Effect of substrates and thickness on optical properties in atomic layer deposition grown ZnO thin films

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Effect of substrates and thickness on optical properties in atomic layer deposition grown ZnO thin films Dipayan Pal a , Jaya Singhal b , Aakash Mathur a , Ajaib Singh a , Surjendu Dutta c , Stefan Zollner d , Sudeshna Chattopadhyay a,b,c,∗ a

Discipline of Metallurgy Engineering and Materials Science, Indian Institute of Technology Indore, Simrol, Indore 453552, India Centre for Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Indore 453552, India c Discipline of Physics, Indian Institute of Technology Indore, Indore 453552, India d Department of Physics, New Mexico State University, Las Cruces, NM 88003, USA b

a r t i c l e

i n f o

Article history: Received 24 July 2016 Received in revised form 19 October 2016 Accepted 20 October 2016 Available online xxx Keywords: Atomic layer deposition Spectroscopic ellipsometry Zinc oxide thin film Thickness dependence Tunable optical property

a b s t r a c t Atomic Layer Deposition technique was used to grow high quality, very low roughness, crystalline, Zinc Oxide (ZnO) thin films on silicon (Si) and fused quartz (SiO2 ) substrates to study the optical properties. Spectroscopic ellipsometry results of ZnO/Si system, staggered type-II quantum well, demonstrate that there is a significant drop in the magnitudes of both the real and imaginary parts of complex dielectric constants and in near-band gap absorption along with a blue shift of the absorption edge with decreasing film thickness at and below ∼20 nm. Conversely, UV–vis absorption spectroscopy of ZnO/SiO2 , thin type-I quantum well, consisting of a narrower-band gap semiconductor grown on a wider-band gap (insulator) substrate, shows the similar thickness dependent blue-shift of the absorption edge but with an increase in the magnitude of near-band gap absorption with decreasing film thickness. Thickness dependent blue shift, energy vs. 1/d2 , in two different systems, ZnO/Si and ZnO/SiO2 , show a difference in their slopes. The observed phenomena can be consistently explained by the corresponding exciton (or carrier/s) deconfinement and confinement effects at the ZnO/Si and ZnO/SiO2 interface respectively, where TanguyElliott amplitude pre-factor plays the key role through the electron-hole overlap factor at the interface. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Owing to its direct and wide band gap, large exciton binding energy, high thermal and chemical stability, zinc oxide (ZnO) has gained intensive interest in the research community in the past few years [1–4]. Its distinct properties like wide band gap and large excitonic binding energy (60 meV, which is more than twice exciton binding energy of GaN) [4], ensure efficient excitonic emission in ZnO at room temperature and even at higher temperatures [5], which makes ZnO a promising material for short-wavelength optoelectronic devices, especially for ultraviolet light-emitting diodes and laser diodes [6]. ZnO has also been extensively investigated in various applications such as solar cells [7], thin film transistors [8], transparent conducting oxide [9], gas sensors [10] and nanogenerators [11]. Furthermore, due to its wide band gap and a very good optical transmittance, ZnO has also attracted a lot of interest

∗ Corresponding author at: Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore, India. Tel.: +919981991590. E-mail addresses: [email protected], [email protected] (S. Chattopadhyay).

as an efficient cathode buffer layer or a transparent electrode in organic and hybrid solar cells [12]. On account of the above facts, for optimal device performance, tuning of the structural and optical properties of ZnO films is of great benefit [13]. Earlier experimental studies show that within the dimensions of 20 nm or less, the quantum effect in ZnO becomes apparent [14–16]. Therefore, a careful and systematic study of the influence of film thickness on the optical properties of ZnO thin films in this regime is highly desirable, and convincing scientific explanation of the observed phenomena needs to be addressed. Over the past few years, Atomic layer deposition (ALD) technique has gained substantial interest for growing ZnO thin films in nanometer length scale in a controlled manner [17–19]. Due to two self-limiting surface reactions, ALD grown films are typically smooth, uniform, homogeneous, pinhole-free and extremely conformal to the underlying substrate [20–22]. Herein we demonstrate and explain the contrary trends in the thickness induced change in optical properties of Atomic Layer Deposition (ALD) grown high quality, crystalline, smooth ZnO thin films, for silicon (Si) and fused quartz (SiO2 ) substrates. It has been clearly shown by spectroscopic ellipsometry studies that in the ZnO film with decreasing film thickness at and below ∼20 nm, there is

