Optical absorption spectra as a useful tool to find parameters of deep impurity centers in semiconductors Viktor P. Makhniy,1,* Paul P. Horley,2 Oksana V. Kinzerskaya,1 and Elena V. Stets3 1
Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi, Ukraine
2 3
Centro de Investigación en Materiales Avanzados S.C., 120 Miguel de Cervantes, 31109 Chihuahua, Mexico
National Technical University of Ukraine “Kyiv Polytechnic Institute,” 37 Prospekt Peremohy, 03056 Kyiv, Ukraine *Corresponding author: [email protected] Received 15 November 2013; accepted 29 November 2013; posted 11 December 2013 (Doc. ID 199072); published 3 February 2014
We analyze physical models accounting for deep-level conduction band transitions to describe impurity absorption spectra in tetrahedral-structured semiconductors. The investigations were carried out for ZnSe crystals doped with transition metals (Ti, V, Cr, Mn, Fe, Co, Ni) from a vapor phase. It was shown that the impurities provide acceptor centers with ground state energy offset by 0.3–0.6 eV from the edge of the conduction band, forming long-wave bands in the absorption spectra of the materials studied. © 2014 Optical Society of America OCIS codes: (300.1030) Absorption; (300.6170) Spectra; (160.1890) Detector materials. http://dx.doi.org/10.1364/AO.53.0000B8
1. Introduction
Deep-level impurities in semiconductor materials are responsible for a multitude of physical effects, either useful for electronic applications or undesirable [1]. Therefore, more research should be focused on such impurities to discover details on physical and chemical phenomena occurring in such systems, energy spectra corresponding to deep levels, as well as controllable doping techniques required to achieve desired impurity parameters. Answering these questions is important for semiconductor material science and may provide useful hints for improvement of electronic devices. The situation is quite complicated due to the absence of a unified theory describing deep impurity centers so that experimental investigations in this field are extremely important to produce the data required for in-depth theoretical analysis. The preference should be given to nondestructive 1559-128X/14/1000B8-04$15.00/0 © 2014 Optical Society of America B8
APPLIED OPTICS / Vol. 53, No. 10 / 1 April 2014
methods that can be implied to monitor the sample practically at every stage of its formation and processing, i.e., during synthesis, annealing, doping, and so on. The obtained information will form a solid base for developing semiconductor materials with predetermined properties, also offering detailed data for analysis and understanding of deep impurity centers that is important for development of a unified theory explaining the physical processes that occurs at these impurities. This paper is dedicated to a partial solution of the aforementioned problem. We report the successful use of optical absorption spectra to study deep-level impurities as a useful tool to determine parameters of deep centers in different semiconductor materials. 2. Impurity Absorption Models
In the first place, it is necessary to emphasize that analytical expression describing the absorption spectra cannot be obtained from the first principles, at least at the present level of this numerical technique. Therefore, scientists have to use available physical
models, including those for tetrahedral crystals [2], where the wave function for the impurity is represented by the Bloch wave. As a consequence, the optical phenomena are described by excitation of an electron into conduction band EC and formation of a hole in the valence band EV , Fig. 1. In the spherical-symmetry band approximation one can obtain four expressions for cross-section σ in the absorption limit [2]. Taking into account that σ essentially defines the absorption process, one can find spectral dependence of the absorption coefficient αω as αB ω ∼
ℏω − Et 1∕2 ; ℏωℏω − Et ℏ2 γ 2 ∕2m 2
(1)
αAω ∼
ℏω − Et 3∕2 ; ℏωℏω − Et ℏ2 γ 2 ∕2m 2
(2)
1∕2 · ℏω−1 ; αD ω ∼ ℏω − Et
(3)
3∕2 · ℏω−1 : αC ω ∼ ℏω − Et
(4)
Here γ is the wavevector of the complex bandstructure, m is the particle’s effective mass, and Et is the energy of impurity level. Equations (1)–(4) describe direct permitted transitions αB ω , direct forbidden transitions αAω , indirect permitted transitions αD ω, and indirect forbidden transitions αC ω . Applying effective mass approximation Et ℏ2 γ 2 ∕2m to Eq. (2), one can obtain Lucovsky formula [3] that was written for δ-function potential of the impurity center. In this case transition number 1 shown in Fig. 1 should yield the absorption coefficient: αAω ∼ ℏω − Eg − Et 1∕2 · ℏω−1 ;
(5)
whereas transition number 2 should be characterized with αAω ∼ ℏω − Et 3∕2 · ℏω−3 :
(6)
In both cases, the ionization energy Et is measured from the edge of the valence band EV and the quantity Eg corresponds to the band gap of semiconductor. The Lucovsky formula predicts that αmax ≈ 2Et . ω
Fig. 1. Sketch of electron transitions involving a deep level Et .
