The impact of thickness and thermal annealing on refractive index for aluminum oxide thin films deposited by atomic layer deposition

The aluminum oxide (Al2O3) thin films with various thicknesses under 50 nm were deposited by atomic layer deposition (ALD) on silicon substrate. The surface topography investigated by atomic force microscopy (AFM) revealed that the samples were smooth and crack-free. The ellipsometric spectra of Al2O3 thin films were measured and analyzed before and after annealing in nitrogen condition in the wavelength range from 250 to 1,000 nm, respectively. The refractive index of Al2O3 thin films was described by Cauchy model and the ellipsometric spectra data were fitted to a five-medium model consisting of Si substrate/SiO2 layer/Al2O3 layer/surface roughness/air ambient structure. It is found that the refractive index of Al2O3 thin films decrease with increasing film thickness and the changing trend revised after annealing. The phenomenon is believed to arise from the mechanical stress in ALD-Al2O3 thin films. A thickness transition is also found by transmission electron microscopy (TEM) and SE after 900°C annealing.


Background
Aluminum oxide (Al 2 O 3 ) thin films are used as gate dielectric films in electronic devices [1], protective coating layer in magnetic read heads [2], encapsulation layer in light emitting diodes [3], antireflection coating in solar thermal cells [4], and many other areas [5][6][7]. These applications benefit from the excellent optical and electrical properties of Al 2 O 3 films such as wide bandgap, high conduction, high compatibility with Si substrate, and high dielectric constant [8]. The properties of Al 2 O 3 films have been studied a lot [9][10][11]. However, most articles focused on electrical and mechanical properties of Al 2 O 3 films. The research on optical properties of Al 2 O 3 films , especially for Al 2 O 3 films thinner than 50 nm, is still lacking. The applications of optical critical dimension, in situ spectroscopic ellipsometry (SE) and phase measurements in inspection are widely used in semiconductor process and solar cells. These applications are dependent on the accuracy of dielectric constants. The inaccurate optical constant of Al 2 O 3 can introduce errors in fabricating procedure and further influence the performance of devices. So the study of optical properties of Al 2 O 3 thin films is needed.
Atomic layer deposition (ALD) is one of the most popular chemical vapor deposition methods used in oxide film fabrication [12]. For its low temperature and monolayer deposition, Al 2 O 3 ultrathin films with a smooth and defectfree surface can be deposited. Therefore, ALD-Al 2 O 3 films are widely used in recent researches [13,14].
SE is routinely used in optical characterization and film thickness determination. In the SE measurement, a linearly polarized light is illuminated on the sample. The polarization state will be changed after the light reflected. Two parameters, the amplitude ratio (Ψ) and phase shift (Δ) between reflected pand s-polarized light, are obtained from the measurement [15]. The ellipsometric spectra can be fitted to the optical model based on the film structure, then the optical properties and film thickness of the measured material can be revealed [16][17][18]. Its noncontact, nondestructive characteristics are ideal for many situations when film thickness or dielectric constants are needed [19,20].
In this paper, the thickness dependence of refractive index for ALD-Al 2 O 3 films is investigated by SE. An anomaly change trend of refractive index for Al 2 O 3 films was reported. The changing trend reversed after the Al 2 O 3 films were annealed in nitrogen condition at different temperatures. The thickness transition was observed through transmission electron microscopy (TEM) and SE. The change of dielectric constant was explained by the changing of dielectric polarization after annealing.

Methods
The Al 2 O 3 films were deposited by a thermal ALD reactor (Picosun R-series, Espoo, Finland) on Si substrate. Trimethylaluminum (TMA; Al(CH 3 ) 3 ) and water (H 2 O) were used as metal and oxidation precursors, respectively. The reacting temperature is 100°C. The characteristic analysis of surface morphology was performed by atomic force microscopy (AFM; Bruker Dimension Icon VT-1000, Santa Barbara, CA, USA) in tapping mode. The ellipsometric spectra were measured by a SE system (J.A. Woollam Co. M2000X-FB-300XTF, Lincoln, NE, USA) over the wavelength range of 250 to 1,000 nm at incident angle of 65°. The thickness of SiO 2 and Al 2 O 3 layers were identified by TEM (FEI Tecnai G2 F20, Hillsboro, OR,  USA), Then the ALD-Al 2 O 3 samples were cut into three pieces and annealed at 400°C, 600°C, and 900°C in nitrogen atmosphere. A rapid thermal process system (RTP; AS-ONE, Montpellier, France) was used. The annealed samples were researched by AFM, TEM, and SE again to perform further analysis.
Considering the Si substrate always have a native oxide layer [21], the ellipsometric spectra were collected for the Si substrate with oxide layer and ALD-Al 2 O 3 thin film, respectively. The RMS roughness obtained from AFM helps determining the thickness of roughness layer. So the optical model used in SE fitting is Si substrate/SiO 2 layer/ Al 2 O 3 layer/surface roughness/air ambient, as shown in Figure 1. The dispersion model of Al 2 O 3 used in SE fitting is Cauchy model [22].

