- Email: [email protected]
Stacking faults in silicon carbide
ARTICLE IN PRESS
Physica B 340–342 (2003) 165–170
Stacking faults in silicon carbide b . H.P. Iwataa,b,*, U. Lindefelta, S. Oberg , P.R. Briddonc a
Department of Physics and Measurement Technology, Linkoping University, SE-58183 Linkoping, Sweden . . b ( Sweden Department of Mathematics, Lulea( University of Technology, SE-97187 Lulea, c Department of Physics, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK
Abstract We review of our theoretical work on various stacking faults in SiC polytypes. Since the discovery of the electronic degradation phenomenon in 4H–SiC p–i–n diodes, stacking faults in SiC have become a subject of intensive study around the globe. At the beginning of our research project, the aim was to find the culprit for the degradation phenomenon, but in the course of this work we uncovered a wealth of information for the general properties of stacking faults in SiC. An intuitive perspective to the diverse nature of stacking faults in SiC will be given in this conference report. r 2003 Published by Elsevier B.V. Keywords: Stacking fault; Dislocations; Quantum well; Solid–solid phase transition
We have reported a series of theoretical studies on various stacking faults in SiC polytypes, based on first-principles density functional modelling, which lead to a detailed insight into general electronic properties of stacking disordered system [1]. This work is largely motivated by the discovery in 1999 by ABB Corporate Research of the electronic degradation phenomenon in 4H–SiC p–i–n diodes [2,3]. The p–i–n diodes gradually degraded in the sense that the voltage drop across the diode, for a constant current, increased gradually with the time of operation. More significantly, the timing of the electronic deterioration was correlated with the occurrence of structural defects, mainly interpreted as stacking *Corresponding author. Department of Physics and Mea. surement Technology, Linkoping University, SE-58183 Link. oping 58183, Sweden. Fax: +46-(0)13142337. E-mail address: [email protected] (H.P. Iwata). 0921-4526/$ - see front matter r 2003 Published by Elsevier B.V. doi:10.1016/j.physb.2003.09.045
faults in the basal planes. At the initial stage, our primary goal was to answer a simple question: even if stacking faults are created in connection with diode degradation, are they the culprit for degradation? However, later on, we encountered the unexpected diverse nature of stacking faults in SiC polytypes. In Ref. [4], we reported the discovery of localized electronic states around stacking faults in silicon carbide. It was found that certain types of stacking faults in 4H– and 6H–SiC can create very clear quantum-well-like structures. Additionally, all geometrically distinguishable intrinsic stacking faults in 3C–, 4H–, and 6H–SiC were recognized. Miao et al. also reached a similar conclusion for the interface states due to stacking faults by an ab initio calculation [5]. In Ref. [6], the stacking fault energies for all the different stacking faults in 3C–, 4H–, and 6H–SiC were calculated. These are in agreement with available experiments
ARTICLE IN PRESS 166
H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
[7,8]. In Ref. [9], a detailed investigation of cubic inclusions in 4H–SiC was performed. Moreover, strong evidence for the rich occurrence of doublestacking fault structure in 4H–SiC was revealed [9,10]. In Ref. [11], it was found that a wide variety of electronic properties of stacking faults in 3C–, 4H–, 6H–, and 15R–SiC can actually be classified into three classes according to the dominant factors that determine their electronic properties: (1) quantum-well class, (2) spontaneous-polarization class, and (3) electrically inactive class. In Ref. [12], a microscopic model to account for the effect of the spontaneous polarization on the electronic structures of stacking faults was developed. Some analysis based on a simple rectangular quantumwell model was also done. In Ref. [13], a theoretical investigation of stacking faults in 15R–SiC was reported. There are as many as five different stacking faults with different properties in this polytype. In Ref. [14], multiple stacking faults in 6H–SiC were investigated, and some differences from those in 4H–SiC were discussed. In Ref. [15], effective masses for two-dimensional electron gases around stacking faults, which are actually very novel two-dimensional quantum structures, were calculated. In Ref. [16], twin boundaries in 3C–SiC were studied in detail in comparison with those in Si and diamond, and we discovered that interacting twin boundaries which are separated by only two or three Si–C bilayers are actually favourable in energy. It is regrettable that the limited space