However, in real crystals one often obtains Et > ℏ2 γ 2 ∕2m , which results in red-shift of the αAω peak bringing it closer to Et . In general, functions corresponding to real impurity centers will receive contributions from different band peaks. At the same time, such contributions will differ on energy scale so that the excitation process can be localized in the vicinity of a corresponding band. Moreover, the intensity of the absorption processes connected with different basis functions will be also different. As permitted transitions are more intensive than forbidden ones, as well as direct transitions are more probable than indirect ones, it is A D natural to expect that the inequality αB ω > αω > αω > will hold. In this way, if the deep impurity state is αC ω formed by contributions from different peaks, one will be able to distinguish the major coefficient value αω at the corresponding absorption threshold. Moreover, the spectral data can be used to extract information about the energy associated with the impurity level as well as information about the nature of the impurity state. These considerations form the theoretical base of experimental methodology proposed in this paper. 3. Samples and Experimental Methodology
The discussed methodology was applied to monocrystalline zinc selenide samples doped with transitional metals. The choice of the material is caused by a considerable research to ZnSe:Me, which features stimulated IR radiation at room temperature [4,5] because transition metal ions enter tetrahedral lattice where they become characterized with short life times and high quantum yield of luminescence. Moreover, the low value of the maximum phonon energy in ZnSe (ℏω0 ≈ 30 meV) increases quantum yield by lowering the nonradiative recombination rate. Also, ZnSe:Me crystals exhibit nonlinear absorption in mid-IR spectral ranges that offer promising perspective for Q-switches for μm lasers [6,7]. The presence of noncompensated magnetic moment in II–VI compounds doped with transitional metals is also promising for spintronics applications [8]. It is worth noting that all these properties can be observed if transitional metals enter into a cathion sub-lattice of ZnSe, where no charge compensation for 3D elements is necessary so that the crystalline matrix remains undistorted due to similarity of tetrahedral radii of zinc and impurity elements. As transitional metals technically can enter into any sub-lattice as well as into interstitial states, one should ensure their placement namely into the cathion sub-lattice, which can be achieved by optimal doping technology. One of the promising solutions concerns diffusion of 3D elements from a vapor phase in a closed volume in the presence of selenium vapors [9]. The latter prevent formation of vacancies in anion sub-lattice and discourage insertion of transitional metal atoms. Moreover, this technology maintains that the sample surface mirrors are smooth, 1 April 2014 / Vol. 53, No. 10 / APPLIED OPTICS
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Fig. 2. Transmission of ZnSe (1) and ZnSe:V (2) at 300 K.
