# Structural and Optical Properties of Amorphous Al2O3 Thin Film Deposited by Atomic Layer Deposition

Authors: Shuzheng Shi; Shuo Qian; Xiaojuan Hou; Jiliang Mu; Jian He; Xiujian Chou
Journal: Advances in Condensed Matter Physics
 (2018)

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## Abstract

Aluminum oxide (Al2O3) amorphous structure with short-range order and long-range disorder has presented promising applications in optical and optoelectronic devices. In this paper, the Al2O3 films with different thickness were prepared by atomic layer deposition (ALD) technology at 200°C in order to achieve amorphous structure. X-ray diffraction (XRD) and energy dispersive spectrum (EDS) results indicated that the Al2O3 films were amorphous structure and stable O/Al ratio. The surface topography investigated by atomic force microscopy (AFM) showed that the samples were smooth and crack-free. Spectroscopic ellipsometer (SE) measurements were operated to investigate the effect of thickness on the structure and optical properties of films with Tauc-Lorentz model. It is found that the band gap exhibits a steady value ~2.3 eV by the UV-VIS transmittance method, but the T-L model was ~3.0 eV. The refractive index and extinction coefficient are related to the variation of thickness and the samples surface quality of amorphous network structure in the thin films. The outstanding optoelectronic properties and facile fabrication of Al2O3 films amorphous structure can be extended to other similar oxides, which could display wide applications in various engineering and industrial fields.


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## Body

## 1. Introduction

Aluminum oxide (Al2O3) is a technologically promising material in optics, machinery, batteries, and microelectronics applications because of its advantages like high dielectric constant, excellent stability, favorable thermal conductivity, high hardness, and low refractive index [1]. Al2O3 film can be fabricated by several methods, including chemical vapor deposition [2], electron beam evaporation [3], magnetron sputtering [4], the sol-gel process [5], pulsed laser deposition [6], and atomic layer deposition [7]. Among these techniques, Atomic Layer Deposition (ALD), a low-temperature atomic chemical vapor deposition technique, has advantages in homogeneity, compactness, precise composition, and thickness controllability of the target material on Ågstrom or monolayer level [8, 9]. Therefore, ALD is one of the most effective methods used in Al2O3 film fabrication, especially the application in optical lenses, refractory coatings, microelectronic devices, anticorrosive coatings, heat sinks in integrated circuits, and the passivation of metal surfaces. Al2O3 has complex and variable lattice structures based on the strong Al-O bonds and the atomic spatial sequence. When deposited on below 400°C, the Al2O3 films form amorphous structure with “short-range order and long-range disorder” [9, 10]. Amorphous Al2O3 plays an important role in optical applications like optical lenses and windows, antireflection coatings, and optical wave guides. As we know, a certain property of material originates from its special atomic structures. However, the complication in amorphous matrix and its sensitivity to process conditions makes it very difficult to control or predict the material performance. Therefore, a detailed investigation on the optical and structural properties of amorphous Al2O3 thin films is crucial to the improvement of device performance. In the last few decades, although there exist numerous related reports about crystalline Al2O3 film, the research on the optical and structural properties of amorphous counterpart is rare.In this paper, the effect of structure evolution on the optical properties of amorphous Al2O3 films deposited by ALD has been examined. By means of X-Ray Diffraction and Scanning Electron Microscopy-Energy Dispersive Spectrometer, the atomic configuration, the surface morphology, and the element composition were characterized. Furthermore, the optical properties of samples were analyzed by spectroscopic ellipsometer (SE) in spectral range [300 nm, 800 nm]. The ellipsometer spectra were fitted by Tauc-Lorentz dispersion model. The ultraviolet and visible transmission spectrum were used to confirm the band gap evolution and support the SE results. This investigation enables a better understanding of the structural and optical properties of amorphous Al2O3 films, also providing a new reference for other similar materials.


## 2. Experimental Method

### 2.1. Samples Preparation

A single crystal silicon substrate was used as the substrate for Al2O3 films growth, with 4 inches’ N type, 100 crystalline phase, 375 μm, and resistivity of 1–10 Ω·cm. The glass wafer was cut into 1×1 cm2. The Si and glass substrates were cleaned by acetone, anhydrous ethanol, and deionized water for 15 minutes to remove the organic impurities and the “stain trap” of the substrate surface, ensuring the purity and compliance of the Al2O3 film with silicon wafer. Then, the substrates were heated on the heating plate to remove excessive water in the temperatures of 300°C.In the experiment, Al2O3 films were deposited on Si and glass substrates by ALD (TFS-200, Bene, Finland). Trimethylaluminum (TMA; (Al(CH3)3)) and H2O were used as the precursor of metallic aluminum and oxygen ions. Simultaneously, high purity N2 (99.999%) was used as the carrier and purge gas. To ensure the vacuum of the reaction chamber, the pressure differences about 3 Torr between internal and external chamber were controlled. The reacting temperature remained constant at 200°C. The Al2O3 films were deposited on silicon wafer and glass for 100, 200, 300, 400, and 500 cycles, respectively. TMA and H2O were alternately entrained in the N2 carrier flow using gas switching valves. The N2 carrier gas pressure was 2.0 Torr. Each ALD cycle was as follows: 0.2 s to pulse TMA, 0.2 s to pulse H2O as the second reactant, 2 s and 3 s to purging the chamber with high purity N2 in 1st and 2st. Total time of a deposition cycle is 5.4 s.


