DOI: 10.1016/s0081-1947(08)60104-6. Shallow Impurity States in Silicon and Germanium

Shallow Impurity States in Silicon and Germanium

10.1016/s0081-1947(08)60104-6

Crossref book-chapter

Elsevier

Solid State Physics (78)

Bibliography

Kohn, W. (1957). Shallow Impurity States in Silicon and Germanium. Solid State Physics, 257â320.

Authors 1

W. Kohn (first)

References 91 Referenced 435

{'key': '10.1016/S0081-1947(08)60104-6_bib1', 'series-title': 'Electronic Procession in Ionic Crystals', 'first-page': '166', 'author': 'Mott', 'year': '1940'} / Electronic Procession in Ionic Crystals by Mott (1940)
The actual band structures of silicon and germanium are rather complex, which requires a modification of the kinetic energy term (see Settions 5 and 9).
10.1021/j150509a023 / J. Phys. Chem. by Burstein (1953)
{'key': '10.1016/S0081-1947(08)60104-6_bib4', 'series-title': '“Electrons and Holes in Semiconductors,” Section 16.4.', 'author': 'Shockley', 'year': '1950'} / “Electrons and Holes in Semiconductors,” Section 16.4. by Shockley (1950)
10.1103/PhysRev.93.693 / Phys. Rev. by Debye (1954)
10.1103/PhysRev.95.1085 / Phys. Rev. by Geballe (1954)
{'key': '10.1016/S0081-1947(08)60104-6_bib7', 'first-page': '833', 'volume': '96', 'author': 'Morin', 'year': '1953', 'journal-title': 'Phys. Rev.'} / Phys. Rev. by Morin (1953)
F. J. Morin private communication.
10.1016/0022-3697(56)90012-9 / J. Phys. Chem. Solids by Burstein (1956)
10.1016/0022-3697(56)90013-0 / J. Phys. Chem. Solids by Picus (1956)
This suggests the following “chemical” models: A group V donor enters the lattice substitutionally. It contributes four of its five valence electrons to saturate all covalent bonds. The fifth electron is weakly bound by the Coulomb field of the resulting positive donor ion. Similarly, a group III acceptor enters the lattice substitutionally. Its three valence electrons saturate all but one of the covalent bonds. The remaining “hole” in the bond structure circulates in a large orbit around the net negative charge in the vicinity of the acceptor ion. The energy required to remove this hole to infinity is the ionization energy of the acceptor.
G. S. Picus private communication. These data supersede those quoted in ref. 10.
10.1103/PhysRev.99.465 / Phya. Rev. by Newman (1955)
10.1103/PhysRev.103.103 / Phys. Rev. by Newman (1956)
{'issue': '2', 'key': '10.1016/S0081-1947(08)60104-6_bib15', 'first-page': '66', 'volume': '2', 'author': 'Hrostowski', 'year': '1957', 'journal-title': 'Bull. Am. Phys. Soc.'} / Bull. Am. Phys. Soc. by Hrostowski (1957)
10.1103/PhysRev.100.592 / Phys. Rev. by Lax (1955)
This behavior is probably not typical of shallow impurity states and connected with the large ionization energy (0.16 ev) of In acceptors.
10.1103/PhysRev.94.1392.2 / Phys. Rev. by Fletcher (1954)
10.1103/PhysRev.95.844 / Phys. Rev. by Fletcher (1954)
10.1103/PhysRev.95.1686.2 / Phys. Rev. by Honig (1954)
10.1103/PhysRev.103.834 / Phys. Rev. by Feher (1956)
10.1103/PhysRev.91.1071 / Phys. Rev. by Portis (1955)
G. Feher private communication.
10.1103/PhysRev.106.489 / Phys. Rev. by Pines (1957)
{'key': '10.1016/S0081-1947(08)60104-6_bib25', 'first-page': '576', 'volume': '243', 'author': 'Abragam', 'year': '1956', 'journal-title': 'Compt. rend.'} / Compt. rend. by Abragam (1956)
