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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 12 — Jun. 17, 2013
  • pp: 14131–14138
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Effects of free electrons and quantum confinement in ultrathin ZnO films: a comparison between undoped and Al-doped ZnO

X.D. Li, T. P. Chen, P. Liu, Y. Liu, and K. C. Leong  »View Author Affiliations


Optics Express, Vol. 21, Issue 12, pp. 14131-14138 (2013)
http://dx.doi.org/10.1364/OE.21.014131


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Abstract

Band gaps and exciton binding energies of undoped and Al-doped ZnO thin films were determined from optical absorption measurement based on the Elliott’s exciton absorption theory. As compared to the undoped films, the doped films exhibit a band gap expansion and a reduction in the exciton binding energies due to the free electron screening effect, which suppresses the excitonic absorption and results in a blue shift of the absorption edge. The undoped and doped films show the same quantum size dependence, i.e. both the exciton binding energies and band gap energies increase with decreasing grain size of the oxides.

© 2013 OSA

In this work, a comparison of the free-electron screening effect and quantum confinement effect between the undoped ZnO and AZO is conducted. The undoped ZnO thin films show strong excitonic absorptions at room temperatures; while the excitonic absorptions are greatly suppressed in AZO. As compared to the undoped ZnO, the AZO films exhibit an expansion in the band gap and a reduction in the exciton binding energies due to the free electron screening effect. On the other hand, the undoped ZnO and AZO thin films show the same quantum size dependence as a result of quantum confinement effect, i.e. both the exciton binding energies and band gap energies increase with decreasing grain size of the oxides. The quantum confinement effect on the optical properties is very significant for the ultra-thin films, e.g., as compared to the undoped ZnO film with the thickness of 90 nm, the undoped ZnO film with the thickness of 20 nm shows an increase of ~40% in the absorption coefficient at 3.6 eV, an increase of ~35 meV in the exciton binding energy and an increase of ~0.1 eV in the bandgap energy. Therefore, it is important to consider the quantum confinement effect on the optical properties when an ultra-thin ZnO film is used in optoelectronic and photonic applications.

The undoped ZnO and AZO thin films were deposited on quartz substrates by RF magnetron sputtering of a pure ZnO target (99.99% purity) and an AZO target (2% Al2O3, 99.99% purity), respectively, under the same deposition condition. The chamber was pumped down to 7×106 Torr prior to the deposition process. The sputtering deposition was carried out at room temperature in argon ambient with the background pressure of 9×103Torr, and the RF power was maintained at 80 W. The pure argon environment was to ensure that the influence of oxygen on the structural and optical properties of the deposited films is minimized [13

13. S. Kishimoto, T. Yamada, K. Ikeda, H. Makino, and T. Yamamoto, “Effects of oxygen partial pressure on film growth and electrical properties of undoped ZnO films with thickness below 100 nm,” Surf. Coat. Tech. 201(7), 4000–4003 (2006). [CrossRef]

, 14

14. S. S. Kim and B.-T. Lee, “Effects of oxygen pressure on the growth of pulsed laser deposited ZnO films on Si(0 0 1),” Thin Solid Films 446(2), 307–312 (2004). [CrossRef]

]. The thicknesses of the as-deposited films for both the undoped ZnO and AZO were 20, 40, 90 and 185 nm, as determined by spectroscopic ellipsometry (Woollam VB-250). The crystalline structures of the thin films were characterized by X-ray diffraction (XRD) (Siemens D5005) using Cu Kα radiation (40kV, 40mA) in the θ–2θ geometry; and the film surface morphology was investigated by using scanning electron microscope (SEM) (LEO 1550 Gemini). Optical absorbance measurement was carried out with an UV-Vis spectrophotometer (Perkin-Elmer 950) in the wavelength range of 250-800 nm.

