Limits...
Spherical, cylindrical and tetrahedral symmetries; hydrogenic states at high magnetic field in Si:P.

Lewis RA, Bruno-Alfonso A, de Souza GV, Vickers RE, Colla JA, Constable E - Sci Rep (2013)

Bottom Line: While the hydrogen atom is spherically symmetric, an applied magnetic field imposes cylindrical symmetry, and the solid-state analogue involves, in addition, the symmetry of the Si crystal.For one magnetic field direction, all six conduction-band valleys of Si:P become equivalent.New experimental data to high laboratory fields (30 T), supported by new calculations, demonstrate that this high symmetry field orientation allows the most direct comparison with free hydrogen.

View Article: PubMed Central - PubMed

Affiliation: Institute for Superconducting and Electronic Materials, University of Wollongong, Wollongong, New South Wales 2522, Australia.

ABSTRACT
Phosphorous donors in silicon have an electronic structure that mimics the hydrogen atom, albeit on a larger length, smaller energy and smaller magnetic field scale. While the hydrogen atom is spherically symmetric, an applied magnetic field imposes cylindrical symmetry, and the solid-state analogue involves, in addition, the symmetry of the Si crystal. For one magnetic field direction, all six conduction-band valleys of Si:P become equivalent. New experimental data to high laboratory fields (30 T), supported by new calculations, demonstrate that this high symmetry field orientation allows the most direct comparison with free hydrogen.

No MeSH data available.


Related in: MedlinePlus

Experimental spectra of Si:P at magnetic fields of B = 0, 1 and 2 T with B//〈111〉.The absorption coefficient has been calculated in the usual way. For clarity, the spectra for 1 and 2 T have been offset on the vertical axis by 10 and 20 cm−1, respectively. As highlighted, the lower branch of the transition labelled 3p± interacts with the transition labelled 4p0 at around 1 T and the upper branch of transition labelled 3p± interacts with the transition labelled 4f0 (not evident at 0 T) at around 2 T.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC3860012&req=5

f3: Experimental spectra of Si:P at magnetic fields of B = 0, 1 and 2 T with B//〈111〉.The absorption coefficient has been calculated in the usual way. For clarity, the spectra for 1 and 2 T have been offset on the vertical axis by 10 and 20 cm−1, respectively. As highlighted, the lower branch of the transition labelled 3p± interacts with the transition labelled 4p0 at around 1 T and the upper branch of transition labelled 3p± interacts with the transition labelled 4f0 (not evident at 0 T) at around 2 T.

Mentions: Finally, to better deal with transitions of higher energies than the 2p+ transition, we will focus on the low-field region 0–6 T (Fig. 2, Fig. 3). Both the positions and the intensities of the observed and calculated transitions are shown. In comparison to Fig. 5 of ref. 1, at the lowest energies and fields we distinctly observe the 4p0 transition. The data for that transition, and the repulsion of the adjacent 3p− transition, are very distinct and in excellent agreement with the calculations. In the same way, the data for the 3p− transition follows the calculation very precisely, with a second anti-crossing evident at about 5 T. The simpler crystallographic orientation means the whole region is less cluttered than for B//〈100〉; in particular, the most intense transitions of Fig. 5 of ref. 1, occurring between the 3p± and 4p± zero-field energies, do not appear at all for B//〈111〉, leaving a striking example of a crossing at around 2 T in the middle of this energy range. Further such detailed observations may be made; however, this becomes progressively more difficult at higher energies due to the diminishing intensities and increasing number of the transitions.


Spherical, cylindrical and tetrahedral symmetries; hydrogenic states at high magnetic field in Si:P.

Lewis RA, Bruno-Alfonso A, de Souza GV, Vickers RE, Colla JA, Constable E - Sci Rep (2013)

Experimental spectra of Si:P at magnetic fields of B = 0, 1 and 2 T with B//〈111〉.The absorption coefficient has been calculated in the usual way. For clarity, the spectra for 1 and 2 T have been offset on the vertical axis by 10 and 20 cm−1, respectively. As highlighted, the lower branch of the transition labelled 3p± interacts with the transition labelled 4p0 at around 1 T and the upper branch of transition labelled 3p± interacts with the transition labelled 4f0 (not evident at 0 T) at around 2 T.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3860012&req=5

f3: Experimental spectra of Si:P at magnetic fields of B = 0, 1 and 2 T with B//〈111〉.The absorption coefficient has been calculated in the usual way. For clarity, the spectra for 1 and 2 T have been offset on the vertical axis by 10 and 20 cm−1, respectively. As highlighted, the lower branch of the transition labelled 3p± interacts with the transition labelled 4p0 at around 1 T and the upper branch of transition labelled 3p± interacts with the transition labelled 4f0 (not evident at 0 T) at around 2 T.
Mentions: Finally, to better deal with transitions of higher energies than the 2p+ transition, we will focus on the low-field region 0–6 T (Fig. 2, Fig. 3). Both the positions and the intensities of the observed and calculated transitions are shown. In comparison to Fig. 5 of ref. 1, at the lowest energies and fields we distinctly observe the 4p0 transition. The data for that transition, and the repulsion of the adjacent 3p− transition, are very distinct and in excellent agreement with the calculations. In the same way, the data for the 3p− transition follows the calculation very precisely, with a second anti-crossing evident at about 5 T. The simpler crystallographic orientation means the whole region is less cluttered than for B//〈100〉; in particular, the most intense transitions of Fig. 5 of ref. 1, occurring between the 3p± and 4p± zero-field energies, do not appear at all for B//〈111〉, leaving a striking example of a crossing at around 2 T in the middle of this energy range. Further such detailed observations may be made; however, this becomes progressively more difficult at higher energies due to the diminishing intensities and increasing number of the transitions.

Bottom Line: While the hydrogen atom is spherically symmetric, an applied magnetic field imposes cylindrical symmetry, and the solid-state analogue involves, in addition, the symmetry of the Si crystal.For one magnetic field direction, all six conduction-band valleys of Si:P become equivalent.New experimental data to high laboratory fields (30 T), supported by new calculations, demonstrate that this high symmetry field orientation allows the most direct comparison with free hydrogen.

View Article: PubMed Central - PubMed

Affiliation: Institute for Superconducting and Electronic Materials, University of Wollongong, Wollongong, New South Wales 2522, Australia.

ABSTRACT
Phosphorous donors in silicon have an electronic structure that mimics the hydrogen atom, albeit on a larger length, smaller energy and smaller magnetic field scale. While the hydrogen atom is spherically symmetric, an applied magnetic field imposes cylindrical symmetry, and the solid-state analogue involves, in addition, the symmetry of the Si crystal. For one magnetic field direction, all six conduction-band valleys of Si:P become equivalent. New experimental data to high laboratory fields (30 T), supported by new calculations, demonstrate that this high symmetry field orientation allows the most direct comparison with free hydrogen.

No MeSH data available.


Related in: MedlinePlus