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Muonium transitions in 4H silicon carbide
ARTICLE IN PRESS Physica B 404 (2009) 845–848
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Muonium transitions in 4H silicon carbide Y.G. Celebi a,, R.L. Lichti b, H.N. Bani-Salameh b, A.G. Meyer b, B.R. Carroll b, J.E. Vernon b, P.J.C. King c, S.F.J. Cox c,d a
Department of Physics, Istanbul University, 34459 Beyazit, Istanbul, Turkey Department of Physics, Texas Tech University, Lubbock, TX 79409-1051, USA STFC ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxon OX11 OQX, UK d Condensed Matter and Materials Physics, University College, London WC1E 6BT, UK b c
a r t i c l e in fo
Keywords: Hydrogen Muonium SiC
abstract Preliminary low-field data on the diamagnetic muon spin rotation signal in 4H-SiC are presented. The initial results on all three electrical types of 4H-SiC are compared with those for the 6H polytype. Analysis of amplitude transitions at low temperatures in n- and p-type samples indicates carrier capture. At temperatures above 600 K, an increase in diamagnetic amplitude and an associated dip in the phase indicate a slowly formed state in the p-type material. We discuss possible identification of transitions evident from temperature dependent diamagnetic amplitudes and correlations with neutral muonium centers. & 2008 Elsevier B.V. All rights reserved.
1. Introduction Hydrogen in SiC, as in any other semiconductor, is an unavoidable impurity. Its common existence in semiconductor materials as the simplest impurity, belies its very complicated behavior. In most cases, hydrogen is a beneficial impurity since it quickly ties up dangling bonds and forms bound states with existing defects, modifying electrical and optical properties associated with those defects. It is therefore of interest both theoretically and experimentally to determine the properties of hydrogen in these materials. With its ability to tolerate extreme conditions such as high temperatures and high powers, there has been an increased interest in device fabrication using SiC. Among over a hundred known crystal structures, SiC with stacking sequences of 4H and 6H are more easily produced by the current technology. Hence, these two structures are studied heavily, and are being developed for practical applications in adverse environments. Because of its ability to take part in many interactions, it is rarely possible to study isolated hydrogen. Muonium, now commonly considered as an isotope of hydrogen, can almost always be studied in isolated form because of its short lifetime ð2:2 msÞ. In SiC, Mu0 states formed by the end of muon thermalization following implantation are long lived on the mSR time scale at low temperatures, making it possible to observe charge-state
Corresponding author. Tel.: +90 212 455 5700; fax: +90 212 519 0834.
E-mail address: [email protected] (Y.G. Celebi). 0921-4526/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2008.11.155
transitions as the temperature is raised [1]. Therefore, in order to investigate these transitions, we have performed transverse-field measurements to monitor the diamagnetic fractions over a wide temperature range. For the measurements reported in this paper, we have used the EMU spectrometer at the ISIS Facility, where 100% spin polarized muons were implanted into the three electrical types of commercially available 4H-SiC wafers commonly used as substrates for thin film deposition. As we have already reported [2] on the high transverse-field data on these 4H-SiC samples, here we mainly present preliminary results on the temperature dependence of amplitudes of the lowfield diamagnetic muon spin rotation (mSR) signals in the 4H-SiC samples and compare with those obtained for the 6H polytype [1].
2. Experimental results Muonium hyperfine spectroscopy performed in a field of 6.0 T using TRIUMF HiTime spectrometer on all electrical types of 4H-SiC has shown two isotropic Mu0 centers whereas a total of four were detected in the 6H polytype [2]. Fig. 1 shows the Fourier spectrum for p-type 4H-SiC as an example. The hyperfine constants for each observed neutral are virtually the same in all three electrical types of 4H-SiC. Extrapolated values for AHF at T ¼ 0 K are 3029.9 MHz for the state labelled as Mu1 and 2825.1 MHz for Mu2 [1,2]. We found no dependence on c-axis orientation with respect to the applied magnetic field for the frequency of these lines, indicating that these signals are due to isotropic muonium centers.
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Fig. 1. The muon spin precession spectrum at 6 T for p-type 4H-SiC, adapted from Ref. [2]. The same Mu0 centers are observed for high-resistivity and n-type samples.
