of the integrated photon yield of 4.7 between linear and circular pumping, if we assumed a three photon absorption coefficient of ${{\alpha }_{3,lin}}\sim 0.5\cdot {{10}^{-27}}\,{{{\rm m}}^{3}}\,{{{\rm W}}^{-2}}~$ for linear radiation and ${{\alpha }_{3,circ~}}=\left( \frac{1}{1.8} \right){{\alpha }_{3,lin}}$ for circular polarization, respectively, according to the results for spontaneous emission. Thus, the excellent agreement between experiment and simulation proofs that the three photon absorption coefficients for circularly polarized light can be directly determined from the absorption coefficient for linear polarized light and the ratio of the photoluminescence given in figure 2(b) and 3(b).

In conclusion, we demonstrated stimulated emission from rf magnetron sputtered polycrystalline ZnO thin films pumped by femtosecond laser pulses via three photon absorption with a threshold of about 1.3 TW cm⁻². This threshold was lowered to 0.95 TW cm⁻² (by a factor of 0.73) by doping the polycrystalline ZnO thin film samples with 0.5 at.% aluminum due to an enhanced EHP formation and a reduced reabsorption rate caused by state blocking. The sharp intensity threshold for the stimulated emission makes thin film samples an ideal system for investigating the polarization dependent nonlinear absorption. The maximum emission yield was observed for pumping situation with linearly polarized light and dropped significantly for circular polarization. Furthermore, this polarization anisotropy for nonlinear excitation is not affected by the density of free carriers. The ratio for three photon absorption coefficients in ZnO thin films was determined to be 1.8, which is in a good agreement with the theoretically predicted value of 1.5. These findings are backed by simulations based on solving three coupled rate equations. Our results show that the ellipticity of the laser pulse can be used to precisely control the number of excited carriers and thus may be an adaptive control knob for many applications such as material processing or optically pumped nano-lasers. Furthermore, our approach based on measurements of the luminescence yield can be applied for studying the polarization dependence of nonlinear absorption in a wide range of different semiconductor materials and excitation mechanism [28]. Therefore, a precise knowledge of the laser polarization dependent damage threshold in semiconductors and dielectrics is of great importance for the design of novel high-energy laser beamlines and their related applications [29, 30].

Acknowledgment

Supplementary material