### 2.2. Characterization and Measurement Methods

The film crystal structure was examined by X-ray diffraction (XRD, X’Pert PRO, PANalytical B.V., Netherlands). The compositions were evaluated by Scanning Electron Microscopy-Energy Dispersive Spectrometer (SEM-EDS, Zeiss 1450VP Scanning Electron Microscope). The roughness and surface topography were characterized by atomic force microscopy (AFM; Bruker Dimension Icon VT-1000, Santa Barbara, CA, USA). The optical properties of Al2O3 films were investigated by spectroscopic ellipsometer (SE, SENTECH SE850 UV/VIS/NIR, spectroscopic ellipsometer, Germany), of which the wavelength ranges from 300 to 800 nm at the incident angle of 65°. Besides, the ultraviolet-visible spectra were examined with ultraviolet and visible spectrophotometer (UV, SHIMADZU UV-1700 ultraviolet and visible spectrophotometer) which can extract the band gap evolution to support the SE results.


### 2.3. Spectroscopic Ellipsometer Principle of Measurement

When a beam of light enters a membrane at a certain angle, the thickness and optical parameters of the film can be determined by the polarization state variations of reflected light and transmitted light.The ellipsometric parametersψ and Δ are defined by the ellipsometric ratio ρ as the following equation [11]:(1)ρ=RpRs=RpRseiΔp-Δs=tan⁡ψexp⁡jΔ,where Rp and Rs are complex Fresnel reflection coefficients for “p” and “s” polarization, respectively. Δp and Δs represents the phase for each polarization. Ellipsometry measures the two values ψ and Δ, which express the amplitude ratio and phase difference between p polarization and s polarization, shown in (1). Based on the above calculation, dielectric function of film can be expressed as(2)ε=ε1+ε2=ε0sin2⁡ϕ01+tan2⁡ϕ01-ρ1+ρ2,where ϕ0,ε0 represent the incident angle and the vacuum dielectric function, respectively.In this case, the refractive indexn and extinction coefficient k can be extracted from the two ellipsometry parameters. For single layer film, the amplitude ratio ψ is characterized by the refractive index n, while Δ represents light absorption by applying the Fresnel equations. The ellipsometer fitting iterative are evaluated by an objective optimization function [11, 12]. The mean square deviation can be described by Root Mean Square Error (RMSE) between the theoretical and experimental value, which is given as follows:(3)RMSE=12N-M-1∑i=1Nψical-ψiexp⁡2+Δical-Δiexp⁡2,where N is the number of measured wavelengths, M is the number of variables, ψical and Δical represent the theoretical values, and ψiexp⁡ and Δiexp⁡ are experimental measurements, respectively. When the RMSE value is less than 1, the fitting results are reliable [11–13].


## 2.1. Samples Preparation

A single crystal silicon substrate was used as the substrate for Al2O3 films growth, with 4 inches’ N type, 100 crystalline phase, 375 μm, and resistivity of 1–10 Ω·cm. The glass wafer was cut into 1×1 cm2. The Si and glass substrates were cleaned by acetone, anhydrous ethanol, and deionized water for 15 minutes to remove the organic impurities and the “stain trap” of the substrate surface, ensuring the purity and compliance of the Al2O3 film with silicon wafer. Then, the substrates were heated on the heating plate to remove excessive water in the temperatures of 300°C.In the experiment, Al2O3 films were deposited on Si and glass substrates by ALD (TFS-200, Bene, Finland). Trimethylaluminum (TMA; (Al(CH3)3)) and H2O were used as the precursor of metallic aluminum and oxygen ions. Simultaneously, high purity N2 (99.999%) was used as the carrier and purge gas. To ensure the vacuum of the reaction chamber, the pressure differences about 3 Torr between internal and external chamber were controlled. The reacting temperature remained constant at 200°C. The Al2O3 films were deposited on silicon wafer and glass for 100, 200, 300, 400, and 500 cycles, respectively. TMA and H2O were alternately entrained in the N2 carrier flow using gas switching valves. The N2 carrier gas pressure was 2.0 Torr. Each ALD cycle was as follows: 0.2 s to pulse TMA, 0.2 s to pulse H2O as the second reactant, 2 s and 3 s to purging the chamber with high purity N2 in 1st and 2st. Total time of a deposition cycle is 5.4 s.


## 2.2. Characterization and Measurement Methods

The film crystal structure was examined by X-ray diffraction (XRD, X’Pert PRO, PANalytical B.V., Netherlands). The compositions were evaluated by Scanning Electron Microscopy-Energy Dispersive Spectrometer (SEM-EDS, Zeiss 1450VP Scanning Electron Microscope). The roughness and surface topography were characterized by atomic force microscopy (AFM; Bruker Dimension Icon VT-1000, Santa Barbara, CA, USA). The optical properties of Al2O3 films were investigated by spectroscopic ellipsometer (SE, SENTECH SE850 UV/VIS/NIR, spectroscopic ellipsometer, Germany), of which the wavelength ranges from 300 to 800 nm at the incident angle of 65°. Besides, the ultraviolet-visible spectra were examined with ultraviolet and visible spectrophotometer (UV, SHIMADZU UV-1700 ultraviolet and visible spectrophotometer) which can extract the band gap evolution to support the SE results.


