Negative-U Properties for Point Defects in Silicon
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Inc.
Narayan, and Tan,eds. Defects
in
Semiconductors
21 NEGATIVE-U PROPERTIES FOR POINT DEFECTS IN SILICON*
G. D. WATKINS Department of Physics and Sherman Fairchild Laboratory, Bethlehem, Pennsylvania 18015
Lehigh University,
ABSTRACT A defect has negative-U properties if it can trap two electrons (or holes) with the second bound more strongly than the first. It is as if there were a net attraction between the two carriers (negative Hubbard correlation energy U) at the defect, and the defect energy levels in the gap are therefore inverted from their normal order. Experimental evidence is presented that interstitial boron and the lattice vacancy, both common simple point defects produced by electron irradiation of silicon, have this unusual property. These defects represent the first and only concrete examples of negative-U centers in any material and serve as models for an understanding of the phenomenon.
WHAT IS U? An impurity, or other simple point defect, often introduces more than one electrically active level in the forbidden gap of a semiconductor. For such a defect, it is normally found that if one electron is trapped, the level position for the next trapped electron is raised in energy, closer to the conduction band. This is illustrated in Fig. l(a) for a typical defect with both a single donor (0/+) and acceptor (-/0) level. (The notation i/j means //////////////////EC -
(0)
D 0--
+
U I A
(+)I
-D
-0
+
;'
(0)
0
U
Fig.
A
H
ceptor level (A) above the donor level (B).
l(a).
Normal positive-U level
ordering for a defect with its ac-
(b) Inverted negative-U ordering.
Ev
11111111117117=111-1/
(a)
(b)
that the defect has charge i if the level is filled with an electron, j if empty.) The acceptor level is expected to be above the donor level because the second electron, although possibly trapped into a similar orbital as the first, and experiencing therefore the same attractive interaction to the core of the defect, is repelled by the Coulomb interaction with the first electron. This added Coulomb repulsion energy is defined as U and in Fig. l(a) is the Research supported by the U.S. Navy, ONR Electronics and Solid State Sciences Program, Contract No. N00014-76-C-1097.
22 separation between the donor and acceptor levels. (U is often called the Hubbard "correlation energy," being first introduced by Hubbard in his treatment of conductivity in narrow band semiconductors [i]). POSITIVE-U All defectswhich introduce more than one level in a crystalline semiconductor are either known to have positive-U behavior or have been assumed to have this property. For the defect example of Fig. la, for instance, the normal positive-U ordering of levels means that each of the three charge states D+, D°, D- can be the thermodynamically stable one depending upon the position of the Fermi level, EF. The donor and acceptor levels have unambiguous meanings and can be measured either by a Hall measurement (Fermi level position determination under thermodynamic equilibrium conditions for the electronic
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