Analysis of the Urbach tails in absorption

spectra of undoped ZnO thin films

Cite as: J. Appl. Phys. 113, 153508 (2013); https://doi.org/10.1063/1.4801900
Submitted: 21 December 2012 • Accepted: 01 April 2013 • Published Online: 18 April 2013

R. C. Rai

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J. Appl. Phys. 113, 153508 (2013); https://doi.org/10.1063/1.4801900 113, 153508

© 2013 AIP Publishing LLC.

 JOURNAL OF APPLIED PHYSICS 113, 153508 (2013)

Analysis of the Urbach tails in absorption spectra of undoped ZnO thin films
R. C. Raia)
Department of Physics, SUNY College at Buffalo, New York 14222, USA
(Received 21 December 2012; accepted 1 April 2013; published online 18 April 2013)
We report the analysis of the Urbach effect in the absorption spectra of the undoped ZnO thin
films. The absorption coefficients of the ZnO thin films show the exponential rise, also known as
the Urbach tails, just below the free exciton peak. Fitting of the steepness parameter of the Urbach
tails yields the phonon energy to be hxp ¼ 76 6 4 meV, consistent with hxp ¼ 72 meV measured
from the photoluminescence spectra of ZnO. The temperature dependence of the Urbach energy,
the steepness parameter, and the energy gap strongly suggests that the observed Urbach effect is a
result of the cumulative effect of impurities, structural disorders, and electron-phonon interaction
C 2013 AIP Publishing LLC [http://dx.doi.org/10.1063/1.4801900]
in the absorption processes. V

I. INTRODUCTION of the absorption edge. The free exciton peak just below the
fundamental absorption edge also plays role for the observed
Zinc oxide is a wide band gap (Eg  3.40 eV) semicon-
exponential tails.
ductor with potential to impact the future technologies. An
undoped ZnO is an n-type semiconductor having a free exci- II. EXPERIMENTAL
ton with a large binding energy of 60 meV.1 For the develop-
ment of ZnO based devices, however, it is essential to make ZnO has a hexagonal wurtzite structure (P63mc) with
p-type ZnO. While there have been the reports of p-type the lattice constants a ¼ 3.252 Å and c ¼ 5.313 Å.14 One
ZnO by doping with P, N, As, Sb, and Li,2–5 these reports particular substrate suitable for ZnO thin film deposition is
have been controversial due to their reproducibility issues. sapphire because it also has a hexagonal lattice with the
Therefore, the p-type doping has been a major challenge for lattice constants a ¼ 4.758 Å and c ¼ 12.992 Å. Although the
the development of potential ZnO based devices. mismatch between ZnO and sapphire substrate is large
Despite that ZnO has been intensely investigated for its (18%), ZnO grows epitaxially on sapphire.1,2,10,13,15,16
various properties, ranging from transport to optoelectronic All optical measurements have been carried out on the
properties, and p-type doping of ZnO, the past research has undoped ZnO thin films deposited on (001) sapphire at
not produced any significant development as far as its tech- 600  C by an electron beam deposition technique, as
nological applications. Perhaps, the answer to the difficulties described in details in our earlier paper.15 The thin films
in p-type doping lies in understanding the electronic proper- were annealed at 500  C in the mixture of O2 and air for
ties in the sub-band gap region, where ZnO shows an expo- about 3 h to improve the stoichiometry and the crystal qual-
nential rise of the optical absorption spectrum, widely ity. The X-ray diffraction pattern of our ZnO thin films
known as the Urbach tail.6 There have been many reports of confirmed that the (002) was the preferred crystalline orien-
the Urbach tails in the optical spectra of ZnO in single crys- tation. We did not observe any other orientation, confirming
tal as well as in thin film forms.7–13 However, the systematic the epitaxial nature of the film. Variable-temperature
study of the Urbach tails and understanding of their origin (78–450 K) transmittance has been measured in the wave-
are still lacking, and thus need further attention. In addition, length range of 200–3000 nm (0.41–6.2 eV), with a spectral
understanding the optical properties, such as reflectance, resolution of 1 nm, using a dual-beam ultraviolet visible
transmittance, and absorption coefficients, of ZnO is impor- near-infrared spectrophotometer (Shimadzu UV 3101PC)
tant for the development of possible optical and photonic coupled with a continuous flow helium cryostat. In order to
devices. minimize the light scattering effect from the substrate, we
In this paper, we report the analysis of the Urbach effect selected two-side polished sapphire substrates to deposit
in the optical absorption spectra of the undoped single crystal ZnO thin films.
ZnO thin films deposited by electron beam deposition. We The absorption coefficients (a) were extracted from
have extracted the Urbach energy, the steepness parameter, the transmittance data using the equation, a ¼ lnðTÞ=d,
and the energy gap for a wide temperature range (78–450 K) where T is the transmittance and d is the film thickness. In
by fitting the absorption data to the theoretical models. To addition, for room temperature data, we also used equation
identify the cause of the Urbach tails, we discuss the role of a ¼ ln½T=ð1  RÞ2 =d, where R is the reflectance, in order
the disorders, impurities, and phonon in the ZnO thin films. to estimate the contribution of the reflectance in the absorp-
Our analysis suggests that these parameters strongly influ- tion spectra. Both the equations for a resulted in very similar
ence the absorption processes, leading to the exponential rise absorption spectra at 300 K, indicating that the small reflec-
tance of ZnO thin film does not contribute much to the
optical properties. Therefore, we only present the absorption
a)
Electronic mail: rairc@buffalostate.edu spectra extracted using the first equation with transmittance.

