Figures 5.12 and 5.13 show two independently measured experimental data of non-annealing
and annealing of ZnO thin film at 70 and 75 incidence angles and the model curves are in good agreement. Figures 5.14 ~ 5.21 display two independently measured experimental data of various Dy
doped ZnO thin film at 70 and 75 incidence angles without and with annealing. Figures 5.22 ~ 5.28 illustrate two independently measured experimental data of various Gd doped ZnO thin film at
70 and 75 incidence angles without annealing. We fitted the ellipsometric spectra using the stacked layer model consisting of sapphire structure / thin film / surface roughness / air ambient
structure. Figure 5.29 illustrates the structure of the stacked layer. First, the thickness of the
c-sapphire substrate was approximately 0.5 mm. Second, we added the Cauchy model and fitted the
data in the range of 450 ~ 1700 nm (0.73 ~ 2.75 eV). The thickness of ZnO thin film was mainly
determined by using the Cauchy model. The Cauchy model can be described by [106,107]
( )
B2 C4 where n is the refractive index, k is the extinction coefficient, and A, B and C are the Cauchyparameters. Third, we fitted the data in the range of 180 ~ 450 nm (2.75 ~ 6.9 eV) by using the
Lorentz oscillator model. The Lorentz model is described by [73,108]
( )
2( )
1 2 2nadopted the Bruggeman effective medium approximation (EMA). The Bruggeman EMA layer can be
used to represent inhomogeneous materials as well as interface roughness in terms of effective dielectric functions denoted εeff . The Bruggeman EMA can be described by [72]
1 1
complex dielectric function of component. Finally, we added the surface roughness and air ambient
structure. Tables 5.6 ~ 5.8 contain a list of fitting parameters of the stacked layer model.
The complex optical constants of non-annealing and annealing ZnO thin films are shown in
Figure 5.30. The refractive index of ZnO thin films is independent of annealing in the range of 0.73 ~
3.5 eV. The peaks at approximately 3.3 eV are caused by free exciton absorption. The refractive
index values of non-annealing and annealing samples are 1.9 and 1.88 at 6.5 eV. In Fig. 5.30, the
extinction coefficient of ZnO thin films shows a strong absorption at 3.3 eV. This peak is due to free
exciton absorption. The differences of the complex optical constants in non-annealing and annealing
ZnO thin films may be induced by the changes in the local structures of the thin films and the
interface layer between ZnO thin film and sapphire substrate [109].
Figure 5.31 shows the complex optical constants of various Dy doped ZnO thin films without
annealing. With an increase in Dy doping, the intensity of free exciton absorption is decreased and its
position shifts to higher energies. Moreover, the extinction coefficient edge clearly shifts to lower
energies.
Figure 5.32 illustrates the complex optical constants of various Dy doped ZnO thin films with
annealing. The doping dependence of refractive index is different from that in non-annealing thin
films. The extinction coefficient edge shows a slightly redshift with increasing Dy concentration.
These results suggest that annealing plays an important role on the optical properties of Dy doped
ZnO thin films [109,110].
Figure 5.33 shows the complex optical constants of various Gd doped ZnO thin films without
annealing. These complex optical constants exhibit strong doping dependent behavior. The intensity
of free exciton absorption is reduced and its position moves to higher energies with increasing Gd
doping. For higher Gd doped (> 20%) samples, the refractive index spectra show an irregurlar
doping dependence. Furthermore, the extinction coefficient edge shifts to lower energies with
increasing up to Gd 15% doped. The samples with more than Gd 20% doped show the S-curve
behavior.
Figures 5.34 and 5.35 show the room-temperature optical absorption spectra of non-annealing
and annealing ZnO thin films. The absorption coefficient α is related to the extinction coefficient
k. It can be described by [111]
4 kπ
α = λ , (5.3.7)
where λ is the wavelength. The absorption spectra of non-annealing and annealing ZnO thin films
can be divided into three region. No optical absorption was observed in the range of 0.73 ~ 3.2 eV.