The amplitude dependence on electrical type for Mu1 indicates acceptor-like properties [2]. Thus, this signal has been assigned to the T Si site, which is predicted [3] to be the lowest energy location for both the neutral and negative charge states of Mu in SiC. Based on calculated site energies for H impurities [3], the primary donor location in the hexagonal structures of SiC is a site anti-bonding to a carbon atom, ABC , with the muon residing in the short c-axis channels. One also expects a secondary acceptor site antibonding to a silicon atom, ABSi , in the same structural region. It is not clear from previous data which of these metastable Mu0 locations results in the signal labelled as Mu2. The diamagnetic signal appears to show a small frequency shift in the high-field data below about 100 K [4]. For some cases, two separate precession frequencies can be obtained. These observations are interpreted as an indication of two different diamagnetic muonium centers, most likely Muþ and Mu . The appearance of two diamagnetic states at low temperatures is a consistent feature observed in all SiC samples investigated thus far. Fig. 2 shows previously unreported magnetic field and temperature dependencies of the low-field diamagnetic precession data in n-type 4H SiC. At low temperatures, the amplitude of this signal decreases with applied field strength as displayed in the inset. This indicates delayed formation of a diamagnetic state from a paramagnetic precursor. An increase in the slope of amplitude vs. temperature as the temperature is increased presents evidence for an additional transition process, and perhaps a second slowly formed ionic state. Evidence for two slowly formed diamagnetic states is more pronounced in the 6H samples as reported previously [1,2]. A dip in diamagnetic amplitude near 50 K in n-type 6H-SiC [1] was interpreted as electron capture by Muþ. A steep increase starting at a slightly higher temperature was assigned to electron capture by a Mu0 state, consistent with a smaller capture cross section. The 4H data do not clearly show such a separation, but the general features in Fig. 3 are very similar to those seen for the 6H polytype. Together with the 6H results, the current data at least suggest the presence of two separate low-temperature diamagnetic states; these are assigned to Muþ and Mu . Fig. 3 displays our recent results for the temperature dependence of the diamagnetic fractions for each 4H-SiC electrical type up to 1000 K. The low temperature transitions and associated
Fig. 2. Diamagnetic amplitudes as a function of temperature at a few magnetic fields. The inset shows the decrease in the diamagnetic fraction with applied field strength. These data imply a paramagnetic precursor to a slowly formed diamagnetic state.
Fig. 3. Temperature dependence of the diamagnetic muonium amplitudes in low transverse field for the 4H-SiC. The low-T behavior gives energies characteristic of carrier capture. Above 920 K all samples show the onset of an additional transition.
energies suggest carrier capture processes, as were observed in each sample of the 6H SiC polytype [1]. Donors have a much lower ionization energy in SiC than acceptors [5]. Thus, the most likely assignment for the lowest temperature transition in n-type SiC is that one of the Mu0 states converts to Mu by an electron capture process. Similarly, for the p-type data, the transition just below 200 K is most likely hole capture by Mu to form a paramagnetic Mu0 state. In this intermediate temperature region, high-field muon spin precession data indicate quite complicated transitions [6]. The amplitude associated with the Mu1 signal in p-type 4H-SiC decreases with temperature, while at the same time the amplitude of the Mu2 signal shows a slight increase. Diamagnetic signals observed both at high and low fields show a narrow peak in the relaxation rate around 200 K (not shown), near the decreasing diamagnetic amplitude step, indicating a transition out of that state. There could be a simple site change from Mu01 to
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847