Figure 1(a)
Fig. 1 XRD measurements and SEM images of the undoped ZnO (a) and AZO films (b) with the thicknesses of 20 nm and 90 nm; and c) average grain sizes of the undoped ZnO and AZO films estimated from the XRD and SEM measurements as a function of film thickness.
shows the XRD and SEM measurements of the 20 nm and 90 nm undoped ZnO thin films; and Fig. 1(b) shows the same measurements of the 20 nm and 90 nm AZO thin films. The XRD patterns indicate the polycrystalline growth of wurtzite structure along (002) direction. The average sizes of the grains in the oxide thin films can be estimated from the broadening of the Bragg peak in the XRD patterns based on the Scherrer’s equation [15

15. S.-S. Lin and J.-L. Huang, “Effect of thickness on the structural and optical properties of ZnO films by r.f. magnetron sputtering,” Surf. Coat. Tech. 185(2-3), 222–227 (2004). [CrossRef]

]. The estimated grain size DXRD as a function of the film thickness for both undoped ZnO and AZO thin films is shown in Fig. 1(c). The in-plane average grains size DSEM estimated from the SEM images as a function of film thickness for both undoped ZnO and AZO thin films is shown in Fig. 1(c) also. As can be observed in Fig. 1(c), the DSEM is generally comparable with the DXRD.

Figures 2(a)
Fig. 2 Absorption spectra of the undoped ZnO (a) and AZO films (b) with the thicknesses of 20 nm and 90 nm; and (c) comparison of the absorption between the undoped ZnO and AZO for the thickness of 20 nm. The modeling based on Eqs. (1) and (2) for the undoped ZnO and AZO films is shown in the figure also.
and 2(b) show the absorption spectra in the UV-visible range at room temperature of the undoped ZnO and AZO thin films, respectively, with the thicknesses of 20 nm and 90 nm; and Fig. 2(c) shows the comparison of the absorption between the undoped ZnO and AZO for the thickness of 20 nm. It can be observed from Fig. 2 that there is remarkable difference in the absorption spectrum between the undoped ZnO and AZO thin films and the film thickness has a significant impact on the absorption also. The difference between the undoped ZnO and AZO can be attributed to the large difference in the carrier concentration. As shown in Fig. 2(a) for the undoped ZnO thin films, a broaden absorption peak is observed at ~3.5 eV, which is attributed to the excitonic absorptions. In contrast, as shown in Fig. 2(b), such peak is not evident in the AZO thin films. This indicates that the abundant free electrons (the carrier concentration in 90 nm AZO is in the order of 1018 cm−3 as determined from the Hall effect measurement) in the AZO thin films greatly suppress the excitonic absorptions as a result of the free-electron screening effect. It has been known that the three valence bands of wurtzite ZnO result in the formation of the excitons labeled in order of the valence bands as “A”, “B”, and “C” [16

16. S. Adachi, Optical Properties of Crystalline and Amorphous Semiconductors: Materials and Fundamental Principles (Kluwer Academic Publishers, 1999), Chap. 1.

]. The three excitons can be resolved usually at low temperatures; they can merge into a broadened peak at room temperature due to the broadening caused by the exciton-phonon interactions [9

9. J. C. Nie, J. Y. Yang, Y. Piao, H. Li, Y. Sun, Q. M. Xue, C. M. Xiong, R. F. Dou, and Q. Y. Tu, “Quantum confinement effect in ZnO thin films grown by pulsed laser deposition,” Appl. Phys. Lett. 93(17), 173104 (2008). [CrossRef]

], which is the case observed in Fig. 2(a). On the other hand, the dependence of the absorption coefficient on the film thickness can be attributed to the following two factors. As shown in Fig. 1(c), the grain size is smaller for a thinner film. As discussed later, the quantum confinement effect on both the bandgap energies and the exciton binding energies is more significant in a smaller grain. The carrier concentration may be also lower in a thinner film [8

8. B.-Z. Dong, G.-J. Fang, J.-F. Wang, W.-J. Guan, and X.-Z. Zhao, “Effect of thickness on structural, electrical, and optical properties of ZnO: Al films deposited by pulsed laser deposition,” J. Appl. Phys. 101(3), 033713–033719 (2007). [CrossRef]

]. Thus the free-electron screening effect may be less significant in a thinner film. As such, the excitonic absorption may be more significant in a thinner film, which is indeed observed in Fig. 2.