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a significant drop in the magnitudes of both the real and imaginary parts of complex dielectric constants and in near-band gap absorption for ZnO/Si system. On the other hand, UV–vis absorption study demonstrates that, for ZnO/SiO2 system, the thinner ZnO films show higher absorption coefficient at band edge and a sharper blue shift in the band gap energy with decreasing film thickness, corresponding to the stronger exciton confinement effect. The observations have been consistently explained through the delocalization effect of holes in Si from ZnO at the ZnO/Si interface, which leads to the deconfinement of exciton and consequently the lowering of electron-hole overlap factor at the interface, thus causing a decrease in strength of optical interband transition, governed by the Tanguy-Elliott amplitude pre-factor [23,24]. The proposition is consistent in case of ZnO/SiO2 system, where both the electron and the hole are confined in ZnO thin film, which leads to an increase in the electron-hole overlap matrix element with decreasing film thickness, resulting in enhancement of excitonic absorption in thinner ZnO films, and sharper thickness dependent blue shift in the band gap energy.

2. Experimental ZnO thin films were deposited at 200 ◦ C using a BENEQ TFS-200 ALD reactor. Two different substrates, Si (100) and fused quartz (SiO2 ), were used in this study. The substrates were cleaned using an ultrasonic bath in acetone and ethanol and then kept in deionized (DI) water and finally dried in nitrogen (N2 , 99.999% purity). Subsequently, the cleaned dried substrates were loaded into the ALD reactor for the deposition. Diethyl zinc (DEZn, Zn(C2 H5 )2 , Sigma-Aldrich) and DI water were used respectively as precursors for zinc and oxygen. Nitrogen (N2 , 99.999% purity) was used both as a carrier and purging gas. The precursors were alternately pulsed into the reactor chamber using their intrinsic vapor pressures from external containers kept at 18 ◦ C. The sequence for ALD reaction cycle is 0.2 s exposure to DEZ/0.75 s N2 purge/0.2 s exposure to H2 O/0.75 s N2 purge. The number of ALD cycles varied from 30 to 410 to achieve ZnO film thickness range from ∼5 nm to ∼70 nm. The growth rate of ZnO determined with X-ray reflectivity (XRR) from the deposited films on Si and SiO2 was about 1.6 Å/cycle (at 200 ◦ C), which is in agreement with previous studies of ZnO growth by ALD [25,26]. ZnO films with different thickness (∼5 nm to ∼70 nm) were grown on Si and fused quartz (SiO2 ) substrates to explore the substrate and thickness induced change in optical properties. The crystalline structures of the as-grown ZnO films were observed by X-ray diffraction (XRD) with CuK␣ radiation (␭ = 1.54 Å) using Rigaku SmartLab automated multipurpose X-ray diffractometer. Thickness and electron density profile (EDP) of the ZnO film were obtained by using X-ray reflectivity measurements. Xray reflectivity data of ZnO films were collected with CuK␣ radiation using Rigaku SmartLab automated multipurpose X-ray diffractometer. Specular reflectivity scans, i.e., scans in the plane containing the incident beam and normal to the sample surface, with incident angle  in = scattering angle  sc , were performed with  in varying from 0◦ to 3◦ . If q = ks -ki is the momentum transfer vector and ks and ki being the scattered and incident X-ray wave vector respectively, then this geometry makes the components in the sample plane, qx = qy = 0, and the value of qz (= (4/) Sin in ), the component normal to the sample surface varies from 0 to 0.43 Å−1 . The X-ray reflectivity, R(qz ), calculated from any electron density profile, (z), is [27]:

R (qz ) = RF (qz ) |

1 



d (z) −iz e dz



2 qz (q2 z −qc )

1/2

2

|

(1)

