Optical and electronic properties of Cu-Mn solid solutions
The optical properties of Cu-Mn alloys with Mn concentrations of 2, 5, 10 and 17.5% (which corresponds to the γ-solid solutions) were studied within a wide spectral range of 0.23 to 2.8 μm (0.44…5.39 eV). Real and imaginary parts of the refractive index were measured, other optical properties...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2013
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irk-123456789-1176802017-05-27T03:06:43Z Optical and electronic properties of Cu-Mn solid solutions Bondar, V.M. Stashchuk, V.S. Polianska, O.P. Chernukha, Ie.O. Tsuk, B.A. Lysiuk, V.O. The optical properties of Cu-Mn alloys with Mn concentrations of 2, 5, 10 and 17.5% (which corresponds to the γ-solid solutions) were studied within a wide spectral range of 0.23 to 2.8 μm (0.44…5.39 eV). Real and imaginary parts of the refractive index were measured, other optical properties such as dielectric constant, optical conductivity and the coefficient of specular reflectance at normal incidence were calculated being based on them. The analysis of the dispersion dependences ε(hν), R(hν) and σ(hν) enabled us to offer the electronic structure model for these alloys. According to this model, the electronic spectra (dependence of the density of electronic states on energy N(E)) of alloys with the indicated concentrations of components are the superposition of electronic spectra of Cu host, with weights equal to Cu concentrations, and the density of states within the impurity band, calculated using the experimental data. Remove selected 2013 Article Optical and electronic properties of Cu-Mn solid solutions / V.M. Bondar, V.S. Stashchuk, O.P. Polianska, Ie.O. Chernukha, B.A. Tsuk, V.O. Lysiuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 2. — С. 166-169. — Бібліогр.: 12 назв. — англ. 1560-8034 PACS 71.20.Be, Eh, Gj http://dspace.nbuv.gov.ua/handle/123456789/117680 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
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English |
| description |
The optical properties of Cu-Mn alloys with Mn concentrations of 2, 5, 10 and
17.5% (which corresponds to the γ-solid solutions) were studied within a wide spectral
range of 0.23 to 2.8 μm (0.44…5.39 eV). Real and imaginary parts of the refractive index
were measured, other optical properties such as dielectric constant, optical conductivity
and the coefficient of specular reflectance at normal incidence were calculated being
based on them. The analysis of the dispersion dependences ε(hν), R(hν) and σ(hν)
enabled us to offer the electronic structure model for these alloys. According to this
model, the electronic spectra (dependence of the density of electronic states on energy
N(E)) of alloys with the indicated concentrations of components are the superposition of
electronic spectra of Cu host, with weights equal to Cu concentrations, and the density of
states within the impurity band, calculated using the experimental data.
Remove selected |
| format |
Article |
| author |
Bondar, V.M. Stashchuk, V.S. Polianska, O.P. Chernukha, Ie.O. Tsuk, B.A. Lysiuk, V.O. |
| spellingShingle |
Bondar, V.M. Stashchuk, V.S. Polianska, O.P. Chernukha, Ie.O. Tsuk, B.A. Lysiuk, V.O. Optical and electronic properties of Cu-Mn solid solutions Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Bondar, V.M. Stashchuk, V.S. Polianska, O.P. Chernukha, Ie.O. Tsuk, B.A. Lysiuk, V.O. |
| author_sort |
Bondar, V.M. |
| title |
Optical and electronic properties of Cu-Mn solid solutions |
| title_short |
Optical and electronic properties of Cu-Mn solid solutions |
| title_full |
Optical and electronic properties of Cu-Mn solid solutions |
| title_fullStr |
Optical and electronic properties of Cu-Mn solid solutions |
| title_full_unstemmed |
Optical and electronic properties of Cu-Mn solid solutions |
| title_sort |
optical and electronic properties of cu-mn solid solutions |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117680 |
| citation_txt |
Optical and electronic properties of Cu-Mn solid solutions / V.M. Bondar, V.S. Stashchuk, O.P. Polianska, Ie.O. Chernukha, B.A. Tsuk, V.O. Lysiuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2013. — Т. 16, № 2. — С. 166-169. — Бібліогр.: 12 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT bondarvm opticalandelectronicpropertiesofcumnsolidsolutions AT stashchukvs opticalandelectronicpropertiesofcumnsolidsolutions AT polianskaop opticalandelectronicpropertiesofcumnsolidsolutions AT chernukhaieo opticalandelectronicpropertiesofcumnsolidsolutions AT tsukba opticalandelectronicpropertiesofcumnsolidsolutions AT lysiukvo opticalandelectronicpropertiesofcumnsolidsolutions |
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2025-07-08T12:36:47Z |
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2025-07-08T12:36:47Z |