making them suitable for optical measurements without any additional treatment. The spectra of optical transmission were measured with the infrared spectrometer IKS-21 in the energy ranges 0.5–2.6 eV at 300 K. To avoid optical recharge of the impurity, the samples were placed beyond the monochromator. Also, spectral scanning was performed from low-energy values onward [10]. To obtain absorption spectra from the transmission data, we used the relation for transmission T ω , absorption αω , and reflection Rω : T ω αω Rω 1:
(7)
Our studies have shown that in the spectral range of 0.5–2.6 eV, reflection spectra are almost independent on frequency, so that Eq. (7) can be simplified into T ω αω ≈ const. As we are interested in normalized values of T ω and αω , one can assume that αω ≈ 1 − T ω ;
(8)
where αω is normalized optical absorption spectra. The absorption data can be used to determine the ionization energy of the impurity level, as well as to provide information about the nature of the impurity state itself, which will be discussed in detail below. 4. Results and Discussion
The base substrates of ZnSe featured pronounced transparency exceeding 40% in wide energy ranges. This can be seen from optical transmission spectra showing a smooth curve for energies 0.5–2.5 eV, as
in Fig. 2. An abrupt decrease of T ω for photon energies approaching Eg of zinc selenide is caused by an increasing absorption coefficient that reaches 104 cm−1 for ℏω ≥ Eg. It is important that the highenergy tail of curve 1 reaches zero transparency at 2.7 eV, corresponding to Eg of ZnSe at 300 K. Doping ZnSe substrates with 3D elements decreases their absorption coefficient in different ways according to the impurity element. For ℏω < Eg, the optical transmission spectrum becomes structured (Fig. 2, curve 2 corresponding to ZnSe:V sample). It is worth mentioning that the shape of T ω curves and energy position of their structural irregularities is also defined by the doping element. Therefore, the optical absorption spectra contain a considerable amount of information on deep level parameters. To extract this data, it is most convenient to use absorption spectra calculated with Eq. (8) and presented in Fig. 3. As a 3D element can be in different charge states, it may produce energy levels located above or below the ground level of the impurity. Thus, the ground level of multi-charge impurity can be defined looking for the lowest energy band in the optical absorption spectra. As one can see from Fig. 3, for every ZnSe: Me sample there exists a specific low-energy absorption band, which was chosen for comparisons with analytical models of absorption. This procedure is illustrated below for the ZnSe:V sample. As one can see from Fig. 3, the absorption spectra of ZnSe:V contains the longest-wave band with a wide peak αmax at 0.8 eV, which according to the ω Lucovsky formula produces impurity level energy Et ≈ αmax ω ∕2 ≈ 0.4 eV. At the same time, the exact determination of Et (as well as optical transitions types) requires comparison of experimental curves with absorption coefficient models Eqs. (1)–(4). For this purpose, they must be converted to such a form that the resulting construct in the coordinates αn · ℏωm obtained from ℏω a linear relationship. Thus, the exponents n and m are determined by the type of optical transition and respectively, equal 2/3 and C 2 for αAω, 2 and 6 for αB ω, 2/3 and 2/3 for αω, 2 and 2 D for αω. The results of such comparison are shown in Fig. 4, which proves that the low-energy band is
Fig. 3. Optical absorption spectra for ZnSe:Me samples measured at 300 K. B10
APPLIED OPTICS / Vol. 53, No. 10 / 1 April 2014
Table 1.
3D Element Et (eV)
Ionization Energy of Deep Impurity Centers
Ti
V
Cr
Mn
Fe
Co
Ni
0.38
0.60
0.40
0.30
0.45
0.40
0.30
of the impurity absorption band corresponding to the transition mechanism illustrated in Fig. 1. It is worth noting that a reliable observation of this effect requires high-resistive samples to ensure low dark currents. The ZnSe:Me samples studied in this paper completely satisfy this requirement with their specific resistivity of 108 Ω · cm at room temperature [9]. 5. Conclusions Fig. 4. Low-energy tail of impurity absorption band in ZnSe:V A D C (open circles) fitted with Eqs. (1)–(4) for αB ω, αω , αω , and αω , respectively.