## 2.3. Spectroscopic Ellipsometer Principle of Measurement

When a beam of light enters a membrane at a certain angle, the thickness and optical parameters of the film can be determined by the polarization state variations of reflected light and transmitted light.The ellipsometric parametersψ and Δ are defined by the ellipsometric ratio ρ as the following equation [11]:(1)ρ=RpRs=RpRseiΔp-Δs=tan⁡ψexp⁡jΔ,where Rp and Rs are complex Fresnel reflection coefficients for “p” and “s” polarization, respectively. Δp and Δs represents the phase for each polarization. Ellipsometry measures the two values ψ and Δ, which express the amplitude ratio and phase difference between p polarization and s polarization, shown in (1). Based on the above calculation, dielectric function of film can be expressed as(2)ε=ε1+ε2=ε0sin2⁡ϕ01+tan2⁡ϕ01-ρ1+ρ2,where ϕ0,ε0 represent the incident angle and the vacuum dielectric function, respectively.In this case, the refractive indexn and extinction coefficient k can be extracted from the two ellipsometry parameters. For single layer film, the amplitude ratio ψ is characterized by the refractive index n, while Δ represents light absorption by applying the Fresnel equations. The ellipsometer fitting iterative are evaluated by an objective optimization function [11, 12]. The mean square deviation can be described by Root Mean Square Error (RMSE) between the theoretical and experimental value, which is given as follows:(3)RMSE=12N-M-1∑i=1Nψical-ψiexp⁡2+Δical-Δiexp⁡2,where N is the number of measured wavelengths, M is the number of variables, ψical and Δical represent the theoretical values, and ψiexp⁡ and Δiexp⁡ are experimental measurements, respectively. When the RMSE value is less than 1, the fitting results are reliable [11–13].


## 3. Results and Discussion

### 3.1. Crystal Structure and Compositional Analysis

The intensity of XRD is sensitive to the atomic arrangement of material, so it is capable of analyzing crystal structure. Figure1 gives the XRD patterns of naked Si substrate and deposited films with different cycles. It can be seen from Figure 1(a) that Si XRD exhibits three diffraction peaks at 61.86°, 66.02°, and 69.16°, respectively. Likewise, the XRD patterns of all deposited films almost completely overlap the Si XRD [14], and no other peaks are observed, implying the amorphous structure of the obtained samples.Figure 1
XRD patterns of Si (100) and all films of different cycles grown on Si (100) substrates.
(a) (b)In ALD, the monolayer deposition and the alternating precursor pulse can guarantee an excellent film deposition quality and uniform rate [7, 8]. Figure 2 shows the whole reaction cycle consisting of four steps. (1) Precursor TMA vapor is pulsed into the reaction chamber, and the chemical adsorption reaction 4 occurs on the surface of the substrate. (2) Excess precursor TMA and reaction by-products CH4 are purged with inert carrier gas N2. (3) Precursor deionized H2O vapor is pulsed into the reaction chamber, the surface chemical reactions 4 is proceeded on surface of the adsorption by TMA. (4) Excess precursor H2O and reaction by-products CH4 are purged with inert carrier gas N2.Figure 2
ALD process schematic.The surface chemistry reaction for ALD-Al2O3 can be expressed asAAlCH33g+Al-OH∗s⟶Al-O-AlCH32∗s+CH4gBAlCH3∗s+H2Os⟶Al-OH∗s+CH4gThe overall reaction isC2AlCH33g+3H2Os⟶Al2O3s+6CH4g∗ refers to the functional groups adsorbed on the deposition surface, showing that self-stop gas-solid reaction is the basis of ALD. TMA/H2O ALD process can be divided into 4 and 4 two half reactions, and the precursor molecule performs the chemical adsorption firstly on the deposition surface in each half reaction. Through ligand exchange between TMA and surface hydroxyl groups form the bridging oxygen bonds Al-O-Al on the surface and in the meantime release methane molecules. The reaction between the precursor and the deposition surface is chemical adsorption, the monolayer adsorption, which is also related to the steric hindrance of methyl groups. Therefore, the gas-solid surface reactions of ALD include adsorption, chemical reactions and desorption, and other processes.The chemical composition of the films was evaluated using SEM-EDS. As shown in Table1, result indicates that the atomic ratio O/Al in all samples is around 5, which is different from the value 1.5 in crystalline state [15]. In the report of Kääriäinen and Cameron [16], the O/Al value varies between 2.5 and 3.6 due to some oxygen ion contribution from precursor O2. Gupta and Saleh [17] demonstrated that it is almost impossible to precisely control the atomic ratio in metal oxides, because some oxygen contribution comes from the oxygen-containing functional groups, such as carbonyl or carboxyl groups, on the growth surface. In our case, there are a large number of carbonyl groups adsorbed on the growth surface during reaction process leading to increased oxygen contribution because of the precursor H2O shown in Figure 2. In addition, due to the limitation of SEM-EDS measurement accuracy, the extremely low Al content in the sample with 10.5833 nm of thickness cannot be detected. The EDS result combined with XRD result confirms that our samples deposited at 200°C is amorphous.Table 1
EDS data of different cycles Al2O3 film on silicon wafer (oxygen, aluminum, and silicon (%); the total = 100%).
ALD cycles Elements Wt.% At. (%) d (nm) O/Al ratio 100 O 2.3 3.97 11.62 —— Al 0 0 Si 97.7 96.03  200 O 4.05 6.90 19.63 4.964029 Al 1.38 1.39 Si 94.57 91.71  300 O 5.85 9.82 30.95 5.223404 Al 1.89 1.88 Si 92.27 88.30  400 O 7.97 13.18 39.05 4.592334 Al 2.93 2.87 Si 89.1 83.95  500 O 11.23 18.15 50.40 5.385757 Al 3.52 3.37 Si 85.25 78.48