| _version_ |
1837082316258672640 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 166-169.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
166
PACS 71.20.Be, Eh, Gj
Optical and electronic properties of Cu-Mn solid solutions
V.M. Bondar1, V.S. Stashchuk1, O.P. Polianska1, Ie.O. Chernukha1, B.A. Tsuk1, V.O. Lysiuk2
1Taras Shevchenko Kyiv National University, Physics Department,
64, Volodymyrska str., 01601 Kyiv, Ukraine; e-mail: bond270587@i.ua
2V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine
Abstract. The optical properties of Cu-Mn alloys with Mn concentrations of 2, 5, 10 and
17.5% (which corresponds to the γ-solid solutions) were studied within a wide spectral
range of 0.23 to 2.8 μm (0.44…5.39 eV). Real and imaginary parts of the refractive index
were measured, other optical properties such as dielectric constant, optical conductivity
and the coefficient of specular reflectance at normal incidence were calculated being
based on them. The analysis of the dispersion dependences ε(h), R(h) and h)
enabled us to offer the electronic structure model for these alloys. According to this
model, the electronic spectra (dependence of the density of electronic states on energy
N(E)) of alloys with the indicated concentrations of components are the superposition of
electronic spectra of Cu host, with weights equal to Cu concentrations, and the density of
states within the impurity band, calculated using the experimental data.
Keywords: Cu-Mn alloy, electronic structure, impurity band, collision rate, density of
electronic states, optical conductivity spectrum.
Manuscript received 19.12.12; revised version received 28.02.13; accepted for
publication 19.03.13; published online 25.06.13.
1. Introduction
Cu-Mn alloys, unlike Cu-Ni alloys, which are single-
phase [1] in a wide range of concentrations, form two-
phase solid solutions with γ-phase Cu and ε-phase Mn.
At the same time, other transition metals such as Fe, Co
or Cr are almost insoluble in Cu [2]. On the other hand,
it is well known that the impurities of 3d-transition
metals form localized magnetic moments [3], which
gave impetus to theoretical studies of electronic
properties of the compounds with 3d-transition metals
[4]. It was found that with the addition of 3d-transition
metals to copper, new impurity bands are formed in the
electronic spectrum of the solvent. They are located
below the Fermi level EF [5]. This enabled to determine
the parameters that characterize the impurity band, as in
the case of alloys Cu-Fe [6], Cu-Co [7] and Cu-Cr [8].
However, so far, to our knowledge, the optical properties
of alloys of copper with another 3d-transition metal –
antiferromagnetic Mn – were not studied. Therefore, in
this work we study the optical properties and, being
based on them, the electronic structure of Cu-Mn
compounds rich in Cu.
2. Experimental procedure
Optical properties of solid solutions of Cu-Mn with Mn
concentrations of 2, 5, 10 and 17.5%, and pure Cu and
Mn were investigated within the spectral range λ =
0.23…2.8 μm (hν = 0.44…5.39 eV) by Beattie
ellipsometric method using an original spectral
ellipsometer [9]. The ellipsometer included the
following functional units: block of light sources,
consisting of deuterium-mercury lamp ART-250,
hydrogen lamp ICE-25 and halogen lamp КГМ-150;
block of radiation detectors, which included
photoelectron multipliers PEM-39A and PEM-62; G-5
goniometer, which housed the Glan prism polarizer and
analyzer. The studied samples were located on the
goniometer sample stage. The setup also included the
electrical components for amplifying electrical signals
and their registration by standard digital voltmeters and
PC. Ellipsometric parameters Δ (phase shift between p-
and s-polarization components) and ψ (azimuth of the
restored linear polarization) were measured within this
setup in the specified spectral range at a fixed angle of
incidence close to the principal one. Based on Δ and ψ
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 166-169.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
167
the refraction and absorption indices n and χ were
calculated, and then the dielectric constant 22 n ,
optical conductivity σ = 4πε0nχν (ν – light frequency)
and the reflection coefficient at normal incidence
22
22
1)(
1)(
n
n
R were obtained.
Cu-Mn alloy samples were obtained by vacuum-arc
melting of pure Cu and Mn with corresponding weights
in argon atmosphere by repeated melting. To achieve
greater uniformity samples were annealed in the same
atmosphere at 900 ºС for 24 h. Sample mirror surfaces
were prepared by mechanical grinding and polishing
with diamond paste with subsequent recrystallization
annealing and electropolishing. X-ray structure and
phase analysis of alloy samples was also performed with
ДРОН-3.0 X-ray diffractometer.
