Nonradiative processes in the Zn
1 x
Co
x
Se system
Marek Grinberg
Institute of Experimental Physics, University of Gdansk, Wita Stwosza 57, 80-952 Gdansk, Poland
A. C. Felici, T. Papa, and M. Piacentini
Dipartimento di Energetica, Universita di Roma ‘‘La Sapienza,’’ Via A. Scarpa 14, 00161 Roma, Italy
and Istituto Nazionale di Fisica della Materia, Sezione di Roma I, Roma, Italy
Received 10 May 1999
We report the photoacoustic investigations of the Zn
1-x
Co
x
Se system. The qualitative analysis of possible
nonradiative deexcitation paths in the Co
2+
ion is performed. It is shown that the pseudo-Jahn-Teller effect is
responsible for accumulation of the electron-lattice interaction energy in the lowest
2
T
1
state. As a result, the
effective path for nonradiative deexcitation of the system is opened. S0163-18299901736-1
I. INTRODUCTION
The purpose of this paper is the interpretation of the pho-
toacoustic spectrum of Zn
1 -x
Co
x
Se and the qualitative
analysis of possible nonradiative deexcitation paths in the
Co
2 +
ion.
A Co atom has nine valence electrons in the 3 d
7
4 s
2
con-
figuration. When it replaces the Zn
2 +
ions in the zincblende
ZnSe lattice, the two s electrons are shared with the Se atoms
to form tetrahedraly coordinated bonds. The internal ener-
getic structure of the Co
2 +
ion is determined by the remain-
ing seven d-electrons, which are influenced by the crystal
field of tetrahedral symmetry. The electronic energy levels
scheme of the Co
2 +
ion is determined within the framework
of the crystal-field theory
1–3
by the values of the Racah pa-
rameters B and C, by the crystal-field splitting parameter
10Dq and by the spin-orbit interaction parameter .
4
The
next parameter that determines the transitions’ line shape is
the electron-lattice coupling S . According to the spin-
selection rules, in the energy region below the ZnSe funda-
mental energy gap one expects to observe three strong ab-
sorption bands related to the spin-allowed transitions from
the quartet
4
A
2
ground state to the quartet
4
T
2
,
4
T
1
(a), and
4
T
1
(b) final states for increasing photon energy. In the case
of
4
T
1
states we have indicated them by a and b instead of
the respective atomic quartet states ‘‘F ’’ and ‘‘P ’’ since they
are completely mixed by the off-diagonal part of the Tanabe-
Sugano matrix, equal to 6 B . Many weak absorption bands
have been also observed and assigned to final doublet states.
The energies of the lowest
2
E ,
2
T
1
, and
2
T
2
doublet states
fall between the
4
T
1
(a) and
4
T
1
(b) quartet states. Specifi-
cally the
2
T
1
state, which is just above the
4
T
1
(b) state, can
produce significant absorption due to large spin-orbit mixing
with the close quartet level.
2
As far as the luminescence is considered, the IR emission
related to the
4
T
2
→
4
A
2
transition, which accompanies the
respective absorption band
4
A
2
→
4
T
2
, can be detected.
5
In
the last decade also the emission from the next excited state
4
T
1
(a) has been observed.
6
As far as we know, the emission
from higher excited states (
2
E and
2
T
1
doublets or a
4
T
1
(b)
quartet, which would be excited only by the
4
A
2
→
4
T
1
(b)
absorption band, has not been observed. The sharp lines at
2.36 eV, 2.43 eV, and 2.54 eV, observed in the low-
temperature absorption spectra
7,8
and the one at 2.36 eV de-
tected in the emission
8
were attributed to transitions to the
states belonging to the mixed ( d
7
, d
6
) electronic
configuration.
7
The electronic energetic structure of the Co
2 +
ion is
strongly influenced by the electron-lattice interaction, which
is related to the interaction of the ligand ions with the
Co
2 +
d electrons cloud. In that paper we have considered
the coupling of the seven d electrons system with the full
symmetric a
1
vibrational mode and to the two-dimensional
vibrational mode. We have performed the calculations in the
strong crystal-field scheme
4
and the results have been visu-
alized in the form of several configurational coordinate dia-
grams, which represent separately the electron system
coupled to the a
1
mode only, and then to the mode. In the
latter case the calculations also included the Pseudo-Jahn-
Teller coupling, which results from coupling between differ-
ent states of T symmetry via the distortion of the symme-
try. From these configurational coordinate diagrams we have
estimated the energy barriers for the nonradiative processes.
As a particular, quite fundamental result, we have found that
the existence of the Jahn-Teller effect, the Pseudo-Jahn-
Teller effect, and the coupling by the B Racah parameter,
cause an effective exchange of the Jahn-Teller relaxation en-
ergy between the coupled states. It has been found that this
effect leads to the accumulation of the lattice relaxation en-
ergy in the lowest
2
T
1
state and, therefore, it reduces signifi-
cantly the barrier for the nonradiative process between them
and the excited state
4
T
1
(a).
In Sec. II we describe the photoacoustic experiment. In
Sec. III we discuss the configurational coordinate diagrams.
In the Appendix we discuss the analytical result obtained for
the simplified case of the
4
T
1
(a) and
4
T
1
(b) states coupled
to the mode.
II. EXPERIMENT
Photoacoustic spectroscopy is a technique, which allows
the measurement of absorption coefficients by detection of
the heat generated in a sample by the absorption of modu-
PHYSICAL REVIEW B 15 SEPTEMBER 1999-II VOLUME 60, NUMBER 12
PRB 60 0163-1829/99/6012/85957/$15.00 8595 ©1999 The American Physical Society