### 3.2. Morphological Analysis

The film surface quality has a direct influence on the optical and electrical performance of device, such as the optical scattering and electrical contact. Therefore, a precise control of surface morphology during film growth process is very crucial to device performance. In this work, AFM is used to characterize the surface structure of the amorphous Al2O3 films. Figure 3 gives the AFM results of Al2O3 film with different ALD cycles. The AFM scan is carried out on a 3 μm × 3 μm area with the tapping mode.Figure 3
AFM micrographs of deposited Al2O3 films with different thicknesses. (a) 100 cycles. (b) 200 cycles. (c) 300 cycles. (d) 400 cycles. (e) 500 cycles. (f) Trend chart of roughness for the five samples. RMS represents root mean square roughness.
(a) (b) (c) (d) (e) (f)The surface morphologies of all samples are smooth and crack-free with similar root mean square (RMS) surface roughness values, which indicates that Al2O3 films were well fabricated. In order to study the cause of different growth rates of those of 50 cycles, we also studied the growth rate of films with ALD cycles below 50. The ALD surface reactions are very efficient, and Steps 1 and 3 are also known as the half reaction with the self-limitation and complementarity, while the self-limiting reaction is determined by the saturation adsorption of the group and the number of surface activated groups. Each group has a certain size, and the bonding location is blocked by adjacent chemical group, so the remaining groups can only be adsorbed in the next cycle. The number of surface activation groups determines the number of molecules per cycle. The Al2O3 films growth occurs during alternating exposures to TMA and H2O. The main driver for the efficient reactions is the formation of a very strong Al-O bond. The films tend to be smooth and pinhole-free because the randomness of the precursor flux and the self-limiting of the surface reactions. The reaction dose, deposition temperature, and so forth have little or no effect on the reaction. Thus, the growth rate is constant in the ALD process, which is insensitive to changes in process parameters, and the deposited films have excellent thickness uniformity and three-dimensional conformity.


