Alkali atoms as acceptor impurities in ZnSe

~

Solid State Communications, Printed in Great Britain.

Vol.64,No.6,

pp.863-866,

1987.

ALKALI ATOMS AS ACCEPTOR IMPURITIES H~lio Chacham, Departamento

0038-1098/87 $3.00 + .00 ©1987 Pergamon Journals Ltd.

IN ZnSe

J.L.A. Alves, and M.L. De Siqueira

de FIsica, ICEx, Universidade Federal de Minas Gerais C.P. 702, 30.161, Belo Horizonte, MG, Brazil

( Received on July |3th,|987,by R.C.C. Leite ) The electronic structure of L~, Na, and K substitutional impurities in ZnSe are calculated within the framework of the self-consistent-field multiplescattering molecular cluster model. The Li and Na impurities induce an a I resonance in the valence band and a t 2 state in the band gap. According to our results, the Li and Na acceptor states originate from the t 2 orbital in the gap. The degree of localization of the gap state increases with atomic number, as a result from core repulsion effects and from the orthogonality between the impurity states. We suggest that the latter mechanism could be applied to Li and Na acceptors in other II-Vl compounds.

I. INTRODUCTION The II-VI semiconductors with wide band gaps (such as ZnSe, ZnTe, ZnS and CdS) are materials with luminescence properties at the optical range of the visible and ultraviolet light. The use of those compounds in optoelectronic devices is limited, however, by the difficulties encountered on making p-n homojunctlons. In particular, ZnSe is a "blue"gap compound which is difficult to prepare with good p-type conductivltyl. In this context, the role of acceptor impurities in ZnSe is a subject of particular interest. Single acceptors in ZnSe originate from IA- or IB- group substitutional impurities on the cation site or from V-group impurities on the anion site. Among the cationic impurities, Li and Na are the ones that give rise to the shallowest acceptors in ZnSe. Luminescence studies have been performed2-~ in which the acceptor levels involved are LiEn and Nazn. An electron trap associated to one of those centers have been also observed in photocapacitance studies 5. The ionization energies of the Lizn and Nazn acceptors, as obtained by experiments3,4, are estimated to be 0.114 eV and 0.126 eV, respectively. Variational ~ffective-mass-theory (EMT) calculations6 for single acceptors in ZnSe predict an ionization energy of 0.ii0 eV and a radial extent for the hole, < r >, of about 13 ~. Therefore, EMT reproduces the experimental ionization energies within fifteen percent. However,the EMT fails when predicting the radial extent of the hole wave function for the Na impurity. The spatial extent of an acceptor wave function can be estimated experimentally from the decay characteristics of donor-acceptorpalrs(DAP) lumlnescence 7-9. This kind of experiment have been performed9,quite recently, for the DAP luminescence in ZnSe where the donor level involved is AIZn and the acceptor level involved is Nazn. In Ref. 9 the author confirmed that the donor satisfies EMT relations between the effective Bohr radius and the binding energy. However, the experimental results required an effective Bohr radius for the Na acceptor (rA = 4.7 ~) which is less than half of the

predicted value by EMT 6. Indeed, the Bohr radius obtained from the experimental fitting is smaller than the lattice constant of ZnSe (5.67 ~). Such an apparent disagreement between experiments 9 and EMT 6 for the Na acceptor in ZnSe stimulates a theoretical investigation on the microscopic nature of this center and similar systems. In the present work we undertake an investigation on the electronic structure of substitutional Li, Na, and K impurities in ZnSe by means of first-prlnclples calculations. We use a localized description of the defects through the Watson-sphere-termlnated cluster model I0. This model utilizes the self-consistent multlple-scattering X~ formalism II and presents a suitable treatment of the surface orbltals of the clusters. The model used in our calculations consists of a central zinc or impurity atom surrounded by four selenium first neighbors and twelve zinc second neighbors. The 18 dangllng-bond electrons at surface are transferred to an external sphere. The eigenvalues of the 3d orbitals of the external Zn atoms are chosen to be a common energy reference to all calculations. The atomic X~ parameters are those suggested by Schwarz 12. The perfect crystal geometry is used in all calculations, i.e., we do not consider explicitly lattice distortions due to the impurities. More details on the model can be found in previous worksl3,14. II. THE Na A C C E P T O R A N D

THE IB-GROUP IMPURITIES

The one-electron self-consistent spectrum for the cluster NaSe4Znl2, representing the system ZnSe:Na, is shown in fig. i. We depict only the "impurity" levels, that is, the states that are significantly affected by the central impurity. The levels are classified according to the irreducible representations of the T d point group. The band edges are defined by the "perfect" ZnSe4Znl2 cluster (see refs. 13 and 14), in such a way that the highest occupied orbital is identified as the valence-band maximum and the lowest unoccupied orbital as the conduction-band minimum.