0021-8979/2013/113(15)/153508/5/$30.00 113, 153508-1 C 2013 AIP Publishing LLC

V
153508-2 R. C. Rai J. Appl. Phys. 113, 153508 (2013)

III. RESULTS AND DISCUSSION

Figure 1 shows the absorption spectra of an undoped
150 nm ZnO thin film on (001) sapphire at temperatures
ranging from 78 to 450 K. The absorption spectra show that
the absorption increases exponentially as a function of pho-
ton energy for all the measured temperatures, as shown in
Fig. 2.17 As indicated by an arrow, the exponential absorp-
tion edge redshifts with increasing temperature due to a com-
bination of the thermal effect and the Urbach effect.6,18,19
The absorption spectra, particularly at low temperatures,
show a strong free exciton peak at 3.45 eV in agreement
with the published data.20–22 The observation of exciton in a
thin film sample is a strong indication of the high quality
nature of the thin film. Further, the intensity of the exciton
peak displays a strong temperature dependence, i.e., the exci- FIG. 2. Logarithm of absorption coefficients of the ZnO thin film as a func-
ton peak area decreases as temperature increases, and it tion of photon energy. The solid lines represent the fitting of the logarithmic
can be used to measure the binding energy of the exciton. absorption data below the free exciton peak to Eq. (1). All the absorption
The Arrhenius best-fit to the integrated intensity of the coefficients converge to the point, E0 ¼ 3.62 eV and a0 ¼ 2:8  106 cm1 .
exciton peak yields the free exciton binding energy to be
E0 ¼ 64 6 7 meV, which is consistent with the known value where aðEÞ is the absorption coefficient as a function of pho-
of 60 meV.15 ton energy (E), E0 and a0 are the characteristic parameters of
In semiconductors and insulators, the fundamental the materials, r is the steepness parameter, and kB is the
absorption edge below the energy band gap increases expo- Boltzmann constant. The Urbach energy is defined as
nentially, and the absorption edge is known as the Urbach EU ¼ kBT/r(T), which indicates the width of the exponential
tail.6 The exact cause of the Urbach tails in materials has tail in the absorption spectra at temperature T.
been extensively investigated over the years.23–29 In litera- In Fig. 2, we show the logarithmic absorption coeffi-
tures, phonons, impurities, excitons, and structural disorders cients of the ZnO thin film as a function of photon energy at
in the materials have been associated with the observed temperatures ranging from 78 to 450 K. The spectra show the
exponential tails.6,18,30,31 Here, we analyze and discuss the Urbach tails below the free exciton energy for all the meas-
Urbach tails in the absorption spectra of the undoped ZnO ured temperatures: a linear increase of log(a) with increasing
thin film using the phenomenological models that have been photon energy. In order to extract a0 , E0, and the steepness
extensively used for semiconductors. First, we model the parameter (r) at each temperature, we fitted the Urbach tails
absorption coefficients of the ZnO thin film below the free in the logarithmic absorption spectra (the solid lines) between
exciton peak using the Urbach’s rule:6 a ¼ 4000 and a ¼ 120 000 cm1 to Eq. (1). We note that the
  absorption data below 4000 cm1 were rather complex and
ðE  E0 Þ were not included for the analysis. Our fittings show that the
aðEÞ ¼ a0 exp rðTÞ ; (1)
kB T Urbach tails in the absorption spectra converged to the point,
E0 ¼ 3.62 eV and a0 ¼ 2:8  106 cm1 . These extracted
parameters have been used below to further analyze and dis-
cuss the origin of the Urbach tails in the undoped ZnO thin
film.
Based on the phonon theory, the steepness parameter (r)
of the Urbach tail depends on temperature and photon energy
as given by Dow and Redfield,18
 