### 3.3. Optical Property Analysis

Spectroscopic ellipsometer (SE) is an important thin film measurement technology for its nondestructive and sensitive advantages [18]. It is necessary to develop a proper optical model for the SE measurement and thus the extraction of optical and structural parameters. Our optical model for fit analysis is established as follows: Si substrate/bulk Al2O3 layer/surface roughness/air ambient, as shown in Figure 4. The surface roughness layer was modeled as a mixture of 50% bulk Al2O3 layer and 50% voids based on the Bruggeman effective medium approximation (EMA). Meanwhile, a reasonable material dispersion relationship is required during ellipsometry analysis. In our measurement, the Tauc-Lorentz model has been used. It is established by Jellison et al. in 1996 based on combined density and Lorentz oscillator model and more suitable for amorphous thin film compared to FB model [18, 19]. This model is defined as follows:(4)ε1E=ε1∞+2πP∫Eg∞τε2ττ2-E2dτ,ε2E=ACEE0E2-E022+C2E2E-EgE2forE>Eg,0forE≤Eg,where P represents the Cauchy principal value of the integral. The dielectric function of the films is determined by five parameters A,C,E0,Eg,andε1∞. In the T-L model, ε2 is modeled as the product of Tauc gap and Lorentz oscillator and ε1 is derived by the Kramers–Kronig relations.Figure 4
Spectroscopic ellipsometer schematic of Al2O3 film micronanosystem.The ellipsometry spectra of Al2O3 thin film with different ALD cycles have been obtained using the above theoretical model. Since the related parameters of all samples are extracted from Ψ and Δ fits, we give both the experimental and calculated data, respectively, as shown in Figure 5. The fitting parameters are listed in Table 2. It can be seen that the calculated outcomes fit the experimental points well. The objective function value fRMSE in all samples is less than 1, demonstrating the acceptable optimization in our case.Table 2
Structural and electronic parameters extracted from SE analysis of the five different samples.
ALD cycle ε 1 ∞ A C E 0/eV E g/eV d/nm d s/nm f RMSE 100 1.66 118.24 644.70 74.33 3.08 11.62 0.08 0.68 200 1.39 156.83 393.56 70.30 2.99 19.63 0.25 0.67 300 1.22 72.65 39.07 25.23 2.98 30.95 0.89 0.58 400 0.59 334.78 430.62 92.86 2.92 39.05 0.15 0.53 500 1.11 207.70 295.86 59.76 2.92 50.40 0.21 0.73Figure 5
Al2O3 films ellipsometry spectra of fit data (continued curves) and measured data (gauge points).SE measurement shows that the fundamental structural parameter, film thickness, increases regularly with the increase of ALD cycles, corresponding to a growth rate of ~0.1 nm/cycle. The relationship between thickness and cycle can be described by a linear fit functiond=0.097nc+1.2328 nm, as shown in Figure 6. As we know, SE analysis is an indirect measurement method, and the obtained result could be a local minimum and not the global minimum. Hence, in order to confirm the reliability of our result, the above fit function is extrapolated to 1000 cycles and then the calculated thickness is supposed to be 98.23 nm. On the other hand, a sample has been deposited at 1000 cycles and its thickness has been examined using SEM. The derived thickness by SEM is 96.89 nm (see the inset in Figure 6), which indicates our SE analysis is reliable. Regarding the 1.34 nm thickness difference, it can be attributed to the following three reasons. First, the ALD growth speed is not constant in each cycle. Second, the thickness calculated by SE analysis has about 0.5 nm error. Third, the two thickness measurement methods, SE and SEM, have distinct principles, so there is an inherent difference in the results from them.Figure 6
Trend chart of thickness for the five different cycle samples. The inset is SEM image of 1000 cycles ALD-Al2O3 film, where d and nc represent film thickness and number of ALD cycles, respectively.The optical band gapETL of Al2O3 has been extracted from the SE analysis. An obvious fluctuation of ETL is not observed in all samples with different thickness. ETL of five samples are ~3.0 eV, as shown in Table 2. Similarly, another optical measurement method, UV-VIS transmittance spectrum, is used to verify the obtained SE results. Figure 7 gives the UV-VIS transmittance spectra of samples in the wavelength range from 300 to 800 nm. The absorption coefficient α can be calculated from the transmittance spectra. The optical band gap is derived by Tauc plot. Generally, the Tauc equation can be expressed as(5)aE=AE-ETuacn,where A is a constant, E is the photon energy (hν), ETuac is the optical band gap, and n is the value decided by the transition process which is specifically divided into two kinds of situations: n=2 for indirect transition and n=1/2 for direct transition. The amorphous Al2O3 films have an indirect band gap, so n=2 is adopted in this work.Figure 7
Optical transmittance spectra by UV-VIS transmittance measurement. The inset shows the optical band gaps from the plots ofαE1/2 versus ETauc of 200 and 400 cycles (cycles).According to the Tauc theory [12], the direct consequence of electron energy parabolic distribution is the linear feature of Tauc curve, so the band gap ETauc can be extracted from the linear extrapolation of curve to αE=0. As shown in Figure 8, the band gap ETauc of all samples is around 2.3 eV and has no significant fluctuation. The corresponding slope is near zero. This low slope is the same as the situation in SE measurement, which also convincingly verifies the reliability of our SE results. It is understandable because the amorphous Al2O3 films with different thickness have the identical atomic ratio Al/O as demonstrated by EDS. As to the difference between ETL and ETauc, there are probably two reasons. First, the localization of electron wave functions and the subgap absorption in forbidden band is incorporated in Tauc model. However, the optical transition below band gap is zero by forcing ε(E) to be 0 for E≤ETL in the T-L model (see (5)). Second, in the UV-VIS measurement, only transmittance is recorded and other information, like polarization state, is lost.Figure 8
The optical band gap changes with the ALD cycles.Another important structural parameter extracted from SE analysis is the surface roughnessds of thin film. As indicated by AFM measurement, ds of all samples are relatively low, showing the good surface quality of Al2O3 thin film fabricated by ALD technology. drms from AFM measurement is found inconsistent with ds from SE analysis. It is likely because of the different testing principle in the two methods. The AFM scanning process is a mechanical tapping method, which cannot detect the microstructure located below at surface, and the scanning area is micrometer level. In SE analysis, however, the surface roughness is a calculation outcome and the laser spot size is millimeter level. Further, the surface roughness is modeled as a mixture of 50% bulk Al2O3 layer and 50% voids based on EMA, which includes both the microstructure on surface and the microstructure in bulk layer. On the other hand, the relationship between ds and drms is shown in Figure 9. An apparent mathematical relationship between the two sets of value cannot be found. This is different from the report of Koh et al. [20] in 1996, where an obvious linear relationship is observed in amorphous SixC1-x:H thin film. It could be ascribed to the different testing material.Figure 9
RMS roughnessdrms measured by AFM with tapping mode versus surface roughness ds extracted from T-L model.The refractive indexn and extinction coefficient k are also the key parameters to characterize the optical properties of amorphous Al2O3 films with different thickness. As shown in Figure 10(a), the n/k value of Al2O3 films is calculated based on the obtained SE fitting parameters. Result shows that n/k value of samples is dependent on film thickness. It exhibits a similar variation trend, which increases with different thickness. The sample with 500 cycles has the maximum n/k values and the sample with 100 cycles has the minimum ones. At 400 nm wavelength, n increases from 1.536 to 1.721 with the thickness increasing from 11.62 nm to 50.40 nm. The inflection point at ~400 nm wavelength (~3 eV) in k curves means the onset of optical absorption, which is in agreement with the above results. The surface defects may exist in the films, including the stress and strain change or the imperfect crystal. This surface defect of Al2O3 films in the ALD is determined by the number of activation groups and saturation adsorption capacity. The thicker samples may exhibit stress and strain, and thinner films may have amorphous phase [21]. The ratio of defects and the volume ratio of air have an effect on the film surface with different thickness. The n/k values can be improved by the thickness variation of films [22]. Meanwhile, the interfacial layer always has influence on the n/k values of the Al2O3 samples, because the refractive index and the layer thickness in any layer have a direct influence on analysis result according to the Snell law and transfer matrix. As the films thickness increases, the defects may be decreased, the values of n/k tend to be similar with the Al2O3 bulk layer. However, the influences are inevitable resulting from the interfacial layer. In our work, the interfacial layer plays a main role in the n/k values of Al2O3 samples and the roughness of the surface was subordinate. These results demonstrate that thickness plays an important role in the optical properties of Al2O3 thin films.Figure 10
(a) Refractive indexn (continued curves) and extinction coefficient k (open symbols) spectra derived from the Al2O3 films with different thicknesses. (b) Absorption spectra of Al2O3 films with different thickness.
(a) (b)The absorption coefficient also can be calculated from analysis through the relationshipα=4kπ/λ [23]. It can be seen that the increased film thickness enhance the absorption capacity of materials.The electronic response of material depends on its dielectric function, which reflects the interaction between the electrons and the applied field in materials. Figure11 provides the calculated dielectric function spectra of amorphous Al2O3 film with different thickness. It can be observed that the spectra display a systematic change with the increase of cycles. For all Al2O3 film samples, the value of ε2(E) is zero when the photon energy is between 0 and ETL (~3.0 eV), because the electron transitions less than ETL are forbidden in the Tauc-Lorentz mode [24]. The nonzero value of the curve front end shows the occurrence of the absorption of Al2O3 films, and the boundary point of zero and nonzero values is the optical band gap.Figure 11
The dielectric functions of Al2O3 films with different thickness samples by the T-L model: real part (a) and imaginary part (b).
(a) (b)