Mu02 , but we previously claimed that Mu01 was located at the lowest energy site for a neutral [2]. Therefore, we argue that the combination of features observed in p-type 4H-SiC should be interpreted as a series of hole capture events. We propose two independent sets of transitions, both involving a site change, Mu01 ! Muþ and separately a Mu ! Mu02 ! Muþ conversion sequence. The first process is consistent with the change in Mu1 amplitude, while the second sequence would explain the Mu2 feature and diamagnetic features in Fig. 3. The quoted energy of 400 meV might therefore be appropriate for a site change initiated by the hole capture. Because it is present as a decrease in the diamagnetic amplitude this should be associated with the first step of our second sequence. As implied above, the second sequence is the one seen in the þ p-type data of Fig. 3; this involves two h capture steps starting as þ Mu and ending up as Mu in a different site. Since Mu1 was assigned to the acceptor state at T Si , the same site as expected for Mu , the decrease in amplitude near 200 K probably represents hole capture by Mu driving the resulting Mu0 to a donor site, with most of the transition energy assigned to the barrier for site change. The increase in amplitude around 450 K in p-type 4H-SiC gives an energy of 250 meV, roughly consistent with ionization of standard acceptors [5] in SiC. We thus identify this feature as a hole capture at the donor site as the final step of the second sequence. From the combination of results for neutral amplitude changes and these assignments, we can infer that Mu2 most likely represents the ABC donor site. In the high-resistivity sample, the temperature dependence of the amplitude is quite flat with several small-amplitude transitions spread over the scanned temperature range. An upper limit on the low temperature transition energy in this sample is around 80 meV, appropriate for an electron capture process. Other small features in the high-resistivity and n-type data may be related to either a precursor site change or carrier capture by one or another of the observed states. None of these small features appear to be characteristic of an ionization transition. At higher temperatures, there are additional slowly formed diamagnetic states in each of the 4H-SiC samples. This is most obvious in the p-type data, where the large-amplitude transition between 700 and 800 K yields an energy that roughly agrees with that expected for donor ionization in 4H-SiC based on our extrapolations from 6H results [1]. Additional information for
Fig. 5 shows the diamagnetic amplitude in a temperature range of 100–1100 K for the high-resistivity 6H-SiC sample [1]. This is a composite of two different data sets, one set (solid triangles) was collected at TRIUMF in a field of 1.5 mT, and the other one (open circles) was taken in 10 mT with the sample placed in an optical furnace at ISIS. The resulting temperature dependence shows two main transitions indicating the donor and acceptor ionization steps. With the sample in the optical furnace, amplitudes in this region followed the hole capture curve (p-type sample, data not shown) until about 400 K and then followed TRIUMF data taken in the dark. This behavior prompted us to assign the 300–500 K transition in the dark to Mu donor ionization ðED ¼ 280 meVÞ and the step above 700 K to Mu acceptor ionization ðEA ¼ 860 meVÞ. For 6H-SiC, we developed a model that explains many of the features observed for muonium centers [1]. Dynamics in the 4H polytype have proven to be more complicated than anticipated. In 6H-SiC, nearly the maximum diamagnetic asymmetry is reached by 1000 K. Considering that neutrals never dominate the equilibrium populations in a negative-U system, one expects Muþ to dominate in p-type and Mu in n-type samples under thermodynamic equilibrium conditions [7]. This might be the case in 6H-SiC, but is thus far much less clear for 4H.
Fig. 4. Fitted phases for diamagnetic amplitudes of p-type SiC displayed in Fig. 3. The dip seen in these data is interpreted as an indication for delayed formation of the ionic state.
Fig. 5. Results from a high-resistivity 6H-SiC sample show Mu donor and acceptor ionization transitions locating the Mu defect levels relative to band edges [1].
charge-state dynamics can be drawn from the temperature dependence of the phases associated with the monitored diamagnetic states. Fig. 4 displays the phase for the diamagnetic signal as a function of temperature in p-type sample. Both the high-resistivity and p-type samples show a pronounced dip in phase around 700 K, while phases for n-type 4H-SiC remain almost flat over the scanned temperature range relative to the high-resistivity and p-type samples. The increase in amplitude above 600 K in Fig. 3 for the p-type sample suggests two overlapping transitions and additional data at higher temperatures are needed to accurately establish the related energies. However, these transitions are most likely the ionization transitions from the Mu donor and acceptor sites in the 4H polytype of SiC. Since the diamagnetic fractions are still low at 1000 K, transitions at even higher temperatures will be crucial to establishing Mu defect levels in this material.
