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Tunneling phenomena of trapped holes in ZnO: Li
ARTICLE IN PRESS
Physica B 376–377 (2006) 682–685 www.elsevier.com/locate/physb
Tunneling phenomena of trapped holes in ZnO: Li B.K. Meyera, A. Hofstaettera, V.V. Lagutab a
Physics Institute, Justus Liebig University Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany Institute for Problems of Material Sciences, NASc of Ukraine, Krjijanovskogo 3, 03142 Kiev, Ukraine
b
Abstract We report on magnetic resonance (ESR) experiments on the group-I-acceptor Li in ZnO. As shown in previous investigations Li produces deep acceptor states whose properties are studied by temperature dependent ESR. A tunneling process between axial and nonaxial centers is observed and analyzed in detail. r 2006 Elsevier B.V. All rights reserved. Keywords: ZnO; Li-center; Tunneling
1. Introduction Many attempts have been undertaken to dope ZnO ptype, and still now the subject is very controversial and contradictory. Lander [1] reported in 1960 on the donor and acceptor action of Li, and already gave hints as to the possible defect structures. For the donor center he proposed a molecular ion like defect LiO, and for the acceptor Li substitutional on Zn site. In 1963 Schneider et al. [2] reported on the electron paramagnetic resonance (ESR) of ZnO:Li which was extended in 1968 by a very detailed work of Schirmer [3]. The acceptor seen in ESR was assigned to an isolated LiZn, but the analysis of the hyperfine structure showed a substantial relaxation of the Li-O bonds resulting in a deep, distorted center with a binding energy of 800 meV. The crystal structure of zinc oxide is hexagonal (P63mc) with a ¼ 3.25 A˚ and c ¼ 5.12 A˚. The Zn2+ ions are tetragonally coordinated to four O2 ions, and the Zn d-electrons hybridize with the O pelectrons. In addition, it was found recently that lithium also induces a ferroelectric-like behavior in ZnO with a dielectric susceptibility anomaly around 330 K [4,5] that may indicate an off-center position of Li+ with respect to the Zn2+ lattice site. From electron spin resonance investigations [3], in particular, it was found that ultraviolet irradiation of E-mail address: [email protected] (B.K. Meyer). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.171
ZnO crystals doped with lithium at temperatures below 200 K leads to the creation of O—Li+ hole centers, i.e., a hole is trapped by a host oxygen ion in the neighborhood of the Li+ ion (axial center, when the hole is trapped on an oxygen atom along the c-axis, non-axial center otherwise; see Fig. 1). In principle, a hole can be trapped at each of the four oxygens of the tetrahedron with equal probability. However, when the irradiation is stopped, the hole populations on different positions relax to an equilibrium state because in ZnO lattice the four oxygen positions are not equivalent. For ZnO:Li the axial configuration is favored over the non-axial configuration. There is an energetic barrier between the two configurations which is 15 meV for ZnO:Li and 35 meV for ZnO:Na, where contrary to ZnO:Li the axial configuration is metastable.
2. Experimental details The bulk ZnO:Li (Na) samples were grown by a vapor phase deposition technique and provided by R. Helbig. They are of hexagonal shape with three non-equivalent axes of growth, are colorless, transparent, and highly resistive. ESR was performed on a Bruker ESP 900E spectrometer operating at a microwave frequency of 9.5 GHz. The temperature of the sample could be adjusted between 3.7 K and room temperature. A HeCd laser working at 325 and
ARTICLE IN PRESS B.K. Meyer et al. / Physica B 376–377 (2006) 682–685
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Fig. 2. Temperature dependence of the equilibrium intensity ratio between axial and non-axial centers measured after turning off the light irradiation. The slope of the line gives the energy difference E eq between two non-equivalent lattice sites for trapped holes as it is shown in the insert together with the corresponding energy diagram.
Fig. 1. ESR spectra of O—Li+ centers in ZnO: Li: (a) under light irradiation and (b) after turning off the light irradiation. The insert shows a fragment of ZnO lattice with O—Li+ centers.
