Electronically-enhanced Atomic Processes in Condensed Matter
Yuzo Shinozuka
Faculty of Systems Engineering, Wakayama University, Sakaedani 930 Wakayama 640-8510, JAPANe-mail: yuzo@sys.wakayanma-u.ac.jp
Abstract
An overview is presented on various electronic-atomic processes in nonmetallic materials. The off-center instability of aself-trapped exciton in alkalihalides and a substitutional impurity in covalent semiconductors are discussed in connection
with (pseudo) Jahn-Teller effect. Mesatable configurations of (sp3) tetrahedral systems are examined with T d T-U-S model
including the effect of electron-lattice interaction and electron-electron interaction. Strategy to fabricate new structures isproposed upon multiple excitation mechanism.
Keywords: electronic excitation, structural change, Jahn-Teller effect, sp3-, sp2- hybridazation
Introduction
In condensed matter, a crystal structure is realized
when electrons and atoms are in the lowest ground state.
In the given structure, characterized by a translational
space group, each atom cooperatively vibrates around eachequilibrium position. The atomic elementary excitations
are called phonons.
The electronic elementaryexcita-tions in crystals are all delocalized as a result of theBloch’s theorem. In nonmetallic materials it is a pair of aconduction electron and a valence hole, sometimes they
form into an exciton. These elementary excitations are
the main actors and actresses on the “stage” of the crystalstructures. In order to discuss the physics of elementallyexcitations and their interaction, we usually introduce theexcitation (creation) operator ak* which operates on thevacuum 0 , asa k* 0 ,(1)which indicates the ground state electronic and atomic
structure.
Electronic Property
electron, hole,exciton

Electrons（ ({r i})）H (r 1, ..., rN)=E (r 1, ..., r N)

excitations as a result of their mutual interaction have been
main interests in the solid state physics, especially insemiconductor physics. This is schematically shown in theleft part of Fig. 1.
Recently, however, there have been found various
phenomena (Fig. 2) which break out this “solid statephysics” [1, 2]. When we excite valence electrons insolids, it sometimes induces a local structural change:
several atoms show large displacement. For example, alocalized electronic excitation induces large lattice
distortion at a point defect, desorption of an atom from asurface, defect reaction, bond switching, and so on. All
these phenomena cannot be treated as a small perturbation.
We would rather say that the vacuum 0 itself isdestroyed, or locally changes into a new vacuum 0 .
Then several fundamental questions on the structure arise:
why the original vacuum 0 has such configuration?
Do another vacuum(s) 0 really exist? How can they bestabilized? What kind of elementally excitations are

Electronic Transition

ElementaryExcitation
Interaction

Atoms（{Rj }）phononStructure(The Stage) {Rj } G

Old Solid State Phy sics

{Rj }Electronic-Atomic Processes(structural chnage, desorption,diffusion, cohesion,phase transition, ... )New Materials ScienceFig. 1The physics of the elementary excitations insolids and the new stage of materials science by electronicexcitation.
The energy spectrums of these excitations and composed

Fig. 2 Various electronically-enhanced atomic processes
in non-metallic solids.

there in the new vacuum 0 ? .… The purpose of mytalk is to give an overview on various electronic-atomic
processes in nonmetallic materials.

eVIVVV

Localization
Since electronically excitations in perfect crystals
are all delocalized, their localization process is necessary
to induce a local structural change. This is realized bya) absence of translational symmetry such as impurity,vacancy, dislocation, surface, …
b) self-localization of an electron (hole, exciton) as aresult of the strong electron-lattice interaction.

Off-center Instability
Self-trapping of an exciton in alkali halides has been
intensively studied in connection with the F-H defect pairformation [2]. It is recently found that self-trapped
excitons in alkali halides have an off-center configuration(type III (II)) as well as an on-center configuration (type I)[3], as shown in Fig. 3(b). Their stabilities depend on thematerial.
In the type I configuration, a hole isself-trapped by attracting two halogen ions to form a V kcenter by which an electron is loosely bound. The
effective charge of the Vk center seen by an electron awayfrom it would be +e, because the charges of anions andcations are canceled. On the other hand, if an electron
comes close to the Vk center, it feels the bare charge of twoanions: the effective charge would be (1-1-1)e = -e. Thus
the effective potential between an electron and a Vk center
will be attractive at large distance and repulsive for shortdistance. Then an electron can be strongly localizedpushing away the Vk center to the [110] direction to createa pair of an F center (anion vacancy) and an H center(interstitial anion pair): the type III (II) configuration.
In covalent semiconductors, when IV or VI
elements are doped into III-V compound semiconductors,
there appears a deep donor level in addition to a normal
shallow donor level. This deep level, called DX-levelcan be interchanged by a photoexcitation or a carrier
trapping, and is considered as the origin of the persistent
photoconductivity. The shallow-deep transition is caused