## 3.1. Crystal Structure and Compositional Analysis

The intensity of XRD is sensitive to the atomic arrangement of material, so it is capable of analyzing crystal structure. Figure1 gives the XRD patterns of naked Si substrate and deposited films with different cycles. It can be seen from Figure 1(a) that Si XRD exhibits three diffraction peaks at 61.86°, 66.02°, and 69.16°, respectively. Likewise, the XRD patterns of all deposited films almost completely overlap the Si XRD [14], and no other peaks are observed, implying the amorphous structure of the obtained samples.Figure 1
XRD patterns of Si (100) and all films of different cycles grown on Si (100) substrates.
(a) (b)In ALD, the monolayer deposition and the alternating precursor pulse can guarantee an excellent film deposition quality and uniform rate [7, 8]. Figure 2 shows the whole reaction cycle consisting of four steps. (1) Precursor TMA vapor is pulsed into the reaction chamber, and the chemical adsorption reaction 4 occurs on the surface of the substrate. (2) Excess precursor TMA and reaction by-products CH4 are purged with inert carrier gas N2. (3) Precursor deionized H2O vapor is pulsed into the reaction chamber, the surface chemical reactions 4 is proceeded on surface of the adsorption by TMA. (4) Excess precursor H2O and reaction by-products CH4 are purged with inert carrier gas N2.Figure 2
ALD process schematic.The surface chemistry reaction for ALD-Al2O3 can be expressed asAAlCH33g+Al-OH∗s⟶Al-O-AlCH32∗s+CH4gBAlCH3∗s+H2Os⟶Al-OH∗s+CH4gThe overall reaction isC2AlCH33g+3H2Os⟶Al2O3s+6CH4g∗ refers to the functional groups adsorbed on the deposition surface, showing that self-stop gas-solid reaction is the basis of ALD. TMA/H2O ALD process can be divided into 4 and 4 two half reactions, and the precursor molecule performs the chemical adsorption firstly on the deposition surface in each half reaction. Through ligand exchange between TMA and surface hydroxyl groups form the bridging oxygen bonds Al-O-Al on the surface and in the meantime release methane molecules. The reaction between the precursor and the deposition surface is chemical adsorption, the monolayer adsorption, which is also related to the steric hindrance of methyl groups. Therefore, the gas-solid surface reactions of ALD include adsorption, chemical reactions and desorption, and other processes.The chemical composition of the films was evaluated using SEM-EDS. As shown in Table1, result indicates that the atomic ratio O/Al in all samples is around 5, which is different from the value 1.5 in crystalline state [15]. In the report of Kääriäinen and Cameron [16], the O/Al value varies between 2.5 and 3.6 due to some oxygen ion contribution from precursor O2. Gupta and Saleh [17] demonstrated that it is almost impossible to precisely control the atomic ratio in metal oxides, because some oxygen contribution comes from the oxygen-containing functional groups, such as carbonyl or carboxyl groups, on the growth surface. In our case, there are a large number of carbonyl groups adsorbed on the growth surface during reaction process leading to increased oxygen contribution because of the precursor H2O shown in Figure 2. In addition, due to the limitation of SEM-EDS measurement accuracy, the extremely low Al content in the sample with 10.5833 nm of thickness cannot be detected. The EDS result combined with XRD result confirms that our samples deposited at 200°C is amorphous.Table 1
EDS data of different cycles Al2O3 film on silicon wafer (oxygen, aluminum, and silicon (%); the total = 100%).
ALD cycles Elements Wt.% At. (%) d (nm) O/Al ratio 100 O 2.3 3.97 11.62 —— Al 0 0 Si 97.7 96.03  200 O 4.05 6.90 19.63 4.964029 Al 1.38 1.39 Si 94.57 91.71  300 O 5.85 9.82 30.95 5.223404 Al 1.89 1.88 Si 92.27 88.30  400 O 7.97 13.18 39.05 4.592334 Al 2.93 2.87 Si 89.1 83.95  500 O 11.23 18.15 50.40 5.385757 Al 3.52 3.37 Si 85.25 78.48


## 3.2. Morphological Analysis

The film surface quality has a direct influence on the optical and electrical performance of device, such as the optical scattering and electrical contact. Therefore, a precise control of surface morphology during film growth process is very crucial to device performance. In this work, AFM is used to characterize the surface structure of the amorphous Al2O3 films. Figure 3 gives the AFM results of Al2O3 film with different ALD cycles. The AFM scan is carried out on a 3 μm × 3 μm area with the tapping mode.Figure 3
AFM micrographs of deposited Al2O3 films with different thicknesses. (a) 100 cycles. (b) 200 cycles. (c) 300 cycles. (d) 400 cycles. (e) 500 cycles. (f) Trend chart of roughness for the five samples. RMS represents root mean square roughness.
(a) (b) (c) (d) (e) (f)The surface morphologies of all samples are smooth and crack-free with similar root mean square (RMS) surface roughness values, which indicates that Al2O3 films were well fabricated. In order to study the cause of different growth rates of those of 50 cycles, we also studied the growth rate of films with ALD cycles below 50. The ALD surface reactions are very efficient, and Steps 1 and 3 are also known as the half reaction with the self-limitation and complementarity, while the self-limiting reaction is determined by the saturation adsorption of the group and the number of surface activated groups. Each group has a certain size, and the bonding location is blocked by adjacent chemical group, so the remaining groups can only be adsorbed in the next cycle. The number of surface activation groups determines the number of molecules per cycle. The Al2O3 films growth occurs during alternating exposures to TMA and H2O. The main driver for the efficient reactions is the formation of a very strong Al-O bond. The films tend to be smooth and pinhole-free because the randomness of the precursor flux and the self-limiting of the surface reactions. The reaction dose, deposition temperature, and so forth have little or no effect on the reaction. Thus, the growth rate is constant in the ALD process, which is insensitive to changes in process parameters, and the deposited films have excellent thickness uniformity and three-dimensional conformity.


