Electric dipole polarizabilities of isolated gallium arsenide clusters

24 November

1995

CHEMICAL PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 246 (1995) 315-320

Electric dipole polarizabilities of isolated gallium arsenide clusters S. Schlecht, R. Schiifer, J. Woenckhaus, J.A. Becker lnstitutfir Physikalische Chemie und Wissenschaftliches Zentrum fir Materialwissenschafien, Philipps-Unioersitiit Mat-burg, D-35032 Marburg, Germany Received 26 July 1995

Abstract clusters with N + M = 4-30 atoms and approximatly 1 : 1 The static electric dipole polarizabilities of isolated Ga,As, composition have been measured in dependence of the cluster size N + M by means of a molecular beam deflection technique. A striking size-dependent behaviour has been observed for small Ga,As, clusters with up to 15 atoms. Within this size range the polarizability oscillates strongly between low values for even and high values for odd numbers of atoms N + M. For clusters with N + M < 12 the polarizabiiity of gallium rich clusters is significantly larger than the values obtained for arsenic rich clusters whereas the opposite effect was observed for larger clusters with N + M > 12.

1. Introduction In the last years a lot of effort has been concentrated on the investigation of chemical reactions between isolated semiconductor clusters like Ga,As, [1,2] or Si, clusters [3,4] and molecules like e.g. H,O, NO, NH, or C,H,. The reactivity of the clusters is predominately explained in terms of its electronic structure and the number of its dangling bonds. However, there is only rare experimental information on the electronic structure of the neutral semiconductor clusters. No direct measurements of physical properties of size-selected isolated neutral semiconductor clusters were performed up to now apart from the existing crucial knowledge of their ionization potentials [5]. Most of the studies were performed on cationic or anionic clusters as measurements of drift mobilities and photodissociation experiments on Sii or Gei clusters [4,6] or photo0009.2614/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0009.2614(95)01095-5

electron spectroscopy on cluster anions like Si, clusters [7,8] or Ga,As, clusters [8]. Moreover, the interpretation of one- and two-colour photodissociation spectra in terms of the electronic structure of the participating clusters and cluster fragments [9,103 is even more difficult. Actually, there have been no successful two-colour photoionization experiments on the neutral semiconductor clusters. Up to now these spectra could only be obtained for small semiconductor molecules like GaAs [ 111. Therefore, one tries to compensate this lack of experimental information by means of quantum chemical calculations. There are several theoretical investigations on the electronic and geometrical structures of neutral semiconductors like Si, [ 12- 161 clusters [17-211. However, pure theoand Ga,As, retical investigations often suffer from the lack of measurable properties, that can be interpreted in terms of well-defined quantum mechanical quanti-

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Physics Letters 246 (1995) 315-320

ties. An ideal quantity to investigate is the absorption spectra and hence the dynamic polarizability Q(W). However, the experimental determination of this quantity is still a challenge. The purpose of the present Letter therefore is to show an experimental way of determining the static polarizability a(O) of semiconductor clusters which is a small step towards the dynamic polarizability a(w). Such a measurement is at a first glance only a determination of one single value of a(w) for w = 0. However, the static value of a(o) is related to the whole absorption spectra i.e. to the imaginary part Im[ a( w)] of the cluster polarizability by the Kramers-Kronig integral relation [22]

already measured [23] and quite a lot of theoretical work has been done on this field.

2. Experimental

(1) To our knowledge, polarizabilities have only been calculated for Si,, Si,, and Si,, clusters [14,15]. Hence we also hope to stimulate more quantum mechanical calculations of semiconductor cluster polarizabilities by delivering the corresponding experimental values for gallium arsenide clusters with N + M = 4-30 atoms. It should also be noted that the polarizabilities of sodium, potassium and aluminum clusters have been

The experimental apparatus is schematically shown in Fig. 1 and the details have already been described elsewhere [24]. Gallium arsenide clusters are generated by a pulsed laser vaporization cluster source [25], leave the source through a cooled nozzle and form a molecular beam. The beam is skimmed and collimated by two slits. The clusters in the beam are then deflected by an inhomogeneous electric field and the deflections are measured for each cluster size 1.2 m downstream the deflection field by means of a scanning collimated ionization laser beam in combination with a large ionization volume timeof-flight mass spectrometer [26]. The velocity of the clusters in the beam is measured by means of a chopper that is located directly behind the nozzle of the cluster source. The polarizability can be calculated from the measured deflections 6z of the clusters via the formula %luster =

B‘4,,v2U2~z*

TOFMS scintillator ,,/y-j-“:\ ,

chopper expansion chamber

slit collimators

pulsed ’ accelleration plates (grids)

Fig. 1. Experimental

apparatus (see text).

