- Email: [email protected]
Deep centers in bulk AlN and their relation to low-angle dislocation boundaries
ARTICLE IN PRESS Physica B 404 (2009) 4939–4941
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Deep centers in bulk AlN and their relation to low-angle dislocation boundaries A.Y. Polyakov a,, N.B. Smirnov a, A.V. Govorkov a, T.G. Yugova a, K.D. Scherbatchev a, O.A. Avdeev b, T.Yu. Chemekova b, E.N. Mokhov b, S.S. Nagalyuk b, H. Helava b, Yu.N. Makarov b a b
Institute of Rare Metals, B. Tolmachevsky, 5, Moscow, 119017, Russia Nitride Crystals Ltd., 27 Engels Av., St. Petersburg, Russia
a r t i c l e in fo
Keywords: Bulk AlN Physical vapor transport Deep traps Dislocation boundaries
abstract Structural properties, electrical properties, deep traps spectra, optical properties of bulk 50-mmdiameter AlN crystals prepared by physical vapor transport (PVT) were studied by means of X-ray diffraction, selective etching, admittance spectroscopy, microcathodoluminescence (MCL). The crystals had a low dislocation density with dislocations forming a well defined cellular structure. The dominant electron traps had the ionization energy of 0.26 and 0.65 eV with low concentrations close to some 1013 cm 3 and some 1015 cm 3, respectively. The Fermi level was pinned near the 0.26 eV electron traps. These traps were shown to give rise to a strong persistent photoconductivity and photocapacitance. MCL spectra of the studied crystal were dominated by the 3.3, 4.2 and 5.5 eV luminescence bands. The intensity of the strongest 3.3 eV band was greatly enhanced in the vicinity of low-angle dislocation boundaries. & 2009 Published by Elsevier B.V.
1. Introduction Bulk AlN crystals with low dislocation density can be prepared by modified physical vapor transport (PVT) technique [1,2] and such crystals are of great interest as substrates for heteroepitaxial growth of Al-rich AlGaN-based light emitting diodes and of AlGaN/GaN-based high electron mobility transistor structures. Despite the obvious practical and scientific interest of studying the properties of such bulk AlN crystals the nature of deep traps determining the Fermi level pinning, the recombination lifetime and the type of optical transitions in such crystals is not well understood. In this paper we present the results of our studies of the properties of large diameter undoped bulk AlN crystals.
grow about 10-mm-long AlN crystal that was then sliced into 0.5 mm-thick wafers and chemo-mechanically polished. The wafer we studied was the closest to the seed AlN crystal. It was characterized by selective etching in KOH/NaOH eutectic and by high resolution X-ray diffraction (HRXRD) (triple-axis arrangement, Bede System 1 spectrometer with Cu Ka radiation). Electrical properties were studied using current–voltage (I–V), capacitance–voltage (C–V) and admittance spectra [4] measurements on Au Schottky diodes deposited in vacuum through a shadow mask [5]. MCL spectra measurements and MCL imaging of the sample was performed as described in Ref. [6].
3. Results and discussion 2. Experimental 50-mm-diameter bulk AlN crystal studied in this paper was grown by two-stage modified PVT process described in some detail in Ref. [3]. Growth was performed in carbonized Ta crucibles, from pre-synthesized polycrystalline AlN charge. At the first stage AlN layer with thickness of about 2 mm was deposited on a high quality 6H-SiC seed crystal, the AlN layer was cut from the SiC and used at the second stage of the process to Corresponding author. Tel.: + 7499 788 90 90; fax: +7499 88 90 90.
E-mail address: [email protected] (A.Y. Polyakov). 0921-4526/$ - see front matter & 2009 Published by Elsevier B.V. doi:10.1016/j.physb.2009.09.052
The full width at half maximum of the triple-axis HRXRD (0 0 0 2) reflection was 0.171, but the diffraction pattern also showed side peaks indicating the presence of misoriented grains with misorientation up to 21. Selective etching patterns revealed the presence of well defined dislocation etch pits and showed that the majority of dislocations are agglomerated in low-angle dislocation boundaries with characteristic grain size from some 10 to 100 mm. I–V characteristics of the Au Schottky diodes prepared on the studied sample showed that it had n-type conductivity with the room temperature resistivity deduced from the series resistance of the forward I–V characteristic close to 107 Ocm. The temperature dependence of the forward current at
ARTICLE IN PRESS A.Y. Polyakov et al. / Physica B 404 (2009) 4939–4941
10-3
Current (A)
10-5 after GaN LED
10-7 10-9
Dark
10-11 Ea=260 meV 10
-13
0
2
4
6 1000/T (1/K)
8
10
12
Fig. 1. The temperature dependence of the forward current at 10 V for the Au Schottky diode prepared on the studied AlN sample, the solid curve was measured in the dark, the dashed curve (marked as ‘‘PPC’’) was measured after illumination at 85 K with 2.8 eV GaN light emitting diode.