e-V

e-(a)

shallow neutral donor

deep negative donor

sp 3-like,4-coodination,on-centersp 2-like,3-coordination,off-center

e＋＋＋＋＋＋＋＋

creation ofan exciton＋

alkali halogen

In three and two dimensional system, self-localization only
occurs when the electron-lattice coupling exceeds a criticalstrength. In one-dimensional systems all the electronic
excitations are predicted to be always self-localized(self-trapping) without potential barrier.
The energy of an elementally electronic excitationin semiconductors is around 1eV. Then this seems notenough to break a bond because the bonding energy per
atom is usually around several eV. Thus structuralchange takes place by eithera) bond switching where the potential barrier needs lowerenergy.
b) multiple electronic excitation.

ca pture o f
a no th e r ele ctro n＋＋h+＋＋＋＋h+e＋＋＋＋＋＋＋＋＋(b)type I, on-center

type III (II), off-center

Fig. 3(a) The off-center instability of a substitutional
donor (IV) in III-V semiconductors and (b) theself-trapping of an exciton in alkali halides.

by the on-off instability of a substitutional donoratom itself[4, 5]. The similar off-center instability are found inmany impurity, such as EL2 in GaAs and N in Si [6, 7].
When a III element is replaced by a IV element such as Si,
it behaves as a single donor (Fig. 3(a)).
The local
chemical bonding of Si needs three valence electrons (Td,sp3). The rest one electron feels +e positive charge of theSi impurity when it is far away from. The Si atom canattract one more electron, and if it displaces from thecenter (C3v, sp2), two electrons will occupy a createddangling bond. The Anderson’s negative U is realized.
Finally four electrons which have to occupy in a Si-As
bond repel each other to create a pair of dangling bonds.
In this case, the As becomes neutral and satisfies the localvalency, while the Si is singly charged -e.
Structural Change of a Tetrahedral Point DefectIn case of strong electron localization we must also
take account of the electron-electron interaction. Even if
we start with a single electron in the conduction band, as it
becomes strongly localized around a particular bond, itinteracts with another valence electrons which have been
regarded to be combined with ions to form the lattice
medium in the first place. Then we have to extend theconcept of the electron-lattice interaction, which can beconsistently treated with the many-electron scheme (see areview article [8]).
Most of covalent semiconductors have either thediamond, zincblende or wurtzite structures, which areconstructed by the four-fold coordination network with sp3
hybridization of valence electrons. There the tetrahedral
symmetry (Td) is the most frequent and important point
symmetry. Several point defects have been found toshow symmetry breaking structural changes from T d toTCs(2)n=5S=1/2 (doublet)
20×22T1electroncapture

CholecaptureC3v(1)
USCs(3)T

n=4S=0 (singlet )
20×1

C2v

C3v(1)

1E

M

Tdelectron
captureFig. 4 (a) a vacancy and (b) a substitutional impurity insemiconductors.
(c) the four-site Td T-U-S model.
Hatching in (c) represents (a) sp3 dangling bond and (b)bonding or antibonding orbitals.
(d) One-electron
scheme for U=S=0, where  is one-electron orbital at
the -th site.
D2d, C2v or C3v when the electronic occupation is changed.
The stable structure is governed by the electron-electroninteraction and the electron-lattice interaction.
The
simplest model to discuss the cooperation and competition
between them would be the T-U-S model, which consistsof several interacting electrons coupled with a deformablelattice. Recently El-Maghraby and Shinozuka [9] havedone a comprehensive study on a tetrahedral (T d) four-site
system to discuss the competition between theseinteractions and the metamorphosis of the stable structures.
Figure 4 schematically shows (a) a vacancy and (b)a substitutional impurity in the diamond (zincblende)
lattice. As a first step of approximation we cut them outof the crystal and form them into the T d T-U-S model
shown in Fig. 4(c). It is characterized by the electronictransfer energy, -T, describing the quantum hopping of anelectron from site to site, the on-site Coulomb repulsion
energy, U, between two electrons, the lattice relaxationenergy, S, due to the short range interaction of an electronwith the lattice mode, Q , at the site(=1~4) and thenumber n (=0~8) of the occupied electrons. The site
represents either atomic or molecular orbital: four dangling
bonds for a vacancy and four bonding (or antibonding)orbitals for a substitutional impurity.
In the rigid lattice ( Q =0), if the electron-electroninteraction is neglected (U=0), one electron eigenstates are
one a1 state with an eigenenergy -3T and three t2 stateswith T. Then the system does not have the electron-holesymmetry. If we allow the lattice to deform ( Q ≠0) andC2v