3. Results and discussion
Analysis of optical properties’ dependence on the
photon energy hν in the investigated spectral range
hν = 0.44…5.39 eV provides information about
changes in the electronic structure of Cu with the
addition of Mn. First, we consider the dispersion curves
of reflection coefficient R(hν) of studied Cu-Mn alloys
and pure Cu and Mn, shown in Fig. 1. The figure
shows that the reflection curve R(hν) for pure Cu is a
smooth curve without any anomalies, although the
value of R varies within wide limits (35…99%), except
for the shallow minimum located at about 4.2 eV,
caused by electron interband transitions. At the same
time, the value of R of Mn is much lower than that for
Cu, especially in the ultraviolet region, where the
values of R differ by almost 3.5 times. A broad
maximum is observed in the infrared region
(hν <1.1 eV) for Mn, located at about 0.95 eV. It is
seen that in this area R value for Cu depends weakly on
energy, indicating the dominance of interband electron
transitions. With addition of Mn, the R value in the
ultraviolet spectral region (hν >3.0 eV) decreases with
increasing the Mn concentration, and the minimum at
4.2 eV characteristic for pure Cu does not appear in
R(hν) curves of alloys with Mn concentrations higher
than 10%. The behavior of the curve R(hν) for Cu-
17.5% Mn alloy is quite peculiar, as a maximum at
3.85 eV clearly appears in the curve, which is virtually
absent in other alloys. It is speculated that with further
increase in the manganese concentration this maximum
intensity will increase, as it is observed in the R(hν)
curve of pure manganese. Therefore, the most
significant changes in the R(hν) spectra of alloys are
observed in the infrared region (with hν < 1.5 eV),
which indicates the increasing role of interband
transitions with the increase of manganese
concentrations.
In what follows, we proceed to analyze the
dispersion of the dielectric constant ε(hν), shown in
Fig. 2. The figure shows that the ε(hν) curves for alloys
with a low Mn content are similar to the pure copper
ε(hν) curve, which decreases monotonically with the
decrease in energy, which is typical for normal
dispersion. In the samples with high Mn concentrations,
as well as for pure Mn, the anomalous dispersion is
observed in ε(hν) curves at 1.0…3.0 eV, which indicates
the dominance of interband electron transitions within
this spectral range. Additional information can be
obtained by analyzing the ε(hν) curves at
(hν) = 3.3…4.5 eV, where the value of ε for all studied
alloys is close to zero, which is a necessary condition for
the excitation of plasma oscillations.
Let us make a more detailed look at the dispersion
of optical conductivity σ(hν), which is proportional to
the interband density of electronic states G(hν) [10].
Experimental ε(hν) curves of the investigated alloys
and pure Cu and Mn are shown in Fig. 3. The features
of σ(hν) spectra of pure Cu and Mn are significantly
different. At the energies (hν) <1.5 eV, the optical
conductivity value for Cu increases monotonically with
the decrease in the energy hν, which indicates the
dominance of intraband transitions that occur within
each of the bands that cross the Fermi level EF.
Characteristic features of ε(hν) spectrum of Cu are the
sharp interband absorption edge at hν = 2.1…2.3 eV,
centered at 2.2 eV, and an intense absorption band with
a maximum near 4.72 eV, as well as minor spectrum
features at 3.5…4.4 eV. σ(hν) curve of Mn is in turn
characterized by a wide maximum at 2.2 eV and a
slight increase in σ value in the IR range (hν < 0.5 eV)
caused by intraband electron transitions. We analyze
further the dispersion of optical conductivity σ(hν) of
Cu-Mn alloys with the increase in the Mn
concentration (Fig. 3).
Fig. 1. Dispersion curves of reflectance R(hν) for Cu (1),
Mn (6) and their alloys containing 2 (2), 5 (3), 10 (4) and
17.5% Mn (5).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 166-169.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
168
Fig. 2. Dispersion curves of the dielectric permittivity ε(hν) for
pure Cu (1) and Mn (6), and Cu-Mn alloys containing 2 (2),
5 (3), 10 (4) and 17.5% Mn (5).
Fig. 3. Dispersion curves of interband optical conductivity
σ(hν) for pure Cu (1) and Mn (2) and Cu-Mn alloys containing
2 (3), 5 (4), 10 (5) and 17.5% Mn (6). Curves (1) and (2) for
the pure component raised by 0.1 M (Ohmm)–1.