(2)

S. Schlecht er al. /Chemical Physics Lerrers 246 (1995) 315-320 0.20

3. Results and discussion 3.1. Polarizabilities

.z21 0.15 P Y c -cl 0.10 ._% f

in dependence of cluster size

N-FM

0.05

0.00

317

Q

-2

-1

0

scanning position

+I

+2

(mm)

Fig. 2. Typical beam profiles (raw data) of gallium arsenide clusters with N + M = 14 atoms. The whole profile is shifted by the applied field, whereas the shape of the profile remains unchanged.

where u is the velocity of the clusters, U denotes the electric potential between the deflection plates and B App is an apparatus constant that depends on the geometry of the deflection field and has already been described in detail in Ref. [24]. Since the clusters are rotating in the molecular beam the measured polarizability c+luster is the average of the diagonal elements ox+, oyy and cr,, of the clusters polarizability tensor %uster = f< ax, + ayy + %,)*

The polarizability has been evaluated for each cluster size N + M from its corresponding deflection Sz and its velocity U. Fig. 3 shows the polarizability per atom (yN+ M = %uster /(N + M) of the cluster in dependence of the cluster size N + M for a nozzle temperature of T = 38 K. The profiles have also been measured for beams with a nozzle temperature T = 300 K. The polarizability of the clusters is not influenced by the nozzle temperature. The polarizabilities per atom show significant and regular oscillations in dependence of the cluster size for N < 15. The polarizability of the clusters with an odd number of atoms N + M is thereby significantly higher than for clusters with an even number of atoms N + M. Similar odd-even effects have been observed in the intensities of the mass spectra, the ionization potentials [5] and the electron affinities of the gallium arsenide clusters [8]. The photodissociation spectra of III-V-semiconductor clusters like InNPM also show such odd-even effects [9]. For the present work the most interesting result concemes the ionization potentials of the Ga,As, clusters. One finds high ionization thresholds for even N + M

(3)

Fig. 2 shows a typical beam profile of Ga,As,,, clusters containing N + M = 14 atoms with and without deflecting field (E = 20 kV/mm) and a nozzle temperature of T = 38 K. Within our mass resolution a distribution of the clusters with all N : M compositions contributes to the profile with N + M = 14. However, the abundances in the mass spectra demonstrate that the stoichiometries with N = M and N = M &- 1 are dominant for even and for odd numbers of atoms N + M, respectively. Hence, the profiles shown in Fig. 2 belong predominantly to Ga,As, clusters. The intensities of the other compositions are significantly weaker [5]. Additionally, it was possible to measure the polarizabilities of gallium rich clusters and gallium poor clusters, i.e. clusters with N > M and N < M respectively, in order to study the influence of the cluster composition on the polarizabilitiy.

0

10

20

30

40

cluster size N+M Fig. 3. Polarizability per atom arv+ M of gallium arsenide clusters in dependence of the cluster size N + M. The figure includes the calculated values for the Ga and As atoms [34].