## 3.3. Optical Property Analysis

Spectroscopic ellipsometer (SE) is an important thin film measurement technology for its nondestructive and sensitive advantages [18]. It is necessary to develop a proper optical model for the SE measurement and thus the extraction of optical and structural parameters. Our optical model for fit analysis is established as follows: Si substrate/bulk Al2O3 layer/surface roughness/air ambient, as shown in Figure 4. The surface roughness layer was modeled as a mixture of 50% bulk Al2O3 layer and 50% voids based on the Bruggeman effective medium approximation (EMA). Meanwhile, a reasonable material dispersion relationship is required during ellipsometry analysis. In our measurement, the Tauc-Lorentz model has been used. It is established by Jellison et al. in 1996 based on combined density and Lorentz oscillator model and more suitable for amorphous thin film compared to FB model [18, 19]. This model is defined as follows:(4)ε1E=ε1∞+2πP∫Eg∞τε2ττ2-E2dτ,ε2E=ACEE0E2-E022+C2E2E-EgE2forE>Eg,0forE≤Eg,where P represents the Cauchy principal value of the integral. The dielectric function of the films is determined by five parameters A,C,E0,Eg,andε1∞. In the T-L model, ε2 is modeled as the product of Tauc gap and Lorentz oscillator and ε1 is derived by the Kramers–Kronig relations.Figure 4
Spectroscopic ellipsometer schematic of Al2O3 film micronanosystem.The ellipsometry spectra of Al2O3 thin film with different ALD cycles have been obtained using the above theoretical model. Since the related parameters of all samples are extracted from Ψ and Δ fits, we give both the experimental and calculated data, respectively, as shown in Figure 5. The fitting parameters are listed in Table 2. It can be seen that the calculated outcomes fit the experimental points well. The objective function value fRMSE in all samples is less than 1, demonstrating the acceptable optimization in our case.Table 2
Structural and electronic parameters extracted from SE analysis of the five different samples.
ALD cycle ε 1 ∞ A C E 0/eV E g/eV d/nm d s/nm f RMSE 100 1.66 118.24 644.70 74.33 3.08 11.62 0.08 0.68 200 1.39 156.83 393.56 70.30 2.99 19.63 0.25 0.67 300 1.22 72.65 39.07 25.23 2.98 30.95 0.89 0.58 400 0.59 334.78 430.62 92.86 2.92 39.05 0.15 0.53 500 1.11 207.70 295.86 59.76 2.92 50.40 0.21 0.73Figure 5
Al2O3 films ellipsometry spectra of fit data (continued curves) and measured data (gauge points).SE measurement shows that the fundamental structural parameter, film thickness, increases regularly with the increase of ALD cycles, corresponding to a growth rate of ~0.1 nm/cycle. The relationship between thickness and cycle can be described by a linear fit functiond=0.097nc+1.2328 nm, as shown in Figure 6. As we know, SE analysis is an indirect measurement method, and the obtained result could be a local minimum and not the global minimum. Hence, in order to confirm the reliability of our result, the above fit function is extrapolated to 1000 cycles and then the calculated thickness is supposed to be 98.23 nm. On the other hand, a sample has been deposited at 1000 cycles and its thickness has been examined using SEM. The derived thickness by SEM is 96.89 nm (see the inset in Figure 6), which indicates our SE analysis is reliable. Regarding the 1.34 nm thickness difference, it can be attributed to the following three reasons. First, the ALD growth speed is not constant in each cycle. Second, the thickness calculated by SE analysis has about 0.5 nm error. Third, the two thickness measurement methods, SE and SEM, have distinct principles, so there is an inherent difference in the results from them.Figure 6
Trend chart of thickness for the five different cycle samples. The inset is SEM image of 1000 cycles ALD-Al2O3 film, where d and nc represent film thickness and number of ALD cycles, respectively.The optical band gapETL of Al2O3 has been extracted from the SE analysis. An obvious fluctuation of ETL is not observed in all samples with different thickness. ETL of five samples are ~3.0 eV, as shown in Table 2. Similarly, another optical measurement method, UV-VIS transmittance spectrum, is used to verify the obtained SE results. Figure 7 gives the UV-VIS transmittance spectra of samples in the wavelength range from 300 to 800 nm. The absorption coefficient α can be calculated from the transmittance spectra. The optical band gap is derived by Tauc plot. Generally, the Tauc equation can be expressed as(5)aE=AE-ETuacn,where A is a constant, E is the photon energy (hν), ETuac is the optical band gap, and n is the value decided by the transition process which is specifically divided into two kinds of situations: n=2 for indirect transition and n=1/2 for direct transition. The amorphous Al2O3 films have an indirect band gap, so n=2 is adopted in this work.Figure 7
Optical transmittance spectra by UV-VIS transmittance measurement. The inset shows the optical band gaps from the plots ofαE1/2 versus ETauc of 200 and 400 cycles (cycles).According to the Tauc theory [12], the direct consequence of electron energy parabolic distribution is the linear feature of Tauc curve, so the band gap ETauc can be extracted from the linear extrapolation of curve to αE=0. As shown in Figure 8, the band gap ETauc of all samples is around 2.3 eV and has no significant fluctuation. The corresponding slope is near zero. This low slope is the same as the situation in SE measurement, which also convincingly verifies the reliability of our SE results. It is understandable because the amorphous Al2O3 films with different thickness have the identical atomic ratio Al/O as demonstrated by EDS. As to the difference between ETL and ETauc, there are probably two reasons. First, the localization of electron wave functions and the subgap absorption in forbidden band is incorporated in Tauc model. However, the optical transition below band gap is zero by forcing ε(E) to be 0 for E≤ETL in the T-L model (see (5)). Second, in the UV-VIS measurement, only transmittance is recorded and other information, like polarization state, is lost.Figure 8