Fig. 3 shows that the addition of low quantities of
manganese to copper does not introduce significant
changes in the overall shape of the absorption spectrum
of copper. Characteristic features of the σ(hν) spectrum
of pure copper, in particular a short peak at 4.72 eV and
a sharp edge at 2.1…2.3 eV, to some extent, appear in
all the investigated Cu-Mn alloys, as in Cu-Co alloys
[7]. It is found that the peak at 4.72 eV is observed in all
the alloys, hardly shifting along the energy scale. The
sharp absorption edge at 2.2 eV appears only in samples
with the concentration of manganese below 10%. At the
same time, in the infrared spectral range hν =
0.8…1.8 eV it is found that with addition of only 2% Mn
to Cu the contribution of “free” electrons in the overall
absorption decreases sharply. At high concentrations of
Mn, this spectral area completely dominates due to
interband electron transitions. This is due to the sharp
increase of relaxation frequency of electrons in alloys as
compared to pure components. It is found that addition
of Mn to Cu at Mn concentrations higher than 5% gives
a very strong effect – the appearance of an intense
absorption band in the σ(hν) curves in the near-IR range
with a peak at hν = 1.9…2.0 eV. Fig. 3 shows that a
minimum is observed in the Cu σ(hν) curve in this
region, while the maximum of absorption of pure Mn,
according to our experimental data, is located at 2.2 eV.
Consequently, this band is not associated with pure Cu
and Mn, and is most likely associated with the resonant
states arising in the electronic spectrum of Cu by
addition of Mn. The maximum, which is located at
2.5 eV for the Cu-2% Mn alloy, shifts in high-energy
region of the spectrum, for example, for the Cu-
17.5% Mn alloy it is located at 2.15 eV (see Fig. 3).
Clearly, the formation of an additional band in alloys is
due to changes in the electronic spectra of Cu-Mn alloys.
These changes are associated with the restructuring the
energy spectrum of Cu and the appearance, as noted
above, of resonant impurity states [10].
Further, we analyze the dispersion curves of the
residual optical conductivity σ(hν), which represents
the difference between the experimental values σ(hν)
for alloys and the values of the optical conductivity of
pure copper σCu(hν) and pure manganese σMn(hν) with
respective weights σ(hν) =
hchch MnCu1 (c is the Mn
concentration), which for Cu-Mn alloys containing 2,
5, 10, and 17.5% are shown in Fig. 4.
It is seen that for all the investigated alloys a new
absorption band with a maximum at 2.05…2.15 eV
appears. From the obtained data presented in Figs 3 and
4, the following conclusions can be made: first, at low
concentrations of Mn (5%) it solves almost completely
Fig. 4. Dispersion of residual optical conductivity Δσ(hν) for
Cu-Mn alloys containing 2 (1), 5 (2), 10 (3) and 17.5%
Mn (4). All the curves are shifted upwards by
0.1 M(Ohmm)–1. Inset shows the density of states N(E)
curves for Cu [11] and Cu-Mn alloys within the impurity
band (dashed lines).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 166-169.
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
169
in Cu, second, the solubility increases with increasing
the Mn concentration, and third, the impurity d-band
forms in the electronic spectrum of the Cu-Mn solid
solution, associated with Mn, which is located at
2.05…2.15 eV below the Fermi level EF.
Using the results of studies of the electronic structure
of pure copper and its optical spectrum [12], we can
propose a model of the electronic structure of Cu-Mn
solid solutions. According to [12], the absorption edge in
pure copper at 2.1…2.2 eV is associated with transitions
of electrons from the peaks of d-band near the L3 Brillouin
zone (BZ) to free states of s-p-bands 2L in the vicinity of
the Fermi level (FL) EF. Based on the data of
experimental studying the optical properties of Cu-Mn
alloys, it follows that the energy gap between the top of d-
Cu bands and Fermi level with addition of Mn remains
unchanged. That is, the position of d-band relative to
Fermi level is virtually unchanged in the electronic
spectrum of alloys. Intense interband absorption is
observed above the absorption edge, which is associated
with transitions in the large volume of BZ from 2-nd, 3-rd
and 4-th bands into the free states of the sixth band in
WL and XD directions of the Brillouin zone [10].
Taking into account that the high-energy peak in the σ(hν)
curve of copper at 4.7 eV is related to transitions from the
sixth to the seventh band, mainly from d-states of L1 to
free sp-band levels of 2L [11], one arrives to conclusion
that the structure of d-bands located at 4.0…4.95 eV
lower than the Fermi level is not changed in the alloys and
is similar to the d-bands of copper. Thus, the energy bands
in the investigated Cu-Mn alloys retain the characteristics
of the electron spectrum inherent to pure copper.