better described with the absorption coefficient αAω , Eq. (2), which corresponds to optical transitions from the valence band EV to the acceptor level of vanadium. It is worth mentioning that if vanadium centers would be of donor type (i.e., related to the conduction band), the transitions to such levels in the center of the Brillouin zone will be direct and permitted, and the corresponding absorption spectrum will be described with Eq. (1). However, as one can clearly see from Fig. 4, the experimental spectrum of the impurity band in ZnSe:V do not agree with any other absorption mechanism described with Eqs. (1), (3), and (4). The similar results were obtained for other metal impurities (Ti, Cr, Mn, Fe, Co, and Ni) introduced to ZnSe crystals. Performing the similar curve fitting, we defined ionization energy for each impurity level (measured from EV ), which is presented here in Table 1. Therefore, it is possible to confirm that 3D elements form acceptor centers in zinc selenide and the main absorption mechanism responsible for optical properties involves direct forbidden transitions from the valence band to the ground level of impurity. Obtained values of Et and optical transition information provide information on shape of impurity absorption bands. Calculations with Eq. (2) make an accurate description of experimental data for the low photon energies. The high-energy bands of absorption spectra are completely different, involving inter-center transitions between the ground and the excited states of 3D elements [11,12], so that these bands would not fit to any of the models, Eqs. (1)–(4). For the spectral ranges studied, no photoconductivity was observed because inter-band transitions do no lead to photo-generation of nonequilibrium carriers in a permitted energy band. Therefore, one can consider the presence of long-wave photoconductivity as an additional criterion proving the correct definition
We report that impurity absorption spectra can be used as a powerful tool for identification of ionization energy and nature of the deep impurity centers. These parameters can be found by comparison of the experimental spectra with analytical expressions accounting for interactions of a local center with the permitted energy bands. We used this methodology to study ZnSe:Me samples, showing that transitional metals form acceptor centers in zinc selenide with ionization energy ranging in 0.3–0.6 eV. The longwave absorption band observed in these materials is caused by direct forbidden transitions of electrons from the valence band to the ground state of impurity. The described methodology can be also used to study deep center parameters and absorption mechanisms involving them in other semiconductor crystals with tetrahedral crystalline lattice. References 1. A. G. Milnes, Deep Impurities in Semiconductors (Wiley, 1973). 2. J. C. Inkson, “Deep impurities in semiconductors. II. The optical cross sections,” J. Phys. C 14, 1093–1101 (1981). 3. G. Lucovsky, “On the photo-ionisation of deep impurity centres in semiconductors,” Solid State Commun. 3, 299–302 (1965). 4. V. I. Kozlovskii, Y. V. Korostelin, A. I. Landman, Y. P. Podmar’kov, and M. P. Frolov, “Efficient lasing of a Cr2+:ZnSe crystal grown from a vapour phase,” Quantum Electron. 33, 408–410 (2003). 5. N. N. Il’ichev, V. P. Danilov, V. P. Kalinushkin, M. I. Studenikin, P. V. Shapkin, and A. S. Nasibov, “Superluminescent roomtemperature Fe2+:ZnSe IR radiation source,” Quantum Electron. 38, 95–96 (2008). 6. A. V. Podlipensky, V. G. Shcherbitsky, N. V. Kuleshov, V. P. Mikhailov, V. I. Levchenko, and V. N. Yakimovich, “Cr2+:ZnSe and Co2+:ZnSe saturable-absorber Q-switches for 1.54 μm Er: glass laser,” Opt. Lett. 24, 960–962 (1999). 7. A. A. Voronov, V. I. Kozlovskii, Y. V. Korostelin, A. I. Landman, Y. P. Podmar’kov, V. G. Polushkin, and M. P. Frolov, “Passive Fe2+:ZnSe single-crystal Q switch for 3 μm lasers,” Quantum Electron. 36, 1–2 (2006). 8. M. Ziese and M. J. Thornton, Spin Electronics: Lecture Notes in Physics (Springer, 2001). 9. O. V. Kinzerska, “Physical properties of zinc selenide crystals doped with transitional metals,” Ph.D. dissertation (Chernivtsi, 2012). 10. O. V. Vakulenko and M. P. Lisitsa, Optical Recharge of Impurity in Semiconductors (Naukova, 1992). 11. E. M. Omel’yanovskiy and V. I. Fistul’, Impurities of Transitional Metals in Semiconductors (Metallurgia, 1984). 12. K. A. Kikoin, Electron Properties of Transition Metal Impurities in Semiconductors (Energoatomizdat, 1991).