Results and discussion
The numbers of ALD cycles in the deposition were 50, 100, 300, and 500. Figure 2 shows the AFM images of selected ALD-Al 2 O 3 thin film. The surface of the samples is smooth and crack-free, which indicates that Al 2 O 3 films were well fabricated. The root mean square roughness (RMS roughness) information of all samples is listed in Table 1. The thickness of surface roughness layer used in SE fitting is fixed as the RMS value. And the roughness layer is described by a Bruggeman effective medium approximation mixed by 50% Al 2 O 3 and 50% void [23].  Considering Al 2 O 3 is transparent in visible region, the optical model of Al 2 O 3 used in SE fitting is Cauchy model, which is defined as follows [22]: where A, B, and C are the material coeffients that define the real part of the refractive index n(λ). Figure 3a illustrates the thickness dependence of refractive index for as deposited ALD-Al 2 O 3 films revealed by SE fitting. It can be found that with increasing thickness, the refractive index of Al 2 O 3 is decreasing, which is contrary to Al 2 O 3 films thicker than 50 nm [24][25][26]. From the inset of Figure 3a, we can know that the Al 2 O 3 films were grown at a speed of 0.88 Å/cycle. The growth rate becomes stable when ALD cycle is higher than 100. The Al 2 O 3 thin films were then annealed at 400°C, 600°C, and 900°C, respectively. The changing trend of refractive index at each annealing temperature is illustrated in Figure 3b,c,d. It is indicated that the thickness dependence of refractive index for Al 2 O 3 films reversed and shows regular evolution rule after annealing. Furthermore, the thicknesses of Al 2 O 3 films show a significant decrease after 900°C annealing. TEM pictures in Figure 4 also support the SE results. The thickness of SiO 2 , 300cycles of Al 2 O 3 , and RMS layer at different annealing temperatures in SE fitting and TEM measurements are compared in Table 2. The thickness of SiO 2 layer slightly increased after annealing. And the Al 2 O 3 film went through a densification process after annealing.
Generally, the ALD-Al 2 O 3 film will be under a stress state after it is deposited. And for thin films under 50 nm, the effect of internal stress is strongly related to thickness [27,28]. The anomaly changing trend of refractive index for Al 2 O 3 thin films is only observed in the as deposited samples. The reverse of changing trend may be contributed to two reasons caused by annealing process: stress release and phase transition.
To further understand the effect of annealing process, the refractive index depending on annealing temperature for each sample are researched and given in Figure 5. A significant increase in refractive index after 900°C annealing can be noted. This variation can also be observed from the thickness decreasing illustrated in Figures 3 and 4, which means the films are more compact or may become crystallized. But the crystal grain is not observed from TEM pictures in Figure 4b,c. The Al 2 O 3 thin films are not crystallized after annealing. The transition of the films is due to stress release and densification caused by annealing.
The refractive index of Al 2 O 3 films increased after thickness transition. This phenomenon can be explained by classical dielectric theory. For a transparent material, the dielectric constant ε is given by [22].
where P is the dielectric polarization, n is the refractive index, ε 0 is the free-space permittivity, and E is the electric field. The q i and l i are electric charge of electric dipole and distance between the charge pair, respectively. So the dielectric polarization is related to the electric charge and distances of dipoles in the material. The dielectric constant will become larger if the dielectric polarization is larger.
In the process of annealing, the vacancies are filled during annealing and the thickness of Al 2 O 3 films will decrease. The charge of electric dipole is then increased and leads to a higher dielectric polarization. This is often accompanied with a decreasing of total binding energy [29], which agrees with previous reports on Al 2 O 3 films [10,27].
The annealing process, which is believed as an efficient method to release the stress or leads to a thickness transition, turned the changing trend of refractive index back to normal. The stress in ALD-Al 2 O 3 thin films caused the anomaly trend. And the stress has been released after a 400°C annealing. A higher annealing temperature further led to a thickness transition of Al 2 O 3 films. Both stress release and thickness transition will have a significant influence on the refractive index of Al 2 O 3 films.

Conclusions
In summary, the ALD-Al 2 O 3 thin films with various thicknesses were fabricated and annealed at different temperatures. The AFM measurement indicated that the surface roughness of Al 2 O 3 thin films was less than 1 nm. The SE analysis revealed that the refractive index of as deposited Al 2 O 3 thin films decreases with increasing film thickness. And this anomaly phenomenon disappeared after annealing. Further analysis on SE and TEM data shows that the stress of as deposited Al 2 O 3 caused the anomaly changing trend of refractive index. And the refractive index becomes higher after 900°C annealing, which is contributed by vacancy filling induced higher dielectric polarization. The revolution of optical constant will affect other properties of Al 2 O 3 thin films and leads to new features. The results given in this work will be helpful in further fabrication and application of Al 2 O 3 thin films.