10.1016/S0031-8914(56)90013-1 / Physica by Van Itterbeck (1956)
10.1103/PhysRev.98.368 / Phys. Rev. by Dresselhaus (1955)
10.1103/PhysRev.95.847 / Phys. Rev. by Herman (1955)
{'key': '10.1016/S0081-1947(08)60104-6_bib29', 'first-page': '1965', 'volume': '98', 'author': 'McFarlane', 'year': '1955', 'journal-title': 'Phys. Rev.'} / Phys. Rev. by McFarlane (1955)
{'key': '10.1016/S0081-1947(08)60104-6_bib30', 'first-page': '1222', 'volume': '96', 'author': 'Dexter', 'year': '1954', 'journal-title': 'Phys. Rev.'} / Phys. Rev. by Dexter (1954)
10.1103/PhysRev.100.1084 / Phys. Rev. by Stevens (1955)
10.1103/PhysRev.100.747 / Phys. Rev. by Fletcher (1955)
10.1103/PhysRev.77.287 / Phys. Rev. by Briggs (1950)
(Fi0) and (ui0) real and positive for all j.
10.1103/PhysRev.52.191 / Phys. Rev. by Wannier (1937)
{'key': '10.1016/S0081-1947(08)60104-6_bib36', 'first-page': '1', 'volume': 'XIX', 'author': 'Slater', 'year': '1956'} by Slater (1956)
10.1103/PhysRev.105.509 / Phys. Rev. by Kohn (1957)
10.1103/PhysRev.96.1488 / Phys. Rev. by Kittel (1954)
10.1103/PhysRev.97.352 / Phys. Rev. by Lampert (1955)
10.1103/PhysRev.97.1721 / Phys. Rev. by Kohn (1955)
10.1103/PhysRev.97.1722 / Phys. Rev. by Kleiner (1955)
{'key': '10.1016/S0081-1947(08)60104-6_bib42', 'series-title': 'Quantum Chemistry', 'first-page': '388', 'author': 'Eyring', 'year': '1944'} / Quantum Chemistry by Eyring (1944)
If the latter type of wave functions are used one obtains instead of (5.52) the result (F0)(r), PαFe)(r); i.e., one loses the essential factor m/m*.
10.1103/PhysRev.98.1856 / Phys. Rev. by Kohn (1955)
W. Kohn unpublished.
G. Feher private communication.
10.1103/PhysRev.103.1127 / Phys. Rev. by Shulman (1956)
The reason for concentrating on P (Z=15) is that there exists a mathematical limit where the effective mass wave function (6.3) should become exact everywhere, even at the position of the P nucleus. This is the limit in which the charge on the P nucleus is imagined to be only infinitesimally larger than that on the Si nuclei (i.e., Zp = 14 + q). In this limit the orbits become very large and the wave function is, locally, just like a superposition of silicon conduction band functions. On the other hand, consider another donor such as As (Z = 33). Here even in the limit in which the Coulomb attraction is imagined to be very weak (Z = 32 + q), the donor wave function in the cell of the As ion will resemble conduction band wave functions of Ge (Z = 32) more than those of Si. This fact is not allowed for in the effective mass expression (6.3).
W. Kohn ref. 34.
Unpublished calculations by the author.
10.1103/PhysRev.97.883 / Phys. Rev. by Kohn (1955)
Other ways of choosing m*, for example by the condition that F(0) should have the same value as that calculated with m1 and m2 give very nearly the same result.
For normalization purposes one can use the singular solution of (7.5), (7.6) for all r, since it is square integrable and the “interior” region makes a negligible contribution because of its small volume.
W. Kohn ref. 26.
10.1103/PhysRev.98.368 / Phys. Rev. by Dresselhaus (1955)
10.1016/S0031-8914(54)80194-7 / Physica by Lax (1954)
10.1016/0022-3697(56)90014-2 / J. Phys. Chem. Solids by Kane (1956)