Assuming by analogy between Cu-Fe and Cu-Cr
alloys [6, 8] that the absorption band with a peak at 2 eV
in the σ(hν) optical spectra is related to electron transitions
from the impurity d-subband to free electron states in the
vicinity of the Fermi level EF and using the obtained data,
one can find the distance of the energy center of the
impurity band from the Fermi level FEEd as well as its
half-width Δ. According to the experimental data in Cu-
Mn solid solution the value of FEEd is about 2.1 eV
and almost independent of the Mn concentration, and Δ
increases slightly with increasing the Mn content in the
solution and equals 1.35 eV (Cu-2% Mn), 1.4 eV (Cu-
17.5% Mn). Based on the obtained FEEd density of
electronic states, N(E) was calculated for Cu-Mn alloys
within the impurity band shown in the inset to Fig. 4.
Consequently, the resulting electron spectrum of any alloy
is a superposition of the spectrum of pure copper with a
weight equal to the concentration of Cu in the alloy, and
the density of states of the alloy within the impurity band.
4. Conclusions
It is found that a new impurity energy band forms in the
electronic spectrum of Cu with the addition of
antiferromagnetic Mn impurities, located approximately
2.1 eV below the Fermi level EF, which may split into
two energy subbands due to exchange interaction. It is
shown that the electron spectrum N(E) of Cu-Mn alloys
is, in a rough approximation, the superposition of
densities of electronic states N(E) of pure copper with a
weight equal to its concentration in the alloy, and the
density of states within the impurity band.
It has been shown that the optical properties of Cu-
Mn alloys are determined by solvent (Cu) d-bands and
impurity bands (Mn). Due to interband transitions from
the solvent d-band to its sp-band, the main absorption
band in the σ(hν) spectra of Cu-Mn alloys is formed.
Additional bands appear due to transitions of electrons
from the impurity band to the Fermi level EF.
References
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Non-equilibrium phase diagrams of ternary
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calculations for optical constants of copper // Phys.
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and characterization of Ba2Cu3O7−δ/LaMnO3/
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(1997).
8. V.S. Stashchuk, Optical properties of Cu-Cr two-
component systems in intraband transition region //
Ukr. Phys. J., 43, p. 282 (1996).
9. H. Fujiwara, Spectroscopic Ellipsometry Principles
and Applications. Atrium. Wiley, 2007.
10. L.V. Poperenko, I.A. Shaikevych, V.S. Stashcuk,
V.A. Odarych, Diagnostics of Surface with
Polarized Light. Kyiv University Publ. House,
Kyiv, 2007, p. 130-136 (in Ukrainian).
11. Y. Kakehashi, M. Atiqur, R. Patoary, and
T. Tamashiro, Dynamical coherent-potential
approximation approach to excitation spectra in 3d
transition metals // Phys Rev. B, 81, 245133 (2010).
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2013. V. 16, N 2. P. 166-169.
PACS 71.20.Be, Eh, Gj
Optical and electronic properties of Cu-Mn solid solutions
V.M. Bondar1, V.S. Stashchuk1, O.P. Polianska1, Ie.O. Chernukha1, B.A. Tsuk1, V.O. Lysiuk2
1Taras Shevchenko Kyiv National University, Physics Department,
64, Volodymyrska str., 01601 Kyiv, Ukraine; e-mail: bond270587@i.ua
2V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 03028 Kyiv, Ukraine
Abstract. The optical properties of Cu-Mn alloys with Mn concentrations of 2, 5, 10 and 17.5% (which corresponds to the γ-solid solutions) were studied within a wide spectral range of 0.23 to 2.8 μm (0.44…5.39 eV). Real and imaginary parts of the refractive index were measured, other optical properties such as dielectric constant, optical conductivity and the coefficient of specular reflectance at normal incidence were calculated being based on them. The analysis of the dispersion dependences ε(h), R(h) and h) enabled us to offer the electronic structure model for these alloys. According to this model, the electronic spectra (dependence of the density of electronic states on energy N(E)) of alloys with the indicated concentrations of components are the superposition of electronic spectra of Cu host, with weights equal to Cu concentrations, and the density of states within the impurity band, calculated using the experimental data.
Keywords: Cu-Mn alloy, electronic structure, impurity band, collision rate, density of electronic states, optical conductivity spectrum.
Manuscript received 19.12.12; revised version received 28.02.13; accepted for publication 19.03.13; published online 25.06.13.
