4-1 XRD
The thickness of ZnO film was measured about 1 µm by surface profile offered by Nano Facility Center (NFC) at NCTU. Result of X-ray diffraction measurement is shown in Fig.
4-1. By comparing with JCPDS#36-145 and our diffraction pattern in Fig. 4-1, strong diffraction lines were observed only from the (002) and (004) planes. This result indicates that the ZnO sample growth is highly-qualify single crystal thin film with the crystallographic c-axis being parallel to the growth direction (perpendicular the surface of this sample).
30 40 50 60 70
Intensity(a.u.)
2 θ( degree )
ZnO(002)
ZnO(004)
Fig. 4-1 Result of X-ray diffraction measurement
4-2 Photoluminescence Spectra
With using the PL spectra shows in 3-2, the near-band edge emission and band-gap of this ZnO thin film can be investigated. As Fig. 4-2 shows, the near band edge emission of this ZnO film is around 381 nm. This emission is the near-band edge emission of ZnO in most epitaxial method. The broad band emission of 450-550 nm is contributed from the substrate of fused silica and deep level of ZnO. This is due to lattice mismatch of fused silica and ZnO. This can be solved to replace the substrate of fused silica by double-side polished sapphire. But this kind of sapphire substrate can contribute the nonlinear absorption and refraction when the wavelength of incident pulse is near two-photon resonance of ZnO thin film. It will lead some errors in calculation of nonlinear absorption and refraction of ZnO thin film. Moreover, this contribution of deep level of ZnO is tenfold smaller than the near-band edge emission; this will not induce a large amount of nonlinearities in Z-scan measurements and misunderstanding of this ZnO thin film. The sapphire, hence, may not the proper candidate of substrate for the ZnO thin film in our Z-scan measurement.
350 400 450 500 550 600 650 700
381
Intensity(a.u.)
Wavelength(nm) Quartz & deep level
Fig. 4-2 Result of Photoluminescence spectra measurement
4-3 Transmission Spectra
A simple formula 4-1(Ref R. Swanepoel .pdf) can be used for the calculation of sample thickness via transmission spectra for our measurement.
1 2 thickness d is about 1023 nm which is close to the result of surface profile measurement.
300 400 500 600 700 800 900
0
Fig. 4-3 Result of transmission spectra measurement
4-4 Measurement of Z-scan
A Z-scan with a fully open aperture (S=1) is in sensitive to nonlinear refraction (thin sample approximation). Such Z-scan traces with no aperture are expected to be symmetric with respect to the focus (z=0) where has a minimum transmittance (e.g., multiphoton absorption) or maximum transmittance (e.g., saturation of absorption). Thus, the coefficients of nonlinear absorption can be easily calculated from such transmittance curves.
The low-irradiance (I0=0.54GW/cm2) open aperture and closed aperture Z-scan traces of single crystal ZnO thin film with c-axis orientation thin film at 748 nm-wavelength are shown in Fig. 4-4. (a) and (b) respectively. Figure 4-4(a) shows normalized open-aperture Z-scan transmittance of ZnO (filled squares) and the best fitting curve (solid line). The significant decrease in the normalized transmittance was observed as the sample approached to the focus (Z=0). Figure 4-4(b) shows normalized closed-aperture (S=0.4) Z-scan transmittance (filled squares) and the best fitting curve (solid line). As seen in Fig. 4-4(a), the change in transmittance for the measurement without an aperture is symmetric with respect to the focus.
The observations imply that two-photon absorption can be occurred at 748nm-wavelength of input laser beam. As seen in Fig. 4-4(b), the asymmetric curve is observed and it implies a nonlinear refractive phenomenon takes place. A prefocal transmittance minimum (valley) followed by a postfocal transmittance maximum (peak) is the Z-scan signature of a positive refractive nonlinearity. Therefore, it reveals this ZnO thin film is a positive nonlinear refractive medium when the wavelength of input laser beam is around 748 nm. To remove nonlinear absorption from closed-aperture data and obtain the purely nonlinear refraction, the closed-aperture measurement is divided by the open-aperture one at the same irradiance.
The division of the intensity-dependent Z-scans results (Fig. 4-4(b)/(a)) is shown in Fig. 4-5(a) where the filled squares are the experimental result and the solid lines are the theoretical fitting result. The valley-peak configuration is clearer than Fig. 4-4(b) showed symmetric result. By fitting the division data, the phase distortion can be obtained. And the nonlinear index can be deduced from this phase distortion at this irradiance. The theoretical fit is obtained by setting β= 1440 cm/GW in fig. 4-4(a) and γ = 2.8 × 10-11 cm2/W (1.323 × 10-11 esu) in fig. 4-4(b) with the peak irradiance 0.538 GW/cm2 at the focus within sample.