10.1103/PhysRev.78.173 / Phys. Rev. by Shockley (1950)
10.1103/PhysRev.97.869 / Phys. Rev. by Luttinger (1955)
These values were kindly communicated by. Dr. H. J. Zeiger of the M.I.T. Lincoln laboratories.
More precisely, this means that E(k) - E(0) must be small compared to λ.
10.1103/PhysRev.97.1647 / Phys. Rev. by Kahn (1955)
10.1103/PhysRev.99.1903 / Phys. Rev. by Kohn (1955)
10.1103/PhysRev.100.573 / Phys. Rev. by Parmenter (1955)
W. Kohn, D. Schechter. 80
R. G. Shulman private communication.
A variation of 10% of the absolute energies of the excited states corresponds of course to a much longer fractional variation in their energy differences.
The first experimental spectrum obtained by Burstein and co-workers3 for B had a fortuitous resemblance to a simple hydrogenic spectrum. Therefore these authors labeled their optically excited states in order as 2p3p and 4p. It is now known that this labeling has no significance. First of all, Hrostowski13 has discovered an additional lower-lying state for B which removes any similarity with the hydrogenic spectrum. Also the other acceptor spectra show no such similarity. Finally, from a theoretical point of view, no resemblance to the hydrogen spectrum is to be expected. In fact, the four lowest strong transitions are all believed to be 2p-like states.
10.1016/0001-6160(57)90164-5 / Acta Met. by Pearson (1957)
10.1103/PhysRev.101.944 / Phys. Rev. by Herring (1956)
10.1103/PhysRev.104.1223 / Phys. Rev. by Price (1956)
10.1103/PhysRev.105.525 / Phya. Rev. by Morin (1956)
According to Kramers' theorem (time reversal), at least twofold degeneracy remains unless there is an external magnetic field.
The full Hamiltonian of the impurity problem has only tetrahedral symmetry and is not invariant under inversion. As a result, if the effective mass theory is seriously in error, states belonging to the representations T1T2and T3 can have an appreciable first-order Stark effect. This might possibly be of significance for the acceptor ground state (T3) in silicon.
I am indebted to. Dr. Burstein for a conversation on this question.
G. Feher private communication.
δE2 vanishes for m1=m2
10.1103/PhysRev.102.1030 / Phys. Rev. by Luttinger (1956)
10.1016/0022-3697(56)90020-8 / J. Phys. Chem. Solids by Yafet (1956)
10.1016/0022-3697(56)90021-X / J. Phys. Chem. Solids by Keyes (1956)
10.1103/PhysRev.100.592 / Phys. Rev. by Lax (1955)
The width due to the finite lifetime of the excited state is negligible.
10.1103/PhysRev.80.72 / Phys. Rev. by Bardeen (1950)
This question has not yet been fully analyzed. Preliminary studies indicate a very complicated line shape with peaks whose widths may be an order of magnitude smaller than the optical width of 10−3 ev.
10.1103/PhysRev.85.945 / Phys. Rev. by Dunlap (1952)
10.1103/PhysRev.105.84 / Phys. Rev. by Woodbury (1957)
10.1103/PhysRev.93.64 / Phys. Rev. by Taft (1950)
10.1103/PhysRev.105.1168 / Phys. Rev. by Collins (1957)
10.1103/PhysRev.105.379 / Phys. Rev. by Fuller (1957)
10.1103/PhysRev.104.937 / Phys. Rev. by Carlson (1956)
{'issue': '2', 'key': '10.1016/S0081-1947(08)60104-6_bib91', 'first-page': '48', 'volume': '1', 'author': 'Collins', 'year': '1956', 'journal-title': 'Bull. Am. Phys. Soc.'} / Bull. Am. Phys. Soc. by Collins (1956)

