Impurity band states in SI(P)

doi:10.1016/0038-1098(76)90301-X

Solid State Communications

Volume 20, Issue 8, November 1976, Pages 811-813

https://doi.org/10.1016/0038-1098(76)90301-X Get rights and content

Abstract

A comparison is made between calculated impurity band densities of state in Si(P) for donor concentrations below that of the semiconductor-to-metal transition and experimental results obtained from photoluminescence spectra after subtracting an electron-hole droplet line. The theoretical results were obtained within the large interaction limit of the Hubbard model, assuming the impurities to be randomly distributed. The density of states was computed from cumulants appropriate to the low and high impurity density limit.

References (12)

J.A. Rostworowski et al.
Solid State Commun.
(1976)
B. Bergersen et al.
Phys. Rev.
(1976)
R.E. Halliwell et al.
Solid State Commun.
(1974)
Can. J. Phys.
(1974)
B. Bergersen et al.
J. Phys.
(1975)
R.B. Hammond et al.
Phys. Rev. Lett.
(1975)
J. Hubbard

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Cited by (11)

On the composition of luminescence spectra from heavily doped p-type silicon under low and high excitation
2017, Journal of Luminescence
Citation Excerpt :
Firstly, the conduction band and valence band rigidly shift towards one another due to increasing interactions among free carriers, and between free carriers and dopant atoms, causing a reduction in the band gap [21–23]. Secondly, the two band edges are perturbed and band tails are formed, yielding not only an effectively-smaller band gap but also a wider distribution of free carriers at the two band edges [24–27]. Thirdly, the shallow dopant band, located slightly above the valence band (for p-type silicon), broadens due to an increasing interaction among the dopant atoms.
We present a systematic investigation of the effects of doping on the luminescence spectra from p-type crystalline silicon wafers. First, we explain the difference in the approaches between the line shape analysis and the generalized Planck’s law in modeling the spectral shape, and connect the two methods together. After that, we elucidate the separate impacts of individual phenomena including band gap narrowing, band tails and dopant bands, Fermi level shifting, and hot carriers on the luminescence spectra in heavily-doped silicon. Finally, employing appropriate excitation levels, we can unambiguously re-examine the growing of the band tails and the broadening of the shallow dopant band, as well as the merging of the valence and shallow dopant bands together, on measured luminescence spectra.
Analytic expression for electronic density of states in random media with weak scattering potential
2008, Solid State Communications
Citation Excerpt :
The examples are heavily doped semiconductors, amorphous materials, nanoporous materials and large-molecule organic crystals. We are interested in the electronic properties of these materials as they exhibit some common experimental-observed features [1–5], such as bandtails, an energy shift or band gap narrowing, and a sharp turning point at the intersection between the band edge and the tail. Furthermore, these features affect the physical properties, such as the specific heat and the optical absorption of the materials, and the diffusion of minority carriers in semiconductors [6].
We evaluate the electronic density of states (DOS) in random media by using the expression from the variational path integral theory. The scattering potential is modeled by a Gaussian function. By imposing the limit of weak scattering, the full spectrum DOS can be approximated by an analytical method. The solution has several features; in the extended states, it is essentially proportional to $\sqrt{E}$ . In the localized states, it resembles an exponential tail. However, this tail has less population than that of the compatible Kane DOS. The total energy of the system is lowered by $E_{α}$ , depending linearly on the density of scatterers. Our results give good description to the photoluminescence spectra of Si:P and the tunneling measurement of GaAs.
Density of states of a disordered Hubbard model using the modified moments method
1980, Solid State Communications
We apply the modified-moments method to compute the density of states of the impurity band of a doped semi-conductor in the intermediate region of impurity concentrations. This method is used to correct the density of states obtained by interpolating between the high and low concentration limit asymptotic expressions. The calculation is based on the Hubbard model in the atomic limit without spin ordering. The overlap integral is assumed to be a Gaussian function of the impurity separation. Use is made of the first seven moments of the exact distribution and of the low and high concentration limit approximations previously calculated. The first six moments are employed to determine the orthogonal polynomial expansion of the density of states while the seventh moment is used as a check on the accuracy of the distribution obtained. The results are similar to the previous ones using a truncated Edgeworth series for the correction term but the present method has the advantage of being a more systematic approach.
On the origin of photoluminescence in heavily-doped silicon
1979, Solid State Communications
The origin of the photoluminescence in heavily-doped silicon is examined. Transient photoluminescence data for Si(P) are presented and used to identify the “Low Level” emission bands in terms of recombination of impurity band electrons with holes bound to acceptor sites. The “High Level” bands are attributed to recombination of impurity band electrons with free holes. The energies of the band gap and optical band gap in heavily-doped silicon are determined from the photoluminescence measurements.
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2022, Japanese Journal of Applied Physics
Semi-classical Monte Carlo study of the impact of contact geometry and transmissivity on quasi-ballistic nanoscale Si and In<inf>0.53</inf>Ga<inf>0.47</inf>As n-channel FinFETs
2019, Journal of Applied Physics

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Solid State Communications

Abstract

References (12)

Solid State Commun.

Phys. Rev.

Solid State Commun.

Can. J. Phys.

J. Phys.

Phys. Rev. Lett.

Cited by (11)

On the composition of luminescence spectra from heavily doped p-type silicon under low and high excitation

Analytic expression for electronic density of states in random media with weak scattering potential

Density of states of a disordered Hubbard model using the modified moments method

On the origin of photoluminescence in heavily-doped silicon

Systematic variation of photoluminescence spectra with donor and acceptor concentrations ranging from 1 × 10<sup>10</sup>to 1 × 10<sup>20</sup>cm<sup>-3</sup>in Si

Semi-classical Monte Carlo study of the impact of contact geometry and transmissivity on quasi-ballistic nanoscale Si and In<inf>0.53</inf>Ga<inf>0.47</inf>As n-channel FinFETs