3. Discussion and conclusion
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In conclusion, with the presently available data, assignments for the transitions in 4H-SiC are less certain than for the 6H polytype. The main result up to 1000 K is that Mu ionization from either the donor or acceptor sites occurs at higher temperatures in 4H-SiC than in 6H-SiC. The lowest temperature (below 50 K) transition in n-type 6H-SiC is electron capture by a positively charged muonium center [1]. In n-type 4H SiC, the lowest temperature transition is assigned to electron capture by Mu0 at an acceptor location, most likely T Si which is the predicted lowest energy Mu0 site [3]. For p-type 4H SiC and also for p-type 6H-SiC, the first transition with increasing temperature is a hole capture by Mu. Only the p-type 4H sample shows a transition that can be considered ionization; however, the data suggest two processes with overlapping temperature dependencies, such that the existing measurements are insufficient to cleanly separate the dynamics. In high-resistivity 6H-SiC, two transitions dominated between 100 and 1000 K, from which we extracted the Mu donor and acceptor ionization energies. In contrast, for high-resistivity 4H-SiC, the diamagnetic fraction remains quite flat over the whole range up to 1000 K. Additional dynamics are present at higher temperatures for 4H-SiC, as can be seen from Fig. 3.
Above approximately 950 K diamagnetic amplitudes in all three electrical types show a steep increase. Data will therefore be required in this higher temperature regime above 1000 K in order to assign either the donor or acceptor ionization energy for Mu in the 4H polytype of SiC.
Acknowledgments This work was supported by the US National Science Foundation (DMR-0604501) and the R.A. Welch Foundation (D-1321) and by the Royal Society of London. References [1] [2] [3] [4] [5] [6]
H.N. Bani-Salameh, et al., Physica B 401–402 (2007) 631. R.L. Lichti, W.A. Nussbaum, K.H. Chow, Phys. Rev. B 70 (2004) 165204. M. Kaukonen, C.J. Fall, J. Lento, Appl. Phys. Lett. 83 (2003) 923. H.N. Bani-Salameh, et al., Physica B 374–375 (2006) 368. O. Madelung (Ed.), Properties of Semiconductors, Springer, Berlin, 1996. H.N. Bani-Salameh, Ph.D. Dissertation, Texas Tech University, 2007, Unpublished. [7] C. Herring, N.M. Johnson, C.G. Van de Walle, Phys. Rev. B 64 (2001) 125209.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Muonium transitions in 4H silicon carbide Y.G. Celebi a,, R.L. Lichti b, H.N. Bani-Salameh b, A.G. Meyer b, B.R. Carroll b, J.E. Vernon b, P.J.C. King c, S.F.J. Cox c,d a
Department of Physics, Istanbul University, 34459 Beyazit, Istanbul, Turkey Department of Physics, Texas Tech University, Lubbock, TX 79409-1051, USA STFC ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxon OX11 OQX, UK d Condensed Matter and Materials Physics, University College, London WC1E 6BT, UK b c
a r t i c l e in fo
Keywords: Hydrogen Muonium SiC
abstract Preliminary low-field data on the diamagnetic muon spin rotation signal in 4H-SiC are presented. The initial results on all three electrical types of 4H-SiC are compared with those for the 6H polytype. Analysis of amplitude transitions at low temperatures in n- and p-type samples indicates carrier capture. At temperatures above 600 K, an increase in diamagnetic amplitude and an associated dip in the phase indicate a slowly formed state in the p-type material. We discuss possible identification of transitions evident from temperature dependent diamagnetic amplitudes and correlations with neutral muonium centers. & 2008 Elsevier B.V. All rights reserved.
1. Introduction Hydrogen in SiC, as in any other semiconductor, is an unavoidable impurity. Its common existence in semiconductor materials as the simplest impurity, belies its very complicated behavior. In most cases, hydrogen is a beneficial impurity since it quickly ties up dangling bonds and forms bound states with existing defects, modifying electrical and optical properties associated with those defects. It is therefore of interest both theoretically and experimentally to determine the properties of hydrogen in these materials. With its ability to tolerate extreme conditions such as high temperatures and high powers, there has been an increased interest in device fabrication using SiC. Among over a hundred known crystal structures, SiC with stacking sequences of 4H and 6H are more easily produced by the current technology. Hence, these two structures are studied heavily, and are being developed for practical applications in adverse environments. Because of its ability to take part in many interactions, it is rarely possible to study isolated hydrogen. Muonium, now commonly considered as an isotope of hydrogen, can almost always be studied in isolated form because of its short lifetime ð2:2 msÞ. In SiC, Mu0 states formed by the end of muon thermalization following implantation are long lived on the mSR time scale at low temperatures, making it possible to observe charge-state
Corresponding author. Tel.: +90 212 455 5700; fax: +90 212 519 0834.