2kB T hx
rðTÞ ¼ r0 tanh ; (2)
hx 2kB T

where r0 is a temperature independent constant and hx rep-

resents the phonon energy associated with the Urbach tail. In
this model, the interaction of electrons and/or excitons with
a phonon in semiconductors causes the Urbach effect. The
effects of impurities and disorders on the Urbach tail, how-
ever, are not included in this model.
FIG. 1. Absorption spectra of a 150 nm ZnO thin film on (001) sapphire sub- The temperature dependence of the steepness parameter
strate at temperatures ranging from 78 to 450 K. At each temperature, the of the ZnO thin film is shown in Fig. 3(a). As discussed
absorption data show an exponentially rising edge of the free exciton located
at 3:45 eV. The exponential edge shifts to the lower energy region with
above, the steepness parameter at each temperature has been
increasing temperature. The arrow shows the direction of the increasing extracted by fitting the absorption data to Eq. (1). In order to
temperature. estimate the possible phonon energy associated with the
153508-3 R. C. Rai J. Appl. Phys. 113, 153508 (2013)

 
kB H 1 þ P N
EU ðTÞ ¼ þ ; (3)
r0 2 expðH=TÞ  1

where H is the characteristic temperature (proportional to

the Debye temperature HD and H  34 HD ) and P and N are
adjustable parameters. Here, P represents the structural disor-
der related to stoichiometry of the sample, whereas N repre-
sents the thermal term that accounts for the excitation of a
fraction of the total phonon modes at a given temperature,
which interacts with excitons/electrons, due to existence of
structural disorder.31 In this model, a system with P ¼ 0 and
N ¼ 1 represents a perfectly ordered crystal. Note that N ¼ 1
for the Cody’s model.
The Urbach energy (EU) of the ZnO thin film varies
from 74 meV at 78 K to 99 meV at 450 K. In Fig. 3(b), we
plot the Urbach energy data (䉱) as a function of temperature,
which displays a strong temperature dependence. The EU
data have been fitted (the solid green line) to Eq. (3) with
N ¼ 1 and P as an adjustable parameter (the Cody’s model).
The fitting yields H ¼ 800 6 40 K and the structural disorder
parameter to be P ¼ 0.05 6 0.03, indicating a very low struc-
tural disorder in the sample. As shown, P has a large uncer-
tainty and this fitting does not fit the data well. Also, the
characteristic temperature of 800 K is relatively higher than
the known value for ZnO. It means that the temperature
FIG. 3. (a) The steepness parameter of the ZnO thin film as a function of
dependence of the Urbach energy of the sample cannot be
temperature. The solid line represents the fitting of the steepness parameters described just with the structural disorders. On the contrary,
to Eq. (2). (b) The Urbach energy (EU) of the ZnO thin film as a function of the fitting (the dashed red line in Fig. 3(b)) of the same
temperature. The solid (dashed) line represents the fitting of the Urbach data to Eq. (3) with P and N as adjustable parameters (the
energy data to the Cody’s (Wasim’s) model.
Wasim’s model) appears very good. The fitting parameters
are found to be P ¼ 0.66 6 0.07, N ¼ 0.64 6 0.05, and
Urbach tail, we have fitted the steepness parameter versus H ¼ 515 6 20 K. The extracted characteristic temperature of
temperature graph to Eq. (2) with r0 and hxp as adjustable 515 K translates into HD ¼ 685 K, which reasonably falls
parameters. From the fitting, the phonon associated with the within the reported values for ZnO.9,32,33,42–44 We note that
Urbach tail has been estimated to be hxp ¼ 76 6 4 meV and the values of P, obtained from these two models, vary signifi-
the temperature independent constant has been measured to cantly, and the value of P ¼ 0.66, extracted using the
be r0 ¼ 0:498 6 0:008. The extracted phonon energy value Wasim’s model, seems more reasonable.
of 76 6 4 meV agrees very well with the phonon energy of As shown in Fig. 3(b), the Urbach energy increases very
72 meV observed in the photoluminescence spectra of slowly between 78 and 200 K, whereas it increases more rap-
ZnO.32,33 In fact, ZnO has several infrared and Raman active idly above 200 K. At low temperatures, the number of the
phonon modes, ranging in energy from 12 meV (100 cm1) thermally induced phonon is very low, and hence the weak
to 73 meV (590 cm1).34,35 Therefore, the phonon energy temperature dependence of EU is mainly associated with the
associated with the Urbach effect in the ZnO thin film could structural disorders. In contrast, a stronger temperature de-
be either a single phonon or a combination of multiple pho- pendence of EU in the high temperature region comes from
nons with the energy value of 76 meV. the enhanced electron-phonon interaction as the number of
On the other hand, the correlations between the Urbach phonon significantly increases with increasing temperature.
energy and the disorders in several materials have widely Further, thin film samples, in general, are known to contain a
been quantified using the two models.30,31,36–40 Cody et al. significant number of structural disorders due to the presence
have used a model for the Urbach energy (EU) on the basis of a large number of unintended impurities and vacancies.
of the effect of structural disorders and thermal effect on Overall, our fittings show that a significant number of struc-
the electronic property of silicon.30 Meanwhile, the tural disorders are present in the ZnO thin films, which domi-
Wasim’s model for the Urbach energy of the Cu ternaries nates the temperature dependence of EU at low temperatures.
differs from the Cody’s model by an additional parameter On the other hand, the electron-phonon interaction strongly
to account for the interaction of phonon(s) with exci- dominates the temperature dependence of EU at high temper-
ton(s).31,40,41 To investigate the role of impurities, struc- atures. Moreover, these two effects are cumulative and
tural disorders, and the thermal effect on the Urbach tails in strongly affect the absorption tails.
the ZnO optical spectra, we have used both of these models. In order to understand the origin of the temperature
According to the Wasim’s model, the Urbach energy is dependence of the Urbach energy, we also plot the exciton
given by peak energy (Eexc) of ZnO as a function of temperature, as
153508-4 R. C. Rai J. Appl. Phys. 113, 153508 (2013)