45 40
PPC
Capacitance (pF)
35 30
Dark
25
0.65 eV
20 15 10
0.26 eV
5 0 150
200
250 300 Temperature (K)
350
400
Fig. 2. The temperature dependence of capacitance at 500 Hz measured on the studied Au/AlN Schottky diode in the dark (solid curve) and after illumination with 2.8 eV GaN light emitting diode (dash-dotted curve marked as PPC).
high forward voltage of 10 V that is equivalent to the temperature dependence of conductivity showed the activation energy of 0.26 eV that should be close to the position of the trap pinning the Fermi level (Fig. 1). Fig. 2 shows the temperature dependence of capacitance measured at low frequency of 500 Hz. Two steps in capacitance can be clearly seen. Standard admittance spectroscopy analysis of the dependence of the temperature of the step on measurement frequency [4] showed that the lowtemperature step corresponded to electron trap with activation energy of 0.26 eV, while the high temperature step was due to the electron traps with ionization energy 0.65 eV (AC conductance spectra not shown here to save space had well defined peaks corresponding to the steps in C–T curves and the peaks temperature was shifted in the expected way with changing the measurement frequency). The concentration of the centers could be determined as usual from C–V measurements at the temperatures corresponding to the upper plateau of the C–T steps [4]. Such low-frequency C–V measurements yielded the concentration of the 0.26 eV trap as 6.7 1013 cm 3 and the 0.65 eV trap as 5 1015 cm 3. The 0.26 eV trap was obviously the one that was
pinning the Fermi level and determined the temperature dependence of the dark conductivity in Fig. 1. As this trap froze out the capacitance went down to zero. Interestingly, illumination of the sample led to persistent increase of capacitance and conductivity (corresponding persistent photocapacitance and persistent photoconductivity curves are marked as PPC in Figs. 1 and 2). It can be seen that after illumination the lower temperature step in capacitance is eaten up as it should if the PPC-active center were the 0.26 eV trap. The closeness of the concentration deduced from C–V measurements at 85 K after illumination to the concentration deduced from C–V measurements in the dark at 250 K also point to the main contribution of the 0.26 eV centers to the effect at low temperature. At these temperatures the conductivity also returns almost to its dark values (Fig. 1). However, one can see that the capacitance after illumination is still quite measurably higher than the dark capacitance indicating that some other PPC-active centers exist. These centers are not related to the 0.65 eV traps because instead of eating up the corresponding step in capacitance illumination simply shifts the step upwards. Thus the centers in question should be deeper than the 0.65 eV traps, but their exact location is not known at present. Only at about 400 K the capture of electrons by these centers becomes fast enough to equalize the dark and PPC capacitance curves. Measurements of the optical threshold position for the observed PPC phenomena are underway currently. At this point we can only say that the effect is observed for photons with energy higher than 2 eV. The 0.26 eV centers observed in our work are quite similar to previously reported 0.3 eV traps observed in Si doped AlN [7] and could be preliminarily attributed to Si donors. The question of whether such donors can behave as DX-like centers with an appreciable barrier for capture of electrons [8] is currently under debate (see e.g. a discussion in a recent review [9]). Theory predicts that Si donors should become DX-like for Al compositions in AlGaN higher than 60% which would explain our findings for AlN in the present paper. One question that arises is why the activation energy of the 0.26 eV centers is similar in conductivity versus temperature (Fig. 1) and admittance spectra (Fig. 2) measurements. In principle the activation energy in the latter should be higher by approximately the capture barrier [8]. However, our previous measurements on AlGaAs films with DX-centers show a similar relation. It can be explained if one takes into account that the activation energy deduced from admittance spectra can be related either to the activation energy of the emission coefficient of electrons or to the effect of the
MCL intensity (Arb. units)
4940
10
1
0.1 2.5
3.0
3.5
4.0 4.5 5.0 Photon energy (eV)
5.5
6.0
Fig. 3. MCL spectra measured on our AlN sample at 90 K.