Where, RF is the Fresnel reflectivity from a single ideal stepfunction interface,  is the total change in electron density across the interface and qc is the momentum transfer at the critical angle for total external reflection. The Eq. (1) can be used to calculate R(qz ) from a given analytic function (z), but, the reverse is not simple. When R(qz ) is experimental data collected over a finite range and with finite accuracy, (z) cannot be directly calculated from it. The general procedure to solve the inverse problems has been employed for the analysis of x-ray reflectivity data: a model (z), specifically a slab model, is assumed, and parameters in the model are adjusted until good fits to the data have been achieved, following the Parratt formalism [28–32]. The extracted values of film thickness, electron density and interface width or roughness from the best fit of reflectivity data, were used to construct the electron density profiles (EDPs), i.e., the electron density as a function of film depth from the top for ZnO films, after convoluting the profile with the interface widths. Spectroscopic ellipsometry (SE) measurements were performed on ZnO thin films deposited on Si substrate with an ellipsometer (J.A. Woollam Co., Lincoln, NE, Model: VASE) in the photon ◦ ◦ ◦ energy range of 0.8–6.5 eV at four incident angles of 60 ,65 , 70 and ◦ 75 , similar to the technique described elsewhere [33]. Ellipsometry techniques have been extensively used to explore the optical properties of the as-grown ZnO films, namely, complex dielectric function, absorption coefficient and band gap along with the film thickness and surface roughness, using WVASE, Woollam software. The UV–vis absorption spectra of ZnO films, deposited on fused quartz substrates, were measured using a UV–vis spectrophotometer in transmission mode (Perkin Elmer, lambda-35) in the wavelength (␭) range of 190–1100 nm. The absorption coefficient, ␣, can be calculated using the Beer-Lambert’s law as [34]: ˛=

2.303 × Abs () d

(2)

where d and Abs (␭) are the film thickness and film absorbance respectively. 3. Results and discussion The optical properties of as-deposited ZnO thin films, i.e., the complex dielectric function and absorption coefficient have been investigated using Spectroscopic Ellipsometry (SE) in the photon energy range (0.8–6.5 eV). Spectroscopic ellipsometry measures the Jones ratio, J, versus photon energy E and angle of incidence , described by the equation [35–37]: J(E, ) = (r p /rs ) = (tan )ei

(3)

rp and rs are the complex Fresnel reflectance ratios for p and s polarand  are known as the ellipsometric ized light respectively. angles which correspond to the amplitude ratio and the relative phase change respectively [36,38]. Fig. 1(a) and (b) show the ellipsometric angles, ␺ and , for asdeposited 38 nm and 9 nm ZnO films on Si substrate respectively. It is found that the calculated ␺ and  are in good agreement with the experimental data. Excellent fittings with MSE (mean-squarederror) < 5 were achieved for all the samples. In this SE study, to extract the optical constants of the ZnO films, we used a three layer model (i.e. air/ZnO layer/Si substrate) for ZnO film thickness of 5 nm, 9 nm and 19 nm. For ZnO film thickness of 38 nm, 52 nm and 69 nm, a four layer model (i.e. air/surfaceroughness layer/ZnO layer/Si substrate) was employed, where the Si substrate is about 1 mm thick and has been treated as infinite. The optical constants of Si are well known [39]. In this work, Tauc-Lorentz (T-L) model has been used to fit the experimental ellipsometry data. The complex dielectric function (␧ = ␧1 + i␧2 )

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Fig. 2. Evolution of real part (␧1 ) (Inset), and imaginary part (␧2 ) of the dielectric function with the thickness of ZnO film grown on Si, at 200 ◦ C.

Fig. 1. Ellipsometric angles ␺ and  as a function of photon energy for ZnO films of (a) 38 nm, and (b) 9 nm film thickness, grown on Si substrates, acquired with incidence angles ranging from 60◦ to 75◦ ; circles and lines represent experimental data and theoretical fit respectively.

versus photon energy E for ZnO thin films can be written in the following functional form known as the Tauc-Lorentz model [40–42]:



ε2 (E) =

=0





AE0 C E − Eg E2



2 − E02

E ≤ Eg

2

+ C 2 E2

·

1 E

(E > Eg )

(4)



2P ε1 (E) = ε∞ + 



 

ε2

2 − E2

d

(5)