1. Introduction
Cu-Mn alloys, unlike Cu-Ni alloys, which are single-phase [1] in a wide range of concentrations, form two-phase solid solutions with γ-phase Cu and ε-phase Mn. At the same time, other transition metals such as Fe, Co or Cr are almost insoluble in Cu [2]. On the other hand, it is well known that the impurities of 3d-transition metals form localized magnetic moments [3], which gave impetus to theoretical studies of electronic properties of the compounds with 3d-transition metals [4]. It was found that with the addition of 3d-transition metals to copper, new impurity bands are formed in the electronic spectrum of the solvent. They are located below the Fermi level EF [5]. This enabled to determine the parameters that characterize the impurity band, as in the case of alloys Cu-Fe [6], Cu-Co [7] and Cu-Cr [8]. However, so far, to our knowledge, the optical properties of alloys of copper with another 3d-transition metal – antiferromagnetic Mn – were not studied. Therefore, in this work we study the optical properties and, being based on them, the electronic structure of Cu-Mn compounds rich in Cu.
2. Experimental procedure
Optical properties of solid solutions of Cu-Mn with Mn concentrations of 2, 5, 10 and 17.5%, and pure Cu and Mn were investigated within the spectral range λ = 0.23…2.8 μm (hν = 0.44…5.39 eV) by Beattie ellipsometric method using an original spectral ellipsometer [9]. The ellipsometer included the following functional units: block of light sources, consisting of deuterium-mercury lamp ART-250, hydrogen lamp ICE-25 and halogen lamp КГМ-150; block of radiation detectors, which included photoelectron multipliers PEM-39A and PEM-62; G-5 goniometer, which housed the Glan prism polarizer and analyzer. The studied samples were located on the goniometer sample stage. The setup also included the electrical components for amplifying electrical signals and their registration by standard digital voltmeters and PC. Ellipsometric parameters Δ (phase shift between p- and s-polarization components) and ψ (azimuth of the restored linear polarization) were measured within this setup in the specified spectral range at a fixed angle of incidence close to the principal one. Based on Δ and ψ the refraction and absorption indices n and χ were calculated, and then the dielectric constant
2
2
c
-
=
e
n
, optical conductivity σ = 4πε0nχν (ν – light frequency) and the reflection coefficient at normal incidence
2
2
2
2
1)
(
1)
(
c
+
+
c
+
-
=
n
n
R
were obtained.
Cu-Mn alloy samples were obtained by vacuum-arc melting of pure Cu and Mn with corresponding weights in argon atmosphere by repeated melting. To achieve greater uniformity samples were annealed in the same atmosphere at 900 ºС for 24 h. Sample mirror surfaces were prepared by mechanical grinding and polishing with diamond paste with subsequent recrystallization annealing and electropolishing. X-ray structure and phase analysis of alloy samples was also performed with ДРОН-3.0 X-ray diffractometer.
3. Results and discussion
Analysis of optical properties’ dependence on the photon energy hν in the investigated spectral range hν = 0.44…5.39 eV provides information about changes in the electronic structure of Cu with the addition of Mn. First, we consider the dispersion curves of reflection coefficient R(hν) of studied Cu-Mn alloys and pure Cu and Mn, shown in Fig. 1. The figure shows that the reflection curve R(hν) for pure Cu is a smooth curve without any anomalies, although the value of R varies within wide limits (35…99%), except for the shallow minimum located at about 4.2 eV, caused by electron interband transitions. At the same time, the value of R of Mn is much lower than that for Cu, especially in the ultraviolet region, where the values of R differ by almost 3.5 times. A broad maximum is observed in the infrared region (hν <1.1 eV) for Mn, located at about 0.95 eV. It is seen that in this area R value for Cu depends weakly on energy, indicating the dominance of interband electron transitions. With addition of Mn, the R value in the ultraviolet spectral region (hν >3.0 eV) decreases with increasing the Mn concentration, and the minimum at 4.2 eV characteristic for pure Cu does not appear in R(hν) curves of alloys with Mn concentrations higher than 10%. The behavior of the curve R(hν) for Cu-17.5% Mn alloy is quite peculiar, as a maximum at 3.85 eV clearly appears in the curve, which is virtually absent in other alloys. It is speculated that with further increase in the manganese concentration this maximum intensity will increase, as it is observed in the R(hν) curve of pure manganese. Therefore, the most significant changes in the R(hν) spectra of alloys are observed in the infrared region (with hν < 1.5 eV), which indicates the increasing role of interband transitions with the increase of manganese concentrations.