Dates

Type	When
Created	14 years, 7 months ago (Dec. 22, 2010, 2:35 a.m.)
Deposited	6 years, 2 months ago (June 7, 2019, 3:22 a.m.)
Indexed	1 month, 2 weeks ago (July 2, 2025, 11:17 a.m.)
Issued	68 years, 7 months ago (Jan. 1, 1957)
Published	68 years, 7 months ago (Jan. 1, 1957)
Published Print	68 years, 7 months ago (Jan. 1, 1957)

Funders 0

None

BibTeX

@inbook{Kohn_1957, title={Shallow Impurity States in Silicon and Germanium}, ISSN={0081-1947}, url={http://dx.doi.org/10.1016/s0081-1947(08)60104-6}, DOI={10.1016/s0081-1947(08)60104-6}, booktitle={Solid State Physics}, publisher={Elsevier}, author={Kohn, W.}, year={1957}, pages={257–320} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        2
      ]
    ],
    "date-time": "2025-07-02T15:17:47Z",
    "timestamp": 1751469467346
  },
  "reference-count": 91,
  "publisher": "Elsevier",
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1957
      ]
    ]
  },
  "DOI": "10.1016/s0081-1947(08)60104-6",
  "type": "book-chapter",
  "created": {
    "date-parts": [
      [
        2010,
        12,
        22
      ]
    ],
    "date-time": "2010-12-22T07:35:37Z",
    "timestamp": 1293003337000
  },
  "page": "257-320",
  "source": "Crossref",
  "is-referenced-by-count": 435,
  "title": "Shallow Impurity States in Silicon and Germanium",
  "prefix": "10.1016",
  "author": [
    {
      "given": "W.",
      "family": "Kohn",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib1",
      "series-title": "Electronic Procession in Ionic Crystals",
      "first-page": "166",
      "author": "Mott",
      "year": "1940"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib2",
      "unstructured": "The actual band structures of silicon and germanium are rather complex, which requires a modification of the kinetic energy term (see Settions 5 and 9)."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib3",
      "doi-asserted-by": "crossref",
      "first-page": "849",
      "DOI": "10.1021/j150509a023",
      "volume": "57",
      "author": "Burstein",
      "year": "1953",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib4",
      "series-title": "\u201cElectrons and Holes in Semiconductors,\u201d Section 16.4.",
      "author": "Shockley",
      "year": "1950"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib5",
      "doi-asserted-by": "crossref",
      "first-page": "693",
      "DOI": "10.1103/PhysRev.93.693",
      "volume": "93",
      "author": "Debye",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib6",
      "doi-asserted-by": "crossref",
      "first-page": "1085",
      "DOI": "10.1103/PhysRev.95.1085",
      "volume": "95",
      "author": "Geballe",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib7",
      "first-page": "833",
      "volume": "96",
      "author": "Morin",
      "year": "1953",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib8",
      "unstructured": "F. J. Morin private communication."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib9",
      "doi-asserted-by": "crossref",
      "first-page": "65",
      "DOI": "10.1016/0022-3697(56)90012-9",
      "volume": "1",
      "author": "Burstein",
      "year": "1956",
      "journal-title": "J. Phys. Chem. Solids"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib10",
      "doi-asserted-by": "crossref",
      "first-page": "75",
      "DOI": "10.1016/0022-3697(56)90013-0",
      "volume": "1",
      "author": "Picus",
      "year": "1956",
      "journal-title": "J. Phys. Chem. Solids"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib11",
      "unstructured": "This suggests the following \u201cchemical\u201d models: A group V donor enters the lattice substitutionally. It contributes four of its five valence electrons to saturate all covalent bonds. The fifth electron is weakly bound by the Coulomb field of the resulting positive donor ion. Similarly, a group III acceptor enters the lattice substitutionally. Its three valence electrons saturate all but one of the covalent bonds. The remaining \u201chole\u201d in the bond structure circulates in a large orbit around the net negative charge in the vicinity of the acceptor ion. The energy required to remove this hole to infinity is the ionization energy of the acceptor."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib12",
      "unstructured": "G. S. Picus private communication. These data supersede those quoted in ref. 10."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib13",
      "doi-asserted-by": "crossref",
      "first-page": "465",
      "DOI": "10.1103/PhysRev.99.465",