of this article does not allow us to give all relevant references and introduce the diverse nature of these stacking faults in SiC in detail. Instead, we will give an intuitive perspective for the stacking disordered system in SiC. A wide range of structural, electronic, and thermodynamical properties of stacking faults in SiC, from solid–solid phase transition to electronic band structures can be understood in a consistent way. First, it is very important to understand the properties of perfect SiC polytypes. Let us review band gaps variation and band offsets in SiC polytypes. The indirect band gaps vary in a wide range from 2.4 to 3.3 eV as the hexagonality increases from 0% (3C–SiC) to 100% (2H–SiC). The well known Choyke-Hamiliton-Patrick rule
predicts that there is a linear relationship between the band gap and the degree of hexagonality up to 50% (4H–SiC) [17]. The valence band offset between 3C– and 2H–SiC have been calculated to be around 0.13 eV with the top of the valence band for 2H–SiC higher than that of 3C–SiC [18]. Assuming a linear dependence between the valence band offset and the hexagonality of each polytype, the valence band offsets for 3C–, 4H–, 15R–, 6H–, and 2H–SiC can be estimated. Since the experimental band gap values for these six polytypes are relatively well established, we can thereby estimate the conduction band offsets as well. This situation is shown in Fig. 1. There are very large conduction band offsets between the cubic and the other structures. These large conduction band offsets play a vital role for understanding of the electronic structures of stacking faults in SiC. Next, we review the crystalline structures of perfect and faulted SiC polytypes. We consider the stacking faults which can be created by the motion of partial dislocations after growth, since such stacking faults are closely associated with the electronic degradation in SiC-based bipolar devices. Moreover, recent advances in crystal growth technology can avoid the grown-in-type stacking faults to a great extent, except for narrow stacking fault ribbons between pairs of dissociated dislocations. Within this scheme, i.e., glide-type stacking faults, we have classified all possible structures for stacking faults in 3C–, 4H–, 6H–, and 15R–SiC. There exist one, two, three, and five geometrically distinguishable stacking faults in 3C–, 4H–, 6H–,
Ec=3.04
Ec=3.05
Ec=3.43
Ec=3.27
Ec=2.4 Eg=3.3 Eg=3.2 Eg=3.0
Eg=3.0
Eg=2.4
Ev=0[eV] 3C-SiC
Ev=0.04 6H-SiC
Ev=0.05 15R-SiC
Ev=0.13
Ev=0.07 4H-SiC
2H-SiC
Fig. 1. Band offsets of the SiC polytypes.
ARTICLE IN PRESS H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
and 15R–SiC, respectively. These situations are illustrated in Fig. 2. SF(31) and SF(13) in 4H–SiC are interrelated through the interchange of Si and C atoms. The same interrelationship is also found between SF(42) and SF(24) in 6H–SiC, as well as between SF(41) and SF(14) in 15R–SiC. There is of course only one glide-type stacking fault in 3C– SiC, which is called an intrinsic stacking fault, where a 2H-like (zigzag) region around the slip plane is seen. 2H-like regions also appear around SF(3111) in 6H–SiC and SF(1112) in 15R–SiC. On the other hand, SF(31) and SF(13) in 4H–SiC, SF(42) and SF(24) in 6H–SiC, and SF(41) and SF(14) in 15R–SiC create 3C-like (straight) regions, where the hexagonal turns (turning points in the zigzag stacking sequences) are shifted up or
3C-SiC (1120)
2
[0001] [1100]
2 2 Slip plane
2 2
Perfect
down along the c-axis, consequently more 3C-like regions emerge as indicated by the closed curves in Fig. 2. Finally, two stacking faults are left. SF(3322) and SF(2233) in 15R–SiC do not have any 3C-like or 2H-like regions, but the sequences become 6H-like below (above) the stacking fault plane and 4H-like above (below) the plane in SF(3322) [SF(2233)]. Now we are ready for exploring the electronic structures of stacking faults in the light of their geometric structures. Among a series of our theoretical studies, the most crucial finding is probably that certain types of stacking faults in SiC can create well-defined quantum-well structures for the conduction band electrons. Gap states and wave function localization in semiconductors are usually associated with
4H-SiC 2
6H-SiC
+ + + + + + -
SF
+ + + + + Perfect
SF(31)
167
2 2
3 1 2 2
SF(13)
Perfect
SF(42)
SF(3111)
SF(24)
15R-SiC 15R-SiC Five common SiC polytypes
Slip plane
(1120) y (0001)
A-sites B-sites C-sites
[0001] [1100]
C atom Si atom 6H-SiC
x 4H-SiC (1120) 3C-SiC c-axis 2H-SiC
Perfect
SF(3322)
SF(1112)
SF(2233)
SF(41)
SF(14)
AB
ABC
ABC
ABCA
ABCABC
Fig. 2. Geometrically distinguishable glide-type stacking faults for the 3C, 4H, 6H, and 15R polytypes. The notation system is briefly described using perfect 4H–SiC and 4H–SiC with SF(13).
