Simple Model for Rare-Earth Impurities in the Compound Semiconductors
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SIMPLE MODEL FOR RARE-EARTH IMPURITIES IN THE COMPOUND SDIIXNDUICTORS NICOLAS P.ILYIN and VADIM F.MASTKERV Experimental University, State Technical 195251St.Petersburg, Russia
Physics
Department,
ABSTRACT A model of the ground state for a rare-earth element in a semiconductor is suggested and illustrated for ytterbium in InP.
binary It is
shown that the charge state of Yb3+ with 4f13 shell is more stable than the state of Yb2+ with f 1
shell.
MODEL The purpose of this paper is to present a simple model of the ground state for a rare-earth element in a binary semiconductor by taking into account: i) the effects of intra-atomic correlation leading to the energy difference between the occupied and empty f-levels; ion ii) the stabilizing electrostatic field produced by the RE+ envirorment in the matrix. The general formulation of the model is completed by semi-quantitative estimates for an ytterbium atom in indium
phosphide_
Two-band model of an ideal binary semiconductor can be
introduced
by
a
set of Green function GO(E) defined by the same relation:
a
%(K)
= [EA
2
b,[E +A
2~
b 2 Go(E)]
-1-
]
()
,
but with the different positions of the midgap point B = 0 with respect to for each a [1J- Here index Ca characterizes an irreducible the vacu representation (a1 or t2); parameters A, b1 and b2 are related to the is position of the band edges. Two-band subsystem corresponding to each a represented in Fig.1; the realistic band structure is obtained by the superposition of such subsystems.
Fig. l. Two-band subsystem for a particular aL; EK= A
4,
condh.crtd
91,2--/A
2
+ (bI the "gap width" Sg/A2
2 t b2 )
+ (b1 - b 2 )2
-El Mat. Res. Soc. Symp. Proc. Vol. 301. ©1993 Materials Research Society
410
quasiIt should be noted that the energy E-O -A can be interpreted as a vacancy level (a 1 or t 2 ) corresponding to the removal of a neutral A from
atom
A3 B matrix [2]- This energy is a pole of function: Ga(E 102 Gý(E) = CE + A
1,
2 G()-
(2)
which can be called a "vacancy Green function". We pass to the Green functions G(K) for a rare-earth impurity center by inserting the effective energies Er for 6s (P.= a 1 ) or 4f (aL= t 2 ) electron instead of the first A in formula (1):
a
Gr(E) = [E -
a
2 2 (L -1 -1 -(3) r - bila [E + A-a - b 2 G()]
1
Here we also take into account the perturbation of the bonding with the nearest neighbors (b2.
6b e2);
by inserting A- instead of the second A in
(1) we account for the possible charge transfer from the impurity the surrounding B atoms.
atom
to
The poles of Gr() provide two s-like levels a 1 and a* which do not enter the subsequent calculations in this paper; it should be noted only that a 1 -level is fully occupied and a1-level is empty. It may play a role of the electron trap level observed experimentally (3]. at Our main interest is to estimate the position of the poles of Gr(K) aL= t 2 . It is known that the hybridization of f-states with the host states 2
= S for Kt a = t 2 In this case we get a pure f-level of t 2 symmetry with the energy
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