Excitonic absorption can be described by the Elliott theory [17

17. R. J. Elliott, “Intensity of optical absorption by excitons,” Phys. Rev. 108(6), 1384–1389 (1957). [CrossRef]

] for hydrogenic excitons. As exciton absorption can significantly influence a band-edge absorption spectrum, an excitonic theory instead of the traditional Tauc method of linearly extrapolating the absorption edge should be used for more accurate determination of the band gap energies. The discrete states of the exciton lines can be modeled with a broadened Lorentzian line shape [18

18. S. Ninomiya and S. Adachi, “Optical properties of cubic and hexagonal CdSe,” J. Appl. Phys. 78(7), 4681–4689 (1995). [CrossRef]

]
ε(E)=β=A,B,C[n=1A0βdn31EgβRβn2EiΓn,βd].
(1)
where ε is the complex dielectric function, A0βd is the discrete exciton strength parameter, Rβis the exciton binding energy, Γn,βdis the broadening parameter of the nth discrete state (since the intensity falls with n−3, only the ground state n = 1 is considered in this work), and Egβis the band gap energy corresponding to distinct exciton peaks A, B and C. The discrete absorption below the band gap is summed with the continuum absorption above the band gap, which has the form [19

19. H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys. 36(Part 1, No. 10), 6237–6243 (1997). [CrossRef]

]
ε(E)=β=A,B,CA0βc(EgβRβ)4Rβ(E+iΓβc)2ln(Egβ)2(Egβ)2(E+iΓβc)2.
(2)
Where A0βc is the continuum exciton strength parameter, Γβc is the broadening parameter. (1) and (2) were used to model both the absorption of the undoped ZnO and AZO thin films, as shown in Figs. 2(a) and 2(b), respectively. The exciton binding energies and the band gap energy at exciton peak C (the largest exciton absorption energy) yielded from the modeling as a function of the grain size are shown in Fig. 3
Fig. 3 Exciton binding energies of the undoped ZnO films (a) and the AZO films (b) as a function of the average grain size D (D is determined from the SEM images). The trend lines of the size dependence are for guiding the eyes only.
and Fig. 4
Fig. 4 Band gap energies of the undoped ZnO and AZO films as a function of the average grain size D (D is determined from the SEM images). The trend lines of the size dependence are for guiding the eyes only.
, respectively, for both the undoped ZnO and AZO thin films.

As can be observed in Fig. 3, the exciton binding energies of the AZO thin films are significantly smaller than that of the undoped ZnO thin films for the same grain size. For example, for the average grain size D = 15.5 nm (film thickness = 90 nm), the binding energies of excitons A, B and C of the AZO thin film are lower than that of the undoped ZnO thin film by 18, 17, 14 meV, respectively. One may estimate a screened binding energy with the empirical formulaRb=Rb0kN1/3, where Rb is the screened binding energy and Rb0is the unscreened binding energy, Nis the carrier concentration, and the suggested k value of n-type ZnO is ~1.2×105meVcm [5

5. D. C. Reynolds, D. C. Look, and B. Jogai, “Combined effects of screening and band gap renormalization on the energy of optical transitions in ZnO and GaN,” J. Appl. Phys. 88(10), 5760–5763 (2000). [CrossRef]

, 7

7. T. Makino, Y. Segawa, S. Yoshida, A. Tsukazaki, A. Ohtomo, M. Kawasaki, and H. Koinuma, “Free-carrier effects on zero- and one-phonon absorption onsets of n-type ZnO,” Jpn. J. Appl. Phys. 44(10), 7275–7280 (2005). [CrossRef]