ARTICLE IN PRESS H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
168
distorted or broken bonds such as point defects, dislocations, or surfaces. In the case of stacking faults, however, the crystal retains its perfect structure on both sides of the stacking fault plane. To our knowledge, stacking faults in no other semiconductors have been associated with such a clear quantum-well structure in SiC. The mechanism behind the strong localizations parallel to the c-axis in the vicinity of stacking fault planes can be understood very well in the following way. The conduction band offsets between the cubic and hexagonal polytypes are very large, e.g., the offset between 4H(6H) and 3C is about 0.87 (0.64) eV, while the valence band offset is B10% of them. Therefore the conduction band electrons can be confined in the locally lower conduction bands around thin cubic regions even ( thick, though these 3C-like layers are only B10 A due to a quantum confinement effect, as illustrated in Fig. 3. These bound electrons around the stacking faults can however move freely along the wells, and can be thought as two-dimensional electron gases. These quantum-well-like features of stacking faults are responsible for the electronic degradation, hindering normal carrier transport in the diodes. On the other hand, in intrinsic stacking faults in 3C–SiC, SF(3111) in 6H–SiC, and SF(1112) in 15R–SiC there are in effect 2H-like zigzag sequences in the host crystals. Here, let us remember that all SiC crystals, except for 3C– SiC, are polar materials. According to Qteish et al., in SiC a spontaneous polarization takes place around each hexagonal turn (turning point in the
zigzag stacking sequences), which is quite strongly localized at the turn [18]. Since such spontaneous polarization does not occur in 3C–SiC for symmetry, the macroscopic electric dipole moment of a SiC crystal is approximately promotional to the degree of hexagonality [18]. The hexagonality around these stacking faults is locally greater, i.e., two additional hexagonal turns, compared with their perfect structures, are inserted around the slip planes, and hence the effects of the spontaneous polarization around these defects should be more emphasized than those in the mother structures, leading to the electric dipole moments built in throughout the 2H-like zigzag sequences. Furthermore, these electric dipoles throughout the 2H-like thin layers are directed in the opposite direction along the c-axis, with the lower (upper) ends positively (negatively) charged. The perturbation potential due to the spontaneous polarization for an electron is depicted schematically in Fig. 4 for SF(3111) in 6H–SiC. The electron attractive part (to the left) is capable of pulling the bottom of the conduction band into the band gap, thus giving rise to localized states, while the electron repulsive part (to the right) pushes up the top of the valence band into the gap. Consequently, the perturbation potential in Fig. 4 can give rise to a local band gap narrowing around the stacking fault layer. These 2H-like faulted layers appear to shrink the local band gap by around 0.1–0.2 eV. Finally, two stacking faults structures are left, i.e., SF(3322) and SF(2233) in 15R–SiC. They
Energy Offset between 3C- and 4H-SiC
c-axis
Conduction band
Size of 3C-like region
4H-SiC with SF(31)
Valence band
Fig. 3. A simple quantum-well model for the stacking fault structure.
2H-like region
6H-SiC with SF(3111)
Fig. 4. Spontaneous-polarization-induced perturbation potential for SF(3111) in 6H–SiC.