In what follows, we proceed to analyze the dispersion of the dielectric constant ε(hν), shown in Fig. 2. The figure shows that the ε(hν) curves for alloys with a low Mn content are similar to the pure copper ε(hν) curve, which decreases monotonically with the decrease in energy, which is typical for normal dispersion. In the samples with high Mn concentrations, as well as for pure Mn, the anomalous dispersion is observed in ε(hν) curves at 1.0…3.0 eV, which indicates the dominance of interband electron transitions within this spectral range. Additional information can be obtained by analyzing the ε(hν) curves at (hν) = 3.3…4.5 eV, where the value of ε for all studied alloys is close to zero, which is a necessary condition for the excitation of plasma oscillations.
Let us make a more detailed look at the dispersion of optical conductivity σ(hν), which is proportional to the interband density of electronic states G(hν) [10]. Experimental ε(hν) curves of the investigated alloys and pure Cu and Mn are shown in Fig. 3. The features of σ(hν) spectra of pure Cu and Mn are significantly different. At the energies (hν) <1.5 eV, the optical conductivity value for Cu increases monotonically with the decrease in the energy hν, which indicates the dominance of intraband transitions that occur within each of the bands that cross the Fermi level EF. Characteristic features of ε(hν) spectrum of Cu are the sharp interband absorption edge at hν = 2.1…2.3 eV, centered at 2.2 eV, and an intense absorption band with a maximum near 4.72 eV, as well as minor spectrum features at 3.5…4.4 eV. σ(hν) curve of Mn is in turn characterized by a wide maximum at 2.2 eV and a slight increase in σ value in the IR range (hν < 0.5 eV) caused by intraband electron transitions. We analyze further the dispersion of optical conductivity σ(hν) of Cu-Mn alloys with the increase in the Mn concentration (Fig. 3).
Fig. 1. Dispersion curves of reflectance R(hν) for Cu (1), Mn (6) and their alloys containing 2 (2), 5 (3), 10 (4) and 17.5% Mn (5).
Fig. 2. Dispersion curves of the dielectric permittivity ε(hν) for pure Cu (1) and Mn (6), and Cu-Mn alloys containing 2 (2), 5 (3), 10 (4) and 17.5% Mn (5).
Fig. 3. Dispersion curves of interband optical conductivity σ(hν) for pure Cu (1) and Mn (2) and Cu-Mn alloys containing 2 (3), 5 (4), 10 (5) and 17.5% Mn (6). Curves (1) and (2) for the pure component raised by 0.1 M (Ohm(m)–1.
Fig. 3 shows that the addition of low quantities of manganese to copper does not introduce significant changes in the overall shape of the absorption spectrum of copper. Characteristic features of the σ(hν) spectrum of pure copper, in particular a short peak at 4.72 eV and a sharp edge at 2.1…2.3 eV, to some extent, appear in all the investigated Cu-Mn alloys, as in Cu-Co alloys [7]. It is found that the peak at 4.72 eV is observed in all the alloys, hardly shifting along the energy scale. The sharp absorption edge at 2.2 eV appears only in samples with the concentration of manganese below 10%. At the same time, in the infrared spectral range hν = 0.8…1.8 eV it is found that with addition of only 2% Mn to Cu the contribution of “free” electrons in the overall absorption decreases sharply. At high concentrations of Mn, this spectral area completely dominates due to interband electron transitions. This is due to the sharp increase of relaxation frequency of electrons in alloys as compared to pure components. It is found that addition of Mn to Cu at Mn concentrations higher than 5% gives a very strong effect – the appearance of an intense absorption band in the σ(hν) curves in the near-IR range with a peak at hν = 1.9…2.0 eV. Fig. 3 shows that a minimum is observed in the Cu σ(hν) curve in this region, while the maximum of absorption of pure Mn, according to our experimental data, is located at 2.2 eV. Consequently, this band is not associated with pure Cu and Mn, and is most likely associated with the resonant states arising in the electronic spectrum of Cu by addition of Mn. The maximum, which is located at 2.5 eV for the Cu-2% Mn alloy, shifts in high-energy region of the spectrum, for example, for the Cu-17.5% Mn alloy it is located at 2.15 eV (see Fig. 3). Clearly, the formation of an additional band in alloys is due to changes in the electronic spectra of Cu-Mn alloys. These changes are associated with the restructuring the energy spectrum of Cu and the appearance, as noted above, of resonant impurity states [10].