E-mail address: [email protected] (Y.G. Celebi). 0921-4526/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2008.11.155
transitions as the temperature is raised [1]. Therefore, in order to investigate these transitions, we have performed transverse-field measurements to monitor the diamagnetic fractions over a wide temperature range. For the measurements reported in this paper, we have used the EMU spectrometer at the ISIS Facility, where 100% spin polarized muons were implanted into the three electrical types of commercially available 4H-SiC wafers commonly used as substrates for thin film deposition. As we have already reported [2] on the high transverse-field data on these 4H-SiC samples, here we mainly present preliminary results on the temperature dependence of amplitudes of the lowfield diamagnetic muon spin rotation (mSR) signals in the 4H-SiC samples and compare with those obtained for the 6H polytype [1].
2. Experimental results Muonium hyperfine spectroscopy performed in a field of 6.0 T using TRIUMF HiTime spectrometer on all electrical types of 4H-SiC has shown two isotropic Mu0 centers whereas a total of four were detected in the 6H polytype [2]. Fig. 1 shows the Fourier spectrum for p-type 4H-SiC as an example. The hyperfine constants for each observed neutral are virtually the same in all three electrical types of 4H-SiC. Extrapolated values for AHF at T ¼ 0 K are 3029.9 MHz for the state labelled as Mu1 and 2825.1 MHz for Mu2 [1,2]. We found no dependence on c-axis orientation with respect to the applied magnetic field for the frequency of these lines, indicating that these signals are due to isotropic muonium centers.
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Fig. 1. The muon spin precession spectrum at 6 T for p-type 4H-SiC, adapted from Ref. [2]. The same Mu0 centers are observed for high-resistivity and n-type samples.
The amplitude dependence on electrical type for Mu1 indicates acceptor-like properties [2]. Thus, this signal has been assigned to the T Si site, which is predicted [3] to be the lowest energy location for both the neutral and negative charge states of Mu in SiC. Based on calculated site energies for H impurities [3], the primary donor location in the hexagonal structures of SiC is a site anti-bonding to a carbon atom, ABC , with the muon residing in the short c-axis channels. One also expects a secondary acceptor site antibonding to a silicon atom, ABSi , in the same structural region. It is not clear from previous data which of these metastable Mu0 locations results in the signal labelled as Mu2. The diamagnetic signal appears to show a small frequency shift in the high-field data below about 100 K [4]. For some cases, two separate precession frequencies can be obtained. These observations are interpreted as an indication of two different diamagnetic muonium centers, most likely Muþ and Mu . The appearance of two diamagnetic states at low temperatures is a consistent feature observed in all SiC samples investigated thus far. Fig. 2 shows previously unreported magnetic field and temperature dependencies of the low-field diamagnetic precession data in n-type 4H SiC. At low temperatures, the amplitude of this signal decreases with applied field strength as displayed in the inset. This indicates delayed formation of a diamagnetic state from a paramagnetic precursor. An increase in the slope of amplitude vs. temperature as the temperature is increased presents evidence for an additional transition process, and perhaps a second slowly formed ionic state. Evidence for two slowly formed diamagnetic states is more pronounced in the 6H samples as reported previously [1,2]. A dip in diamagnetic amplitude near 50 K in n-type 6H-SiC [1] was interpreted as electron capture by Muþ. A steep increase starting at a slightly higher temperature was assigned to electron capture by a Mu0 state, consistent with a smaller capture cross section. The 4H data do not clearly show such a separation, but the general features in Fig. 3 are very similar to those seen for the 6H polytype. Together with the 6H results, the current data at least suggest the presence of two separate low-temperature diamagnetic states; these are assigned to Muþ and Mu . Fig. 3 displays our recent results for the temperature dependence of the diamagnetic fractions for each 4H-SiC electrical type up to 1000 K. The low temperature transitions and associated
Fig. 2. Diamagnetic amplitudes as a function of temperature at a few magnetic fields. The inset shows the decrease in the diamagnetic fraction with applied field strength. These data imply a paramagnetic precursor to a slowly formed diamagnetic state.