863

864

ALKALI ATOMS AS ACCEPTOR IMPURITIES IN ZnSe

Figure i shows t h a ~ according to our calculations, the Na impurity introduces a slxfold degenerate t 2 state with a single hole in the band gap, as well as an a I resonance in the valence band. The charge distributions of the t 2 and a I states are depicted in table I and table II, respectively. Both orbltals are rather concentrated in the first shell of neighbors; this suggests that those orbitals contain a certain amount of dangling-bond character on the first neighbors.

Vol. 64, No. 6

the trend of the X a engenvalues of the valence orbitals of the isolated atoms shown in fig. 2. The similarity between the impurity and the atomic trends suggests that the a I resonances retain a certain atomic character. This suggestion is reinforced by the analysis of the charge distribution of the orbitals in the space region close to the impurity site. In figure 3 we show

No

Ag

Cu

0 conduction band No

4

Ag

s-X_

>

Cu

2

hl --J

~rY - 4

0 ~0

LIJ Z bJ

LU 0

>

d

-8

am

< J LU r~

valence band > -4 >(9 o~ LU Z LU

-8

S

0-----

0

/-

Fig. 2 - Calculated valence energy spectra for the Na, Ag, and Au isolated atoms. The symmetry and the occupancy of the valence orbitals are indicated.

t2(d) e (d) >I--

Fig. I - Calculated energy spectra of Na, Ag, and Au substitutional impurities in ZnSe in the neutral charge state. Open circles denote holes in the t 2 gap orbitals.

Z

uJ a

Q-

O

ISOLATED

@

IMPURITY

ATOM

L~ L~ r~ I o

There is a family of impurities in ZnSe that depict some similarities to the Na i m p u r i t ~ to say, the IB group impurities (Cu,Ag, Au) in ZnSe. The comparison between both systems will be elucidative to the nature of the t 2 and a I states mentioned above. The self-consistent spectra for the systems ZnSe:Ag and ZnSe:Cu, obtained in a previous work 13,14, are also shown in figure i. The IB-group impurities induce a t 2 state in the gap and an a I resonance in a similar way to the Na impurity. They also induce an additional feature given by the presence of e and t 2 states which are resonant in the case of Cu, and hyperdeep in the case of Ag and Au. These states have a strong atomic d-character and interact weakly with the lattice; a small part of the atomic "d" character is transferred to the t 2 orbital in the gap. The systems depicted in fig. i are placed in such an order that the degree of admixture between the d-like level and the t 2 gap orbital increases from the left to the right. The degree of localization of the t 2 gap level increases in the same sequence. The trend suggests that the Na impurity behaves as if it were a IB-group impurity in the limit of infinitely hiperdeep d-like levels. Now, we shall compare the trends of the Na, Ag, and Cu impurity levels depicted in fig. i to

04

0,2

r,, IIv(.9 O0 z

I

I

I

I

I

Cu

Ag

Li

Na

K

Fig. 3 - Integrated charge density inside a sphere of radius 1.31 ~ for atomic and impurity orbitals. The closed circles (.) indicate the values for a I levels induced by IA- and IB-group impurities in ZnSe. The open circles (o) indicate the values for the outermost s orbitals of the isolated atoms. the integrated charge density inside a sphere of radius 1.31 ~, centered in the impurity, for the a I resonances induced by Cu, Ag, Li, Na, and K impurities in ZnSe. In the same figure we depict the integrated charge density within the same sphere for the outermost s orbital of the isolated atoms. The integrated charges for the isolated atoms and for the impurities are very close to each other; this result indicates that the charge

865

ALKALI ATOMS AS ACCEPTOR IMPURITIES IN ZnSe

Vol. 64, No. 6

distribution of the a I resonances is similar to that of the atomic "s" orbitals in the space region close to the impurity. Therefore, both the energy position and the charge distribution analyses indicate that the a I resonances induced by the IA- and IB-group impurities still retain characteristics from the outermost s orbitals of the isolated atoms.

.J

Li

O.