ARTICLE IN PRESS H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
169
Table 1 Classification of the single isolated stacking faults in terms of their electronic properties Quantum-well class Spontaneous-polarization class Electrically inactive class
SF(31) and SF(13) in 4H–SiC, SF(42) and SF(24) in 6H–SiC, SF(41) and SF(14) in 15R–SiC Intrinsic SFs in 3C–SiC, SF(3111) in 6H–SiC, SF(1112) in 15R–SiC SF(3322) and SF(2233) in 15R–SiC
have neither 2H-like nor 3C-like sequences. In fact, our supercell calculation indicates that they are almost electrically inactive. The characteristic features in the electronic structures of stacking faults in SiC can be summarized in the following way. 1. If a thin 3C-like straight sequence is created, a split-off band below the conduction band minimum is induced, which is strongly localized around the stacking fault plane along the c-axis but still keeps full dispersion parallel to the stacking fault plane, due to the quantum confinement effect. 2. If a thin 2H-like zigzag sequence is formed, shallow localized states appear at the band edges, where the conduction (valence) band electrons are localized below (above) the stacking fault plane, due to the electric dipole moment induced by the spontaneous polarization around the 2H-like layer. 3. If neither 2H-like zigzag sequence nor 3C-like straight sequence is introduced, no clear states in the fundamental band gap can be seen. Therefore, stacking faults in SiC can be divided into three classes, namely, (1) quantum-well class, (2) spontaneous-polarization class, and (3) electrically inactive class, as summarized in Table 1. We have also done a couple of studies on multiple-stacking fault structures in SiC, i.e., more than two stacking faults are inserted in a crystal. Their interactions lead to several interesting phenomena. Unfortunately, it is not possible to describe them as well as other topics such as stacking fault energy or two-dimensional electron gases around stacking faults in this short report due to lack of space. We would like to encourage the readers to look into the references given in this article for more detailed information.
References . [1] H. Iwata, Ph.D. Thesis no. 817, Linkoping University, 2003. [2] H. Lendenmann, F. Dahlquist, N. Johansson, R. S( Nilsson, J.P. Bergman, P. Skytt, Mater. . oderholm, P.A. Sci. Forum 353–356 (2001) 727. ( Nilsson, U. Lindefelt, [3] J.P. Bergman, H. Lendenmann, P.A. P. Skytt, Mater. Sci. Forum 353–356 (2001) 299. . [4] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 389–393 (2002) 529; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Phys. Rev. B 65 (2002) 033203. [5] M.S. Miao, S. Limpijumnong, W. Lambrecht, Appl. Phys. Lett. 79 (2001) 4360. . [6] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 389–393 (2002) 439. [7] K. Maeda, K. Suzuki, S. Fujita, M. Ichihara, S. Hyodo, Philos. Mag. A 57 (1988) 573. [8] M.H. Hong, A.V. Samant, P. Pirouz, Philos. Mag. A 80 (2000) 919. . [9] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 389–393 (2002) 533; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, J. Appl. Phys. 93 (2003) 1577. [10] T.A. Kuhr, J.Q. Liu, H.J. Chung, M. Skowronski, F. Szmulowicz, J. Appl. Phys. 92 (2002) 5863. . [11] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, J. Phys.: Condens. Matter 14 (2002) 12733. . [12] U. Lindefelt, H. Iwata, S. Oberg, P.R. Briddon, Phys. Rev. B 67 (2003) 155204; . U. Lindefelt, H. Iwata, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 907. . [13] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 531. . [14] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 921; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, J. Appl. Phys., accepted. . [15] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 519; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Microelectronics J. 34 (2003) 371; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Phys. Rev. B, submitted. . [16] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 527;
ARTICLE IN PRESS 170
H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
. H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Phys. Rev. B 68 (2003) 113203. [17] W.J. Choyke, D.R. Hamilton, L. Patrick, Phys. Rev. A 133 (1964) 1163.
[18] A. Qteish, V. Heine, R.J. Needs, Phys. Rev. B 45 (1992) 6534; A. Qteish, V. Heine, R.J. Needs, Phys. Rev. B 45 (1992) 6376.