shown in Fig. 4(a). As shown, the Urbach energy varies from necessary to eliminate the thermal expansion contribution
3.45 eV at 78 K to 3.40 eV at 450 K. The temperature de- from the data. The energy shift DEth due to the thermal
pendence of the exciton peak has been fitted (the solid line) expansion can be written as DEth ¼ 3aath T, where a is the
aT 2
to the Varshni model:45 E0 ðTÞ ¼ E0 ð0Þ  ðTþbÞ , where E0(0) hydrostatic deformation potential and ath is the linear expan-
is the energy band gap at T ¼ 0, and a and b are constants. sion coefficient.47,49 We have estimated the thermal contri-
Further, b is proportional to the Debye temperature.33,45 The bution DEth for our ZnO sample using the available data
fitting confirms a linear relationship in the high temperature a ¼ 4.13 eV and ath  4  106 K1 for ZnO from Refs.
region and a nonlinear character in the low temperature 50 and 51. The exciton peak energy of ZnO minus the ther-
region as consistent with the Varshni model. For our ZnO mal effect (䉮) has been plotted as a function of temperature,
thin film, the extracted fitting parameters are a ¼ (0.00022 as shown in Fig. 4(a). The solid and dashed lines represent
6 0.00002) eV/K, b ¼ ð350 6 25Þ K, and E0 (T ¼ 0 K) the fittings to the Varshni model and the Bose-Einstein
a0 T 2
¼ (3.455 6 0.002) eV. In addition, the temperature depend- model: E0 ðTÞ  DEth ¼ E0 ð0Þ  ðTþb 0Þ and E0 ðTÞ  DEth
2a0 B
ence of the exciton energy has also been fitted to the ¼ E0 ð0Þ  ðexpðH0 B =TÞ1Þ, respectively. With the thermal effect
Bose-Einstein model (the dashed line in Fig. 4(a)):47,48 subtracted from the exciton energy data, the fitting yields the
E0 ðTÞ ¼ E0 ð0Þ  ðexpðH2aB =TÞ1Þ
B
, where E0(0) is the energy Varshni model parameters to be E0 ð0Þ ¼ ð3:452 6 0:002Þ eV;
band gap at T ¼ 0, aB is the strength of the electron-phonon a0 ¼ ð0:00025 6 0:00002Þ eV=K, and b0 ¼ ð250 6 50Þ K.
interaction, and HB is the average phonon temperature. From Similarly, the Bose-Einstein model yields the fitting parame-
the Bose-Einstein model, the fitting parameters are found ters to be E0 ð0Þ ¼ ð3:451 6 0:003Þ eV; a0 B ¼ ð25 6 2Þ meV,
to be E0 ð0Þ ¼ ð3:454 6 0:002Þ eV, aB ¼ (24 6 3) meV, and and H0 B ¼ ð240 6 20Þ K. Eliminating the thermal effect,
HB ¼ ð280 6 25Þ K, respectively. Using HB ¼ 3HD =8,46–48 the Debye temperature for the ZnO thin film is found to be
the Debye temperature for the ZnO thin film is found to be HD ¼ ð640 6 50Þ K, which compares reasonably well with
HD ¼ ð745 6 65Þ K. Overall, all the fitting parameters for HD ¼ 685 K obtained from the fitting of the Urbach energy.
the ZnO thin film compare reasonably well with the previ- Therefore, while the two phenomenological models fit
ously reported values.9,32,33,42,43 the exciton peak energy data nicely, the fitting to the Bose-
The above extracted parameters contain contributions Einstein model seems more appropriate for our sample as it
from both thermal expansion and electron-phonon coupling results in the consistent value for the Debye temperature.