The exciton peak appears in the range of 3.2 ~ 3.4 eV [111,112]. The intensity of exciton peak of
annealing ZnO thin film was higher than that of non-annealing ZnO thin film. Interband transition is
visible in the range of 3.4 ~ 6.9 eV.
Figures 5.36 and 5.37 show the room-temperature optical absorption spectra of different Dy
doped ZnO thin films without annealing and with annealing. The absorption edge shows a redshift
with an increase in Dy doping. By contrast, the absorption edge of Dy 10% doped sample shifts to
higher energies. Moreover, the position of exciton peak shows a blueshift with an increase in Dy
doping. For higher Dy doped samples, the exciton peak is disappeared. The variation of the
absorption edge in Dy doped samples with annealing is less significant than that without annealing.
This difference may be due to changes of free-carrier concentration by annealing.
Figure 5.38 displays the room-temperature optical absorption spectra of different Gd doped
ZnO thin films without annealing. The absorption edge shows a redshift with increasing Gd doping
up to 15%. The position of exciton peak of low Gd doped (3 ~ 15%) samples shows a blueshift. By
contrast, the samples with more than Gd 20% doping show S-curve behavior. The exciton transition
is disappeared for the higher Gd doped (> 20%) samples.
The direct band gap energies were determined by Eq. (5.2.4). Figures 5.39 ~ 5.44 show
(
α⋅E)
2 versus the photon energy for pure and different Dy and Gd doped ZnO thin films. Thedirect optical band gap energy of non-annealing ZnO thin film is 3.27 ± 0.02 eV, which is in good
agreement with the value determined by optical transmission measurements. The direct optical band
gap energy of ZnO thin film with annealing is 3.28 ± 0.02 eV.
Tables 5.9 ~ 5.11 list the direct optical band gap energies of different Dy and Gd doped ZnO
thin films. With an increase in Dy doping from 1%, 3% to 5%, the optical band gap energies of ZnO
thin films without annealing are red shifted. By contrast, the optical band gap energy of Dy 10%
doped ZnO thin film shows a blueshift (Fig. 5.45). For the annealing samples, the optical band gap
energy shows small variation up to Dy 3% doping. By contrast, the optical band gap energy of Dy 10%
doped sample shifts to higher energies. This significant blueshift in band gap can be explained by the
band characteristics of ternary Zn1-xDyxO alloys as the following [113]: Dy doped ZnO thin films can
be considered as ternary Zn1-xDyxO alloys due to the stoichiometry of Dy doping concentration by
percentage. As mentioned, the results of XRD measurements show the c-axis lattice constant of ZnO
thin films decreases with an increase in Dy doping. This phenomenon causes the distance of atoms to
decrease, leading to the increased Coulomb interaction in the Dy doped ZnO thin films [57,114].
Consequently, the Dy 10% doped sample would have a higher band gap energy.
With increased Gd doping from 3% to 30%, optical band gap energies of ZnO thin films
without annealing show blueshift (Fig. 5.46). This significant blueshift in band gap is explained by
band characteristics of ternary Zn1-xGdxO alloys [85]. Gd doped ZnO thin films can be considered
ternary Zn1-xGdxO alloys due to the stoichiometry of Gd doping which occurs with increased doping
percentage. The results of XRD measurements also show the c-axis lattice constant of ZnO thin films
decreases with an increase in Gd doping. This phenomenon causes the distance of atoms to decrease,
leading to the increased Coulomb interaction in the Gd doped ZnO thin films [115]. Consequently,
the Gd doped samples have a higher band gap energy.
The observed peak in the spectral range of 3.2 ~ 3.4 eV is assigned to A excitonic transition
[111]. The discrete states of the exciton observed in all series of ZnO thin films can be described by
using the broadened Lorentzian line shape [116]
0
fitting parameters is given in Tables 5.12 ~ 5.14. At room-temperature, the exciton binding energy
value of non-annealing and annealing ZnO thin films is approximately 60 meV. This value is in good
agreement with that reported earlier by W. Shen et al. [117] They prepared ZnO thin films using
seeded chemical vapor transport method. The free-exciton binding energy is estimated to be 60 meV.