Physica B 340–342 (2003) 165–170
Stacking faults in silicon carbide b . H.P. Iwataa,b,*, U. Lindefelta, S. Oberg , P.R. Briddonc a
Department of Physics and Measurement Technology, Linkoping University, SE-58183 Linkoping, Sweden . . b ( Sweden Department of Mathematics, Lulea( University of Technology, SE-97187 Lulea, c Department of Physics, University of Newcastle upon Tyne, Newcastle NE1 7RU, UK
Abstract We review of our theoretical work on various stacking faults in SiC polytypes. Since the discovery of the electronic degradation phenomenon in 4H–SiC p–i–n diodes, stacking faults in SiC have become a subject of intensive study around the globe. At the beginning of our research project, the aim was to find the culprit for the degradation phenomenon, but in the course of this work we uncovered a wealth of information for the general properties of stacking faults in SiC. An intuitive perspective to the diverse nature of stacking faults in SiC will be given in this conference report. r 2003 Published by Elsevier B.V. Keywords: Stacking fault; Dislocations; Quantum well; Solid–solid phase transition
We have reported a series of theoretical studies on various stacking faults in SiC polytypes, based on first-principles density functional modelling, which lead to a detailed insight into general electronic properties of stacking disordered system [1]. This work is largely motivated by the discovery in 1999 by ABB Corporate Research of the electronic degradation phenomenon in 4H–SiC p–i–n diodes [2,3]. The p–i–n diodes gradually degraded in the sense that the voltage drop across the diode, for a constant current, increased gradually with the time of operation. More significantly, the timing of the electronic deterioration was correlated with the occurrence of structural defects, mainly interpreted as stacking *Corresponding author. Department of Physics and Mea. surement Technology, Linkoping University, SE-58183 Link. oping 58183, Sweden. Fax: +46-(0)13142337. E-mail address: [email protected] (H.P. Iwata). 0921-4526/$ - see front matter r 2003 Published by Elsevier B.V. doi:10.1016/j.physb.2003.09.045
faults in the basal planes. At the initial stage, our primary goal was to answer a simple question: even if stacking faults are created in connection with diode degradation, are they the culprit for degradation? However, later on, we encountered the unexpected diverse nature of stacking faults in SiC polytypes. In Ref. [4], we reported the discovery of localized electronic states around stacking faults in silicon carbide. It was found that certain types of stacking faults in 4H– and 6H–SiC can create very clear quantum-well-like structures. Additionally, all geometrically distinguishable intrinsic stacking faults in 3C–, 4H–, and 6H–SiC were recognized. Miao et al. also reached a similar conclusion for the interface states due to stacking faults by an ab initio calculation [5]. In Ref. [6], the stacking fault energies for all the different stacking faults in 3C–, 4H–, and 6H–SiC were calculated. These are in agreement with available experiments
ARTICLE IN PRESS 166
H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
[7,8]. In Ref. [9], a detailed investigation of cubic inclusions in 4H–SiC was performed. Moreover, strong evidence for the rich occurrence of doublestacking fault structure in 4H–SiC was revealed [9,10]. In Ref. [11], it was found that a wide variety of electronic properties of stacking faults in 3C–, 4H–, 6H–, and 15R–SiC can actually be classified into three classes according to the dominant factors that determine their electronic properties: (1) quantum-well class, (2) spontaneous-polarization class, and (3) electrically inactive class. In Ref. [12], a microscopic model to account for the effect of the spontaneous polarization on the electronic structures of stacking faults was developed. Some analysis based on a simple rectangular quantumwell model was also done. In Ref. [13], a theoretical investigation of stacking faults in 15R–SiC was reported. There are as many as five different stacking faults with different properties in this polytype. In Ref. [14], multiple stacking faults in 6H–SiC were investigated, and some differences from those in 4H–SiC were discussed. In Ref. [15], effective masses for two-dimensional electron gases around stacking faults, which are actually very novel two-dimensional quantum structures, were calculated. In Ref. [16], twin boundaries in 3C–SiC were studied in detail in comparison with those in Si and diamond, and we discovered that interacting twin boundaries which are separated by only two or three Si–C bilayers are actually favourable in energy. It is regrettable that the limited space of this article does not allow us to