1 April 2014 / Vol. 53, No. 10 / APPLIED OPTICS
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Yuri Fedkovych Chernivtsi National University, 2 Kotsyubynsky str., 58012 Chernivtsi, Ukraine
2 3
Centro de Investigación en Materiales Avanzados S.C., 120 Miguel de Cervantes, 31109 Chihuahua, Mexico
National Technical University of Ukraine “Kyiv Polytechnic Institute,” 37 Prospekt Peremohy, 03056 Kyiv, Ukraine *Corresponding author: [email protected] Received 15 November 2013; accepted 29 November 2013; posted 11 December 2013 (Doc. ID 199072); published 3 February 2014
We analyze physical models accounting for deep-level conduction band transitions to describe impurity absorption spectra in tetrahedral-structured semiconductors. The investigations were carried out for ZnSe crystals doped with transition metals (Ti, V, Cr, Mn, Fe, Co, Ni) from a vapor phase. It was shown that the impurities provide acceptor centers with ground state energy offset by 0.3–0.6 eV from the edge of the conduction band, forming long-wave bands in the absorption spectra of the materials studied. © 2014 Optical Society of America OCIS codes: (300.1030) Absorption; (300.6170) Spectra; (160.1890) Detector materials. http://dx.doi.org/10.1364/AO.53.0000B8
1. Introduction
Deep-level impurities in semiconductor materials are responsible for a multitude of physical effects, either useful for electronic applications or undesirable [1]. Therefore, more research should be focused on such impurities to discover details on physical and chemical phenomena occurring in such systems, energy spectra corresponding to deep levels, as well as controllable doping techniques required to achieve desired impurity parameters. Answering these questions is important for semiconductor material science and may provide useful hints for improvement of electronic devices. The situation is quite complicated due to the absence of a unified theory describing deep impurity centers so that experimental investigations in this field are extremely important to produce the data required for in-depth theoretical analysis. The preference should be given to nondestructive 1559-128X/14/1000B8-04$15.00/0 © 2014 Optical Society of America B8
APPLIED OPTICS / Vol. 53, No. 10 / 1 April 2014
methods that can be implied to monitor the sample practically at every stage of its formation and processing, i.e., during synthesis, annealing, doping, and so on. The obtained information will form a solid base for developing semiconductor materials with predetermined properties, also offering detailed data for analysis and understanding of deep impurity centers that is important for development of a unified theory explaining the physical processes that occurs at these impurities. This paper is dedicated to a partial solution of the aforementioned problem. We report the successful use of optical absorption spectra to study deep-level impurities as a useful tool to determine parameters of deep centers in different semiconductor materials. 2. Impurity Absorption Models
In the first place, it is necessary to emphasize that analytical expression describing the absorption spectra cannot be obtained from the first principles, at least at the present level of this numerical technique. Therefore, scientists have to use available physical
models, including those for tetrahedral crystals [2], where the wave function for the impurity is represented by the Bloch wave. As a consequence, the optical phenomena are described by excitation of an electron into conduction band EC and formation of a hole in the valence band EV , Fig. 1. In the spherical-symmetry band approximation one can obtain four expressions for cross-section σ in the absorption limit [2]. Taking into account that σ essentially defines the absorption process, one can find spectral dependence of the absorption coefficient αω as αB ω ∼
ℏω − Et 1∕2 ; ℏωℏω − Et ℏ2 γ 2 ∕2m 2
(1)
αAω ∼
ℏω − Et 3∕2 ; ℏωℏω − Et ℏ2 γ 2 ∕2m 2
(2)
1∕2 · ℏω−1 ; αD ω ∼ ℏω − Et
(3)
3∕2 · ℏω−1 : αC ω ∼ ℏω − Et
(4)
Here γ is the wavevector of the complex bandstructure, m is the particle’s effective mass, and Et is the energy of impurity level. Equations (1)–(4) describe direct permitted transitions αB ω , direct forbidden transitions αAω , indirect permitted transitions αD ω, and indirect forbidden transitions αC ω . Applying effective mass approximation Et ℏ2 γ 2 ∕2m to Eq. (2), one can obtain Lucovsky formula [3] that was written for δ-function potential of the impurity center. In this case transition number 1 shown in Fig. 1 should yield the absorption coefficient: αAω ∼ ℏω − Eg − Et 1∕2 · ℏω−1 ;
(5)
whereas transition number 2 should be characterized with αAω ∼ ℏω − Et 3∕2 · ℏω−3 :
(6)
In both cases, the ionization energy Et is measured from the edge of the valence band EV and the quantity Eg corresponds to the band gap of semiconductor. The Lucovsky formula predicts that αmax ≈ 2Et . ω
Fig. 1. Sketch of electron transitions involving a deep level Et .
