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Abstract
We report the uniaxial anisotropic optical constants of wurtzite-type a-axis oriented AlN films deposited on Si (100) using DC reactive magnetron sputtering as a function of growth temperature (Ts, 35 to 600 °C) using the spectroscopic ellipsometry (SE) technique. The thickness and roughness of these films are determined from the regression analysis of SE data, which are corroborated using TEM and AFM techniques. Highly oriented a-axis AlN film grown at 400 °C, exhibits high n and low k at 210 nm (deep-UV region) with small birefringence (−0.01) and dichroism (0.03) near the band edge. All these AlN films exhibit transparent nature from near-infrared (NIR) to 354 nm, where optical band gap energies vary between 5.7 to 6.1 eV.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the last two decades, aluminum nitride (AlN) films have been attracted extensively in semiconductor industry due to their unique physical and optical properties. AlN and Al-rich AlGaN alloy films find a crucial role in UV-LED (covering wavelength from 210 to 375 nm), where the insulating properties are exploited in the fabrication of III–V materials such as GaN, GaAs and InP based electronic, radio-frequency UV sensor and optical devices [1–3]. In particular, for the wurzite AlN structure, the top of valence band creates excitonic states due to the hexagonal crystal-field and spin-orbital splittings [4,5]. There are therefore two configurations of excitonic transitions i.e. σ (E⊥c, c = axis of wurzite structure) and π (E‖c) configurations. In the application of AlN as LED device in the deep UV region, the extracted light intensity along the surface normal from a-plane or m-plane is 25 times higher as compared to the conventional c-plane structure [6,7]. The extracted light intensity in turn directly depends upon critical angle of light escape cone, which is inversely proportional to the square of refractive index [8]. The plane orientation is thus vital to electro-luminescent diodes like optoelectronic devices and the radiation properties of UV-LED. However in the previous literature, the variation of optical properties of crystaline AlN with growth temperature (Ts) are restricted to isotropic optical response only [9,10]. Although there are reports on anisotropic optical properties of AlN thin films, they are mostly confined to c-axis oriented films [11–15]. It is therefore imperative and pertinent to examine the nature of refractive index of a-axis oriented AlN thin films. As spectroscopic ellipsometry (SE) measurement is a very powerful and unique optical characterization technique to determine the optical properties of materials in the broad range of energy (from deep UV to NIR), which is a non invasive, non-contact and sensitive technique with a high degree of accuracy [16].
2. Experimental details
AlN films were grown by DC reactive magnetron sputtering technique (M/s. MECA 2000, France), using aluminum target, in a mixture (4:1 SCCM) of high pure argon (5N) and nitrogen (5N) gases on Si(100) substrate at different Ts such as 35, 200, 400 and 600 °C. A thin layer of Al was deposited for few seconds to increase the adhesive strength between substrate and deposited AlN films [17,18]. The crystal structure and microstructure of these films were studied by GIXRD and TEM, respectively. AlN film grown at 400 °C showed a strong texture along (100) plane with hexagonal wurtzite structure and a rocking curve of (100) exhibited an FWHM of 0.03913 ± 0.00052 at an angle of 33.2°. This confirms that the film is preferentially oriented along [100] direction to the normal of the surface i.e highly a-axis oriented as described elsewhere [18,19]. Figure 1 shows a dark field cross-sectional TEM (X-TEM) image of the film grown at 400 °C along with the selected area diffraction (SAED) image in the inset. This shows that the film is highly oriented along a-axis with a slanted columnar structure by making few degrees to the substrate normal as described elsewhere [18].
The SE parameters are measured in ambient conditions by a phase modulated spectroscopic ellipsometer (M/s. Horiba Jobin-Yvon, UVISEL2, France) at an incident angle of 70° in the photon energy range of 0.6 to 6.5 eV with 0.01 eV increment as shown in Fig. 2. SE measures change in polarization state of light as it reflects from the sample of interest. The polarization change between the parallel (p) and perpendicular (s) components of the reflected light with respect to the plane of incidence is represented as the change in amplitude (Ψ) and the phase difference (Δ), which are considered as ellipsometric parameters. The ellipsometric parameters Ψ and Δ are defined by the Eq. (1) below.
where rp and rs are the parallel and perpendicular reflection coefficients, respectively. In this experiment, Is and Ic are the experimentally measured parameters from which the pseudo dielectric constants are computed. These are related to Ψ and Δ in the following Eq. (2) below.3. Results and discussion
3.1. Modeling and fitting for the analysis of optical constants
The refractive index (n) and extinction coefficient (k) of these films are computed by fitting Is and Ic with the modified Forouhi-Bloomer dipersion relation with one oscillator term. This relation fits smoothly for broader wavelength range i.e. from normal to anomalous dispersion region [20]. This is also consistent with Kramers-Kronig relation with five independent parameters as described below.