The exciton binding energies of Dy and Gd doped samples show a blueshift. The blue-shifted exciton
binding energy might be caused by higher free-carrier concentration due to the Dy and Gd doping
[118].
Figures 5.47 ~ 5.50 show temperature-dependent optical absorption spectra of pure and
different Dy doped ZnO thin films with annealing. Thermal activation of exciton in ZnO can be
estimated by the integration of the peak intensity of the exciton in the optical absorption spectra.
Figures 5.49 and 5.50 show the temperature-dependent integrated intensity of A exciton for pure and
Dy 3% doped ZnO thin films. The thermal activation process of exciton in the ZnO thin film can be
described by Arrhenius equation as given by [112,119]
( ) (
0 T)
T 1 exp / BT
I I
B E k
= + − , (5.3.9)
where I
( )
T and I are the integrated intensity at a finite temperature T and 0 K, 0 B is the constant, which represents the thermal activation rate for the free exciton, and E is the thermal Tactivation energy, which is related to the free exciton binding energy (E ). The Arrhenius best-fit b
results are shown in Figs. 5.51 and 5.52. In a beat fit, the zero-temperature intensities I of pure and 0
Dy 3% doped ZnO thin films with annealing are 2.33 ± 0.02 and 1.99 ± 0.04. The thermal activation
rates B of pure and Dy 3% doped ZnO thin films with annealing are 1.50 ± 0.01 and 0.98 ± 0.01.
The free exciton binding energies E of pure and Dy 3% doped ZnO thin films with annealing are b
0.061 ± 0.007 and 0.062 ± 0.008 eV. These exciton binding energy values are consistent with those
obtained by using the broadened Lorentzian line shape.
Figures 5.53 ~ 5.56 display
(
α⋅E)
2 versus the photon energy for pure and different Dy doped ZnO thin films with annealing. The temperature-dependent positions and linewidths of excitionictransitions of pure and Dy 3% doped ZnO thin films with annealing are shown in Figs. 5.57 and 5.58.
These values were determined by using the broadened Lorentzian line shape. Figures 5.59 and 5.60
show the temperature dependence of energy gap and exciton binding energy of pure and different Dy
doped ZnO thin films with annealing. The optical band gap of annealing ZnO thin film is 3.30 eV at
240 K and 3.10 eV at 700 K. The exciton binding energy of annealing ZnO thin film is 61.2 meV at
240 K and 56.7 meV at 700 K. The optical band gap of Dy 3% doped ZnO thin film with annealing
is 3.30 eV at 240 K and 3.11 eV at 700 K. The exciton binding energy of Dy 3% doped ZnO thin
film with annealing is 61.7 meV at 240 K and 58.4 meV at 700 K. The optical band gap of annealing
Dy 5% doped ZnO thin film is 3.31 eV at 240 K and 3.12 eV at 700 K. The direct band gap of
annealing Dy 10% doped ZnO thin film is 3.37 eV at 240 K and 3.17 eV at 700 K. Notably, the
band-gap narrowing coefficient of ZnO and Dy 3, 5, 10% doped ZnO thin films can be obtained by using the formula β =dEg /dT. They are approximately -2.5 × 10-4 eV / K, -5.0 × 10-4 eV / K, -2.5
× 10-4 eV / K, and -7.5 × 10-4 eV / K at 300 K, respectively. These values are comparable to those of
other semiconductor materials. For example, GaN is -6.14 × 10-4 eV / K and GaAs is -4.76 × 10-4 eV
/ K [120]. The negative band-gap narrowing coefficient can be explained by two reasons: (i) thermal
expansion of the lattice and renormalization of the band structure by electron- phonon interaction,
and (ii) lattice vibration, leading to a deviation of atoms or ions from balance sites, would destroy the
lattice periodic field, gives rise to an addition potential as a perturbation of electron energy and
transition, even changes the chemical bond length, and further renormalize these bond structure and
band-gap energy [121]. The exciton binding energy narrowing coefficient of annealing of ZnO and Dy 3% doped ZnO thin film can be obtained by using the formula β =dEb/dT. They are
approximately -2.25 × 10-5 eV / K and -5 × 10-6 eV / K at 300 K.