442 nm was used for the optical irradiation of the samples directly in the cavity of the spectrometer. 3. Experimental results The ESR spectra of Li-doped ZnO single crystals, irradiated at 50 K with blue light (442 nm), consist of two sets of lines having, however, different angular dependencies (Fig. 1(a)). One group of lines with well resolved hyperfine (hf) structure has pure axial symmetry around the c-axis of the crystal. In agreement with previous interpretation [3], the paramagnetic center responsible for this spectrum and called ‘‘axial’’ in the following corresponds to a hole trapped at an oxygen ion located along the c-axis of the crystal in the neighborhood of the Li+ ion (see Fig. 1). The second set of ESR lines contains three spectra which are nearly axially symmetric with respect to the non-axial Li— O bond directions. The paramagnetic centers responsible for these spectra (called ‘‘non-axial’’) correspond to a hole trapped at one of the non-axially bound oxygen ions (Fig. 1). The detailed description of the O—Li+ ESR spectra and full set of the spectral parameters (principal values of the g and hf tensors and corresponding principal axes orientations) can be found in Ref. [3]. In the present
paper we pay attention to the problem of the thermal stability of the O—Li+ non-axial centers because they show in some respect an unexpected behavior. When the light irradiation is stopped, the intensity of the non-axial centers decreases to an equilibrium value (Fig. 2), which depends on the temperature. This is due to the fact that the axial sites are favored by the polar part of the crystal field and the equilibrium partition between axial and non-axial centers is determined by their energy separation. In the equilibrium state, i.e., a long time after the light being turned off, the populations of holes between these two energy levels obey a Boltzmann law N axial ¼ expðE eq =kTÞ. N non-axial This ratio is proportional to the ratio of ESR intensities of corresponding centers. The analysis of their temperature dependence is presented in Fig. 2. Here the slope of the line gives the energy difference between the two lattice sites of the O—Li+ centers, i.e., the value of the asymmetry of their double-well potential. We assume that all three non-axial positions are completely equivalent and, thus, have the same potential well. Note that the energy E eq obtained by us is two times larger then reported in Ref. [3]. The reason for such a large discrepancy in the measured energies is not completely clear. It might be due to the fact that in Ref. [3] the ratio I axial =I nonaxial was measured at T480 K, where it changes with temperature only by 2–3 times, while in our measurements this range extended over two orders in magnitude. Therefore, the present measurements should give a more reliable result. At low temperatures this equilibrium state is not established immediately. The decay of the non-axial centers
ARTICLE IN PRESS 684
B.K. Meyer et al. / Physica B 376–377 (2006) 682–685
mechanisms can be distinguished for the O—Li+ hole center: (i) Simple tunneling transitions or more generally phonon-assisted tunneling transitions in the ground state with the relaxation time 1 d , tph tanh d kT where " #1=2 U 2 d¼G þ1 . G
(i) Even at the lowest temperatures used in the investigation, about 8 K, holes trapped at non-axial sites escape to the axial site. (ii) A pre-exponential factor t0 ¼ 1:2 103 s is more than 9 orders of magnitude higher than expected for a ‘‘jump’’ of a charged particle over a potential barrier. For such a process t0 is usually of the order of the classical oscillation frequency (1012–1014 s).