6.5
ARTICLE IN PRESS A.Y. Polyakov et al. / Physica B 404 (2009) 4939–4941
4941
boundaries and selective etching shows that these boundaries coincide closely with the low-angle dislocation boundaries which should indicate attraction of the complex constituents (oxygen and Al vacancies) to the grain boundaries.
4. Conclusions We have shown that the electrical properties of our bulk AlN crystals are determined by electron traps with ionization energies 0.2 and 0.65 eV. The Fermi level is pinned by the shallower traps and the absolute concentrations of both traps are quite low indicating a reasonably high purity of the material. The 0.26 eV traps seem to be similar to the previously described 0.3 eV electron traps that have been associated with Si donors. Our data indicate that these donors are responsible for persistent increase of capacitance and conductivity after illumination at low temperatures and are thus the analogue of DX-centers in AlGaAs. There also are additional unidentified PPC-active centers that manifest themselves at higher temperatures. MCL spectra of our crystals are dominated by the 3.3 eV luminescence band that has been with some grounds attributed to aluminum vacancy–oxygen complexes. The concentration of these centers is enhanced in the vicinity of low-angle dislocation grain boundaries. Fig. 4. MCL image taken on our AlN sample at 90 K for the 3.3 eV luminescence line; the full dimensions of the figure are 200 200 mm.
increasing series resistance of the diode [4]. In the first case the energy should be close to the sum of thermal ionization energy and the barrier for capture of electrons, in the second case it is equal to the ionization energy. The second trap, the 0.65 eV trap, is often observed as the center pinning the Fermi level in more heavily compensated AlN films and crystals. It is most likely associated with a prominent luminescence band at 5.5 eV in MCL spectra of undoped AlN crystals and films. Indeed, in Fig. 3 we present the 90 K MCL spectrum of the studied AlN crystal that shows a well defined 5.5 eV band. In addition, one can see a band at 4.2 eV and a band at 3.3 eV. The latter is absolutely dominant in the spectrum. The attribution of the bands is still somewhat shaky, but the main band at 3.3 eV has been with some grounds attributed to transitions involving Al vacancy–oxygen acceptor complexes [9]. It was interesting to study the spatial distribution of the 3.3 eV MCL band intensity. Fig. 4 presents the result of such mapping. It can be seen that the intensity is greatly enhanced at certain
Acknowledgments The work was supported in part by a grant from Russian Foundation for Basic Research (RFBR grants 08-02-00058)
References [1] L.J. Schowalter, G.A. Slack, J.B. Whitlock, et al., Phys. Stat. Sol. (c) 0 (2003) 1997. [2] Z.G. Herro, D. Zhlesser, R. Colazo, Z. Sitar, J. Cryst. Growth 286 (2006) 205. [3] T.Yu. Chemekova, O.V. Avdeev, I.S. Barash, E.N. Mokhov, S.S. Nagalyuk, A.D. Roenkov, A.S. Segal, Yu.N. Makarov, M.G. Ramm, G. Davis, G. Huminic, H. Helava, Phys. Stat. Sol. (c) 5 (2008) 1612. [4] L.S. Berman, A.A. Lebedev, Capacitance Spectroscopy of Deep Centers in Semiconductors, Nauka, Leningrad, 1981 (in Russian). [5] A.Y. Polyakov, N.B. Smirnov, A.V. Govorkov, M. Shin, M. Skowronski, D.W. Greve, J. Appl. Phys. 84 (1998) 870. [6] A.Y. Polyakov, N.B. Smirnov, A.S. Usikov, A.V. Govorkov, B.V. Pushniy, Solid State Electron. 42 (1998) 1959. [7] R. Zeisel, M.W. Bayerl, S.T.B. Goennenwein, R. Dimitrov, O. Ambacher, M.S. Brandt, M. Stutzmann, Phys. Rev. B 61 (2000) R16283. [8] P.M. Mooney, J. Appl. Phys. 67 (1990) R1. [9] B. Monemar, P.P. Paskov, J.P. Bergman, A.A. Toporov, T.V. Shubina, Phys. Stat. Sol. (b) 244 (2007) 1759.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Deep centers in bulk AlN and their relation to low-angle dislocation boundaries A.Y. Polyakov a,, N.B. Smirnov a, A.V. Govorkov a, T.G. Yugova a, K.D. Scherbatchev a, O.A. Avdeev b, T.Yu. Chemekova b, E.N. Mokhov b, S.S. Nagalyuk b, H. Helava b, Yu.N. Makarov b a b
Institute of Rare Metals, B. Tolmachevsky, 5, Moscow, 119017, Russia Nitride Crystals Ltd., 27 Engels Av., St. Petersburg, Russia
a r t i c l e in fo
Keywords: Bulk AlN Physical vapor transport Deep traps Dislocation boundaries