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S. Schlecht et al./ Chemical Physics Letters 246 (1995) 315-320

single electrons that are due to dopants, i.e. donors or acceptors. The donor-like electron level (d in Fig. 4) will be close to the level of the lowest unoccupied molecular orbital (LUMO) whereas the acceptor-like electron level (a in Fig. 4) will be close lo that of the highest occupied molecular orbital (HOMO) of the closed shell system. The electronic polarizability of the clusters can be calculated by quantum mechanical pertubation the-

Ga6 As, q-Ji

itFig. 4. Energy scheme proposed for the explanation of the alternating polarizability values for even and odd numbers of atoms N-I-M.

ory [271 ~=-$&

and low ionization tresholds for odd N + M [5]. This is consistent with the model that the electrons from the arsenic and the gallium are paired in clusters with even N + M (closed shell), while one unpaired electron is left in clusters with odd N + M (open shell). The energy that is necessary to remove the unpaired electron from the cluster will be rather low. Therefore the clusters with odd N + M will have low ionization potentials. Similar arguments can be used in order to explain the electron affinities. The clusters energy scheme can be modelized as shown in Fig. 4. The clusters with odd numbers of atoms e.g. Ga,As, or Ga,As, are open shell systems. This situation is similar to the solid state picture of special

atom

(4)

where Ear= E, - E,, denotes the energy between the levels E, and Ef and

(5)

Fclf =

represents the oscillator strength for the electronic transition from the ground state IO) of the cluster to an excited state I f). That is described by the dipole operator matrix elements (0 I d I f). The summation is performed over all final states, including states with energies above the ionization threshold. As usual, m denotes the electron mass, e is the electron charge and h is the Planck constant.

bulk

clusters

i. j I 0

‘\ \

n

Ga-rich clusters (N>M)

0 As-rich clusters (N
.

.-- .

difference

I 9

‘r.

-7 20

‘;..

_,Ga-A5 &a-Go

‘.

.,, 8 / 6-

‘AS-AS

1 ti

1 6

8

10

12

14

16

18

20

co

cluster size N+M Fig. 5. Polarizability of Ga,As,,, the expected value corresponding

clusters for gallium-rich to bulk behaviour.

and arsenic-rich

compositions.

Also included are the atomic polarizabilities

and

S. Schlechr et al./ Chemical Physics Letters 246 (1995) 315-320

The donor-like as well as the acceptor-like states allow transitions with very low transition energies Ee, (t in Fig. 4.). Because of the 1 /Et, dependence of the polarizability in IQ. (4) one obtains considerable contributions to the polarizability of the cluster. This gives a simple explanation for the high values for the open shell clusters like Ga, As, or Ga, As, i.e. N + M = 13, whereas no such an enhancement in polarizability can be observed for the closed shell system Ga,As, with N + M = 12. 3.2. Dependence of the polarizability on the composition Fig. 5 shows the polarizabilities for several gallium rich clusters (with N > M) in comparison with the corresponding arsenic rich clusters (with N < M ). For both, odd- and even-number clusters one finds higher polarizabilities for the gallium rich clusters as long as the cluster size is smaller than N + M = 13. For larger clusters the opposite behaviour is observed. The inversion takes place from N + M = 12 to N + M = 13. The inversion points are marked in Fig. 5 by the black dots. The observed behaviour that small Ga-rich clusters are better polarizable than small As-rich clusters is not very surprising since the polarizabilty of the Ga atom is by a factor of two higher than that of the As atom (see Fig. 5). However, the reason for the interchange of the effect remains unclear, especially since the bulk polarizabilities are very similar for Ga-Ga, As-As and Ga-As bonds. These bulk values can be calculated by means of the dielectric sphere model using the bulk densities and bulk dielectric constant [28] as has already been described in detail in Ref. [24]. 3.3. No evidence for permanent dipole moments for N+M>4 The measured profiles do not only contain information about the polarizability of the clusters. It is well known that pure shifts of the profiles due to the deflecting field are only observed for clusters without permanent dipole moment [29,30]. The existence of a permanent dipole moment leads to a broadening of the molecular beam and a intensity reduction on the cluster beam axis when the deflecting field is switched on [31,32]. Such effects have not been

319

observed in the profiles of all the investigated Ga,As,-clusters. However, permanent dipole moments have already been observed in our apparatus e.g. for Ge,Te and Ge,Te, [33]. From these experiments we estimate for example that the dipole moment of the Ga, As, cluster with N + M = 5 is smaller than 0.5 D [33].

Acknowledgement We acknowledge financial support from the Deutsche Forschungsgemeinschaft by Sonderforschungsbereich 383. R. Schafer gratefully acknowledges a grant of the Fonds der Chemischen Industrie.

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