where where, the term fj (in eV) is the oscillator strength, Γj (in eV) is the broadening factor of absorption peak, ωj (in eV) is the energy at which the extinction coefficient is maximum and ωg (in eV) is the minimum energy from which absorption starts.The anisotropic optical properties of single crystals or epitaxial thin films are conventionally studied by generalized ellipsometry [21,22]. However, in the present case, the AlN thin films are predominantly polycrystalline and the film grown at 400 °C is in particular textured and highly oriented along a-axis. The anisotropic optical properties are extracted by suitable models using DeltaPsi2 software based on the approaches mentioned in literature [13–15,23,24]. A systematic approach of inclusion and omission of layers has been followed in which, a five layer model (Air/roughness (AlN + void)/ AlN/ interface (Al+AlN)/ Si) with uniaxial anisotropic conditions is employed for the analysis of optical properties of AlN films. The treatment of roughness and interface layer is based on Bruggeman Effective Medium Approximation (BEMA). The fitting is performed by classical non-linear minimization Levenberg-Marquardt algorithm as described by Modreanu et al and is expressed in terms of χ2 values as shown in Eq. (5) that defines the goodness of fit [25].
where N is the number of data points, P is the number of parameters to be fitted and indices mi and ci are the measured and computed quantity of the ith energy in ellipsometry parameters. The χ2 value for all the fittings are 20 to 30 in the energy range of 0.6 to 6.5 eV. Measured experimental parameters (Is and Ic) for AlN films grown at 35 and 400 °C over a spectral range 0.6 to 6.5 eV and corresponding fit are shown in Fig. 3(a)–3(d) as representatives for all temperatures. It is seen that the fitting of Is and Ic across the whole spectral range is in good agreement with the experimental Is and Ic. The nominal film thicknesses as computed from SE modeling compare well with those obtained from the x-TEM and is shown in Fig. 4.
Fig. 3 Measured experimental ellipsometric parameters as Is and Ic and the corresponding fit of AlN films grown at 35 °C (a, b) and 400 °C (c, d).
The roughness as deduced from SE of these films is found to lie between 7 and 20 nm. These values are higher than the root mean square roughness values (3 to 9 nm) as obtained from atomic force microscopy (AFM). The surface roughness obtained by AFM technique is acquired over an area of 1.5 ×1.5 μm2 and thus basically represents the local roughness values of these films. In SE technique, the data are acquired over a large elliptical area of 2×0.7 mm2. Thus, the difference in the magnitude of roughness is due to the fact that the data for ellipsometry is obtained from a larger area with mixture of material and voids compared to AFM [18,26–28]. Nevertheless, the roughness computed from SE and AFM, both follows a similar trend with Ts. The thickness of interface layer (Al+AlN) between AlN film and Si substrate is extracted from the fitting that decreases from 16 to 5 nm as a function of Ts.
3.2. Behavior of optical constants with growth temperature
The real (n) and imaginary (k) parts of the refractive index of AlN films for different Ts obtained from the five layer model are shown in Fig. 5. The n and k exhibit strong uniaxial anisotropic dispersion and increase monotonically with increasing photon energy in normal dispersion region, while it decreases in anomalous region. Since, AlN is predominantly used in deep-UV region (210 nm), it is worthwhile to explore the behavior of both n and k of these films as a function of Ts in Fig. 6 at 210 nm (5.9 eV).
Fig. 5 A plot of (a) n⊥, (b) n‖ refractive index and (c) k⊥ and (d) k‖ extinction coefficient against to energy of AlN films for different Ts.
With the increase in Ts, both n⊥ and n‖ increase up to 400 °C and then thereafter it falls. While, both k⊥ and k‖ decreased with respect to Ts. All these films show transparent nature up to a photon energy 3.5 eV (354 nm) from NIR. As it is well known that the optical parameter n and k are basically dependent on the crystal structure, disorders like voids, lattice defects and chemical composition of the film under investigation [29, 30]. The crystal parameter such as crystallite size of these AlN films comparatively follows the behavior of refractive index. In the present study, the crystallite size of these films are calculated using Williamson-Hall method and is shown in the inset of Fig. 6. It increases from 35 to 400 °C and there after fall in crystallite size at 600 °C due to dissociation of bonds and strong re-evaporation of ad-atoms at high Ts [18, 31, 32]. The parameter Ts/Tm (Tm = melting temperature of growing material) is important for the growth of film that defines the film orientation and structure [33]. If the film is deposited using sputtering at room temperature, there is a little surface diffusion due to high melting point of AlN and one would expect voids, nitrogen vacancy and defect concentration to be much higher than at equilibrium. But, with increase in Ts, the adatom mobility increases and causes the increase in crystalite size and columnar structure. The higher mobility of adatoms causes the formation of dense AlN films and reduces the residual stress, porosity and defects [18]. Increase in growth or annealing temperature reduces the concentration of defect states like nitrogen, impurity and coordination defects, where refractive index of the film is improved and is proportional to packing density [29, 30]. Hence, n value is increasing linearly with Ts upto 400 °C, then a fall at 600 °C due to decrease in crystallite size. So, highly a-axis oriented AlN film grown at 400 °C, exhibits high n (n⊥ = 2.56, n‖ = 2.55), which is lower than the reported c-axis oriented AlN (∼ 2.7) [14, 15, 34]. Jiang et al and Shokhovets et al have described the optical anisotropic properties of c-axis oriented AlN films using the variable angle spectroscopic ellipsometry (VASE) technique [14,15]. The refractive index values are around 2.30 (n‖) and 2.20 (n⊥) at 4 eV of photon energy. In the present study, the refractive index values are as 2.17 (n‖) and 2.14 (n⊥) at 4 eV for the a-axis oriented AlN films. At 35 °C, the value k is higher due to more vacancies in the film and Al concentration in the interface layer, that additionally contribute to the absorption by creating localized states. But, with increase in Ts, ad-atoms have high surface mobility that reduces the defects and Al concentration in the interface layer. That resulted in the reduction of k value. Thus, the optical parameters n and k strongly depend on Ts as well as crystallite size.