effects.47,49 To study the role of electron-phonon effects, it is Figure 4(b) displays the exciton peak energy versus the
Urbach energy of the ZnO thin film. Coincidently, these two
energies, Eg and EU, roughly vary linearly, which strongly
indicates that their temperature dependence has the similar
functional form. Besides, it could also mean that they are
possibly related in terms of their origin. Cody et al. have
demonstrated such a linear relationship between Eg and EU
for silicon, and they have proposed the model that describes
the equivalence of structural and thermal disorders on these
parameters.30 In particular, they explained that the structural
disorder in the sample directly affects the thermal motion of
the lattice, causing to change the square of the displacement
of the atoms from their equilibrium positions. Therefore, the
effects of structural and thermal disorders on Eg and EU are
directly coupled. We think that the effects of structural and
thermal disorders on Eg and EU in the ZnO thin films are
coupled as well, leading to their linear relationship.
The exponential rise of the fundamental absorption edge
(i.e., the Urbach tails) in the sub-band gap region of the
undoped ZnO thin films indicates that the impurities, struc-
tural and thermal disorders, and interactions of the exciton
with lattice play important roles in the optical properties.
The observed temperature dependence of the Urbach energy,
the steepness parameter, and the exciton peak in the ZnO
thin films unambiguously demonstrate the important role of
these parameters in the absorption edge. Although our ZnO
thin films were undoped and of high quality, the samples do
FIG. 4. (a) The free exciton peak position (䉱: Eexc) and the free exciton
energy minus the thermal effect (䉮: EexcDEth ) of the ZnO thin film as a contain a large number of unintended impurities and defects
function of temperature. The solid (red) and dashed (black) lines represent that were developed during the deposition processes. We
the fitting of the data to the Varshni model45 and the Bose-Einstein model, conclude that the effects of all these factors add up to cause
respectively.47,48 (b) The exciton energy versus the Urbach energy of the
ZnO thin film. The solid line is a guide to the eye. A linear relationship
an exponential rise of the fundamental absorption edge. It
between Eex and EU suggests that the Urbach energy could be associated will be very interesting to see how the absorption edges of
with the cumulative effect of the structural and thermal disorders. lightly and heavily doped ZnO thin films compare with that
153508-5 R. C. Rai J. Appl. Phys. 113, 153508 (2013)

17
of undoped ZnO thin films, and such results will help us Although we present the absorption spectra for only one undoped ZnO
understand the exact role of the impurities and disorders in thin film, we did observe exponentially rising fundamental absorption
edge in all the three different undoped ZnO thin films that we studied.
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