give all relevant references and introduce the diverse nature of these stacking faults in SiC in detail. Instead, we will give an intuitive perspective for the stacking disordered system in SiC. A wide range of structural, electronic, and thermodynamical properties of stacking faults in SiC, from solid–solid phase transition to electronic band structures can be understood in a consistent way. First, it is very important to understand the properties of perfect SiC polytypes. Let us review band gaps variation and band offsets in SiC polytypes. The indirect band gaps vary in a wide range from 2.4 to 3.3 eV as the hexagonality increases from 0% (3C–SiC) to 100% (2H–SiC). The well known Choyke-Hamiliton-Patrick rule
predicts that there is a linear relationship between the band gap and the degree of hexagonality up to 50% (4H–SiC) [17]. The valence band offset between 3C– and 2H–SiC have been calculated to be around 0.13 eV with the top of the valence band for 2H–SiC higher than that of 3C–SiC [18]. Assuming a linear dependence between the valence band offset and the hexagonality of each polytype, the valence band offsets for 3C–, 4H–, 15R–, 6H–, and 2H–SiC can be estimated. Since the experimental band gap values for these six polytypes are relatively well established, we can thereby estimate the conduction band offsets as well. This situation is shown in Fig. 1. There are very large conduction band offsets between the cubic and the other structures. These large conduction band offsets play a vital role for understanding of the electronic structures of stacking faults in SiC. Next, we review the crystalline structures of perfect and faulted SiC polytypes. We consider the stacking faults which can be created by the motion of partial dislocations after growth, since such stacking faults are closely associated with the electronic degradation in SiC-based bipolar devices. Moreover, recent advances in crystal growth technology can avoid the grown-in-type stacking faults to a great extent, except for narrow stacking fault ribbons between pairs of dissociated dislocations. Within this scheme, i.e., glide-type stacking faults, we have classified all possible structures for stacking faults in 3C–, 4H–, 6H–, and 15R–SiC. There exist one, two, three, and five geometrically distinguishable stacking faults in 3C–, 4H–, 6H–,
Ec=3.04
Ec=3.05
Ec=3.43
Ec=3.27
Ec=2.4 Eg=3.3 Eg=3.2 Eg=3.0
Eg=3.0
Eg=2.4
Ev=0[eV] 3C-SiC
Ev=0.04 6H-SiC
Ev=0.05 15R-SiC
Ev=0.13
Ev=0.07 4H-SiC
2H-SiC
Fig. 1. Band offsets of the SiC polytypes.
ARTICLE IN PRESS H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
and 15R–SiC, respectively. These situations are illustrated in Fig. 2. SF(31) and SF(13) in 4H–SiC are interrelated through the interchange of Si and C atoms. The same interrelationship is also found between SF(42) and SF(24) in 6H–SiC, as well as between SF(41) and SF(14) in 15R–SiC. There is of course only one glide-type stacking fault in 3C– SiC, which is called an intrinsic stacking fault, where a 2H-like (zigzag) region around the slip plane is seen. 2H-like regions also appear around SF(3111) in 6H–SiC and SF(1112) in 15R–SiC. On the other hand, SF(31) and SF(13) in 4H–SiC, SF(42) and SF(24) in 6H–SiC, and SF(41) and SF(14) in 15R–SiC create 3C-like (straight) regions, where the hexagonal turns (turning points in the zigzag stacking sequences) are shifted up or
3C-SiC (1120)
2
[0001] [1100]
2 2 Slip plane
2 2
Perfect
down along the c-axis, consequently more 3C-like regions emerge as indicated by the closed curves in Fig. 2. Finally, two stacking faults are left. SF(3322) and SF(2233) in 15R–SiC do not have any 3C-like or 2H-like regions, but the sequences become 6H-like below (above) the stacking fault plane and 4H-like above (below) the plane in SF(3322) [SF(2233)]. Now we are ready for exploring the electronic structures of stacking faults in the light of their geometric structures. Among a series of our theoretical studies, the most crucial finding is probably that certain types of stacking faults in SiC can create well-defined quantum-well structures for the conduction band electrons. Gap states and wave function localization in semiconductors are usually associated with
4H-SiC 2
6H-SiC
+ + + + + + -
SF
+ + + + + Perfect
SF(31)
167
2 2
3 1 2 2
SF(13)
Perfect
SF(42)
SF(3111)
SF(24)
15R-SiC 15R-SiC Five common SiC polytypes
Slip plane
(1120) y (0001)
A-sites B-sites C-sites
[0001] [1100]
C atom Si atom 6H-SiC
x 4H-SiC (1120) 3C-SiC c-axis 2H-SiC
Perfect
SF(3322)
SF(1112)
SF(2233)
SF(41)
SF(14)
AB
ABC
ABC
ABCA
ABCABC
Fig. 2. Geometrically distinguishable glide-type stacking faults for the 3C, 4H, 6H, and 15R polytypes. The notation system is briefly described using perfect 4H–SiC and 4H–SiC with SF(13).