abstract Structural properties, electrical properties, deep traps spectra, optical properties of bulk 50-mmdiameter AlN crystals prepared by physical vapor transport (PVT) were studied by means of X-ray diffraction, selective etching, admittance spectroscopy, microcathodoluminescence (MCL). The crystals had a low dislocation density with dislocations forming a well defined cellular structure. The dominant electron traps had the ionization energy of 0.26 and 0.65 eV with low concentrations close to some 1013 cm 3 and some 1015 cm 3, respectively. The Fermi level was pinned near the 0.26 eV electron traps. These traps were shown to give rise to a strong persistent photoconductivity and photocapacitance. MCL spectra of the studied crystal were dominated by the 3.3, 4.2 and 5.5 eV luminescence bands. The intensity of the strongest 3.3 eV band was greatly enhanced in the vicinity of low-angle dislocation boundaries. & 2009 Published by Elsevier B.V.
1. Introduction Bulk AlN crystals with low dislocation density can be prepared by modified physical vapor transport (PVT) technique [1,2] and such crystals are of great interest as substrates for heteroepitaxial growth of Al-rich AlGaN-based light emitting diodes and of AlGaN/GaN-based high electron mobility transistor structures. Despite the obvious practical and scientific interest of studying the properties of such bulk AlN crystals the nature of deep traps determining the Fermi level pinning, the recombination lifetime and the type of optical transitions in such crystals is not well understood. In this paper we present the results of our studies of the properties of large diameter undoped bulk AlN crystals.
grow about 10-mm-long AlN crystal that was then sliced into 0.5 mm-thick wafers and chemo-mechanically polished. The wafer we studied was the closest to the seed AlN crystal. It was characterized by selective etching in KOH/NaOH eutectic and by high resolution X-ray diffraction (HRXRD) (triple-axis arrangement, Bede System 1 spectrometer with Cu Ka radiation). Electrical properties were studied using current–voltage (I–V), capacitance–voltage (C–V) and admittance spectra [4] measurements on Au Schottky diodes deposited in vacuum through a shadow mask [5]. MCL spectra measurements and MCL imaging of the sample was performed as described in Ref. [6].
3. Results and discussion 2. Experimental 50-mm-diameter bulk AlN crystal studied in this paper was grown by two-stage modified PVT process described in some detail in Ref. [3]. Growth was performed in carbonized Ta crucibles, from pre-synthesized polycrystalline AlN charge. At the first stage AlN layer with thickness of about 2 mm was deposited on a high quality 6H-SiC seed crystal, the AlN layer was cut from the SiC and used at the second stage of the process to Corresponding author. Tel.: + 7499 788 90 90; fax: +7499 88 90 90.
E-mail address: [email protected] (A.Y. Polyakov). 0921-4526/$ - see front matter & 2009 Published by Elsevier B.V. doi:10.1016/j.physb.2009.09.052
The full width at half maximum of the triple-axis HRXRD (0 0 0 2) reflection was 0.171, but the diffraction pattern also showed side peaks indicating the presence of misoriented grains with misorientation up to 21. Selective etching patterns revealed the presence of well defined dislocation etch pits and showed that the majority of dislocations are agglomerated in low-angle dislocation boundaries with characteristic grain size from some 10 to 100 mm. I–V characteristics of the Au Schottky diodes prepared on the studied sample showed that it had n-type conductivity with the room temperature resistivity deduced from the series resistance of the forward I–V characteristic close to 107 Ocm. The temperature dependence of the forward current at
ARTICLE IN PRESS A.Y. Polyakov et al. / Physica B 404 (2009) 4939–4941
10-3
Current (A)
10-5 after GaN LED
10-7 10-9
Dark
10-11 Ea=260 meV 10
-13
0
2
4
6 1000/T (1/K)
8
10
12
Fig. 1. The temperature dependence of the forward current at 10 V for the Au Schottky diode prepared on the studied AlN sample, the solid curve was measured in the dark, the dashed curve (marked as ‘‘PPC’’) was measured after illumination at 85 K with 2.8 eV GaN light emitting diode.