      "volume": "99",
      "author": "Newman",
      "year": "1955",
      "journal-title": "Phya. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib14",
      "doi-asserted-by": "crossref",
      "first-page": "103",
      "DOI": "10.1103/PhysRev.103.103",
      "volume": "103",
      "author": "Newman",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "issue": "2",
      "key": "10.1016/S0081-1947(08)60104-6_bib15",
      "first-page": "66",
      "volume": "2",
      "author": "Hrostowski",
      "year": "1957",
      "journal-title": "Bull. Am. Phys. Soc."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib16",
      "doi-asserted-by": "crossref",
      "first-page": "592",
      "DOI": "10.1103/PhysRev.100.592",
      "volume": "100",
      "author": "Lax",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib17",
      "unstructured": "This behavior is probably not typical of shallow impurity states and connected with the large ionization energy (0.16 ev) of In acceptors."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib18",
      "doi-asserted-by": "crossref",
      "first-page": "1392",
      "DOI": "10.1103/PhysRev.94.1392.2",
      "volume": "94",
      "author": "Fletcher",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib19",
      "doi-asserted-by": "crossref",
      "first-page": "844",
      "DOI": "10.1103/PhysRev.95.844",
      "volume": "93",
      "author": "Fletcher",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib20",
      "doi-asserted-by": "crossref",
      "first-page": "1686",
      "DOI": "10.1103/PhysRev.95.1686.2",
      "volume": "95",
      "author": "Honig",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib21",
      "doi-asserted-by": "crossref",
      "first-page": "834",
      "DOI": "10.1103/PhysRev.103.834",
      "volume": "103",
      "author": "Feher",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib22",
      "doi-asserted-by": "crossref",
      "first-page": "1071",
      "DOI": "10.1103/PhysRev.91.1071",
      "volume": "91",
      "author": "Portis",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib23",
      "unstructured": "G. Feher private communication."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib24",
      "doi-asserted-by": "crossref",
      "first-page": "489",
      "DOI": "10.1103/PhysRev.106.489",
      "volume": "106",
      "author": "Pines",
      "year": "1957",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib25",
      "first-page": "576",
      "volume": "243",
      "author": "Abragam",
      "year": "1956",
      "journal-title": "Compt. rend."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib26",
      "doi-asserted-by": "crossref",
      "first-page": "649",
      "DOI": "10.1016/S0031-8914(56)90013-1",
      "volume": "22",
      "author": "Van Itterbeck",
      "year": "1956",
      "journal-title": "Physica"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib27",
      "doi-asserted-by": "crossref",
      "first-page": "368",
      "DOI": "10.1103/PhysRev.98.368",
      "volume": "98",
      "author": "Dresselhaus",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib28",
      "doi-asserted-by": "crossref",
      "first-page": "847",
      "DOI": "10.1103/PhysRev.95.847",
      "volume": "95",
      "author": "Herman",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib29",
      "first-page": "1965",
      "volume": "98",
      "author": "McFarlane",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib30",
      "first-page": "1222",
      "volume": "96",
      "author": "Dexter",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib31",
      "doi-asserted-by": "crossref",
      "first-page": "1084",
      "DOI": "10.1103/PhysRev.100.1084",
      "volume": "100",
      "author": "Stevens",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib32",
      "doi-asserted-by": "crossref",
      "first-page": "747",
      "DOI": "10.1103/PhysRev.100.747",
      "volume": "100",
      "author": "Fletcher",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib33",
      "doi-asserted-by": "crossref",
      "first-page": "287",
      "DOI": "10.1103/PhysRev.77.287",
      "volume": "77",
      "author": "Briggs",
      "year": "1950",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib34",
      "unstructured": "(Fi0) and (ui0) real and positive for all j."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib35",
      "doi-asserted-by": "crossref",
      "first-page": "191",
      "DOI": "10.1103/PhysRev.52.191",
      "volume": "52",
