Abstract

We find the first, simple, analytical expressions for the bound states of a short-ranged, spherically-symmetric deep center potential in terms of the eigenstates of total (spin plus Bloch plus envelope) angular momentum and the Kane 8×8 k ·p Hamiltonian. We find that the spatial extent of the deep center bound state is proportional to the Kane dipole. This physical size of the deep center bound state is in excellent agreement with both scanning-tunneling-microscopy and measured optical dipoles.

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References

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  1. G. M. Martin, "Optical assessment of the main electron trap in bulk semi-insulating GaAs," Appl. Phys. Lett. 39, 747-749, (1981).
    [CrossRef]
  2. P. Silverberg, P. Omling, and L. Samuelson, "Hole photoionization cross sections of EL2 in GaAs," Appl. Phys. Lett. 52, 1689-1691, (1988).
    [CrossRef]
  3. A. Chantre, G. Vincent, and D. Bois, "Deep-level optical spectroscopy in GaAs," Phys. Rev. B 23, 5335-5359, (1981).
    [CrossRef]
  4. G. A. Baraff and M. A. Schluter, "Electronic aspects of the optical-absorption spectrum of the EL2 defect in GaAs," Phys. Rev. B 45, 8300-8309, (1992).
    [CrossRef]
  5. G. A. Baraff, "Stress splitting of the EL2 zero-phonon line: Need for reinterpretation of the main optical transitions," Phys. Rev. B 41, 9850-9859, (1990).
    [CrossRef]
  6. M. R. Melloch, J. M. Woodall, E. S. Harmon, N. Otsuka, F. H. Pollak, D. D. Nolte, R. M. Feenstra, and M. A. Lutz, "Low-temperature grown III-V materials," Ann. Rev. Mater. Sci. 25, 547-600, (1995).
    [CrossRef]
  7. M. R. Melloch, D. D. Nolte, J. M. Woodall, J. C. P. Chang, D. B. Janes, and E. S. Harmon, "Molecular beam epitaxy of nonstoichiometric semiconductors and multiphase material systems," Crit. Rev. in Sol. St. and Mater. Sci. 21, 189-263, (1996).
    [CrossRef]
  8. G. Lucovsky, "On the photoionization of deep impurity centers in semiconductors," Sold. St. Comm. 3, 299-302, (1965).
    [CrossRef]
  9. S. T. Pantelides, "The electronic structure of impurities and other point defects in semiconductors," Rev. Mod. Phys. 50, 798-858, (1978).
    [CrossRef]
  10. M. Jaros, "Wave functions and optical cross sections associated with deep centers in semiconductors," Phys. Rev. B 16, 3694-3706, (1977).
    [CrossRef]
  11. E. O. Kane, "Band structure of indium antimonide," J. Phys. Chem. Sol. 1, 249-261, (1957).
    [CrossRef]
  12. A. Baldereschi and N. O. Lipari, "Spherical model of shallow acceptor states in semiconductors," Phys. Rev. B 8, 2697-2709, (1973).
    [CrossRef]
  13. P. C. Sercel and K. J. Vahala, "Analytical formalism for determining quantum-wire and quantum-dot band structure in the multiband envelope function approximation," Phys. Rev. B 42, 3690-3710, (1990).
    [CrossRef]
  14. R. M. Feenstra, "Cross-sectional scanning tunneling microscopy of III-V semiconductor structures," Semicond. Sci. Tech. 9, 2157-2168, (1994).
    [CrossRef]
  15. R. M. Feenstra, J. M. Woodall, and G. D. Pettit, "Observation of bulk defects by scanning tunneling microscopy and spectroscopy: Arsenic antisites defects in GaAs," Phys. Rev. Lett. 71, 1176-1179, (1993).
    [CrossRef] [PubMed]
  16. M. E. Rose, Elementary Theory of Angular Momentum, (Wiley, New York, 1957).
  17. We have also assumed the deep center bound states to have a Gaussian distribution with a standard deviation of 0.078eV, as is consistent with the scanning-tunneling-spectroscopy measurements of Feenstra [15].
  18. R. E. Viturro, M. R. Melloch, and J. M. Woodall, "Optical emission properties of semi-insulating GaAs grown at low temperatures by molecular beam epitaxy," Appl. Phys. Lett. 60, 3007-3009 (1992).
    [CrossRef]