Further, we analyze the dispersion curves of the residual optical conductivity σ(hν), which represents the difference between the experimental values σ(hν) for alloys and the values of the optical conductivity of pure copper σCu(hν) and pure manganese σMn(hν) with respective weights (σ(hν) =
(
)
(
)
(
)
(
)
n
s
+
n
s
-
-
n
s
h
c
h
c
h
Mn
Cu
1
(c is the Mn concentration), which for Cu-Mn alloys containing 2, 5, 10, and 17.5% are shown in Fig. 4.
It is seen that for all the investigated alloys a new absorption band with a maximum at 2.05…2.15 eV appears. From the obtained data presented in Figs 3 and 4, the following conclusions can be made: first, at low concentrations of Mn (5%) it solves almost completely in Cu, second, the solubility increases with increasing the Mn concentration, and third, the impurity d-band forms in the electronic spectrum of the Cu-Mn solid solution, associated with Mn, which is located at 2.05…2.15 eV below the Fermi level EF.
Using the results of studies of the electronic structure of pure copper and its optical spectrum [12], we can propose a model of the electronic structure of Cu-Mn solid solutions. According to [12], the absorption edge in pure copper at 2.1…2.2 eV is associated with transitions of electrons from the peaks of d-band near the L3 Brillouin zone (BZ) to free states of s-p-bands
2
L
¢
in the vicinity of the Fermi level (FL) EF. Based on the data of experimental studying the optical properties of Cu-Mn alloys, it follows that the energy gap between the top of d-Cu bands and Fermi level with addition of Mn remains unchanged. That is, the position of d-band relative to Fermi level is virtually unchanged in the electronic spectrum of alloys. Intense interband absorption is observed above the absorption edge, which is associated with transitions in the large volume of BZ from 2-nd, 3-rd and 4-th bands into the free states of the sixth band in
W
L
-
and
X
D
-
directions of the Brillouin zone [10]. Taking into account that the high-energy peak in the σ(hν) curve of copper at 4.7 eV is related to transitions from the sixth to the seventh band, mainly from d-states of L1 to free sp-band levels of
2
L
¢
[11], one arrives to conclusion that the structure of d-bands located at 4.0…4.95 eV lower than the Fermi level is not changed in the alloys and is similar to the d-bands of copper. Thus, the energy bands in the investigated Cu-Mn alloys retain the characteristics of the electron spectrum inherent to pure copper.
Assuming by analogy between Cu-Fe and Cu-Cr alloys [6, 8] that the absorption band with a peak at 2 eV in the σ(hν) optical spectra is related to electron transitions from the impurity d-subband to free electron states in the vicinity of the Fermi level EF and using the obtained data, one can find the distance of the energy center of the impurity band from the Fermi level
F
E
E
d
-
as well as its half-width Δ. According to the experimental data in Cu-Mn solid solution the value of
F
E
E
d
-
is about 2.1 eV and almost independent of the Mn concentration, and Δ increases slightly with increasing the Mn content in the solution and equals 1.35 eV (Cu-2% Mn), 1.4 eV (Cu-17.5% Mn). Based on the obtained
F
E
E
d
-
density of electronic states, N(E) was calculated for Cu-Mn alloys within the impurity band shown in the inset to Fig. 4. Consequently, the resulting electron spectrum of any alloy is a superposition of the spectrum of pure copper with a weight equal to the concentration of Cu in the alloy, and the density of states of the alloy within the impurity band.
4. Conclusions
It is found that a new impurity energy band forms in the electronic spectrum of Cu with the addition of antiferromagnetic Mn impurities, located approximately 2.1 eV below the Fermi level EF, which may split into two energy subbands due to exchange interaction. It is shown that the electron spectrum N(E) of Cu-Mn alloys is, in a rough approximation, the superposition of densities of electronic states N(E) of pure copper with a weight equal to its concentration in the alloy, and the density of states within the impurity band.
It has been shown that the optical properties of Cu-Mn alloys are determined by solvent (Cu) d-bands and impurity bands (Mn). Due to interband transitions from the solvent d-band to its sp-band, the main absorption band in the σ(hν) spectra of Cu-Mn alloys is formed. Additional bands appear due to transitions of electrons from the impurity band to the Fermi level EF.
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Fig. 4. Dispersion of residual optical conductivity Δσ(hν) for Cu-Mn alloys containing 2 (1), 5 (2), 10 (3) and 17.5% Mn (4). All the curves are shifted upwards by 0.1 M(Ohm(m)–1. Inset shows the density of states N(E) curves for Cu [11] and Cu-Mn alloys within the impurity band (dashed lines).
© 2013, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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