      "author": "Wannier",
      "year": "1937",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib36",
      "first-page": "1",
      "volume": "XIX",
      "author": "Slater",
      "year": "1956"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib37",
      "doi-asserted-by": "crossref",
      "first-page": "509",
      "DOI": "10.1103/PhysRev.105.509",
      "volume": "105",
      "author": "Kohn",
      "year": "1957",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib38",
      "doi-asserted-by": "crossref",
      "first-page": "1488",
      "DOI": "10.1103/PhysRev.96.1488",
      "volume": "96",
      "author": "Kittel",
      "year": "1954",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib39",
      "doi-asserted-by": "crossref",
      "first-page": "352",
      "DOI": "10.1103/PhysRev.97.352",
      "volume": "97",
      "author": "Lampert",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib40",
      "doi-asserted-by": "crossref",
      "first-page": "1721",
      "DOI": "10.1103/PhysRev.97.1721",
      "volume": "97",
      "author": "Kohn",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib41",
      "doi-asserted-by": "crossref",
      "first-page": "1722",
      "DOI": "10.1103/PhysRev.97.1722",
      "volume": "97",
      "author": "Kleiner",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib42",
      "series-title": "Quantum Chemistry",
      "first-page": "388",
      "author": "Eyring",
      "year": "1944"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib43",
      "unstructured": "If the latter type of wave functions are used one obtains instead of (5.52) the result (F0)(r), P\u03b1Fe)(r); i.e., one loses the essential factor m/m*."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib44",
      "doi-asserted-by": "crossref",
      "first-page": "1856",
      "DOI": "10.1103/PhysRev.98.1856",
      "volume": "98",
      "author": "Kohn",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib45",
      "unstructured": "W. Kohn unpublished."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib46",
      "unstructured": "G. Feher private communication."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib47",
      "doi-asserted-by": "crossref",
      "first-page": "1127",
      "DOI": "10.1103/PhysRev.103.1127",
      "volume": "103",
      "author": "Shulman",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib48",
      "unstructured": "The reason for concentrating on P (Z=15) is that there exists a mathematical limit where the effective mass wave function (6.3) should become exact everywhere, even at the position of the P nucleus. This is the limit in which the charge on the P nucleus is imagined to be only infinitesimally larger than that on the Si nuclei (i.e., Zp = 14 + q). In this limit the orbits become very large and the wave function is, locally, just like a superposition of silicon conduction band functions. On the other hand, consider another donor such as As (Z = 33). Here even in the limit in which the Coulomb attraction is imagined to be very weak (Z = 32 + q), the donor wave function in the cell of the As ion will resemble conduction band wave functions of Ge (Z = 32) more than those of Si. This fact is not allowed for in the effective mass expression (6.3)."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib49",
      "unstructured": "W. Kohn ref. 34."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib50",
      "unstructured": "Unpublished calculations by the author."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib51",
      "doi-asserted-by": "crossref",
      "first-page": "883",
      "DOI": "10.1103/PhysRev.97.883",
      "volume": "97",
      "author": "Kohn",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib52",
      "unstructured": "Other ways of choosing m*, for example by the condition that F(0) should have the same value as that calculated with m1 and m2 give very nearly the same result."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib53",
      "unstructured": "For normalization purposes one can use the singular solution of (7.5), (7.6) for all r, since it is square integrable and the \u201cinterior\u201d region makes a negligible contribution because of its small volume."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib54",
      "unstructured": "W. Kohn ref. 26."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib55",
      "doi-asserted-by": "crossref",
      "first-page": "368",
      "DOI": "10.1103/PhysRev.98.368",
      "volume": "98",
      "author": "Dresselhaus",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib56",