G and U are the tunneling splitting and the asymmetry of the potential wells, respectively. In our case U is equal to Eeq. Since the asymmetry of the potential wells is large, we can assume d=kTb1, as in the case of the O—Al3+ hole center in SiO2. There the tunneling splitting G is very small, only of the order of 103–104 meV (5–10 mK) [7]. In this approximation tph becomes temperature independent. The tunneling probability in the ground state for the holes in ZnO: Li is very small even for phonon-assisted transitions. Respectively, the correspondent relaxation time is extremely long, around 400 s. Reasons for that are the high potential barrier between the two non-equivalent lattice sites where the hole can localize and, more important, the relatively large width of this potential barrier due to the relatively large distance (E3.3 A˚) between oxygen ions in the relevant tetrahedron. Again, for a comparison, in SiO2 the relaxation times for similar tunneling transitions of holes are of order of 103 s. Here, however, a hole tunnels between two equivalent sites which are separated by a shorter distance (E2.6 A˚). (ii) As the temperature increases, the relaxation becomes much faster. The relaxation time decreases now exponentially with temperature (Fig. 3). This points to tunneling transitions via a high-lying intermediate state at Energy E n . According to Sussmann’s theory [6,7] the expression for the transition probability or, equivalently, relaxation time has the same form as in the case of simple thermal transitions over the potential barrier: " #1=2 _ U 2 tn ¼ t0n expðE n =kTÞ with t0n ¼ þ1 , 2G G
Both experimental facts point to a tunneling mechanism being responsible for the relaxation process of the trapped hole between two possible non-equivalent sites in the lattice of ZnO. In a general case, a charged particle, being situated in the double minimum potential well, can take several paths to cross the potential barrier (see, e.g., Refs. [6,7]). The total transition probability is given by the sum of the transition probabilities of P all different path ways. The relaxation time becomes t1 ¼ ðtn Þ1 , where tn is the relaxation time of the nth relaxation mechanism. In accordance with our experimental data (Fig. 3) two types of the transition
where however, the pre-exponential factor t0 is not only determined by the classical oscillation frequency, but also by the parameters of the potential wells. Using this expression one can calculate the tunneling splitting G, because all other parameters are already known. From the relation t0n ¼ ð_=2G2 Þ 103 s it follows that G is about 2.5 104 meV. This value is comparable with the value obtained for hole tunneling in SiO2, where it was derived from dielectric relaxation data. To summarize briefly, we have investigated the processes how the equilibrium population for the two non-equivalent sites of the holes trapped at oxygen ions near the Li impurity in ZnO is established. Measurements of the
Fig. 3. ESR intensity decay of non-axial O—Li+ centers taken at several temperatures. The insert shows the temperature dependence of the relaxation time of non-axial centers. Solid lines in both the figure and its insert are numerical fits of the data (see text).
and, respectively, the increase in the concentration of the axial centers follows an exponential law (Fig. 3): I ¼ I 0 expðt=tÞ, where I 0 is the initial concentration and t is the decay time or relaxation time for the redistribution of population between axial and non-axial sites. This decay time depends on temperature as depicted in the insert of Fig. 3. It is of the order of 400 s at To25 K and nearly temperature independent in this temperature range. At higher temperatures, a transition to an exponential dependence t ¼ t0 expðE=kTÞ takes place, where E ¼ 33 meV and t0 ¼ 1:2 103 s. Here we note two experimental facts:
ARTICLE IN PRESS B.K. Meyer et al. / Physica B 376–377 (2006) 682–685
temperature dependence of the time at which this equilibrium happens, i.e., the relaxation time, show that at low temperatures To25 K the main mechanism is direct and/or phonon-assisted tunneling in the ground state from the non-axial site to the axial centers. These transitions have a very low probability with slow and temperature-independent relaxation time (E400 s). For T425 K the transitions strongly accelerate and the relaxation time becomes exponentially dependent on temperature. The corresponding relaxation mechanism was described in a model which implies tunneling transitions via excited high-lying levels in the double minimum potential well for the holes. The following parameters are obtained for the potential wells: asymmetry of the potential wells E eq ¼ 0:34ð2Þ meV, distance to the relevant high-lying states E n ¼ 0:33ð1Þ meV, and tunneling splitting G ¼ 2:5 104 meV. One can see from the parameters that the asymmetry of the double minimum
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potential well is very large in comparison to the tunneling splitting. Therefore, the holes in ZnO: Li are strongly localized particles. It should be noted that tunneling transitions of holes between the three equivalent non-axial centers due to negligible asymmetry of their potential wells occur much faster than those between non-axial and axial centers. References [1] [2] [3] [4]
J.J. Lander, J. Phys. Chem. Solids 15 (1960) 324. J. Schneider, O. Schirmer, Z. Naturforsch. A 18 (1963) 20. O.F. Schirmer, J. Phys. Chem. Solids 29 (1968) 1407. A. Onodera, N. Tamaki, Y. Kawamura, T. Sawada, H. Yamashita, Jpn. J. Appl. Phys. 35 (1996) 5160. [5] A. Onodera, N. Tamaki, K. Kazuo, H. Yamashita, Jpn. J. Appl. Phys. 36 (1997) 6008. [6] J.A. Sussmann, J. Phys. Chem. Solids 28 (1967) 1643. [7] W.J. De Vos, J. Volger, Physica 47 (1970) 13.