Fig. 3. Temperature dependence of the diamagnetic muonium amplitudes in low transverse field for the 4H-SiC. The low-T behavior gives energies characteristic of carrier capture. Above 920 K all samples show the onset of an additional transition.
energies suggest carrier capture processes, as were observed in each sample of the 6H SiC polytype [1]. Donors have a much lower ionization energy in SiC than acceptors [5]. Thus, the most likely assignment for the lowest temperature transition in n-type SiC is that one of the Mu0 states converts to Mu by an electron capture process. Similarly, for the p-type data, the transition just below 200 K is most likely hole capture by Mu to form a paramagnetic Mu0 state. In this intermediate temperature region, high-field muon spin precession data indicate quite complicated transitions [6]. The amplitude associated with the Mu1 signal in p-type 4H-SiC decreases with temperature, while at the same time the amplitude of the Mu2 signal shows a slight increase. Diamagnetic signals observed both at high and low fields show a narrow peak in the relaxation rate around 200 K (not shown), near the decreasing diamagnetic amplitude step, indicating a transition out of that state. There could be a simple site change from Mu01 to
ARTICLE IN PRESS Y.G. Celebi et al. / Physica B 404 (2009) 845–848
847
Mu02 , but we previously claimed that Mu01 was located at the lowest energy site for a neutral [2]. Therefore, we argue that the combination of features observed in p-type 4H-SiC should be interpreted as a series of hole capture events. We propose two independent sets of transitions, both involving a site change, Mu01 ! Muþ and separately a Mu ! Mu02 ! Muþ conversion sequence. The first process is consistent with the change in Mu1 amplitude, while the second sequence would explain the Mu2 feature and diamagnetic features in Fig. 3. The quoted energy of 400 meV might therefore be appropriate for a site change initiated by the hole capture. Because it is present as a decrease in the diamagnetic amplitude this should be associated with the first step of our second sequence. As implied above, the second sequence is the one seen in the þ p-type data of Fig. 3; this involves two h capture steps starting as þ Mu and ending up as Mu in a different site. Since Mu1 was assigned to the acceptor state at T Si , the same site as expected for Mu , the decrease in amplitude near 200 K probably represents hole capture by Mu driving the resulting Mu0 to a donor site, with most of the transition energy assigned to the barrier for site change. The increase in amplitude around 450 K in p-type 4H-SiC gives an energy of 250 meV, roughly consistent with ionization of standard acceptors [5] in SiC. We thus identify this feature as a hole capture at the donor site as the final step of the second sequence. From the combination of results for neutral amplitude changes and these assignments, we can infer that Mu2 most likely represents the ABC donor site. In the high-resistivity sample, the temperature dependence of the amplitude is quite flat with several small-amplitude transitions spread over the scanned temperature range. An upper limit on the low temperature transition energy in this sample is around 80 meV, appropriate for an electron capture process. Other small features in the high-resistivity and n-type data may be related to either a precursor site change or carrier capture by one or another of the observed states. None of these small features appear to be characteristic of an ionization transition. At higher temperatures, there are additional slowly formed diamagnetic states in each of the 4H-SiC samples. This is most obvious in the p-type data, where the large-amplitude transition between 700 and 800 K yields an energy that roughly agrees with that expected for donor ionization in 4H-SiC based on our extrapolations from 6H results [1]. Additional information for
Fig. 5 shows the diamagnetic amplitude in a temperature range of 100–1100 K for the high-resistivity 6H-SiC sample [1]. This is a composite of two different data sets, one set (solid triangles) was collected at TRIUMF in a field of 1.5 mT, and the other one (open circles) was taken in 10 mT with the sample placed in an optical furnace at ISIS. The resulting temperature dependence shows two main transitions indicating the donor and acceptor ionization steps. With the sample in the optical furnace, amplitudes in this region followed the hole capture curve (p-type sample, data not shown) until about 400 K and then followed TRIUMF data taken in the dark. This behavior prompted us to assign the 300–500 K transition in the dark to Mu donor ionization ðED ¼ 280 meVÞ and the step above 700 K to Mu acceptor ionization ðEA ¼ 860 meVÞ. For 6H-SiC, we developed a model that explains many of the features observed for muonium centers [1]. Dynamics in the 4H polytype have proven to be more complicated than anticipated. In 6H-SiC, nearly the maximum diamagnetic asymmetry is reached by 1000 K. Considering that neutrals never dominate the equilibrium populations in a negative-U system, one expects Muþ to dominate in p-type and Mu in n-type samples under thermodynamic equilibrium conditions [7]. This might be the case in 6H-SiC, but is thus far much less clear for 4H.
