# A Study of Quantum Confinement Effects in Ultrathin NiO Films Performed by Experiment and Theory

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## Abstract

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^{−2}mbar. The sputtering target was metallic Ni; however, due to the rough vacuum a precursor material was grown in which most of Ni was already oxidized. Subsequent short annealing at temperatures of about 600 °C in a furnace in air resulted in NiO with high crystallinity quality, as atomic force microscopy revealed. The images of surface morphology showed that the NiO films were continuous and follow a normal grain growth mode. UV-Vis light absorption spectroscopy experiments have revealed a blue shift of the direct band gap of NiO. The band gap was determined either by Tauc plots (onset) or by the derivative method (highest rate of absorbance increase just after the onset). The experimental results are interpreted as evidences of quantum confinement effects. Theoretical calculations based on Hartree Fock approximation as applied for an electron-hole system, in the framework of effective mass approximation were carried out. The agreement between theory and experiment supports the quantum confinement interpretation.

## 1. Introduction

_{g}close to 4 eV [1]. NiO is placed in the center of scientific attention for the realization of various applications, such as gas sensing [2,3], nonvolatile storage media [4], battery cathodes [5], and transparent UV detectors in the field of optoelectronics [6]. Moreover, it can be used in photovoltaics as a transparent oxide semiconductor [7,8] and in the formation of modern pn junctions, such as NiO/ZnO ones [9,10]. Among the most important properties of a nanoscaled semiconductor for optoelectronics is the controllable band gap tuning [11,12]. This tuning is achievable through the strong band gap dependence on the particle size or film thickness of the semiconductors and, therefore, it can be tailored by reducing the semiconductor dimensionality.

_{g}determination of NiO thin films and nanoparticles. In most of them, E

_{g}is found to be close to the bulk value, while there are also reports which indicate a “red” shift (towards lower energies) of E

_{g}(see e.g., [13,14,15,16]). However, due to the very small Bohr radius of NiO, it is difficult to find studies where a “blue” shift systematically develops with reduced dimensionality and investigated by experiment and theory. Some preliminary results were published earlier [17]. In the present contribution, we present a complete experimental study which is also supported and complemented by theoretical calculation based on the potential morphing method (PMM). We grow ultrathin NiO thin films with an alternative method which starts from the growth of a precursor NiO material in a rough vacuum followed by a short annealing time at 600 °C [18]. At such elevated temperatures NiO film crystallinity improves [19]. The growth habits of our NiO films with thicknesses ranging from 1 to 27 nm are briefly presented and discussed. Subsequently, our focus is turned on their optical absorption properties, which are found to exhibit a smooth increase of the E

_{g}position as the film thickness decreases. The maximum value of the blue shift observed in our experiments is around 0.4 eV and it corresponds to our thinnest (1 nm) NiO sample. The observed trends remain the same regardless of the adopted method of study (i.e., Tauc plots [20] or derivative method [12]). These two different approaches are compared and discussed in a comprehensive way.

_{g}. Our theoretical results for the dependence of the direct band gap of NiO on the film thickness are in good agreement with the experimental values. This agreement verifies that the experimentally-observed shifts can be safely attributed to quantum confinement effects.

## 2. Materials and Methods

#### 2.1. Experimental Details

^{−2}mbar. The total pressure (including Ar partial pressure) during deposition was about 5 × 10

^{−2}mbar.

#### 2.2. Theory

_{eh}is the electron-hole distance and ${V}_{0}^{e\left(h\right)}$ is the confinement potential of electron (hole). The Hartree-Fock formulation of two particles (electron and one hole) results in the following coupled equations:

_{i}(r

_{i}) that acts on the particles includes the interaction with the confining potential as well as the Coulomb and exchange interaction between the two particles [21,22,23]. Once the numerical solution has been achieved [21,22,23], the total energy of the exciton, is calculated as $E\left(X\right)={\tilde{E}}_{e}+{\tilde{E}}_{h}$, while the corresponding effective band gap is obtained by adding the exciton energy to the band gap of the bulk material:

_{0}outside the film and zero inside. The value of V

_{0}is empirically determined as described in previous studies [22]:

## 3. Results

#### 3.1. Grain Growth

_{rms}, as a function of film thickness for the five NiO samples studied by AFM is plotted in Figure 2b. According to the log-log plot of this figure the roughness increases with thickness following a power law with the form R

_{rms}~ t

^{b}, where b is the slope of the best fitted line which is found to be b = 0.54 ± 0.12. The aforementioned power law has been predicted by many theoretical models for polycrystalline thin films [38,39], where the exponent b is in the range of 0.3–0.9 (see, for example, [34]). Surface roughness measurements made on the same system, i.e., NiO films, grown on Si wafers at 200 °C by atomic layer deposition, with a similar thickness as our films (6–29 nm), resulted in a b = 0.94 [40]. We notice that there is a significant deviation with the exponent value obtained by our measurements. However, we have to bear in mind that the roughness data are nothing more but statistical values about the surface height information and these value depend on many factors, such as the deposition technique, film substrate, substrate temperature, as well as which surface area is studied [34].

#### 3.2. Optical Properties

_{g}. The arrows indicate a clear “blue” shift of the spectra and of the derivative maxima as the film thickness decreases. Although there is a debate on the use of either the derivative, or the more commonly used Tauc plots, for the study of the blue shift of the energy gap and the features of the absorbance spectra, the current NiO samples give us an excellent opportunity to go into some more details since the spectra are almost free of noise.

_{g}and dipole-dipole allowed transitions. In particular, Figure 4a shows the magnitude of (αE)

^{2}as a function of photon energy E, e.g., [13,14,15,16], while Figure 4b depicts the variation of α

^{2}as a function of E [20] (α is the absorption coefficient). One may observe that there is a large almost linear part of the curves near the onset of E

_{g}. The intercept with the energy axis is E

_{g}. In most cases in literature, one deals with relatively thick films. Rayleigh scattering at the grain boundaries, defects or impurities add a parabolic slope to the whole spectrum of the absorbance [20]. This effect limits the linearity of the Tauc plots. Therefore, they exhibit a degree of uncertainty depending on how straight a Tauc curve is. On the contrary, in most cases, the derivative method is found to be more accurate since the maximum of dA/dE can be safely determined. In our case the quality of the data, which reflects the quality of the films, makes the linear part of Tauc plots significant, see Figure 4, and increases the accuracy of the determined onset of E

_{g}.

_{g}determined by the Tauc plots and a vertical shift constant. We see that the two lines coincide, within the experimental accuracy, with the derivative data. Therefore, it is safe to conclude that all these values of the optical-properties (i.e., E

_{g}onset and maximum absorbance increase rate) exhibit the same behavior (i.e., they increase as the film thickness decreases). Indeed, this becomes even more clear if one goes to the thinner films where quantum confinement effects are enhanced since the film thickness becomes comparable to the Bohr radius of the excitons.

^{5}cm

^{−1}, which is in fair agreement with previous reports on high-quality films [1].

## 4. Discussion and Conclusions

_{e}*, m

_{h}*). However, for the case of NiO, the values found in the literature appear to be extremely diverse. It is worth noting that in many cases, even the reported trends, are not consistent with each other [27,41,42,43,44]. To some extent this diversity might be related to changes in the conduction properties (i.e., p-type semiconductor, etc.) which are affected by variations in stoichiometry and, in turn, might also modify the value of the masses. As a result, we performed several benchmark calculations following the diverse literature suggestions, until we finally adopted the conclusion of Irwin et al. [27] who propose that the electron and hole exhibit similar masses which range from 0.5 to 1.0m

_{0}(i.e., m

_{e}* ≈ m

_{h}* = 0.5 − 1.0m

_{0}). Furthermore, in order to include the dependence of the dielectric constant on the film thickness we have chosen to incorporate into our model the size-dependent dielectric function of Hanken [45] with the following parameters: ε

_{∞}= 5.7, ε

_{0}= 12.4 [46] and ω

_{LO}= 64.47 meV [47].