The energy gap with elevating temperature can be described using the Bose-Einstein model
[122,123]
Θ is average phonon temperature. In our fitting results, the band-gap energy of annealing ZnO and B
Dy 3, 5, 10% doped ZnO thin films toward 0 K are approximately 3.34 ± 0.01, 3.35 ± 0.01, 3.35 ± 0.01, and 3.46 ± 0.01 eV. The strength of electron-phonon interaction a of ZnO and Dy 3, 5, 10% B
doped ZnO thin films are 101, 99, 86, and 115 meV. The average phonon temperature Θ of ZnO B
and Dy 3, 5, 10% doped ZnO thin films are 420, 420, 410, and 405 K. These values are comparable to those of other semiconductor materials, such as GaN cubic, a = 170 meV and B Θ = 471 K[124]. B
Temperature-dependent absorption spectra of pure and various Dy doped ZnO thin films with
annealing are observed such that the absorption edge shows redshift with increased temperature. This
phenomenon is caused by the thermal effect and the Urbach effect. The Urbach effect can be
illustrated by the temperature-dependent self-energies of the electrons and holes interacting with the
phonons. Since the phonon number is fluctuating in thermal equilibrium, the optical band gap energy
is also fluctuating, resulting in an exponential absorption tail below the average optical band gap
energy. The exponentially absorption edge below the energy gap at each temperature can be
explained by the Urbach's rule, which is described by [112,125]
(
0)
0exp
U
E E α α E
= − , (5.3.11)
where α0 is the constant, E is the zero-temperature energy band gap, and 0 E is the Urbach U
energy. Our best fitting curves of ZnO thin films without and with annealing are shown in Figures
5.34 and 5.35.
5-4 Summary
In summary, Raman scattering, optical transmission, and spectroscopic ellipsometric spectra of
pure and different Dy and Gd doped ZnO thin films without and with annealing provide us several
important information.
First, Raman scattering spectra of Dy and Gd doped ZnO thin films show that the intensity of both E2low and E2high phonon modes is decreased with increasing Dy and Gd doping, implying Dy
and Gd ions substitute Zn sites in ZnO thin films. The variations of peak position of both E2low and Ehigh phonon modes are possibly due to residual stress and defect-induced changes.
Second, with an increase in Dy and Gd doping, the optical band gap energies of ZnO thin films
show a blueshift. This phenomenon is due to the band characteristics of ternary Zn1-xDyxO
(Zn1-xGdxO) alloys. Consequently, Dy and Gd doped samples would have higher band gap energy as
increasing Dy and Gd doped.
Third, the optical band gap energies of Dy doped ZnO thin films with annealing are larger than
that without annealing. This phenomenon is possibly because of different free-carrier concentration.
The variation of free-carrier concentration is due to the changes in the local structures of the thin
films and the interface layer between thin film and sapphire substrate by annealing.
Fourth, variable temperature absorption spectra of pure and various Dy doped ZnO thin films
with annealing show that both the exciton peak positions and optical absorption edge are affected
with the thermal activation. With increasing temperature, the absorption edge of pure and Dy doped
ZnO thin films with annealing shows a redshift, which is due to thermal effect. The optical band gap
energies of pure and Dy doped ZnO thin films with annealing also show a redshift, which is caused
by thermal expansion and electron-phonon interaction.
Table 5.1 Parameters of a Lorentizan fit for the Raman scattering spectrum of non-annealing
different Dy doped ZnO thin films excited by a 532-nm laser line. All units are cm-1.