]. The 90 nm AZO thin film has an electron concentration in the order of 1018 cm−3 as determined from the Hall measurement; thus the estimated reduction in the binding energy due to the screening effect is ~12 meV, which is comparable with the above differences in the binding energies between the undoped ZnO and AZO thin films. Note that the carrier concentration of the undoped ZnO thin film with the same thickness is 2 – 3 orders lower than that of the AZO thin film and thus the screening effect can be ignored for the undoped ZnO thin films. On the other hand, as can be observed in Fig. 4, the band gap energies of the AZO thin films are larger than that of the undoped ZnO thin films for the same grain size. For example, for the average grain size of 15.5 nm, the band gap energy of the AZO thin film is ~50 meV larger than that of the undoped ZnO thin film. The band gap expansion in the AZO films as compared to the undoped ZnO thin films can be explained by the concept of Bursterin-Moss(BM) shift [6

6. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3:Sn studied by spectroscopic ellipsometry: analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109–075118 (2005). [CrossRef]

, 20

20. I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986). [CrossRef]

]. In the AZO thin films with abundant free electrons in the conduction band, as the direct consequence of Pauli exclusive principle, the filled electron states at the bottom conduction band prevent further electron filling lower energy states, and electron filling can occur only at higher energy states. As a result, the fundamental edge of absorption transitions shifts to a higher energy.

A strong quantum size effect has been observed in both the undoped ZnO and AZO thin films. Both the exciton binding energies and band gap energies increase with decreasing grain size, as shown in Fig. 3 and Fig. 4, respectively. The increase in the exciton binding energies is due to the confinement of the electron-hole wave-functions in the small dimensions [21

21. R. Fausto, G. Guido, M. Oskar, and M. Elisa, “Theory of excitonic confinement in semiconductor quantum wires,” J. Phys. Condens. Matter 11(31), 5969–5988 (1999). [CrossRef]

]. The confinement enhances the columbic interaction of an exciton, giving rise to an increase in the exciton binding energy [22

22. H. Gotoh and H. Ando, “Excitonic quantum confinement effects and exciton electroabsorption in semiconductor thin quantum boxes,” J. Appl. Phys. 82(4), 1667–1677 (1997). [CrossRef]

]. As shown in Fig. 3(a) for the undoped ZnO thin films, the average value (RAV,undoped) of the exciton binding energies tends to reach the bulk ZnO value (60 meV) with increasing grain size, and the size dependence of the average value could be roughly described by the trend line of RAV,undoped(meV)=60+926/D(nm)1.62. As shown in Fig. 3(b), the same size dependence can be observed for the AZO thin films, but the average value (RAV,AZO) of the exciton binding energies of the AZO thin films is lower than that of the undoped ZnO thin films by 12 meV, i.e., RAV,AZO(meV)=[60+926/D(nm)1.62]12. The reduction of 12 meV in the exciton binding energies in the AZO thin films is due to the free-electron screening effect as discussed above. On the other hand, band gap widening as a result of quantum confinement is clearly observed in Fig. 4. The undoped ZnO and AZO thin films show the same size dependence in their band gap energies, but the band gap (Eg,AZO) of the AZO thin films is larger than the counterpart (Eg,undoped)of the undoped ZnO thin films by 60 meV, which is due to the BM shift discussed above. Eg,undopedand Eg,AZOcan be approximately described by Eg,undoped(eV)=3.46+3.23/D(nm)1.65andEg,AZO(eV)=[3.46+3.23/D(nm)1.65]+0.06, respectively. The difference of 60 meV in the bandgap energy between the undoped ZnO and AZO thin films can be considered as an average value for different grain sizes. Note that the bulk value of 3.46 eV is larger than the reported value of ~3.4 eV [1

1. S. J. Pearton, D. P. Norton, K. Ip, Y. W. Heo, and T. Steiner, “Recent progress in processing and properties of ZnO,” Prog. Mater. Sci. 50(3), 293–340 (2005). [CrossRef]

]. This is due to fact that the bulk value is evaluated based on the largest band gap energy at exciton peak C (corresponding to the largest exciton absorption energy). It has been also found that the oscillator strengths of the excitons in the undoped ZnO thin films increase with decreasing grain size. This can be attributed to the enhancement of electron-hole columbic interaction by a smaller size. This is also one of the reasons to explain the result shown in Fig. 2(a) that the exciton peak in the 20 nm film is stronger than that in the 90 nm film.