OUS

P

holecaptureT

n=3
S=1/2 (doublet)
20×2
2T

U

2

C3v(1)

Fig. 5C2v
O C s(1)QC3v(2)

MNSP

Phase diagrams of Td T-U-S model.

if the electron-electron interaction is switched on (U≠0),
however, eigenstates of n electrons become complicatedand structural changes may take place lowering thesymmetry.
Calculated possible stable structures characterized
by point symmetries are Td, C3v, C2v, Cs, C. The obtained
stable configurations for the electronic ground state ofeach subspace (n, S) are summarized in the phase
diagrams [9]. Fig. 5 shows the diagrams for the n=3, 4, 5.
Along the T-U side of each phase diagram, the character ofthe lowest electronic state for the rigid lattice ( Q =0) isindicated. We can see that if it is triply degenerate (T 1and T2) the stable structure is always C3v for S  0, as has
been predicted with the Jahn-Teller effect [10, 11]. For
excited states the Td configuration is more unstablebecause they contain large amplitude of the charge transfer
electronic states. Thus 4-site Td “defect molecule” shows
various stable structures depending on the electron number,n, total spin, S and the strengths of the electron-latticeinteraction, S/T, and the electron-electron interaction, U/T.
When the electron occupation is changed by an electron(hole) capture or a photoexcitation, a structural changetakes place. The corresponding lattice distortion for asubstitutional impurity is illustrated in Fig. 6.

New Stage of Solid State Physics
E''理
Old Solid S. Phys

Relaxa tion

Thermalprocess
Ground stateFig. 6 Several types of the displacement of an impurity
at Td site.
Towards New Materials Science
Recently many nonequilibrium processes have been
proposed to fabricate new materials and nanostructures.
Among them electronic excitation is one of the mostpromising methods because of its high efficiency andselectivity in time, energy and space. Following four
important points should be investigated over the total
process of electronically induced structural change (Fig.7):1) [from] the ground state structure G:
dimensionality, surface, interface, impurity, dislocation,….
2) [how] electronic excitation E:
valence excitation, core excitation, charged state change
by carrier trapping or detrapping, ….
3) [via] relaxation path:
dynamics of the system, change in the character ofexcited electronic state.
4) [to] obtained metastable structure M:
atomic structure, electronic structure, elementaryexcitation, ….
Finally, I would like to comment on multiple
excitation mechanism, which is a key concept of many
proposed mechanisms, for example:a) two hole localization (self-trapping) mechanism fordesorption of atom from surface [12]b) Auger mechanism after core excitation: there are two
localized holes in the intermediate state [13].
c) Anderson’s negative U mechanism in structural changeof defects [14].
d) multiple and coherent carrier capture mechanism fordefect reaction [15].
We are living in a world filled with backgroundradiations from materials around (300 K), Sun (6000 K) in
addition to high energy cosmic ray. Then all materials
must have structures G which are stable against theseradiation: at least stable against single electronic excitation.
(This must be also for M). This is a reason whyelectronically induced structural changes have not been sofrequently met. Then multiple electronic-excitation

Electronic
excitation

Re
lax

Electronic
excitationenergyExcited statea tion

Electronic
excitation

Excited state E ’Thermalprocess M '準態 state
M
Metastable

New Structure

Atomic configuration

Fig. 7 New stage of Solid State Physics by electronic
Excitation.
would be effective because the induced force is
proportional to the electronic charge change n and therelaxation energy is proportional to n2. Thus, multiple
excitation and also co-excitation using several different
excitation would be very effective tools to fabricate newmaterials and nanostructure.
Acknowledgments
The present work is supported by a Grant-in Aid forPriority Area on “Manipulation of Atoms and Molecules
by Electronic Excitations” from the Ministry of Education,Culture, Sports, Science and Technology of Japan.
References
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