However, in real crystals one often obtains Et > ℏ2 γ 2 ∕2m , which results in red-shift of the αAω peak bringing it closer to Et . In general, functions corresponding to real impurity centers will receive contributions from different band peaks. At the same time, such contributions will differ on energy scale so that the excitation process can be localized in the vicinity of a corresponding band. Moreover, the intensity of the absorption processes connected with different basis functions will be also different. As permitted transitions are more intensive than forbidden ones, as well as direct transitions are more probable than indirect ones, it is A D natural to expect that the inequality αB ω > αω > αω > will hold. In this way, if the deep impurity state is αC ω formed by contributions from different peaks, one will be able to distinguish the major coefficient value αω at the corresponding absorption threshold. Moreover, the spectral data can be used to extract information about the energy associated with the impurity level as well as information about the nature of the impurity state. These considerations form the theoretical base of experimental methodology proposed in this paper. 3. Samples and Experimental Methodology
The discussed methodology was applied to monocrystalline zinc selenide samples doped with transitional metals. The choice of the material is caused by a considerable research to ZnSe:Me, which features stimulated IR radiation at room temperature [4,5] because transition metal ions enter tetrahedral lattice where they become characterized with short life times and high quantum yield of luminescence. Moreover, the low value of the maximum phonon energy in ZnSe (ℏω0 ≈ 30 meV) increases quantum yield by lowering the nonradiative recombination rate. Also, ZnSe:Me crystals exhibit nonlinear absorption in mid-IR spectral ranges that offer promising perspective for Q-switches for μm lasers [6,7]. The presence of noncompensated magnetic moment in II–VI compounds doped with transitional metals is also promising for spintronics applications [8]. It is worth noting that all these properties can be observed if transitional metals enter into a cathion sub-lattice of ZnSe, where no charge compensation for 3D elements is necessary so that the crystalline matrix remains undistorted due to similarity of tetrahedral radii of zinc and impurity elements. As transitional metals technically can enter into any sub-lattice as well as into interstitial states, one should ensure their placement namely into the cathion sub-lattice, which can be achieved by optimal doping technology. One of the promising solutions concerns diffusion of 3D elements from a vapor phase in a closed volume in the presence of selenium vapors [9]. The latter prevent formation of vacancies in anion sub-lattice and discourage insertion of transitional metal atoms. Moreover, this technology maintains that the sample surface mirrors are smooth, 1 April 2014 / Vol. 53, No. 10 / APPLIED OPTICS
B9
Fig. 2. Transmission of ZnSe (1) and ZnSe:V (2) at 300 K.