Physica B 376–377 (2006) 682–685 www.elsevier.com/locate/physb
Tunneling phenomena of trapped holes in ZnO: Li B.K. Meyera, A. Hofstaettera, V.V. Lagutab a
Physics Institute, Justus Liebig University Giessen, Heinrich-Buff-Ring 16, 35392 Giessen, Germany Institute for Problems of Material Sciences, NASc of Ukraine, Krjijanovskogo 3, 03142 Kiev, Ukraine
b
Abstract We report on magnetic resonance (ESR) experiments on the group-I-acceptor Li in ZnO. As shown in previous investigations Li produces deep acceptor states whose properties are studied by temperature dependent ESR. A tunneling process between axial and nonaxial centers is observed and analyzed in detail. r 2006 Elsevier B.V. All rights reserved. Keywords: ZnO; Li-center; Tunneling
1. Introduction Many attempts have been undertaken to dope ZnO ptype, and still now the subject is very controversial and contradictory. Lander [1] reported in 1960 on the donor and acceptor action of Li, and already gave hints as to the possible defect structures. For the donor center he proposed a molecular ion like defect LiO, and for the acceptor Li substitutional on Zn site. In 1963 Schneider et al. [2] reported on the electron paramagnetic resonance (ESR) of ZnO:Li which was extended in 1968 by a very detailed work of Schirmer [3]. The acceptor seen in ESR was assigned to an isolated LiZn, but the analysis of the hyperfine structure showed a substantial relaxation of the Li-O bonds resulting in a deep, distorted center with a binding energy of 800 meV. The crystal structure of zinc oxide is hexagonal (P63mc) with a ¼ 3.25 A˚ and c ¼ 5.12 A˚. The Zn2+ ions are tetragonally coordinated to four O2 ions, and the Zn d-electrons hybridize with the O pelectrons. In addition, it was found recently that lithium also induces a ferroelectric-like behavior in ZnO with a dielectric susceptibility anomaly around 330 K [4,5] that may indicate an off-center position of Li+ with respect to the Zn2+ lattice site. From electron spin resonance investigations [3], in particular, it was found that ultraviolet irradiation of E-mail address: [email protected] (B.K. Meyer). 0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.171
ZnO crystals doped with lithium at temperatures below 200 K leads to the creation of O—Li+ hole centers, i.e., a hole is trapped by a host oxygen ion in the neighborhood of the Li+ ion (axial center, when the hole is trapped on an oxygen atom along the c-axis, non-axial center otherwise; see Fig. 1). In principle, a hole can be trapped at each of the four oxygens of the tetrahedron with equal probability. However, when the irradiation is stopped, the hole populations on different positions relax to an equilibrium state because in ZnO lattice the four oxygen positions are not equivalent. For ZnO:Li the axial configuration is favored over the non-axial configuration. There is an energetic barrier between the two configurations which is 15 meV for ZnO:Li and 35 meV for ZnO:Na, where contrary to ZnO:Li the axial configuration is metastable.
2. Experimental details The bulk ZnO:Li (Na) samples were grown by a vapor phase deposition technique and provided by R. Helbig. They are of hexagonal shape with three non-equivalent axes of growth, are colorless, transparent, and highly resistive. ESR was performed on a Bruker ESP 900E spectrometer operating at a microwave frequency of 9.5 GHz. The temperature of the sample could be adjusted between 3.7 K and room temperature. A HeCd laser working at 325 and
ARTICLE IN PRESS B.K. Meyer et al. / Physica B 376–377 (2006) 682–685
683
Fig. 2. Temperature dependence of the equilibrium intensity ratio between axial and non-axial centers measured after turning off the light irradiation. The slope of the line gives the energy difference E eq between two non-equivalent lattice sites for trapped holes as it is shown in the insert together with the corresponding energy diagram.
Fig. 1. ESR spectra of O—Li+ centers in ZnO: Li: (a) under light irradiation and (b) after turning off the light irradiation. The insert shows a fragment of ZnO lattice with O—Li+ centers.