ZnO NA 1 % Dy NA 3 % Dy NA 5 % Dy NA 10 % Dy NA
ωp1 284.9 231.5 125.0 814 -
ω1 98.7 98.7 99.6 99.7 -
γ1 2.7 2.8 2.8 2.9 -
ωp2 494.6 490.4 199.2 116.6 -
ω2 437.1 436.9 436.5 436.1 -
γ2 10.4 10.9 11.1 11.3 -
Table 5.2 Parameters of a Lorentizan fit for the Raman scattering spectrum of annealing different Dy
doped ZnO thin films excited by a 532-nm laser line. All units are cm-1.
ZnO AN 1 % Dy AN 3 % Dy AN 5 % Dy AN 10 % Dy AN
ωp1 203.5 301.3 136.7 - -
ω1 99.0 100.1 100.1 - -
γ1 2.4 2.5 2.5 - -
ωp2 434.6 358.0 273.4 - -
ω2 437.6 437.6 436.8 - -
γ2 13.5 13.7 14.1 - -
Table 5.3 Parameters of a Lorentizan fit for the Raman scattering spectrum of non-annealing
different Gd doped ZnO thin films excited by a 532-nm laser line. All units are cm-1.
ZnO 3 % Gd 5 % Gd 10 % Gd 15 % Gd 20 % Gd 25 % Gd 30 % Gd
ωp1 283.2 234.9 - - - -
ω1 98.8 100.3 - - - -
γ1 2.7 4.2 - - - -
ωp2 422.4 341.9 112.0 - - - - -
ω2 438.0 436.5 435.0 - - - - -
γ2 7.8 14.8 15.1 - - - - -
Table 5.4 The direct optical band gap energies of non-annealing different Dy doped ZnO thin films
were determined by optical transmission measurements. All units are eV.
1 % Dy NA 3 % Dy NA 5 % Dy NA 10 % Dy NA
Eg 3.25 ± 0.02 3.24 ± 0.02 3.26 ± 0.02 -
Table 5.5 The direct optical band gap energies of non-annealing different Gd doped ZnO thin films
were determined by optical transmission measurement. All units are eV.
5 % Gd 10 % Gd 15 % Gd 20 % Gd 25 % Gd 30 % Gd
Eg 3.29 ± 0.02 3.33 ± 0.02 3.31 ± 0.02 - - -
Table 5.6 Parameters of a stacked layer model fit for non-annealing pure and different Dy doped ZnO
thin films.
ZnO NA 1 % Dy NA 3 % Dy NA 5 % Dy NA 10 % Dy NA
Surface roughness 2.1 nm 2.1 nm 3.1 nm 2.2 nm 2.2 nm
Film 107.1 nm 307.3 nm 177.3 nm 65.7 nm 61.6 nm
C-sapphire substrate 0.5 mm 0.5 mm 0.5 mm 0.5 mm 0.5 mm
MSE 6.5 27.08 8.4 10.7 8.1
Table 5.7 Parameters of a stacked layer model fit for annealing pure and different Dy doped ZnO thin
films.
ZnO AN 1 % Dy AN 3 % Dy AN 5 % Dy AN 10 % Dy AN
Surface roughness 2.1 nm - 2.1 nm 2.5 nm 2.2 nm
Film 312.6 nm - 208.2 nm 110.7 nm 61.7 nm
C-sapphire substrate 0.5 mm 0.5 mm 0.5 mm 0.5 mm 0.5 mm
MSE 6.5 - 5.5 10.2 12.2
Table 5.8 Parameters of a stacked layer model fit for non-annealing different Gd doped ZnO thin
films.
3 % Gd 5 % Gd 10 % Gd 15 % Gd 20 % Gd 25 % Gd 30 % Gd Surface roughness 1 nm 1.2 nm 1.7 nm 2 nm 1.4 nm 2.1 nm 2 nm
Film 245 nm 99.2 nm 84.3 nm 62 nm 21.2 nm 21.8 nm 22.3 nm C-sapphire substrate 0.5 mm 0.5 mm 0.5 mm 0.5 mm 0.5 mm 0.5 mm 0.5 mm
MSE 8.5 12.9 8.2 7.5 8.5 9.4 5.28
Table 5.9 The direct optical band gap energies of non-annealing pure and different Dy doped ZnO
thin films determined by spectroscopic ellipsometry. All units are eV.