making them suitable for optical measurements without any additional treatment. The spectra of optical transmission were measured with the infrared spectrometer IKS-21 in the energy ranges 0.5–2.6 eV at 300 K. To avoid optical recharge of the impurity, the samples were placed beyond the monochromator. Also, spectral scanning was performed from low-energy values onward [10]. To obtain absorption spectra from the transmission data, we used the relation for transmission T ω , absorption αω , and reflection Rω : T ω αω Rω 1:
(7)
Our studies have shown that in the spectral range of 0.5–2.6 eV, reflection spectra are almost independent on frequency, so that Eq. (7) can be simplified into T ω αω ≈ const. As we are interested in normalized values of T ω and αω , one can assume that αω ≈ 1 − T ω ;
(8)
where αω is normalized optical absorption spectra. The absorption data can be used to determine the ionization energy of the impurity level, as well as to provide information about the nature of the impurity state itself, which will be discussed in detail below. 4. Results and Discussion
The base substrates of ZnSe featured pronounced transparency exceeding 40% in wide energy ranges. This can be seen from optical transmission spectra showing a smooth curve for energies 0.5–2.5 eV, as
in Fig. 2. An abrupt decrease of T ω for photon energies approaching Eg of zinc selenide is caused by an increasing absorption coefficient that reaches 104 cm−1 for ℏω ≥ Eg. It is important that the highenergy tail of curve 1 reaches zero transparency at 2.7 eV, corresponding to Eg of ZnSe at 300 K. Doping ZnSe substrates with 3D elements decreases their absorption coefficient in different ways according to the impurity element. For ℏω < Eg, the optical transmission spectrum becomes structured (Fig. 2, curve 2 corresponding to ZnSe:V sample). It is worth mentioning that the shape of T ω curves and energy position of their structural irregularities is also defined by the doping element. Therefore, the optical absorption spectra contain a considerable amount of information on deep level parameters. To extract this data, it is most convenient to use absorption spectra calculated with Eq. (8) and presented in Fig. 3. As a 3D element can be in different charge states, it may produce energy levels located above or below the ground level of the impurity. Thus, the ground level of multi-charge impurity can be defined looking for the lowest energy band in the optical absorption spectra. As one can see from Fig. 3, for every ZnSe: Me sample there exists a specific low-energy absorption band, which was chosen for comparisons with analytical models of absorption. This procedure is illustrated below for the ZnSe:V sample. As one can see from Fig. 3, the absorption spectra of ZnSe:V contains the longest-wave band with a wide peak αmax at 0.8 eV, which according to the ω Lucovsky formula produces impurity level energy Et ≈ αmax ω ∕2 ≈ 0.4 eV. At the same time, the exact determination of Et (as well as optical transitions types) requires comparison of experimental curves with absorption coefficient models Eqs. (1)–(4). For this purpose, they must be converted to such a form that the resulting construct in the coordinates αn · ℏωm obtained from ℏω a linear relationship. Thus, the exponents n and m are determined by the type of optical transition and respectively, equal 2/3 and C 2 for αAω, 2 and 6 for αB ω, 2/3 and 2/3 for αω, 2 and 2 D for αω. The results of such comparison are shown in Fig. 4, which proves that the low-energy band is
Fig. 3. Optical absorption spectra for ZnSe:Me samples measured at 300 K. B10
APPLIED OPTICS / Vol. 53, No. 10 / 1 April 2014
Table 1.
3D Element Et (eV)
Ionization Energy of Deep Impurity Centers
Ti
V
Cr
Mn
Fe
Co
Ni
0.38
0.60
0.40
0.30
0.45
0.40
0.30
of the impurity absorption band corresponding to the transition mechanism illustrated in Fig. 1. It is worth noting that a reliable observation of this effect requires high-resistive samples to ensure low dark currents. The ZnSe:Me samples studied in this paper completely satisfy this requirement with their specific resistivity of 108 Ω · cm at room temperature [9]. 5. Conclusions Fig. 4. Low-energy tail of impurity absorption band in ZnSe:V A D C (open circles) fitted with Eqs. (1)–(4) for αB ω, αω , αω , and αω , respectively.