In conclusion, both band gap energies and exciton binding energies of ultrathin undoped and Al-doped ZnO (AZO) films with different thicknesses on quartz substrate have been determined from optical absorption measurement based on the Elliott’s exciton absorption theory. As compared to the undoped ZnO films, the AZO films exhibit an expansion in the band gap and a reduction in the exciton binding energies due to the free electron screening effect, which significantly suppresses the excitonic absorption and results in a blue shift of the absorption edge. The undoped ZnO and AZO thin films show the same quantum size dependence as a result of quantum confinement effect, i.e. both the exciton binding energies and band gap energies increase with decreasing grain size of the oxide. In addition, the oscillator strengths of the excitons in the undoped ZnO thin films increase with decreasing grain size.

Acknowledgments

This work is financially supported by MOE Tier 1 Grant (Grant No. RG 43/12) and A*Star-NTU Si COE Program. Y. Liu would like to acknowledge the support by NSFC under Project No. 61274086.

References and links

1.

S. J. Pearton, D. P. Norton, K. Ip, Y. W. Heo, and T. Steiner, “Recent progress in processing and properties of ZnO,” Prog. Mater. Sci. 50(3), 293–340 (2005). [CrossRef]

2.

U. Özgür, Y. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Dogan, V. Avrutin, S.-J. Cho, and H. Morkoc, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys. 98(4), 041301–041403 (2005). [CrossRef]

3.

T. Minami, “New n-type transparent conducting oxides,” MRS Bull. 25(08), 38–44 (2000). [CrossRef]

4.

J. G. Gay, “Screening of excitons in semiconductors,” Phys. Rev. B 4(8), 2567–2575 (1971). [CrossRef]

5.

D. C. Reynolds, D. C. Look, and B. Jogai, “Combined effects of screening and band gap renormalization on the energy of optical transitions in ZnO and GaN,” J. Appl. Phys. 88(10), 5760–5763 (2000). [CrossRef]

6.

H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3:Sn studied by spectroscopic ellipsometry: analysis of free-carrier and band-edge absorption,” Phys. Rev. B 71(7), 075109–075118 (2005). [CrossRef]

7.

T. Makino, Y. Segawa, S. Yoshida, A. Tsukazaki, A. Ohtomo, M. Kawasaki, and H. Koinuma, “Free-carrier effects on zero- and one-phonon absorption onsets of n-type ZnO,” Jpn. J. Appl. Phys. 44(10), 7275–7280 (2005). [CrossRef]

8.

B.-Z. Dong, G.-J. Fang, J.-F. Wang, W.-J. Guan, and X.-Z. Zhao, “Effect of thickness on structural, electrical, and optical properties of ZnO: Al films deposited by pulsed laser deposition,” J. Appl. Phys. 101(3), 033713–033719 (2007). [CrossRef]

9.

J. C. Nie, J. Y. Yang, Y. Piao, H. Li, Y. Sun, Q. M. Xue, C. M. Xiong, R. F. Dou, and Q. Y. Tu, “Quantum confinement effect in ZnO thin films grown by pulsed laser deposition,” Appl. Phys. Lett. 93(17), 173104 (2008). [CrossRef]

10.

L.-W. Wang and A. Zunger, “Dielectric constants of silicon quantum dots,” Phys. Rev. Lett. 73(7), 1039–1042 (1994). [CrossRef] [PubMed]

11.

H. C. Weissker, J. Furthmuller, and F. Bechstedt, “Optical properties of Ge and Si nanocrystallites from ab initio calculations. II. hydrogenated nanocrystallites,” Phys. Rev. B 65(15), 155328 (2002). [CrossRef]

12.

G. T. Einevoll, “Confinement of excitons in quantum dots,” Phys. Rev. B Condens. Matter 45(7), 3410–3417 (1992). [CrossRef] [PubMed]

13.