      "doi-asserted-by": "crossref",
      "first-page": "818",
      "DOI": "10.1016/S0031-8914(54)80194-7",
      "volume": "20",
      "author": "Lax",
      "year": "1954",
      "journal-title": "Physica"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib57",
      "doi-asserted-by": "crossref",
      "first-page": "83",
      "DOI": "10.1016/0022-3697(56)90014-2",
      "volume": "1",
      "author": "Kane",
      "year": "1956",
      "journal-title": "J. Phys. Chem. Solids"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib58",
      "doi-asserted-by": "crossref",
      "first-page": "173",
      "DOI": "10.1103/PhysRev.78.173",
      "volume": "78",
      "author": "Shockley",
      "year": "1950",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib59",
      "doi-asserted-by": "crossref",
      "first-page": "869",
      "DOI": "10.1103/PhysRev.97.869",
      "volume": "97",
      "author": "Luttinger",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib60",
      "unstructured": "These values were kindly communicated by. Dr. H. J. Zeiger of the M.I.T. Lincoln laboratories."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib61",
      "unstructured": "More precisely, this means that E(k) - E(0) must be small compared to \u03bb."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib62",
      "doi-asserted-by": "crossref",
      "first-page": "1647",
      "DOI": "10.1103/PhysRev.97.1647",
      "volume": "97",
      "author": "Kahn",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib63",
      "doi-asserted-by": "crossref",
      "first-page": "1903",
      "DOI": "10.1103/PhysRev.99.1903",
      "volume": "99",
      "author": "Kohn",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib64",
      "doi-asserted-by": "crossref",
      "first-page": "573",
      "DOI": "10.1103/PhysRev.100.573",
      "volume": "100",
      "author": "Parmenter",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib65",
      "unstructured": "W. Kohn, D. Schechter. 80"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib66",
      "unstructured": "R. G. Shulman private communication."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib67",
      "unstructured": "A variation of 10% of the absolute energies of the excited states corresponds of course to a much longer fractional variation in their energy differences."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib68",
      "unstructured": "The first experimental spectrum obtained by Burstein and co-workers3 for B had a fortuitous resemblance to a simple hydrogenic spectrum. Therefore these authors labeled their optically excited states in order as 2p3p and 4p. It is now known that this labeling has no significance. First of all, Hrostowski13 has discovered an additional lower-lying state for B which removes any similarity with the hydrogenic spectrum. Also the other acceptor spectra show no such similarity. Finally, from a theoretical point of view, no resemblance to the hydrogen spectrum is to be expected. In fact, the four lowest strong transitions are all believed to be 2p-like states."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib69",
      "doi-asserted-by": "crossref",
      "first-page": "181",
      "DOI": "10.1016/0001-6160(57)90164-5",
      "volume": "5",
      "author": "Pearson",
      "year": "1957",
      "journal-title": "Acta Met."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib70",
      "doi-asserted-by": "crossref",
      "first-page": "944",
      "DOI": "10.1103/PhysRev.101.944",
      "volume": "101",
      "author": "Herring",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib71",
      "doi-asserted-by": "crossref",
      "first-page": "1223",
      "DOI": "10.1103/PhysRev.104.1223",
      "volume": "104",
      "author": "Price",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib72",
      "doi-asserted-by": "crossref",
      "first-page": "525",
      "DOI": "10.1103/PhysRev.105.525",
      "volume": "105",
      "author": "Morin",
      "year": "1956",
      "journal-title": "Phya. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib73",
      "unstructured": "According to Kramers' theorem (time reversal), at least twofold degeneracy remains unless there is an external magnetic field."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib74",