45 40
PPC
Capacitance (pF)
35 30
Dark
25
0.65 eV
20 15 10
0.26 eV
5 0 150
200
250 300 Temperature (K)
350
400
Fig. 2. The temperature dependence of capacitance at 500 Hz measured on the studied Au/AlN Schottky diode in the dark (solid curve) and after illumination with 2.8 eV GaN light emitting diode (dash-dotted curve marked as PPC).
high forward voltage of 10 V that is equivalent to the temperature dependence of conductivity showed the activation energy of 0.26 eV that should be close to the position of the trap pinning the Fermi level (Fig. 1). Fig. 2 shows the temperature dependence of capacitance measured at low frequency of 500 Hz. Two steps in capacitance can be clearly seen. Standard admittance spectroscopy analysis of the dependence of the temperature of the step on measurement frequency [4] showed that the lowtemperature step corresponded to electron trap with activation energy of 0.26 eV, while the high temperature step was due to the electron traps with ionization energy 0.65 eV (AC conductance spectra not shown here to save space had well defined peaks corresponding to the steps in C–T curves and the peaks temperature was shifted in the expected way with changing the measurement frequency). The concentration of the centers could be determined as usual from C–V measurements at the temperatures corresponding to the upper plateau of the C–T steps [4]. Such low-frequency C–V measurements yielded the concentration of the 0.26 eV trap as 6.7 1013 cm 3 and the 0.65 eV trap as 5 1015 cm 3. The 0.26 eV trap was obviously the one that was
pinning the Fermi level and determined the temperature dependence of the dark conductivity in Fig. 1. As this trap froze out the capacitance went down to zero. Interestingly, illumination of the sample led to persistent increase of capacitance and conductivity (corresponding persistent photocapacitance and persistent photoconductivity curves are marked as PPC in Figs. 1 and 2). It can be seen that after illumination the lower temperature step in capacitance is eaten up as it should if the PPC-active center were the 0.26 eV trap. The closeness of the concentration deduced from C–V measurements at 85 K after illumination to the concentration deduced from C–V measurements in the dark at 250 K also point to the main contribution of the 0.26 eV centers to the effect at low temperature. At these temperatures the conductivity also returns almost to its dark values (Fig. 1). However, one can see that the capacitance after illumination is still quite measurably higher than the dark capacitance indicating that some other PPC-active centers exist. These centers are not related to the 0.65 eV traps because instead of eating up the corresponding step in capacitance illumination simply shifts the step upwards. Thus the centers in question should be deeper than the 0.65 eV traps, but their exact location is not known at present. Only at about 400 K the capture of electrons by these centers becomes fast enough to equalize the dark and PPC capacitance curves. Measurements of the optical threshold position for the observed PPC phenomena are underway currently. At this point we can only say that the effect is observed for photons with energy higher than 2 eV. The 0.26 eV centers observed in our work are quite similar to previously reported 0.3 eV traps observed in Si doped AlN [7] and could be preliminarily attributed to Si donors. The question of whether such donors can behave as DX-like centers with an appreciable barrier for capture of electrons [8] is currently under debate (see e.g. a discussion in a recent review [9]). Theory predicts that Si donors should become DX-like for Al compositions in AlGaN higher than 60% which would explain our findings for AlN in the present paper. One question that arises is why the activation energy of the 0.26 eV centers is similar in conductivity versus temperature (Fig. 1) and admittance spectra (Fig. 2) measurements. In principle the activation energy in the latter should be higher by approximately the capture barrier [8]. However, our previous measurements on AlGaAs films with DX-centers show a similar relation. It can be explained if one takes into account that the activation energy deduced from admittance spectra can be related either to the activation energy of the emission coefficient of electrons or to the effect of the
MCL intensity (Arb. units)
4940
10
1
0.1 2.5
3.0
3.5
4.0 4.5 5.0 Photon energy (eV)
5.5
6.0
Fig. 3. MCL spectra measured on our AlN sample at 90 K.