Fig. 6 The variation of n and k value at 210 nm and the crystallite size (inset) of AlN films with Ts.
To obtain the optical bandgap of these AlN films, the absorption coefficient (α) (defined as α = 4πk/λ, where λ is the wavelength of the incident light) is calculated over extended energy range (0.6 to 6.5 eV) using the formalism followed by Looper et al [20]. The optical band gaps for the k⊥ and k‖ are obtained using a linear extrapolation of tangential line to the energy axis of (Eα)2, which is shown in Fig. 7. These results agree well with Kar et al, where they have reported the bandgap energy of AlN films after annealed as a function of temperature [35]. The band gap increases with Ts up to 400 °C then it decreases at 600 °C. So, optical band gap also strongly depends on the crystallite size. At low temperatures, the band gap is small compared to bulk AlN that is due to the generation of shallow states caused by the formation of lattice distortion by voids, Al and N vacancy concentrations [29,35]. Whereas, highly a-axis oriented AlN film grown at 400 °C with large crystallite size (∼ 66 nm) shows direct band gap as 6.05 (k‖) and 6.1 eV (k⊥), which is near to the bulk AlN.
To undestand the behavior of anisotropy, the difference in n (birefringence, Δn = n‖ − n⊥) and k (dichroism, Δk = k‖ − k⊥) is shown in Fig. 8. The Δn exhibits a positive value except at higher energy region. Additionally, the value of Δn is larger near band energy region for all these films, whereas AlN film grown at 400 °C shows a maximum birefringence at lower energy range and a minimum birefringence at near band gap. Also, all these films exhibit a strong dichroism near the band edge, whereas 400 °C AlN film shows a negative dichroism after the band edge. Generally, near the band gap, the fundamental absorption occurs due to the contribution of excitonic and band-to-band transitions. For wurzite structure AlN, the excitonic transition strongly depends upon polarization state of light due to the non-cubic crystal-field splittings [4, 5]. Therefore, the anisotropy properties strongly affected near the band gap, which results a strong Δn. In this study, AlN grown at 400 °C is a highly a-axis oriented normal to the substrate compared to other films. Therefore, it shows a strong birefringence (∼ 0.03) at lower energy range. However, birefringence disappears at energies 5.55 and 6.11 eV and reappear with a negative value (−0.01) at 5.9 eV. The birefringence of a-axis oriented AlN film exhibited a lower value compared to the reported c-axis oriented AlN film (Δn = −0.05 at 5.9 eV) [14]. Also, it is seen that a-plane (m-plane) LED exhibited an isotropic emission pattern along the surface normal compared to the c-plane structure at wavelength of 210 nm [6]. So, this film (a-axis) contains a mixed σ and π exciton feature that decreases the value of both Δn and Δk near the band gap.
The parameters of the modified Forouhi-Bloomer dipersion model were extracted from the fitting and shown in Fig. 9. The Γj and fj, both decrease with Ts upto 400 °C. The broadening parameter Γj (= ħ/τj, where τj is the phonon relaxation time), is the inverse of relaxation time, depends on the phonon contribution and microstructural parameters, such as static impurities, defect density, strain, grain boundary, grain sizes, etc [16]. A decrease in Γj is observed with the increase in Ts and implies an increase in phonon relaxation time due to the increase in crystallite size as well as decrease in residual stress. ωj defines the energy at which the extinction coefficient is maximum for a material and it increases with Ts due to increase in band gap, whereas energy from which the absorption starts (ωg) is almost constant. So, at 400 °C, AlN film shows high n as well as low k with higher value of ωj among all due to higher purity, larger crystallite size and also highly oriented.
4. Conclusion
Uniaxial anisotropic optical properties of AlN films with different Ts are investigated by SE technique, which are strongly depended on Ts. A highly a-axis oriented AlN film grown at 400 °C, exhibited high n (n⊥ = 2.56, n‖ = 2.55) and low k (k⊥ = 0.22, k‖ = 0.25) at 210 nm (deep-UV region) with low value of Δn (−0.01) and Δk (0.03). With increase in Ts, the band gap also increased upto 400 °C, which is close to the bulk AlN. So, the anisotropy optical properties of a-axis AlN can be effectively used in UV-LED and electro-luminescent diode based polarization-sensitive optoelectronic applications.
Acknowledgment
One of the authors (PP) acknowledges the research fellowship from the Department of Atomic Energy, Government of India.
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