The optical band gap changes with the ALD cycles.Another important structural parameter extracted from SE analysis is the surface roughnessds of thin film. As indicated by AFM measurement, ds of all samples are relatively low, showing the good surface quality of Al2O3 thin film fabricated by ALD technology. drms from AFM measurement is found inconsistent with ds from SE analysis. It is likely because of the different testing principle in the two methods. The AFM scanning process is a mechanical tapping method, which cannot detect the microstructure located below at surface, and the scanning area is micrometer level. In SE analysis, however, the surface roughness is a calculation outcome and the laser spot size is millimeter level. Further, the surface roughness is modeled as a mixture of 50% bulk Al2O3 layer and 50% voids based on EMA, which includes both the microstructure on surface and the microstructure in bulk layer. On the other hand, the relationship between ds and drms is shown in Figure 9. An apparent mathematical relationship between the two sets of value cannot be found. This is different from the report of Koh et al. [20] in 1996, where an obvious linear relationship is observed in amorphous SixC1-x:H thin film. It could be ascribed to the different testing material.Figure 9
RMS roughnessdrms measured by AFM with tapping mode versus surface roughness ds extracted from T-L model.The refractive indexn and extinction coefficient k are also the key parameters to characterize the optical properties of amorphous Al2O3 films with different thickness. As shown in Figure 10(a), the n/k value of Al2O3 films is calculated based on the obtained SE fitting parameters. Result shows that n/k value of samples is dependent on film thickness. It exhibits a similar variation trend, which increases with different thickness. The sample with 500 cycles has the maximum n/k values and the sample with 100 cycles has the minimum ones. At 400 nm wavelength, n increases from 1.536 to 1.721 with the thickness increasing from 11.62 nm to 50.40 nm. The inflection point at ~400 nm wavelength (~3 eV) in k curves means the onset of optical absorption, which is in agreement with the above results. The surface defects may exist in the films, including the stress and strain change or the imperfect crystal. This surface defect of Al2O3 films in the ALD is determined by the number of activation groups and saturation adsorption capacity. The thicker samples may exhibit stress and strain, and thinner films may have amorphous phase [21]. The ratio of defects and the volume ratio of air have an effect on the film surface with different thickness. The n/k values can be improved by the thickness variation of films [22]. Meanwhile, the interfacial layer always has influence on the n/k values of the Al2O3 samples, because the refractive index and the layer thickness in any layer have a direct influence on analysis result according to the Snell law and transfer matrix. As the films thickness increases, the defects may be decreased, the values of n/k tend to be similar with the Al2O3 bulk layer. However, the influences are inevitable resulting from the interfacial layer. In our work, the interfacial layer plays a main role in the n/k values of Al2O3 samples and the roughness of the surface was subordinate. These results demonstrate that thickness plays an important role in the optical properties of Al2O3 thin films.Figure 10
(a) Refractive indexn (continued curves) and extinction coefficient k (open symbols) spectra derived from the Al2O3 films with different thicknesses. (b) Absorption spectra of Al2O3 films with different thickness.
(a) (b)The absorption coefficient also can be calculated from analysis through the relationshipα=4kπ/λ [23]. It can be seen that the increased film thickness enhance the absorption capacity of materials.The electronic response of material depends on its dielectric function, which reflects the interaction between the electrons and the applied field in materials. Figure11 provides the calculated dielectric function spectra of amorphous Al2O3 film with different thickness. It can be observed that the spectra display a systematic change with the increase of cycles. For all Al2O3 film samples, the value of ε2(E) is zero when the photon energy is between 0 and ETL (~3.0 eV), because the electron transitions less than ETL are forbidden in the Tauc-Lorentz mode [24]. The nonzero value of the curve front end shows the occurrence of the absorption of Al2O3 films, and the boundary point of zero and nonzero values is the optical band gap.Figure 11
The dielectric functions of Al2O3 films with different thickness samples by the T-L model: real part (a) and imaginary part (b).
(a) (b)


## 4. Conclusions

In summary, the amorphous ALD-Al2O3 films with various thicknesses are successfully fabricated at 200°C. The XRD and EDS measurements show that the films were amorphous structure and stable O/Al ratio. The AFM indicates that the surface morphologies of all samples are smooth and crack-free with similar surface roughness values. The SE analysis reveals that the film thickness increases regularly with the increase of ALD cycles, corresponding to a growth rate of ~0.1 nm/cycle. Further analysis on SE and UV-VIS transmittance spectrum shows that the band gap ETL/ETauc of all samples is ~2.3 eV/3.0 eV, with no significant fluctuation. n/k of ALD-Al2O3 films are related to their bulk layer thickness. The bulk layer plays a key role in the n/k values of Al2O3 samples, and the surface roughness is subordinate. The outstanding performances stem from the constructed amorphous thin films. Considering the easy fabrication and excellent performances, this method can be used broadly to deposit other amorphous minerals, and this structure will be promising in practical application for other optoelectronic film materials deposition, especially Ti/Fe/Zn oxides deposition.



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