6.5
ARTICLE IN PRESS A.Y. Polyakov et al. / Physica B 404 (2009) 4939–4941
4941
boundaries and selective etching shows that these boundaries coincide closely with the low-angle dislocation boundaries which should indicate attraction of the complex constituents (oxygen and Al vacancies) to the grain boundaries.
4. Conclusions We have shown that the electrical properties of our bulk AlN crystals are determined by electron traps with ionization energies 0.2 and 0.65 eV. The Fermi level is pinned by the shallower traps and the absolute concentrations of both traps are quite low indicating a reasonably high purity of the material. The 0.26 eV traps seem to be similar to the previously described 0.3 eV electron traps that have been associated with Si donors. Our data indicate that these donors are responsible for persistent increase of capacitance and conductivity after illumination at low temperatures and are thus the analogue of DX-centers in AlGaAs. There also are additional unidentified PPC-active centers that manifest themselves at higher temperatures. MCL spectra of our crystals are dominated by the 3.3 eV luminescence band that has been with some grounds attributed to aluminum vacancy–oxygen complexes. The concentration of these centers is enhanced in the vicinity of low-angle dislocation grain boundaries. Fig. 4. MCL image taken on our AlN sample at 90 K for the 3.3 eV luminescence line; the full dimensions of the figure are 200 200 mm.
increasing series resistance of the diode [4]. In the first case the energy should be close to the sum of thermal ionization energy and the barrier for capture of electrons, in the second case it is equal to the ionization energy. The second trap, the 0.65 eV trap, is often observed as the center pinning the Fermi level in more heavily compensated AlN films and crystals. It is most likely associated with a prominent luminescence band at 5.5 eV in MCL spectra of undoped AlN crystals and films. Indeed, in Fig. 3 we present the 90 K MCL spectrum of the studied AlN crystal that shows a well defined 5.5 eV band. In addition, one can see a band at 4.2 eV and a band at 3.3 eV. The latter is absolutely dominant in the spectrum. The attribution of the bands is still somewhat shaky, but the main band at 3.3 eV has been with some grounds attributed to transitions involving Al vacancy–oxygen acceptor complexes [9]. It was interesting to study the spatial distribution of the 3.3 eV MCL band intensity. Fig. 4 presents the result of such mapping. It can be seen that the intensity is greatly enhanced at certain
Acknowledgments The work was supported in part by a grant from Russian Foundation for Basic Research (RFBR grants 08-02-00058)
References [1] L.J. Schowalter, G.A. Slack, J.B. Whitlock, et al., Phys. Stat. Sol. (c) 0 (2003) 1997. [2] Z.G. Herro, D. Zhlesser, R. Colazo, Z. Sitar, J. Cryst. Growth 286 (2006) 205. [3] T.Yu. Chemekova, O.V. Avdeev, I.S. Barash, E.N. Mokhov, S.S. Nagalyuk, A.D. Roenkov, A.S. Segal, Yu.N. Makarov, M.G. Ramm, G. Davis, G. Huminic, H. Helava, Phys. Stat. Sol. (c) 5 (2008) 1612. [4] L.S. Berman, A.A. Lebedev, Capacitance Spectroscopy of Deep Centers in Semiconductors, Nauka, Leningrad, 1981 (in Russian). [5] A.Y. Polyakov, N.B. Smirnov, A.V. Govorkov, M. Shin, M. Skowronski, D.W. Greve, J. Appl. Phys. 84 (1998) 870. [6] A.Y. Polyakov, N.B. Smirnov, A.S. Usikov, A.V. Govorkov, B.V. Pushniy, Solid State Electron. 42 (1998) 1959. [7] R. Zeisel, M.W. Bayerl, S.T.B. Goennenwein, R. Dimitrov, O. Ambacher, M.S. Brandt, M. Stutzmann, Phys. Rev. B 61 (2000) R16283. [8] P.M. Mooney, J. Appl. Phys. 67 (1990) R1. [9] B. Monemar, P.P. Paskov, J.P. Bergman, A.A. Toporov, T.V. Shubina, Phys. Stat. Sol. (b) 244 (2007) 1759.