_{e}* ≈ m

_{h}* = 0.8m

_{0}are presented in Figure 7 along with experimental data. It is evident that the agreement between theory and experiment is quite good. It is worth noting that when the PMM values (produced by all combinations of masses) are fitted on E

_{g}= a + b/t

^{c}formula, the c exponent ranges from 1.5 to 1.7, while for the experimental data the c parameter is closer to 1.0 (in simple effective mass theory, c is expected to be 2.0). In conclusion, the apparent similarity of the two curves presented in Figure 7 is highly suggestive that the observed shifts are a manifestation of the quantum confinement effect.

_{g}by using Tauc plots and the maximum rate of the absorbance increase after E

_{g}by the derivative method. Both features show a smooth increase, a “blue” shift, with decreasing NiO film thickness down to 1 nm. The experiment is well described by effective mass Hartree Fock calculations revealing that the blue shift is due to quantum confinement.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**AFM images of (

**a**) 13.5 nm and (

**b**) 4 nm thick NiO films. The image size is 500 × 500 nm

^{2}. Grain diameter D size distributions for the (

**c**) 13.5 nm and (

**d**) 4 nm thick NiO films.

**Figure 2.**(

**a**) Grain diameter D as a function of film thickness t in a log-log plot. The slope of the linear fit has a value consistent with normal grain growth mode. The error bar increases with decreasing film thickness due to the finite tip radius of 7 nm. (

**b**) root-mean-square roughness values as a function of film thickness for the same five NiO samples the thickness of which is in the range of 4–27 nm.

**Figure 3.**(

**a**) Absorbance spectra for two NiO films. The film thickness is indicated. The absorbance of the thinner film has been multiplied by 7 for better clarity. One may see a “blue” shift of the energy band gap as determined by the first derivative of the spectra, see (

**b**).

**Figure 4.**Tauc plots for two NiO films. (

**a**) (αE)

^{2}as a function of photon energy E and (

**b**) (α)

^{2}as a function of E. One can clearly observe a “blue” shift of E

_{g}determined with high precision by the extrapolation of a rather large linear part of the plots. The film thickness is indicated.

**Figure 5.**All features of absorbance spectra such as the onset of E

_{g}determined by the Tauc plots and the maximum of absorbance after the onset determined by the derivative maximum, coincide.

**Figure 6.**(−lnT) as a function of film thickness t. The slope of the linear fit is equal to the absorption coefficient. The transmittance T data have been recorded at 5 eV (250 nm).

**Figure 7.**Direct band gap energy E

_{g}of ultrathin NiO films as a function of film thickness t by experiment and theory. Some experimental data from Ref. [17] have been also included. The black dashed line is derived by fitting the calculated values of E

_{g}on E

_{g}= a + b/t

^{c}(a, b, and c are fitting parameters and t is the film thickness) while the red dashed line is a fit of the experimental data on the same function.

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**MDPI and ACS Style**

Garoufalis, C.S.; Barnasas, A.; Stamatelatos, A.; Karoutsos, V.; Grammatikopoulos, S.; Poulopoulos, P.; Baskoutas, S.
A Study of Quantum Confinement Effects in Ultrathin NiO Films Performed by Experiment and Theory. *Materials* **2018**, *11*, 949.
https://doi.org/10.3390/ma11060949

**AMA Style**

Garoufalis CS, Barnasas A, Stamatelatos A, Karoutsos V, Grammatikopoulos S, Poulopoulos P, Baskoutas S.
A Study of Quantum Confinement Effects in Ultrathin NiO Films Performed by Experiment and Theory. *Materials*. 2018; 11(6):949.
https://doi.org/10.3390/ma11060949

**Chicago/Turabian Style**

Garoufalis, Christos S., Alexandros Barnasas, Alkeos Stamatelatos, Vagelis Karoutsos, Spyridon Grammatikopoulos, Panagiotis Poulopoulos, and Sotirios Baskoutas.
2018. "A Study of Quantum Confinement Effects in Ultrathin NiO Films Performed by Experiment and Theory" *Materials* 11, no. 6: 949.
https://doi.org/10.3390/ma11060949