Fig. 4. Fitted phases for diamagnetic amplitudes of p-type SiC displayed in Fig. 3. The dip seen in these data is interpreted as an indication for delayed formation of the ionic state.
Fig. 5. Results from a high-resistivity 6H-SiC sample show Mu donor and acceptor ionization transitions locating the Mu defect levels relative to band edges [1].
charge-state dynamics can be drawn from the temperature dependence of the phases associated with the monitored diamagnetic states. Fig. 4 displays the phase for the diamagnetic signal as a function of temperature in p-type sample. Both the high-resistivity and p-type samples show a pronounced dip in phase around 700 K, while phases for n-type 4H-SiC remain almost flat over the scanned temperature range relative to the high-resistivity and p-type samples. The increase in amplitude above 600 K in Fig. 3 for the p-type sample suggests two overlapping transitions and additional data at higher temperatures are needed to accurately establish the related energies. However, these transitions are most likely the ionization transitions from the Mu donor and acceptor sites in the 4H polytype of SiC. Since the diamagnetic fractions are still low at 1000 K, transitions at even higher temperatures will be crucial to establishing Mu defect levels in this material.
3. Discussion and conclusion
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In conclusion, with the presently available data, assignments for the transitions in 4H-SiC are less certain than for the 6H polytype. The main result up to 1000 K is that Mu ionization from either the donor or acceptor sites occurs at higher temperatures in 4H-SiC than in 6H-SiC. The lowest temperature (below 50 K) transition in n-type 6H-SiC is electron capture by a positively charged muonium center [1]. In n-type 4H SiC, the lowest temperature transition is assigned to electron capture by Mu0 at an acceptor location, most likely T Si which is the predicted lowest energy Mu0 site [3]. For p-type 4H SiC and also for p-type 6H-SiC, the first transition with increasing temperature is a hole capture by Mu. Only the p-type 4H sample shows a transition that can be considered ionization; however, the data suggest two processes with overlapping temperature dependencies, such that the existing measurements are insufficient to cleanly separate the dynamics. In high-resistivity 6H-SiC, two transitions dominated between 100 and 1000 K, from which we extracted the Mu donor and acceptor ionization energies. In contrast, for high-resistivity 4H-SiC, the diamagnetic fraction remains quite flat over the whole range up to 1000 K. Additional dynamics are present at higher temperatures for 4H-SiC, as can be seen from Fig. 3.
Above approximately 950 K diamagnetic amplitudes in all three electrical types show a steep increase. Data will therefore be required in this higher temperature regime above 1000 K in order to assign either the donor or acceptor ionization energy for Mu in the 4H polytype of SiC.
Acknowledgments This work was supported by the US National Science Foundation (DMR-0604501) and the R.A. Welch Foundation (D-1321) and by the Royal Society of London. References [1] [2] [3] [4] [5] [6]
H.N. Bani-Salameh, et al., Physica B 401–402 (2007) 631. R.L. Lichti, W.A. Nussbaum, K.H. Chow, Phys. Rev. B 70 (2004) 165204. M. Kaukonen, C.J. Fall, J. Lento, Appl. Phys. Lett. 83 (2003) 923. H.N. Bani-Salameh, et al., Physica B 374–375 (2006) 368. O. Madelung (Ed.), Properties of Semiconductors, Springer, Berlin, 1996. H.N. Bani-Salameh, Ph.D. Dissertation, Texas Tech University, 2007, Unpublished. [7] C. Herring, N.M. Johnson, C.G. Van de Walle, Phys. Rev. B 64 (2001) 125209.