S. Kishimoto, T. Yamada, K. Ikeda, H. Makino, and T. Yamamoto, “Effects of oxygen partial pressure on film growth and electrical properties of undoped ZnO films with thickness below 100 nm,” Surf. Coat. Tech. 201(7), 4000–4003 (2006). [CrossRef]

14.

S. S. Kim and B.-T. Lee, “Effects of oxygen pressure on the growth of pulsed laser deposited ZnO films on Si(0 0 1),” Thin Solid Films 446(2), 307–312 (2004). [CrossRef]

15.

S.-S. Lin and J.-L. Huang, “Effect of thickness on the structural and optical properties of ZnO films by r.f. magnetron sputtering,” Surf. Coat. Tech. 185(2-3), 222–227 (2004). [CrossRef]

16.

S. Adachi, Optical Properties of Crystalline and Amorphous Semiconductors: Materials and Fundamental Principles (Kluwer Academic Publishers, 1999), Chap. 1.

17.

R. J. Elliott, “Intensity of optical absorption by excitons,” Phys. Rev. 108(6), 1384–1389 (1957). [CrossRef]

18.

S. Ninomiya and S. Adachi, “Optical properties of cubic and hexagonal CdSe,” J. Appl. Phys. 78(7), 4681–4689 (1995). [CrossRef]

19.

H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys. 36(Part 1, No. 10), 6237–6243 (1997). [CrossRef]

20.

I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys. 60(11), R123–R160 (1986). [CrossRef]

21.

R. Fausto, G. Guido, M. Oskar, and M. Elisa, “Theory of excitonic confinement in semiconductor quantum wires,” J. Phys. Condens. Matter 11(31), 5969–5988 (1999). [CrossRef]

22.

H. Gotoh and H. Ando, “Excitonic quantum confinement effects and exciton electroabsorption in semiconductor thin quantum boxes,” J. Appl. Phys. 82(4), 1667–1677 (1997). [CrossRef]

OCIS Codes
(260.7190) Physical optics : Ultraviolet
(300.1030) Spectroscopy : Absorption
(310.6860) Thin films : Thin films, optical properties
(310.6188) Thin films : Spectral properties

ToC Category:
Thin Films

History
Original Manuscript: April 25, 2013
Revised Manuscript: May 23, 2013
Manuscript Accepted: May 23, 2013
Published: June 6, 2013

Citation
X.D. Li, T. P. Chen, P. Liu, Y. Liu, and K. C. Leong, "Effects of free electrons and quantum confinement in ultrathin ZnO films: a comparison between undoped and Al-doped ZnO," Opt. Express 21, 14131-14138 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-12-14131