The T-L dispersion model was obtained from the Tauc joint density of states and the Lorentz oscillator, and the fitting parameters are A, E0 , C, Eg and ε∞ [40,41]. The parameter, A signifies the transition matrix element (proportional to the magnitude of the real and imaginary part of complex dielectric constant) [40]. E0 corresponds to the peak transition energy; C is the broadening term (which can be related to the degree of disorder in the material) [40]. Eg stands for the optical band gap. The four fitting parameters, A, E0 , C and Eg have the units of energy [40]. The additional fitting parameter, ε∞ , is high frequency dielectric constant and P stands for the Cauchy

principal part of the integral [40,41]. Summary of Tauc-Lorentz fit parameters are shown in the Supplementary information, Table 1. A dispersion model-independent determination of the dielectric function is the point-by-point (or direct inversion) method which utilizes the fact that the complex reflection coefficient measured by ellipsometry directly can be converted to both the real and imaginary parts of the refractive index (n and k) or dielectric function (ε1 and ε2 ) if the thickness of the layer is known [38,43]. In our study, with the obtained ZnO layer thickness, n and k were independently varied wavelength-by-wavelength across the entire spectral range to fit the ellipsometric data using the point-by-point method. The extracted ε1 and ε2 using point-by-point inversion of the measured ellipsometric spectra with different thicknesses of the ZnO layer are shown in Fig. 2. This point-by-point fit is a reliable direct method, which doesn’t require any assumption for the dispersion of the refractive index, and therefore can be used as a reference for the further parameterizations [43]. As can be observed in Fig. 2, the film thickness has a significant impact on the complex dielectric functions of ZnO thin films. The magnitudes of both the real and imaginary parts of dielectric constants near the band edge significantly drop in the thinner film thickness window (i.e., at and below ∼20 nm film thickness). In comparison with the thicker films (above ∼20 nm film thickness), the thinner ZnO film with film thickness 9 nm shows a reduction of ∼34% and ∼57% in the real and imaginary parts of the complex dielectric function at the photon energy of ∼3.3 eV, respectively, while the ZnO film with a thickness of 5 nm shows a drastic reduction of ∼46% and ∼73%, respectively. Furthermore, there is also a blue shift in ε1 and ε2 with decreasing film thickness in thinner film thickness window (at and below ∼20 nm). Using the values of ε1 and ε2 , the absorption coefficient, ␣, for ZnO thin films, were calculated, and a plot of (␣h)2 vs energy for direct band gap ZnO is shown in Fig. 3. The results indicate that wider-band gap ZnO deposited on narrower-band gap Si, with staggered type-II alignment, absorbs less light with decreasing film thickness, at and below ∼20 nm. A clear blue shift of the absorption edge has been observed with decreasing film thickness, from 38 nm to 5 nm, Fig. 3. The electronic transitions between the valence band (V.B.) and conduction band (C.B.) in the crystal start at the absorption edge, which corresponds to the band gap energy, Eg [44]. The UV–vis absorption spectroscopy was employed to explore the optical properties of ZnO thin films deposited on fused quartz (SiO2 ) substrate, where measurements were performed in transmission mode. Fig. 4 shows the plot of (␣h)2 vs energy, where

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Fig. 3. A plot of (␣h)2 versus energy (h), where absorption coefficients, ␣ (determined from Ellipsometry) of ZnO films of different thickness grown on Si at 200 ◦ C. Fig. 5. Band gap of ZnO films having different film thickness deposited on Si and SiO2 vs. 1/d2 , d is the film thickness. Dotted lines show the corresponding best linear fits.

Fig. 4. A plot of (␣h)2 versus energy (h), where absorption coefficients, ␣ (determined from UV–vis absorption spectroscopy) of ZnO films of different thickness grown on fused quartz (SiO2 ) at 200 ◦ C.

␣ is the absorption coefficient of ZnO films in ZnO/SiO2 system. It has been observed that in case of ZnO/SiO2 systems, where ZnO deposited on wider band gap SiO2 corresponding to type-I quantum well, the thinner ZnO films show higher absorption coefficient at and above the band edge, which was discussed in details elsewhere [45], in contrast with the ZnO/Si systems, shown in Figs. 3 and 4. The optical band gap of the ZnO films has been determined using the Tauc model [44,46] and the Davis and Mott model [47] in the high absorbance region:



˛ (␯) h␯ = B h␯ − Eg

n

(6)

where Eg is the optical band gap, B is a constant, h is the incident photon energy and ˛() is the absorption coefficient. For the direct transition, n = 1/2 was found to be more appropriate for ZnO films because it gives the best linear curve in the band-edge region [6,48], correspondingly, the relationship between (˛h)2 and h has been plotted in Fig. 4. It can be seen that the absorption edge shifted to higher energy as the film thickness decreases. The band gap energy, Eg , can be obtained by extrapolating the linear portion to (˛h)2 = 0 in that figure. The increase in the band gap energy or band gap expansion induced by the quantum confinement is a well-known phenomenon [14,49,50]. Based on the effective mass approximation (EMA) theory [51], band gap energy, Eg in a confined nanostructure can be written as [14]: Eg (eV ) = Eg,bulk +

F d2

(7)

Where, Eg,bulk is the band gap energy of the bulk, F is the quantum confinement constant and d is the confined dimension, i.e. the film thickness.

The band gap, Eg , calculated for ZnO/Si and ZnO/SiO2 systems for different film thickness, d are shown in Fig. 5. Best linear fits show different slopes, 1.8 eV-nm2 and 6 eV-nm2 , for ZnO/Si and ZnO/SiO2 systems respectively, which attributes to the substrate dependent variation in thickness induced exciton confinement effect. It should be noted that the observed slope for ZnO/SiO2 system, is consistent with the results obtained for ZnO/sapphire system, [14] which also corresponds to a type-I quantum well. Results indicate that thickness induced effective exciton confinement effect is weaker in the case of ZnO/Si system. The fitted bulk band gap energy for ZnO/Si and ZnO/SiO2 systems are 3.27 eV and 3.2 eV respectively, which are in close agreement with the band gap value of bulk ZnO (free exciton emission peak observed at 3.20 eV, corresponding to the band gap) [15]. Summarizing the observation, ellipsometry results clearly demonstrate that for ZnO/Si system, there is significant drop in the magnitudes of both the real and imaginary parts of complex dielectric constants and in near-band gap absorption along with blue shift of the absorption edge in the thinner film thickness window (i.e., at and below ∼20 nm film thickness). On the other hand, UV–vis absorption study demonstrates that, for ZnO/SiO2 system, the thinner ZnO films show higher absorption coefficients at band edge and a sharper blue shift in the band gap energy with decreasing film thickness, corresponding to the stronger exciton confinement effect. To explain the above mentioned observations, the structural study of ZnO thin films were conducted to confirm that whether there is any structural difference in ZnO thin films grown on two different substrates, namely Si and SiO2 , which may cause such kind of effects in optical properties. Fig. 6(a) and (b) shows the X-ray diffraction pattern of ∼38 nm ZnO film grown at 200 ◦ C on Si and SiO2 substrates respectively. The results indicate the formation of hexagonal wurtzite ZnO with a space group of P63mc, which matches with the standard diffraction pattern of hexagonal wurtzite ZnO (JCPDS PDF card number: 01079-2205). XRD pattern of ZnO film shows much stronger ZnO (002) peak with respect to ZnO (101), whereas standard powder XRD pattern of hexagonal wurtzite bulk ZnO shows maximum intensity at ZnO (101) peak (JCPDS PDF card number: 01-079-2205). This clearly indicates that ZnO film exhibits preferred orientation along 0002 direction with c axis perpendicular to the substrate surface. The full width at half maximum (FWHM) of the most intense peak, (002), in the XRD patterns of Fig. 6 is used to determine the out-of-plane mean grain size using Scherrer’s formula [52] and the estimated out-of-plane mean grain size for ZnO is found to be of the order of 20 nm for both the systems, ZnO/Si and ZnO/SiO2 .

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Fig. 6. X-ray diffraction pattern of (a) 38 nm ZnO/Si and (b) 37 nm ZnO/SiO2 grown at 200 ◦ C.