ZnO NA 1 % Dy NA 3 % Dy NA 5 % Dy NA 10 % Dy NA Eg 3.27 ± 0.02 3.25 ± 0.02 3.26 ± 0.02 3.14 ± 0.02 3.49 ± 0.02
Table 5.10 The direct optical band gap energies of annealing pure and different Dy doped ZnO thin
films determined by spectroscopic ellipsometry. All units are eV.
ZnO AN 1 % Dy AN 3 % Dy AN 5 % Dy AN 10 % Dy AN
Eg 3.28 ± 0.02 - 3.27 ± 0.02 3.29 ± 0.02 3.39 ± 0.02
Table 5.11 The direct optical band gap energies of non-annealing different Gd doped ZnO thin films
determined by spectroscopic ellipsometry. All units are eV.
3 % Gd 5 % Gd 10 % Gd 15 % Gd 20 % Gd 25 % Gd 30 % Gd Eg 3.27 ± 0.02 3.30 ± 0.02 3.30 ± 0.02 3.34 ± 0.02 3.42 ± 0.02 3.51 ± 0.02 3.43 ± 0.02
Table 5.12 The exciton binding energies, and exciton broadening parameters of non-annealing pure
and different Dy doped ZnO thin films. All units are eV.
ZnO NA 1 % Dy NA 3 % Dy NA 5 % Dy NA 10 % Dy NA exciton Eb 0.060 ± 0.002 0.061 ± 0.002 0.061 ± 0.002 0.062 ± 0.002 - exciton Γex,1 0.0267 ± 0.005 0.038 ± 0.005 0.051 ± 0.005 0.142 ± 0.005 -
Table 5.13 The exciton binding energies, and exciton broadening parameters of annealing pure and
different Dy doped ZnO thin films. All units are eV.
ZnO AN 1 % Dy AN 3 % Dy AN 5 % Dy AN 10 % Dy AN exciton Eb 0.060 ± 0.002 - 0.061 ± 0.002 0.062 ± 0.002 - exciton Γex,1 0.025 ± 0.005 - 0.053 ± 0.005 0.065 ± 0.005 -
Table 5.14 The exciton binding energies, and exciton broadening parameters of non-annealing pure
and different Gd doped ZnO thin films. All units are eV.
3 % Gd 5 % Gd 10 % Gd 15 % Gd 20 % Gd 25 % Gd 30 % Gd Eb 0.060±0.002 0.061±0.002 0.061±0.002 0.062±0.002 - - - Γex,1 0.062±0.005 0.068±0.005 0.078±0.005 0.089±0.005 - - -
0 100 200 300 400 500 600
Fig. 5.1 Room-temperature Raman scattering spectra of non-annealing (NA) and annealing (AN) of ZnO thin films and a pure sapphire substrate excited by a 532-nm laser line.
0 100 200 300 400 500 600
Fig. 5.2 Room-temperature Raman scattering spectra of various Dy doped ZnO thin films without annealing excited by a 532-nm laser line. The asterisks represent Raman peaks from the sapphire substrate.
0 100 200 300 400 500 600
Fig. 5.3 Room-temperature Raman scattering spectra of various Dy doped ZnO thin films with annealing excited by a 532-nm laser line. The asterisks represent Raman peaks from the sapphire substrate.
Fig. 5.4 Room-temperature Raman scattering spectra of various Gd doped ZnO thin films without annealing excited by a 532-nm laser line. The asterisks represent Raman peaks from the sapphire substrate.
0 1 2 3 4 5 6 7
Fig. 5.5 Room-temperature optical transmission spectrum of non-annealing ZnO thin film.
Fig. 5.5 Room-temperature optical transmission spectrum of non-annealing ZnO thin film.