442 nm was used for the optical irradiation of the samples directly in the cavity of the spectrometer. 3. Experimental results The ESR spectra of Li-doped ZnO single crystals, irradiated at 50 K with blue light (442 nm), consist of two sets of lines having, however, different angular dependencies (Fig. 1(a)). One group of lines with well resolved hyperfine (hf) structure has pure axial symmetry around the c-axis of the crystal. In agreement with previous interpretation [3], the paramagnetic center responsible for this spectrum and called ‘‘axial’’ in the following corresponds to a hole trapped at an oxygen ion located along the c-axis of the crystal in the neighborhood of the Li+ ion (see Fig. 1). The second set of ESR lines contains three spectra which are nearly axially symmetric with respect to the non-axial Li— O bond directions. The paramagnetic centers responsible for these spectra (called ‘‘non-axial’’) correspond to a hole trapped at one of the non-axially bound oxygen ions (Fig. 1). The detailed description of the O—Li+ ESR spectra and full set of the spectral parameters (principal values of the g and hf tensors and corresponding principal axes orientations) can be found in Ref. [3]. In the present
paper we pay attention to the problem of the thermal stability of the O—Li+ non-axial centers because they show in some respect an unexpected behavior. When the light irradiation is stopped, the intensity of the non-axial centers decreases to an equilibrium value (Fig. 2), which depends on the temperature. This is due to the fact that the axial sites are favored by the polar part of the crystal field and the equilibrium partition between axial and non-axial centers is determined by their energy separation. In the equilibrium state, i.e., a long time after the light being turned off, the populations of holes between these two energy levels obey a Boltzmann law N axial ¼ expðE eq =kTÞ. N non-axial This ratio is proportional to the ratio of ESR intensities of corresponding centers. The analysis of their temperature dependence is presented in Fig. 2. Here the slope of the line gives the energy difference between the two lattice sites of the O—Li+ centers, i.e., the value of the asymmetry of their double-well potential. We assume that all three non-axial positions are completely equivalent and, thus, have the same potential well. Note that the energy E eq obtained by us is two times larger then reported in Ref. [3]. The reason for such a large discrepancy in the measured energies is not completely clear. It might be due to the fact that in Ref. [3] the ratio I axial =I nonaxial was measured at T480 K, where it changes with temperature only by 2–3 times, while in our measurements this range extended over two orders in magnitude. Therefore, the present measurements should give a more reliable result. At low temperatures this equilibrium state is not established immediately. The decay of the non-axial centers
ARTICLE IN PRESS 684
B.K. Meyer et al. / Physica B 376–377 (2006) 682–685
mechanisms can be distinguished for the O—Li+ hole center: (i) Simple tunneling transitions or more generally phonon-assisted tunneling transitions in the ground state with the relaxation time 1 d , tph tanh d kT where " #1=2 U 2 d¼G þ1 . G
(i) Even at the lowest temperatures used in the investigation, about 8 K, holes trapped at non-axial sites escape to the axial site. (ii) A pre-exponential factor t0 ¼ 1:2 103 s is more than 9 orders of magnitude higher than expected for a ‘‘jump’’ of a charged particle over a potential barrier. For such a process t0 is usually of the order of the classical oscillation frequency (1012–1014 s).