Other

G. M. Martin, "Optical assessment of the main electron trap in bulk semi-insulating GaAs," Appl. Phys. Lett. 39, 747-749, (1981).
[CrossRef]

P. Silverberg, P. Omling, and L. Samuelson, "Hole photoionization cross sections of EL2 in GaAs," Appl. Phys. Lett. 52, 1689-1691, (1988).
[CrossRef]

A. Chantre, G. Vincent, and D. Bois, "Deep-level optical spectroscopy in GaAs," Phys. Rev. B 23, 5335-5359, (1981).
[CrossRef]

G. A. Baraff and M. A. Schluter, "Electronic aspects of the optical-absorption spectrum of the EL2 defect in GaAs," Phys. Rev. B 45, 8300-8309, (1992).
[CrossRef]

G. A. Baraff, "Stress splitting of the EL2 zero-phonon line: Need for reinterpretation of the main optical transitions," Phys. Rev. B 41, 9850-9859, (1990).
[CrossRef]

M. R. Melloch, J. M. Woodall, E. S. Harmon, N. Otsuka, F. H. Pollak, D. D. Nolte, R. M. Feenstra, and M. A. Lutz, "Low-temperature grown III-V materials," Ann. Rev. Mater. Sci. 25, 547-600, (1995).
[CrossRef]

M. R. Melloch, D. D. Nolte, J. M. Woodall, J. C. P. Chang, D. B. Janes, and E. S. Harmon, "Molecular beam epitaxy of nonstoichiometric semiconductors and multiphase material systems," Crit. Rev. in Sol. St. and Mater. Sci. 21, 189-263, (1996).
[CrossRef]

G. Lucovsky, "On the photoionization of deep impurity centers in semiconductors," Sold. St. Comm. 3, 299-302, (1965).
[CrossRef]

S. T. Pantelides, "The electronic structure of impurities and other point defects in semiconductors," Rev. Mod. Phys. 50, 798-858, (1978).
[CrossRef]

M. Jaros, "Wave functions and optical cross sections associated with deep centers in semiconductors," Phys. Rev. B 16, 3694-3706, (1977).
[CrossRef]

E. O. Kane, "Band structure of indium antimonide," J. Phys. Chem. Sol. 1, 249-261, (1957).
[CrossRef]

A. Baldereschi and N. O. Lipari, "Spherical model of shallow acceptor states in semiconductors," Phys. Rev. B 8, 2697-2709, (1973).
[CrossRef]

P. C. Sercel and K. J. Vahala, "Analytical formalism for determining quantum-wire and quantum-dot band structure in the multiband envelope function approximation," Phys. Rev. B 42, 3690-3710, (1990).
[CrossRef]

R. M. Feenstra, "Cross-sectional scanning tunneling microscopy of III-V semiconductor structures," Semicond. Sci. Tech. 9, 2157-2168, (1994).
[CrossRef]

R. M. Feenstra, J. M. Woodall, and G. D. Pettit, "Observation of bulk defects by scanning tunneling microscopy and spectroscopy: Arsenic antisites defects in GaAs," Phys. Rev. Lett. 71, 1176-1179, (1993).
[CrossRef] [PubMed]

M. E. Rose, Elementary Theory of Angular Momentum, (Wiley, New York, 1957).

We have also assumed the deep center bound states to have a Gaussian distribution with a standard deviation of 0.078eV, as is consistent with the scanning-tunneling-spectroscopy measurements of Feenstra [15].