better described with the absorption coefficient αAω , Eq. (2), which corresponds to optical transitions from the valence band EV to the acceptor level of vanadium. It is worth mentioning that if vanadium centers would be of donor type (i.e., related to the conduction band), the transitions to such levels in the center of the Brillouin zone will be direct and permitted, and the corresponding absorption spectrum will be described with Eq. (1). However, as one can clearly see from Fig. 4, the experimental spectrum of the impurity band in ZnSe:V do not agree with any other absorption mechanism described with Eqs. (1), (3), and (4). The similar results were obtained for other metal impurities (Ti, Cr, Mn, Fe, Co, and Ni) introduced to ZnSe crystals. Performing the similar curve fitting, we defined ionization energy for each impurity level (measured from EV ), which is presented here in Table 1. Therefore, it is possible to confirm that 3D elements form acceptor centers in zinc selenide and the main absorption mechanism responsible for optical properties involves direct forbidden transitions from the valence band to the ground level of impurity. Obtained values of Et and optical transition information provide information on shape of impurity absorption bands. Calculations with Eq. (2) make an accurate description of experimental data for the low photon energies. The high-energy bands of absorption spectra are completely different, involving inter-center transitions between the ground and the excited states of 3D elements [11,12], so that these bands would not fit to any of the models, Eqs. (1)–(4). For the spectral ranges studied, no photoconductivity was observed because inter-band transitions do no lead to photo-generation of nonequilibrium carriers in a permitted energy band. Therefore, one can consider the presence of long-wave photoconductivity as an additional criterion proving the correct definition
We report that impurity absorption spectra can be used as a powerful tool for identification of ionization energy and nature of the deep impurity centers. These parameters can be found by comparison of the experimental spectra with analytical expressions accounting for interactions of a local center with the permitted energy bands. We used this methodology to study ZnSe:Me samples, showing that transitional metals form acceptor centers in zinc selenide with ionization energy ranging in 0.3–0.6 eV. The longwave absorption band observed in these materials is caused by direct forbidden transitions of electrons from the valence band to the ground state of impurity. The described methodology can be also used to study deep center parameters and absorption mechanisms involving them in other semiconductor crystals with tetrahedral crystalline lattice. References 1. A. G. Milnes, Deep Impurities in Semiconductors (Wiley, 1973). 2. J. C. Inkson, “Deep impurities in semiconductors. II. The optical cross sections,” J. Phys. C 14, 1093–1101 (1981). 3. G. Lucovsky, “On the photo-ionisation of deep impurity centres in semiconductors,” Solid State Commun. 3, 299–302 (1965). 4. V. I. Kozlovskii, Y. V. Korostelin, A. I. Landman, Y. P. Podmar’kov, and M. P. Frolov, “Efficient lasing of a Cr2+:ZnSe crystal grown from a vapour phase,” Quantum Electron. 33, 408–410 (2003). 5. N. N. Il’ichev, V. P. Danilov, V. P. Kalinushkin, M. I. Studenikin, P. V. Shapkin, and A. S. Nasibov, “Superluminescent roomtemperature Fe2+:ZnSe IR radiation source,” Quantum Electron. 38, 95–96 (2008). 6. A. V. Podlipensky, V. G. Shcherbitsky, N. V. Kuleshov, V. P. Mikhailov, V. I. Levchenko, and V. N. Yakimovich, “Cr2+:ZnSe and Co2+:ZnSe saturable-absorber Q-switches for 1.54 μm Er: glass laser,” Opt. Lett. 24, 960–962 (1999). 7. A. A. Voronov, V. I. Kozlovskii, Y. V. Korostelin, A. I. Landman, Y. P. Podmar’kov, V. G. Polushkin, and M. P. Frolov, “Passive Fe2+:ZnSe single-crystal Q switch for 3 μm lasers,” Quantum Electron. 36, 1–2 (2006). 8. M. Ziese and M. J. Thornton, Spin Electronics: Lecture Notes in Physics (Springer, 2001). 9. O. V. Kinzerska, “Physical properties of zinc selenide crystals doped with transitional metals,” Ph.D. dissertation (Chernivtsi, 2012). 10. O. V. Vakulenko and M. P. Lisitsa, Optical Recharge of Impurity in Semiconductors (Naukova, 1992). 11. E. M. Omel’yanovskiy and V. I. Fistul’, Impurities of Transitional Metals in Semiconductors (Metallurgia, 1984). 12. K. A. Kikoin, Electron Properties of Transition Metal Impurities in Semiconductors (Energoatomizdat, 1991).
1 April 2014 / Vol. 53, No. 10 / APPLIED OPTICS
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