Results show that crystal structures of ALD grown ZnO on Si and SiO2 substrates are similar. Fig. 7(a) shows specular reflectivity (R) normalized with Fresnel reflectivity (RF ), for ZnO films on two different substrates, Si and SiO2 . XRR of two representative ZnO film thickness, about 38 nm and 9 nm, above and below the threshold film thickness, i.e., 20 nm, are shown. Circles and lines represent experimental data and theoretical fit respectively. The XRR data has been fitted by the well-known Parratt’s exact recursive method [28–32]. XRR profile shows clear strong Kiessig fringes and corresponding extracted electron density indicates the formation of high quality ALD grown ZnO thin films on both Si and SiO2 substrates, with very low surface and interface roughness. Fig. 7(b) shows the electron density (␳) profiles (EDPs) of the respective films extracted from XRR fits. The electron densities of ALD grown ZnO films are very close to its bulk electron density (less than 7% variation even in the thinnest films). It should be noted that the extracted electron density profiles for different ZnO/Si films indicate the presence of very thin SiO2 layer, less than ∼1 nm of thickness, at the ZnO/Si interface, see Supplementary information Table 2. We compare the extracted relative electron density, rel (by fit the XRR data using Parratt formalism), with the relative (ε∞ −1) (which is proportional to valence electron density, unless the transition matrix element changes) of ZnO, vs. ZnO film thickness for ZnO/Si systems, as shown in Fig. 8. Relative electron densities (rel ) of ZnO films on SiO2 substrates have also been included in the figure to show that the electron densities of ZnO films of different film thicknesses have similar trend for Si and SiO2 substrates. The relative electron density (rel ) was estimated using the following equation: rel =

electrondensityofagivenZnOfilm x100 electrondensityofthickestZnOfilm

Fig. 7. (a) Reflectivity profiles, i.e., specular reflectivity (R) normalized with Fresnel reflectivity (RF ), (R/RF ) vs. normal momentum transfer qz (in Å−1 ) for different ZnO film thicknesses grown at 200 ◦ C. (i) and (ii): thin ZnO films, about 9 nm, deposited on Si and SiO2 substrates respectively; (iii) and (iv): thicker ZnO films, about 38 nm, deposited on Si and SiO2 substrates respectively. RF is the theoretical reflectivity from an ideal surface. Circles and lines represent the experimental data and theoretical fit respectively. (b) Corresponding extracted electron density (␳) profile from XRR fits.

Fig. 8. Plot of extracted relative electron density, rel (rel is calculated relative to the thickest ZnO film electron density, where thickest = 1.51 eÅ−3 and 1.48 eÅ−3 for ZnO/Si and ZnO/SiO2 system respectively), and relative (␧∞ −1), i.e., ε , of ZnO vs. ZnO film thickness.

(8)

rel is calculated relative to the thickest ZnO film electron density, thickest . For two different substrates, Si and SiO2 , the ZnO film electron density has been estimated from XRR results. Electron density

of ZnO thin film with highest thickness, thickest , within the thickness range shown in Fig. 8, is close to the bulk electron density (∼1.5 eÅ−3 ).

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␧∞ was calculated at photon energy 0.8 eV. The relative (ε∞ −1), i.e., ε , of ZnO films deposited on Si, was estimated using the following equation: ε = (ε∞ − 1)rel =

(ε∞ − 1) ofagivenZnOfilm x100 (ε∞ − 1) ofthickestZnOfilm

(9)

And in a similar manner as in Eq. (8), ε is calculated relative to the ZnO film with the highest thickness within the thickness range and is shown in Fig. 8. Ellipsometry results show that for ZnO films, in ZnO/Si system, the valence electron density, proportional to (␧∞ −1), starts decreasing sharply at and below 20 nm film thickness, and drops by ∼45% in the thinnest film. Whereas XRR results indicate that the electron density of ZnO films remains constant down to 9 nm thickness, then decreases a little only by less than 7%, as shown in Fig. 8. A slight decrease in electron density for the thinner film thickness range in ZnO/Si system can’t explain the sharp decrease in (␧∞ −1), significant drop in the magnitudes of both the real and imaginary parts of complex dielectric constants and in near-band gap absorption. Similarly, in ZnO/SiO2 system, the slight decrease (less than ∼5%) in electron density of ZnO films with decreasing film thickness, as shown in Fig. 8, can’t be attributed to the sharp increase in near-band gap absorption, obtained from UV–vis absorption spectroscopy, shown in Fig. 4. Fig. 8 clearly indicates that the variation in electron density with ZnO film thickness, obtained from XRR, cannot explain the substrate dependent optical properties of ZnO thin films at and below ∼20 nm thickness (thinner film window), namely, the significant drop in (␧∞ −1) and the significant reduction in near-band gap absorption for ZnO/Si system, on the other hand significant increase in near-band-gap absorption for ZnO/SiO2 system. The observation can be explained by the Tanguy’s proposition on the concept of amplitude pre-factor. The expression for complex dielectric constant (ε = ε1 + iε2 ) of Wannier excitons taking all bound and unbound states exactly into account proposed by Tanguy, can be written [23,24]: ε (E) =