0.97 0.98 0.99 1.00 1.01
Normalized Transmittance
(a)
-10 -5 0 5 10 15
0.96 0.97 0.98 0.99 1.00 1.01
1.02
(b)
Normalized Transmittance
Z(mm)
Fig. 4-4 (a) Open-aperture Z-scan trace (filled squares) of ZnO measured with a pulse intensity of 0.54 GW/cm2
at 748 nm. The solid line is a fitting curve. (b) Closed aperture (S=0.4) Z-scan trace (filled squares) and fitting
curve (solid line). The data in (a) and (b) were fitted with β= 1440 cm/GW and γ = 2.8 × 10-11 cm2/W.
A series of divided Z-scan results versus peak laser irradiance as measured on the same ZnO thin film is shown in Fig. 4-5 (The filled squares are experimental data and solid curve
are theoretical fitting curve). The ? Tp-v (difference between the normalized peak and valley transmittance: Tp-Tv) can be derived directly from the divided results and the phase distortion with various laser irradiances can be obtained easily from these fitting curves. The change of refractive index can be obtained from these phase distortion with
2 1 exp( L)
π n α
λ α
− −
∆Φ = ∆ , where ? is the wavelength of incident laser, a is the absorption coefficient and L is the thickness of sample. A plot of ß and ? n versus peak laser irradiance as measured from various Z-scan on the same ZnO thin film is shown in Fig. 4-6 and 4-7, respectively. The average TPA coefficient, β, is obtained from Fig. 4-6 as 1905 cm/GW with an uncertainty of 15% arising predominantly from the irradiance calibration. This irradiance-dependent Z-scan study of the ZnO thin film indicates that for irradiance I0 < 0.76 GW/cm2, the nonlinear refraction is dominated by a third-order effect. This is depicted in Fig. 4-7 where the measured nonlinear index change ? n varies linearly with the irradiance.
The adjusting γ is obtained from Fig. 4-7 as 2.63 × 10-11 cm2/W (n2 = 1.245× 10-11 esu).
Theoretically, the nonlinear refraction at low irradiance levels is dominated by a third-order effect and this nonlinearity was attributed to n2, the nonlinear refraction caused by bound electrons (electronic Kerr effect). At higher irradiance levels, however, the nonlinear refraction caused by the two photon absorption generated free charge carriers, an effective fifth-order nonlinearity, becomes significant. This is indicated in Fig. 4-7 by the deviation of above I0 =0.76 GW/cm2 from the line representing the cubic nonlinearity.
0.94
Fig. 4-5 The closed aperture trace divided by the open aperture trace with different pulse intensity, the filled squares are experimental data and the solid lines are fitting curves. (a) 0.54 GW/cm2, (b)0.65 GW/cm2, (c) 0.75 GW/cm2, (d)0.81 GW/cm2, (e)0.91 GW/cm2 and (f)0.97 GW/cm2.
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Fig. 4-6 Measured TPA coefficients (filled blocks) plotted as a function of I0. The horizontal solid line is a guide for the eye and yields β = 1905 cm/GW.
Fig. 4-7 ∆n directly derived from ∆Tp-v plotted as a function of I0 for ZnO. The slope of the straight-line best fit to the data yields γ = 2.63 × 10-11 cm2/W. The line represents a cubic (n2 type) nonlinearity. The deviation from the line is indicative of higher order refractive effects arising from two-photon generated charge carriers.
To clearly estimate the free carrier nonlinearity, a simple procedure [30] is present. This procedure is performed at various irradiances, and the results of these fitted ? n are divided by I0. If there were no higher-order nonlinearities, this procedure would give a horizontal line with vertical intercept γ in the plot of ? n/I0 versus I0. Thus, with free-carrier refraction, the curve of a plot of ? n/I0 versus I0 is a straight line with an intercept γ of and a slope of Cσr. where C is given by C;0.23(βt0/h for low linear absorption (ω) α0L < 0.2). t0 is the pulse width of incident laser. A relation is given below
2
0 r 0
n γI Cσ I
∆ ; + (27)
By applying this method to this ZnO thim film, a plot of ? n versus I0 is shown in Fig. 4-7.
Fig. 4-7 shows the low-irradiance results (I0 < 0.76 GW/cm2), the third-order nonlinear refraction is attributed to bound-electronic effects and γ = 2.63 × 10-11 cm2/W is obtained from the vertical intercept of this horizontal line. The higher-irradiance results for I0 > 0.76 GW/cm2 is shown in Fig. 4-7. The bound-electronic nonlinearity γ = 2.21 × 10-11 cm2/W (n2
= 1.155 × 10-8 esu) is obtained from the nonzero-intercept of the fitted parabolic line and the refractive-index change per carrier-pair density σr = 4.51 × 10-20 cm3 is obtained from this parabolic line.
This relation also can be derived as:
0 0 straight line and the refractive-index change per carrier-pair density σr = 4.51 × 10-20 cm3 is obtained from the slope of this straight line. The bound-electronic nonlinearity derived from straight and parabolic line is close, this deviation is mainly from the inaccuracy of experiment.
The data (open squares) in Fig. 4-8 is the TPA coefficients versus incident irradiance and the dashed line is a guide for the eye.