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References

  1. S. J. Pearton, D. P. Norton, K. Ip, Y. W. Heo, and T. Steiner, “Recent progress in processing and properties of ZnO,” Prog. Mater. Sci.50(3), 293–340 (2005). [CrossRef]
  2. U. Özgür, Y. I. Alivov, C. Liu, A. Teke, M. A. Reshchikov, S. Dogan, V. Avrutin, S.-J. Cho, and H. Morkoc, “A comprehensive review of ZnO materials and devices,” J. Appl. Phys.98(4), 041301–041403 (2005). [CrossRef]
  3. T. Minami, “New n-type transparent conducting oxides,” MRS Bull.25(08), 38–44 (2000). [CrossRef]
  4. J. G. Gay, “Screening of excitons in semiconductors,” Phys. Rev. B4(8), 2567–2575 (1971). [CrossRef]
  5. D. C. Reynolds, D. C. Look, and B. Jogai, “Combined effects of screening and band gap renormalization on the energy of optical transitions in ZnO and GaN,” J. Appl. Phys.88(10), 5760–5763 (2000). [CrossRef]
  6. H. Fujiwara and M. Kondo, “Effects of carrier concentration on the dielectric function of ZnO:Ga and In2O3:Sn studied by spectroscopic ellipsometry: analysis of free-carrier and band-edge absorption,” Phys. Rev. B71(7), 075109–075118 (2005). [CrossRef]
  7. T. Makino, Y. Segawa, S. Yoshida, A. Tsukazaki, A. Ohtomo, M. Kawasaki, and H. Koinuma, “Free-carrier effects on zero- and one-phonon absorption onsets of n-type ZnO,” Jpn. J. Appl. Phys.44(10), 7275–7280 (2005). [CrossRef]
  8. B.-Z. Dong, G.-J. Fang, J.-F. Wang, W.-J. Guan, and X.-Z. Zhao, “Effect of thickness on structural, electrical, and optical properties of ZnO: Al films deposited by pulsed laser deposition,” J. Appl. Phys.101(3), 033713–033719 (2007). [CrossRef]
  9. J. C. Nie, J. Y. Yang, Y. Piao, H. Li, Y. Sun, Q. M. Xue, C. M. Xiong, R. F. Dou, and Q. Y. Tu, “Quantum confinement effect in ZnO thin films grown by pulsed laser deposition,” Appl. Phys. Lett.93(17), 173104 (2008). [CrossRef]
  10. L.-W. Wang and A. Zunger, “Dielectric constants of silicon quantum dots,” Phys. Rev. Lett.73(7), 1039–1042 (1994). [CrossRef] [PubMed]
  11. H. C. Weissker, J. Furthmuller, and F. Bechstedt, “Optical properties of Ge and Si nanocrystallites from ab initio calculations. II. hydrogenated nanocrystallites,” Phys. Rev. B65(15), 155328 (2002). [CrossRef]
  12. G. T. Einevoll, “Confinement of excitons in quantum dots,” Phys. Rev. B Condens. Matter45(7), 3410–3417 (1992). [CrossRef] [PubMed]
  13. S. Kishimoto, T. Yamada, K. Ikeda, H. Makino, and T. Yamamoto, “Effects of oxygen partial pressure on film growth and electrical properties of undoped ZnO films with thickness below 100 nm,” Surf. Coat. Tech.201(7), 4000–4003 (2006). [CrossRef]
  14. S. S. Kim and B.-T. Lee, “Effects of oxygen pressure on the growth of pulsed laser deposited ZnO films on Si(0 0 1),” Thin Solid Films446(2), 307–312 (2004). [CrossRef]
  15. S.-S. Lin and J.-L. Huang, “Effect of thickness on the structural and optical properties of ZnO films by r.f. magnetron sputtering,” Surf. Coat. Tech.185(2-3), 222–227 (2004). [CrossRef]
  16. S. Adachi, Optical Properties of Crystalline and Amorphous Semiconductors: Materials and Fundamental Principles (Kluwer Academic Publishers, 1999), Chap. 1.
  17. R. J. Elliott, “Intensity of optical absorption by excitons,” Phys. Rev.108(6), 1384–1389 (1957). [CrossRef]
  18. S. Ninomiya and S. Adachi, “Optical properties of cubic and hexagonal CdSe,” J. Appl. Phys.78(7), 4681–4689 (1995). [CrossRef]
  19. H. Yoshikawa and S. Adachi, “Optical constants of ZnO,” Jpn. J. Appl. Phys.36(Part 1, No. 10), 6237–6243 (1997). [CrossRef]
  20. I. Hamberg and C. G. Granqvist, “Evaporated Sn-doped In2O3 films: basic optical properties and applications to energy-efficient windows,” J. Appl. Phys.60(11), R123–R160 (1986). [CrossRef]
  21. R. Fausto, G. Guido, M. Oskar, and M. Elisa, “Theory of excitonic confinement in semiconductor quantum wires,” J. Phys. Condens. Matter11(31), 5969–5988 (1999). [CrossRef]
  22. H. Gotoh and H. Ando, “Excitonic quantum confinement effects and exciton electroabsorption in semiconductor thin quantum boxes,” J. Appl. Phys.82(4), 1667–1677 (1997). [CrossRef]

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