 

√ A R (E + i )

2









ga (E + i ) + ga (−E − i ) − 2ga (0)



(10)

Where, amplitude pre-factor, A=

2 q2

2 32

2ε0 m20

2

|e · Mcv (0) |2

(11)

where, |e · Mcv (0) | is the dipole matrix element corresponding to the overlap of electron and hole [23]. R is the energy of the fundamental exciton bound state, Eg is the band gap energy, ␮ is the reduced mass of the exciton and is the broadening of the energy levels [23].

 





ga = 2ln − 2 cot  − 2



(z) = (z) =

 

− 1/

(12)

R Eg − z

(13)

dln (z) dz

(14)

In this study, in thinner ZnO films on Si (at or below 20 nm film thickness), the electron remains mostly confined in the ZnO conduction band quantum well (at least at low temperatures, where thermal excitation of the electron across the barrier into the Si substrate can be ignored), while the photoexcited ZnO hole will quickly relax across the interface into the Si substrate, because of the staggered band alignment, as shown in Fig. 9(a) and (b). This causes deconfinement of exciton. As a result, there is a reduction in the overlap of the electron and hole wave functions and thus the amplitude pre-factor, A, in the Tanguy dielectric function (Eq.

Fig. 9. Models/Schematic: (a) and (b) wider-band gap ZnO deposited on narrowerband gap Si, with staggered type-II alignment for thicker and thinner (less than ∼20 nm) films respectively; (c) and (d) ZnO deposited on wider band gap SiO2 corresponding to type-I quantum well for thicker and thinner (less than ∼20 nm) films respectively.

(10)). Delocalization of excitons near the interface plays an important role in determining the optical properties for thinner film, where the thickness is near or below the excitonic Bohr radius, as described in Fig. 9(b). Ellipsometry can effectively probe these excitons, where the magnitude of the real and imaginary parts of the dielectric function are modulated by the excitonic absorption strength (it should be noted that carriers can tunnel through the barrier easily, since the interfacial SiO2 layer thickness is less than ∼1 nm, [53] as estimated from XRR measurement). On the other hand, in case of ZnO on SiO2 , where a thin type-I quantum well, consisting of a narrower-band gap semiconductor grown on a wider-band gap substrate, shown in Fig. 9(c) and (d), both the electron and the hole are confined, which leads to an increase in the electron-hole overlap matrix element, resulting in higher absorption coefficient at the band edge with decreasing film thickness. It should be noted that the absorption coefficients for ZnO/Si systems were calculated from ellipsometry measurements. Whereas absorption coefficients for ZnO/SiO2 films were estimated from UV–vis absorption spectra, where measurements were performed in transmission mode. Results, Fig. 3 and 4, indicate that the absorption coefficients for thicker ZnO film, i.e., ∼38 nm, are more or less constant (∼ 4 × 1011 eV2 -cm−2 ), irrespective of the choice of Si (narrower band gap) or SiO2 (wider band gap) substrates, which indicates that the interface effect is less effective in case of thicker ZnO films (∼38 nm). With decreasing ZnO film thickness at and below ∼20 nm, the systems show significant thickness induced systematic changes/variations in absorption coefficient at band edge, where the trend of variations (i.e., increasing or decreasing) depends on the choice of the substrates. The proposed model can also explain the observed weaker thickness dependency in blue-shift in band gap energy with decreasing film thickness for ZnO/Si system, with respect to ZnO/SiO2 system, which corresponds to the effect of weaker exciton confinement or effectively supports the exciton deconfinement effect in ZnO/Si system. 4. Conclusion High quality, smooth, crystalline ZnO films with varying film thickness, from ∼70 nm to ∼5 nm, were prepared by Atomic Layer Deposition technique and characterized by Ellipsometry, UV–vis absorption spectroscopy, XRR, and XRD. Domain size of ZnO crystals along surface normal is found to be ∼20 nm, for thicker film