Na

K

0 o9 u.I > --

I-

t2

c>

~o

O.C

_J r~

III. Li, Na, AND K: TRENDS AMONG IA-GROUP IMPURITIES.

>

- 0 . ~= valence

We have also calculated the self-consistent electronic structure for theclusters LiSe4Znl2 and KSe4ZnI2, representing the systems ZnSe:Li and ZnSe:K, respectively. The energy position of the Li, Na, and K impurity levels, relative to the top of the valence bands, are depicted in figure 4. The charge distributions of the same levels are shown is tables I and II. According to our calculations, the electronic structure of the Li impurity is quite similar to that of the Na impurity; a t 2 state is induced in the band gap and an a I resonance is induced in the valence band. On the other hand, in the case of the substitutional potassium, both the t 2 and the a I states appear very close to each other in the band gap. This fact can be interpreted by means of the following arguments: The potassium core is much larger than those of Li and Na; in fact, more than 0.4 core electrons appear outside the central sphere. Such a large core acts as a repulsion center for the a I orbital by means of core orthogonality, and causes the a I level to appear in the band gap together with the t 2 level. Such a mechanism has been already found on calculations for He, Ne and Ar substituional impurities in silicon 15. As far as the K impurity in ZnSe is concerned, this mechanism suggests that the impurity would cause outwards distortions

band

>Lo r~ ~LIJ

- I .C

al m

Fig. 4 - Calculated energy spectra of Li, Na, and K substitutional impurities in ZnSe in the neutral charge state. Open circles denote holes in the t 2 gap orbitals. The energies are relative to the top of the valence band. on the first neighborhood (not explicitly considered in our calculations) and that potassium would be less bound to the lattice than Li and Na. This is consistent with the absence of experimental data for potassium as dopant in ZnSe, in contrast to Na and Li which are widely observed I-5 . Let us now analyse the trends among Li, Na, and K impurities in a more detailed way. The charge distribution of the a I levels (see table II and fig. 3) indicates that the degree of localization of those states decreases with atomic number. As we have seen previously, this happens due to the characteristics of the outermost s orbitals of the isolated atoms, or, equivalently, due to the increase of the core "radius" in the sequence. On the other hand, the hehaviour of the

TABLE I - Charge distribution normalized to one electron for the t 2 level introduced in the band gap by Li, Na, and K substitutional impurities in ZnSe.

Impurity

Central Sphere

First neighbors

Second neighbors

Interatomic region

Li

0.03

0.55

0.13

0.29

Na

0.05

0.59

0.08

0.28

K

0.i0

0.57

0.06

0.26

TABLE II - Charge distribution normalized to one electron for the a I resonance introduced by the Li and Na substitutional impurities and for the a I level in the gap introduced by the K impurity in ZnSe.

Impurity

Central Sphere

First neighbors

Second neighbors

Interatomic region

Li

0.20

0.47

0.03

0.30

Na

0.18

0.48

0.03

0.31

K

0.05

0.59

0.05

0.31

866

ALKALI ATOMS AS ACCEPTOR IMPURITIES

t 2 level is on the opposite, that is, the degree of localization of the t 2 orbitals in the gap increases with the atomic number of the IA impurity. We suggest that the opposite behaviour between the a I and t 2 states in the series occurs due to a compensation mechanism; the t 2 orbital charge would tend to occupy the space left by the a I orbital due to the mutual orthogonality. Such a mechanism is consistent with the fact that the Na acceptor is deeper than the Li acceptor 3,4, and it could also explain the small radial extent of the Na acceptor wavefunction 9. We finally suggest that such a mechanism could be applied to Li and Na acceptors in other II-VI compounds. IV. SUMMARY The main results and conclusion obtained from our studies can be summarized as follows: (i) The substitutional Na impurity in ZnSe introduces a t 2 orbital with a single hole in the band gap, and an a I resonance in the valence band. Our results for the IA-group impurities indicate that, in a similar way to the IB-group impurities, the a I resonances behave as hybrids between the dangling-bonds on the nearest neighbors and the atomic "s" valence orbitals of the impurities.

IN ZnSe

Vol. 64, No. 6

(ii) The electronic structure of the Li impurity is quite similar to that of the Na impurity. On the other hand, in the case of the K impurity, both the t 2 and a I states appear close to each other in the band gap. We interpretate the latter fact by means of a corerepulsion mechanism, which could explain why substitutional potassium is not detected in ZnSe, in contrast to lithium and sodium. (iii) We have investigated trends between Li, Na, and K in ZnSe. The degree of localization of the a I states decreases with atomic number, and the degree of localization of the t 2 gap orbitals increases in the same sequence. We suggest that the opposite behaviour between the a I and t 2 states in the series occurs because of a compensation mechanism between these orbitals. The latter mechanism suggests that the acceptor level shall be deeper the heavier the impurity is, which is consistent with experimental results for Li and Na in ZnSe. We also suggest that the same mechanism could be applied to Li and Na acceptors in other II-Vl compounds.

ACKNOWLEDGMENTS: The authors are indebted to Professor Jose R. Leite for a critical reading of the manuscript. REFERENCES

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170 (1985) 06. A. Baldereschi and N,O. Lipari, Phys. Rev. B 8, 2697 (1973) 07. S. Nakashima and A. Nakamura, Solid State Commun. 38, 1289 (1981) 08. Le Si Dang and R. Romenstain, Solid State Commun. 43, 829 (1982)

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