0.0 0.2 0.4 0.6 0.8 1.0
Fig. 4-8 Measured TPA coefficients (open squares) versus irradiance and ∆n/I0 (filled squares) plotted as a function of I0 for the ZnO thin film. The horizontal dashed line is a guide for eye with vertical intercept β = 1905 cm/GW. The intercept of linear best fit to the data gives γ = 2.21 × 10-11 cm2/W, and the slope yields σr = 4.51 × 10-20 cm3.
The measured TPA coefficient, bound-electronic and free-carrier nonlinearity are larger than those with 25-ps laser pulse, frequency-doubled, mode-locked, Q-switched Nd-YAG laser [31]. Excitonic enhanced in optical nonlinearity is dominated when the incident laser light is near two-photon resonance. Thus, a wavelength-dependent Z-scan is performed to investigate this excitonic enhancement of ZnO near two-photon resonance. The measured TPA coefficient versus wavelength of incident laser is shown in Fig 4-9. The dashed line is half of exciton bind energy subtract from half of energy of band-gap of ZnO. The position of arrow is two-photon resonance energy. When the wavelength of incident laser light is far away two-photon resonance, the measured TPA coefficient is smaller. As wavelength of incident laser light is below this dashed line, the measured TPA coefficient is drastically
decreased. It likes a resonance behavior at this dashed line. This is clearly due to excitonic enhancement near two-photon resonance. This behavior could also be observed in ZnTe [32]. In GaN thin film, TPA coefficient is 18 times larger than theoretical value is
observed[33] which is mainly from the excitonic enhancement. There are 12 meV of exciton binding energy in ZnTe and 27 meV one in GaN and 60meV in ZnO. The thermal energy is about 26 meV. At room temperature, the exciton is still exist in ZnO. Due to this large exciton binding energy 60 meV in ZnO, the TPA is drastically enhanced near two-photon resonance. Compared with 25-ps measured TPA coefficient of ZnO single crystal [31], it is about 400 times enhancement when the wavelength of incident laser light is 748 nm.
740 745 750 755 760 765 770 775 780 785 0
Fig. 4-9 Measured TPA coefficients (filled squares) versus wavelength λ(nm) for the ZnO thin film. When the wavelength of incident laser is larger than the half energy of exciton-to-valance band, the TPA coefficients is
smaller. It also reveals an excitonic enhancement near two-photon resonance.
The measured bound-electronic nonlinearity at two-photon resonance is also larger than theoretical value [26]. The measured nonlinear refractive index versus wavelength is shown is Fig. 4-10. When the wavelength of incident laser light is far from two-photon resonance, the nonlinear refractive index is smaller. It reveals a two-photon resonance behavior in this ZnO thin film. This fitted K’ in Fig. 4-11 is 2000 times larger than theoretical value. This behavior could also be obtained in GaN thin film [34]. Because of a smaller exciton bind energy 27 meV than one of ZnO, this enhancement is not remarkable in GaN thin film. By DFWM, a very large third-order optical nonlinearity in ZnO microcrystalline thin film is observed [35]. It is due to absorption strength for excitation near the exciton and the band-to-band transitions. From this, the excitonic enhancement is dominated near two-photon resonance in ZnO thin film.
740 745 750 755 760 765 770 775 780 785 1.0
Fig. 4-12 Measured nonlinear refractive index (filled squares) versus wavelength λ(nm) for the ZnO thin film.
When the wavelength of incident laser is larger than the half energy of exciton-to-valance band, nonlinear refractive index is smaller. It reveals an excitonic enhancement near two-photon resonance.
0.0 0.2 0.4 0.6 0.8 1.0
Fig. 4-11 Measured nonlinear refractive index (open squares) versus h? /Eg for the ZnO thin film. The solid line is the theoretical value with K’ is 2000 times larger than theoretical value.
740 745 750 755 760 765 770 775 780 785 0
Fig. 4-12 Measured free-carrier nonlinearity (filled squares) versus wavelength λ(nm) for the ZnO thin film.
When the wavelength of incident laser is near the half energy of exciton-to-valance band, the free-carrier nonlinearity is larger. It reveals an excitonic enhancement.
The free-carrier nonlinearity versus wavelength of incident laser light is shown in Fig. 4-12.
When the wavelength of incident laser light is near half energy of exciton-to-valance band, the free-carrier nonlinearity is larger. This is also an excitonic enhance behavior.
I0(GW/cm2) ? F Z0(mm) ? n/I0
1 0.54 0.114 1.205 0.0260
2 0.59 0.129 1.570 0.0269
3 0.64 0.137 1.311 0.0264
4 0.70 0.142 1.14 0.0260
5 0.75 0.156 1.250 0.0262
6 0.80 0.176 1.356 0.0279
7 0.86 0.189 1.330 0.0281
8 0.91 0.206 1.386 0.0294
9 0.97 0.226 1.353 0.0304
10 1.02 0.223 1.397 0.0285
11 1.07 0.24 1.430 0.0293
Average 1.334
Table III The fitting results of division of Z-scan.