ARTICLE IN PRESS H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
168
distorted or broken bonds such as point defects, dislocations, or surfaces. In the case of stacking faults, however, the crystal retains its perfect structure on both sides of the stacking fault plane. To our knowledge, stacking faults in no other semiconductors have been associated with such a clear quantum-well structure in SiC. The mechanism behind the strong localizations parallel to the c-axis in the vicinity of stacking fault planes can be understood very well in the following way. The conduction band offsets between the cubic and hexagonal polytypes are very large, e.g., the offset between 4H(6H) and 3C is about 0.87 (0.64) eV, while the valence band offset is B10% of them. Therefore the conduction band electrons can be confined in the locally lower conduction bands around thin cubic regions even ( thick, though these 3C-like layers are only B10 A due to a quantum confinement effect, as illustrated in Fig. 3. These bound electrons around the stacking faults can however move freely along the wells, and can be thought as two-dimensional electron gases. These quantum-well-like features of stacking faults are responsible for the electronic degradation, hindering normal carrier transport in the diodes. On the other hand, in intrinsic stacking faults in 3C–SiC, SF(3111) in 6H–SiC, and SF(1112) in 15R–SiC there are in effect 2H-like zigzag sequences in the host crystals. Here, let us remember that all SiC crystals, except for 3C– SiC, are polar materials. According to Qteish et al., in SiC a spontaneous polarization takes place around each hexagonal turn (turning point in the
zigzag stacking sequences), which is quite strongly localized at the turn [18]. Since such spontaneous polarization does not occur in 3C–SiC for symmetry, the macroscopic electric dipole moment of a SiC crystal is approximately promotional to the degree of hexagonality [18]. The hexagonality around these stacking faults is locally greater, i.e., two additional hexagonal turns, compared with their perfect structures, are inserted around the slip planes, and hence the effects of the spontaneous polarization around these defects should be more emphasized than those in the mother structures, leading to the electric dipole moments built in throughout the 2H-like zigzag sequences. Furthermore, these electric dipoles throughout the 2H-like thin layers are directed in the opposite direction along the c-axis, with the lower (upper) ends positively (negatively) charged. The perturbation potential due to the spontaneous polarization for an electron is depicted schematically in Fig. 4 for SF(3111) in 6H–SiC. The electron attractive part (to the left) is capable of pulling the bottom of the conduction band into the band gap, thus giving rise to localized states, while the electron repulsive part (to the right) pushes up the top of the valence band into the gap. Consequently, the perturbation potential in Fig. 4 can give rise to a local band gap narrowing around the stacking fault layer. These 2H-like faulted layers appear to shrink the local band gap by around 0.1–0.2 eV. Finally, two stacking faults structures are left, i.e., SF(3322) and SF(2233) in 15R–SiC. They
Energy Offset between 3C- and 4H-SiC
c-axis
Conduction band
Size of 3C-like region
4H-SiC with SF(31)
Valence band
Fig. 3. A simple quantum-well model for the stacking fault structure.
2H-like region
6H-SiC with SF(3111)
Fig. 4. Spontaneous-polarization-induced perturbation potential for SF(3111) in 6H–SiC.