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thickness window, i.e, above ∼20 nm film thickness. Ellipsometry results clearly demonstrate that thin wider-band gap ZnO on a narrower-band gap substrate, Si, experience exciton deconfinement (lower absorption, refractive index) at interface, which is pronounced at thinner film thickness window, i.e., at and below ∼20 nm film thickness. Whereas the similar ZnO films deposited on SiO2 substrates, show thickness induced excitonic confinement effect in thinner film thickness window. Furthermore, ZnO thin films in ZnO/Si system show weaker thickness dependency in blueshift in band gap energy with respect to ZnO/SiO2 system, which corresponds to weaker exciton localization effect in ZnO/Si system. The observations were clearly explained in terms of Tanguy-Elliott amplitude pre-factor. Our study established that for high quality thin films, with a proper choice of the substrate, below a certain critical thickness, ∼20 nm for ZnO, the dielectric function changes systematically depending on the film thickness. Because of its unique property, ZnO is already treated as a potential candidate for various important opto-electronic application, e.g., LED, optical recording media, solar cell, nano-electronics etc. The knowledge developed through this study will be useful in choosing the appropriate and optimum film thickness of high quality ZnO films for its various applications in opto- and nano- electronics to achieve the best performance of that particular device. Acknowledgements We would like to acknowledge IIT Indore for all kinds of support to this work. The work at NMSU was supported by the National Science Foundation (DMR-1505172). This work is partially supported by the Department of Science and Technology (DST) Project No. SB/S2/CMP-077/2013 and Council of Scientific and Industrial Research (CSIR) Project No. 03 (1310)/14/EMR-II. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apsusc.2016.10. 130. References [1] J. Anderson, C.G. Van de Walle, Fundamentals of zinc oxide as a semiconductor, Rep. Prog. Phys. 72 (2009) 126501. [2] Ü. Özgür, Y.I. Alivov, C. Liu, A. Teke, M.A. Reshchikov, S. Do˘gan, V. Avrutin, S.-J. Cho, H. Morkoc¸, A comprehensive review of ZnO materials and devices, J. Appl. Phys. 98 (2005) 041301. ´ A.M.C. Ng, X.Y. Chen, ZnO nanostructures for optoelectronics: [3] A.B. Djuriˇsic, material properties and device applications, Prog. Quant. Electron. 34 (2010) 191–259. [4] E. Guziewicz, I.A. Kowalik, M. Godlewski, K. Kopalko, V. Osinniy, A. Wójcik, S. Yatsunenko, E. Łusakowska, W. Paszkowicz, M. Guziewicz, Extremely low temperature growth of ZnO by atomic layer deposition, J. Appl. Phys. 103 (2008) 033515. [5] D.M. Bagnall, Y.F. Chen, Z. Zhu, T. Yao, S. Koyama, M.Y. Shen, T. Goto, Optically pumped lasing of ZnO at room temperature, Appl. Phys. Lett. 70 (1997) 2230–2232. [6] S.T. Tan, B.J. Chen, X.W. Sun, W.J. Fan, H.S. Kwok, X.H. Zhang, S.J. Chua, Blueshift of optical band gap in ZnO thin films grown by metal-organic chemical-vapor deposition, J. Appl. Phys. 98 (2005) 013505. [7] A.M. Peiró, P. Ravirajan, K. Govender, D.S. Boyle, P. O’Brien, D.D. Bradley, J. Nelson, J.R. Durrant, Hybrid polymer/metal oxide solar cells based on ZnO columnar structures, J. Mater. Chem. 16 (2006) 2088–2096. [8] P.F. Carcia, R.S. McLean, M.H. Reilly, High-performance ZnO thin-film transistors on gate dielectrics grown by atomic layer deposition, Appl. Phys. Lett. 88 (2006) 123509. [9] P. Banerjee, W.-J. Lee, K.-R. Bae, S.B. Lee, G.W. Rubloff, Structural, electrical, and optical properties of atomic layer deposition Al-doped ZnO films, J. Appl. Phys. 108 (2010) 043504. [10] M. Suchea, S. Christoulakis, K. Moschovis, N. Katsarakis, G. Kiriakidis, ZnO transparent thin films for gas sensor applications, Thin Solid Films 515 (2006) 551–554.

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