R. E. Viturro, M. R. Melloch, and J. M. Woodall, "Optical emission properties of semi-insulating GaAs grown at low temperatures by molecular beam epitaxy," Appl. Phys. Lett. 60, 3007-3009 (1992).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

F = 1 2 , F z = 1 2 ; L = 0 , J = 1 2 ( L B = 0 ) is the part of |d〉 which has conduction-band character. The spatial extent, α -1, of the bound state is in excellent agreement with STM images by Feenstra [14, 15].

Fig. 2.
Fig. 2.

F = 1 2 , F z = 1 2 ;L=1, J = 3 2 ( L B = 1 ) is the part of |d〉 which has light-hole character. Yellow and green, respectively, denote Bloch and envelope wave functions.

Fig. 3.
Fig. 3.

The antisymmetric linear combination of orbitals |1〉+|2〉-|3〉-|4〉 has the same symmetry as the |L=1, Lz =0〉 envelope function in Fig.2.

Fig. 4.
Fig. 4.

The solid line is the calculated cross-section (from Eq. (6)) for emission from the AsGa antisite to the valence band. The circles denote measurements by Silverberg [2].

Equations (18)

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d = N [ E d E V E G f L = 0 ( r ) F = 1 2 , F z = 1 2 ; L = 0 , J = 1 2 ( L B = 0 ) +
+ 2 3 E C E d E G f L = 1 ( r ) F = 1 2 , F z = 1 2 ; L = 1 , J = 3 2 ( L B = 1 ) +
+ 1 3 E C E d E G f L = 1 ( r ) F = 1 2 , F z = 1 2 ; L = 1 , J = 1 2 ( L B = 1 ) ]
[ E + E + 2 3 ] E ( E E G ) = { P 2 k 2 for E E G , or E < 0 P 2 α 2 for 0 < E < E G
α 1 = < s z z E G E d ( E G E d )
2 < s z z for deep center ,
v = N [ E E V E G f L = 1 ( r ) F = 1 2 , F z = 1 2 ; L = 1 , J = 1 2 ( L B = 0 ) +
+ 2 3 E C E E G f L = 2 ( r ) F = 1 2 , F z = 1 2 ; L = 2 , J = 3 2 ( L B = 1 ) +
+ 1 3 E C E E G f L = 0 ( r ) F = 1 2 , F z = 1 2 ; L = 0 , J = 1 2 ( L B = 1 ) ]
v = N [ E E V E G f L = 1 ( r ) F = 3 2 , F z = 1 2 ; L = 1 , J = 1 2 ( L B = 0 ) +
+ 1 3 E C E E G f L = 0 ( r ) F = 3 2 , F z = 1 2 ; L = 0 , J = 3 2 ( L B = 1 ) +
+ 1 3 E C E E G f L = 2 ( r ) F = 3 2 , F z = 1 2 ; L = 2 , J = 3 2 ( L B = 1 ) +
+ 1 3 E C E E G f L = 2 ( r ) F = 3 2 , F z = 1 2 ; L = 2 , J = 1 2 ( L B = 1 ) ]
f = 2 3 f ( d , l h ) + 1 3 f ( d , h h )
f ( d , h h ) g h h ( E ) = 4 3 π [ 1 E d E ] E P E G { E d 3 / 2 ( E G E d ) 1 / 2 ( E ) 1 / 2 ( E G E ) 3 / 2 [ E d ( E G E d ) + ( E ) ( E G E ) ] 2 }
× [ E G ( α R C / 2 ) E d ( α R C / 2 ) + ( E G E d ) ] ,
f ( d , lh ) glh ( E ) = 4 3 π [ 1 E d E ] E P E G { E d 3 / 2 ( E G E d ) 1 / 2 ( E ) 1 / 2 ( m H H m 0 E P ) 3 / 2 [ E d ( E G E d ) + ( E ) ( m H H m 0 E P ) ] 2 }
× [ E G ( α R C / 2 ) E d ( α R C / 2 ) + ( E G E d ) ] .

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