ARTICLE IN PRESS H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
169
Table 1 Classification of the single isolated stacking faults in terms of their electronic properties Quantum-well class Spontaneous-polarization class Electrically inactive class
SF(31) and SF(13) in 4H–SiC, SF(42) and SF(24) in 6H–SiC, SF(41) and SF(14) in 15R–SiC Intrinsic SFs in 3C–SiC, SF(3111) in 6H–SiC, SF(1112) in 15R–SiC SF(3322) and SF(2233) in 15R–SiC
have neither 2H-like nor 3C-like sequences. In fact, our supercell calculation indicates that they are almost electrically inactive. The characteristic features in the electronic structures of stacking faults in SiC can be summarized in the following way. 1. If a thin 3C-like straight sequence is created, a split-off band below the conduction band minimum is induced, which is strongly localized around the stacking fault plane along the c-axis but still keeps full dispersion parallel to the stacking fault plane, due to the quantum confinement effect. 2. If a thin 2H-like zigzag sequence is formed, shallow localized states appear at the band edges, where the conduction (valence) band electrons are localized below (above) the stacking fault plane, due to the electric dipole moment induced by the spontaneous polarization around the 2H-like layer. 3. If neither 2H-like zigzag sequence nor 3C-like straight sequence is introduced, no clear states in the fundamental band gap can be seen. Therefore, stacking faults in SiC can be divided into three classes, namely, (1) quantum-well class, (2) spontaneous-polarization class, and (3) electrically inactive class, as summarized in Table 1. We have also done a couple of studies on multiple-stacking fault structures in SiC, i.e., more than two stacking faults are inserted in a crystal. Their interactions lead to several interesting phenomena. Unfortunately, it is not possible to describe them as well as other topics such as stacking fault energy or two-dimensional electron gases around stacking faults in this short report due to lack of space. We would like to encourage the readers to look into the references given in this article for more detailed information.
References . [1] H. Iwata, Ph.D. Thesis no. 817, Linkoping University, 2003. [2] H. Lendenmann, F. Dahlquist, N. Johansson, R. S( Nilsson, J.P. Bergman, P. Skytt, Mater. . oderholm, P.A. Sci. Forum 353–356 (2001) 727. ( Nilsson, U. Lindefelt, [3] J.P. Bergman, H. Lendenmann, P.A. P. Skytt, Mater. Sci. Forum 353–356 (2001) 299. . [4] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 389–393 (2002) 529; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Phys. Rev. B 65 (2002) 033203. [5] M.S. Miao, S. Limpijumnong, W. Lambrecht, Appl. Phys. Lett. 79 (2001) 4360. . [6] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 389–393 (2002) 439. [7] K. Maeda, K. Suzuki, S. Fujita, M. Ichihara, S. Hyodo, Philos. Mag. A 57 (1988) 573. [8] M.H. Hong, A.V. Samant, P. Pirouz, Philos. Mag. A 80 (2000) 919. . [9] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 389–393 (2002) 533; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, J. Appl. Phys. 93 (2003) 1577. [10] T.A. Kuhr, J.Q. Liu, H.J. Chung, M. Skowronski, F. Szmulowicz, J. Appl. Phys. 92 (2002) 5863. . [11] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, J. Phys.: Condens. Matter 14 (2002) 12733. . [12] U. Lindefelt, H. Iwata, S. Oberg, P.R. Briddon, Phys. Rev. B 67 (2003) 155204; . U. Lindefelt, H. Iwata, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 907. . [13] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 531. . [14] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 921; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, J. Appl. Phys., accepted. . [15] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 519; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Microelectronics J. 34 (2003) 371; . H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Phys. Rev. B, submitted. . [16] H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Mater. Sci. Forum 433–436 (2002) 527;
ARTICLE IN PRESS 170
H.P. Iwata et al. / Physica B 340–342 (2003) 165–170
. H. Iwata, U. Lindefelt, S. Oberg, P.R. Briddon, Phys. Rev. B 68 (2003) 113203. [17] W.J. Choyke, D.R. Hamilton, L. Patrick, Phys. Rev. A 133 (1964) 1163.
[18] A. Qteish, V. Heine, R.J. Needs, Phys. Rev. B 45 (1992) 6534; A. Qteish, V. Heine, R.J. Needs, Phys. Rev. B 45 (1992) 6376.