G and U are the tunneling splitting and the asymmetry of the potential wells, respectively. In our case U is equal to Eeq. Since the asymmetry of the potential wells is large, we can assume d=kTb1, as in the case of the O—Al3+ hole center in SiO2. There the tunneling splitting G is very small, only of the order of 103–104 meV (5–10 mK) [7]. In this approximation tph becomes temperature independent. The tunneling probability in the ground state for the holes in ZnO: Li is very small even for phonon-assisted transitions. Respectively, the correspondent relaxation time is extremely long, around 400 s. Reasons for that are the high potential barrier between the two non-equivalent lattice sites where the hole can localize and, more important, the relatively large width of this potential barrier due to the relatively large distance (E3.3 A˚) between oxygen ions in the relevant tetrahedron. Again, for a comparison, in SiO2 the relaxation times for similar tunneling transitions of holes are of order of 103 s. Here, however, a hole tunnels between two equivalent sites which are separated by a shorter distance (E2.6 A˚). (ii) As the temperature increases, the relaxation becomes much faster. The relaxation time decreases now exponentially with temperature (Fig. 3). This points to tunneling transitions via a high-lying intermediate state at Energy E n . According to Sussmann’s theory [6,7] the expression for the transition probability or, equivalently, relaxation time has the same form as in the case of simple thermal transitions over the potential barrier: " #1=2 _ U 2 tn ¼ t0n expðE n =kTÞ with t0n ¼ þ1 , 2G G
Both experimental facts point to a tunneling mechanism being responsible for the relaxation process of the trapped hole between two possible non-equivalent sites in the lattice of ZnO. In a general case, a charged particle, being situated in the double minimum potential well, can take several paths to cross the potential barrier (see, e.g., Refs. [6,7]). The total transition probability is given by the sum of the transition probabilities of P all different path ways. The relaxation time becomes t1 ¼ ðtn Þ1 , where tn is the relaxation time of the nth relaxation mechanism. In accordance with our experimental data (Fig. 3) two types of the transition
where however, the pre-exponential factor t0 is not only determined by the classical oscillation frequency, but also by the parameters of the potential wells. Using this expression one can calculate the tunneling splitting G, because all other parameters are already known. From the relation t0n ¼ ð_=2G2 Þ 103 s it follows that G is about 2.5 104 meV. This value is comparable with the value obtained for hole tunneling in SiO2, where it was derived from dielectric relaxation data. To summarize briefly, we have investigated the processes how the equilibrium population for the two non-equivalent sites of the holes trapped at oxygen ions near the Li impurity in ZnO is established. Measurements of the
Fig. 3. ESR intensity decay of non-axial O—Li+ centers taken at several temperatures. The insert shows the temperature dependence of the relaxation time of non-axial centers. Solid lines in both the figure and its insert are numerical fits of the data (see text).
and, respectively, the increase in the concentration of the axial centers follows an exponential law (Fig. 3): I ¼ I 0 expðt=tÞ, where I 0 is the initial concentration and t is the decay time or relaxation time for the redistribution of population between axial and non-axial sites. This decay time depends on temperature as depicted in the insert of Fig. 3. It is of the order of 400 s at To25 K and nearly temperature independent in this temperature range. At higher temperatures, a transition to an exponential dependence t ¼ t0 expðE=kTÞ takes place, where E ¼ 33 meV and t0 ¼ 1:2 103 s. Here we note two experimental facts:
ARTICLE IN PRESS B.K. Meyer et al. / Physica B 376–377 (2006) 682–685
temperature dependence of the time at which this equilibrium happens, i.e., the relaxation time, show that at low temperatures To25 K the main mechanism is direct and/or phonon-assisted tunneling in the ground state from the non-axial site to the axial centers. These transitions have a very low probability with slow and temperature-independent relaxation time (E400 s). For T425 K the transitions strongly accelerate and the relaxation time becomes exponentially dependent on temperature. The corresponding relaxation mechanism was described in a model which implies tunneling transitions via excited high-lying levels in the double minimum potential well for the holes. The following parameters are obtained for the potential wells: asymmetry of the potential wells E eq ¼ 0:34ð2Þ meV, distance to the relevant high-lying states E n ¼ 0:33ð1Þ meV, and tunneling splitting G ¼ 2:5 104 meV. One can see from the parameters that the asymmetry of the double minimum
685
potential well is very large in comparison to the tunneling splitting. Therefore, the holes in ZnO: Li are strongly localized particles. It should be noted that tunneling transitions of holes between the three equivalent non-axial centers due to negligible asymmetry of their potential wells occur much faster than those between non-axial and axial centers. References [1] [2] [3] [4]
J.J. Lander, J. Phys. Chem. Solids 15 (1960) 324. J. Schneider, O. Schirmer, Z. Naturforsch. A 18 (1963) 20. O.F. Schirmer, J. Phys. Chem. Solids 29 (1968) 1407. A. Onodera, N. Tamaki, Y. Kawamura, T. Sawada, H. Yamashita, Jpn. J. Appl. Phys. 35 (1996) 5160. [5] A. Onodera, N. Tamaki, K. Kazuo, H. Yamashita, Jpn. J. Appl. Phys. 36 (1997) 6008. [6] J.A. Sussmann, J. Phys. Chem. Solids 28 (1967) 1643. [7] W.J. De Vos, J. Volger, Physica 47 (1970) 13.