      "unstructured": "The full Hamiltonian of the impurity problem has only tetrahedral symmetry and is not invariant under inversion. As a result, if the effective mass theory is seriously in error, states belonging to the representations T1T2and T3 can have an appreciable first-order Stark effect. This might possibly be of significance for the acceptor ground state (T3) in silicon."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib75",
      "unstructured": "I am indebted to. Dr. Burstein for a conversation on this question."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib76",
      "unstructured": "G. Feher private communication."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib77",
      "unstructured": "\u03b4E2 vanishes for m1=m2"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib78",
      "doi-asserted-by": "crossref",
      "first-page": "1030",
      "DOI": "10.1103/PhysRev.102.1030",
      "volume": "102",
      "author": "Luttinger",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib79",
      "doi-asserted-by": "crossref",
      "first-page": "137",
      "DOI": "10.1016/0022-3697(56)90020-8",
      "volume": "1",
      "author": "Yafet",
      "year": "1956",
      "journal-title": "J. Phys. Chem. Solids"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib80",
      "doi-asserted-by": "crossref",
      "first-page": "143",
      "DOI": "10.1016/0022-3697(56)90021-X",
      "volume": "1",
      "author": "Keyes",
      "year": "1956",
      "journal-title": "J. Phys. Chem. Solids"
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib81",
      "doi-asserted-by": "crossref",
      "first-page": "592",
      "DOI": "10.1103/PhysRev.100.592",
      "volume": "100",
      "author": "Lax",
      "year": "1955",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib82",
      "unstructured": "The width due to the finite lifetime of the excited state is negligible."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib83",
      "doi-asserted-by": "crossref",
      "first-page": "72",
      "DOI": "10.1103/PhysRev.80.72",
      "volume": "80",
      "author": "Bardeen",
      "year": "1950",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib84",
      "unstructured": "This question has not yet been fully analyzed. Preliminary studies indicate a very complicated line shape with peaks whose widths may be an order of magnitude smaller than the optical width of 10\u22123 ev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib85",
      "doi-asserted-by": "crossref",
      "first-page": "945",
      "DOI": "10.1103/PhysRev.85.945",
      "volume": "86",
      "author": "Dunlap",
      "year": "1952",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib86",
      "doi-asserted-by": "crossref",
      "first-page": "84",
      "DOI": "10.1103/PhysRev.105.84",
      "volume": "105",
      "author": "Woodbury",
      "year": "1957",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib87",
      "doi-asserted-by": "crossref",
      "first-page": "64",
      "DOI": "10.1103/PhysRev.93.64",
      "volume": "93",
      "author": "Taft",
      "year": "1950",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib88",
      "doi-asserted-by": "crossref",
      "first-page": "1168",
      "DOI": "10.1103/PhysRev.105.1168",
      "volume": "105",
      "author": "Collins",
      "year": "1957",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib89",
      "doi-asserted-by": "crossref",
      "first-page": "379",
      "DOI": "10.1103/PhysRev.105.379",
      "volume": "105",
      "author": "Fuller",
      "year": "1957",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "10.1016/S0081-1947(08)60104-6_bib90",
      "doi-asserted-by": "crossref",
      "first-page": "937",
      "DOI": "10.1103/PhysRev.104.937",
      "volume": "104",
      "author": "Carlson",
      "year": "1956",
      "journal-title": "Phys. Rev."
    },
    {
      "issue": "2",
      "key": "10.1016/S0081-1947(08)60104-6_bib91",
      "first-page": "48",
      "volume": "1",
      "author": "Collins",
      "year": "1956",
      "journal-title": "Bull. Am. Phys. Soc."
    }
  ],
  "container-title": "Solid State Physics",
  "original-title": [],
  "deposited": {
    "date-parts": [
      [
        2019,
        6,
        7
      ]
    ],
    "date-time": "2019-06-07T07:22:03Z",
    "timestamp": 1559892123000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0081194708601046"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1957
      ]
    ]
  },
  "references-count": 91,
  "URL": "http://dx.doi.org/10.1016/S0081-1947(08)60104-6",
  "relation": {},
  "ISSN": [
    "0081-1947"
  ],
  "subject": [],
  "published": {
    "date-parts": [
      [
        1957
      ]
    ]
  }
}