Destabilization of a self-trapped exciton

PHYSICAL REVIE%

8

VOLUME 26, NUMBER 6 15SEPTEMBER 1982

Destabilization of a self-trapped exciton

in

a

quasi-one-dimensional

semiconductor:

Mg[Pt(CN)4]. 7H20

^with

hydrostatic pressure U.

Rossler

Institut fur Theoretische Physik, Uniuersitat Regensburg, D 8400-Regensburg, Germany

H.

Yersin

Institut fiir Physikalische und Theoretische Chemic, Uniuersitat Regensburg, D-8400Regensburg, Germany

(Received 21 April 1982)

Optical data from single-crystal Mg[Pt(CN)4] 7H20 together with calculations ofthe ex- citon energies allow us todraw conclusions on the existence ofaself-trapped exciton, which becomes metastable by changing the relevant material parameters with hydrostatic pressure.

An exciton in a deformable lattice is in a stable localized (self-trapped) state

if

the exciton-lattice interaction is stronger than the energy transfer be- tween lattice sites; otherwise, the stable exciton state is delocalized. ' The relative strengths

of

exciton-lattice interaction and energy transfer de- pend on the material parameters, which in a con- tinuum model are the exciton mass, the deforma-

tion potential, and the elastic constants. By a proper change

of

these parameters it isconceivable to destabilize aself-trapped exciton

(STE}.

An ef- ficient variation

of

the intrinsic material constants is possible in the highly anisotropic (quasi-one- dimensional) semiconductor Mg[Pt(CN)4] 7H20 by the application

of

hydrostatic pressure. Optical emission spectra

of

this system together with cal- culations

of

the exciton energies give evidence that due

to

stress-induced alteration

of

the intrinsic parameters a

STE

is destabilized. The high aniso- tropy (quasi-one-dimensionality)

of

Mg[Pt(CN)4] 7H20 ^seems tobe crucial for this ef- fect which, toour knowledge, has not been ob- served sofar in other solids.

The fundamental optical transition energies

of M„[Pt(CN}4].

nH20, ^which for different cations

M

and crystal water content n can be varied from the uv to the red spectral region, are correlated ^with the in-chain metal-metal distance A. In partic- ular, for Mg[Pt(CN)4]. 7H20 with

R =3.

155 A these transition peak energies are

19400

crn from reflectivity data and

17600

cm ' _{from emis-} sion spectra (at 295

K).

The Pt-Pt distance

R

can be further decreased by hydrostatic pressure and

giX+&&&t'r'ee exciton state's,

self-_trapped exciton states V

KU

intrinsic photoconductivity

Il

~absorpt~ion

~E

^llc

~o~+~

i

~ ~emission Eic

CO CL

C

C0

lhIh

E ^ct

OQ ^V

OJ CLtW

&t

ground state

FIG.

1. Phenomenological energy-level diagram for the lowest electronic states and schematic (simplified) optical spectra oftetracyanoplatinates (II).

becomes for Mg[Pt(CN)4] 7H20, at about 20 kbar, R

=3. ⁰

^{A3 with} optical transition energies

of

about

13 300cm ^' in reflectivity and 11800cm ' in emission. Calculations for the [Pt(CN)4] ^dimer demonstrate the strong overlap

of

Pt6p, (hybri- dized with ligand CNn. e orbitals) and

of Pt

5d

„6s

orbitals on neighboring complexes. As a conse- quence one expects the formation

of

energy bands for the periodic structure. '

In fact, it is possible to ascribe the R dependence

of

the optical data to a decrease

of

the energy gap ^between the conduc- tion band, which originates mainly from

(Pt6p„CNa

)orbitals, and the

(Pt5d

&,

6s)

valence band with decreasing

R. "

3187

1982

The American Physical Society

The available information on the nature

of

the excited electron states is summarized in the phenomenological energy-level diagram for tetra- cyanoplatinates in

Fig. 1.

^' The optical absorption is _highly polarized with the electric field vector E~~c (cbeing the chain axis), as is expected from the _symmetry

of

the valence-band _edge (a_~s) and the conduction-band edge

(a2„)

ⁱⁿ the crystal-point group D4s. The ^details

of

the optical spectra (Fig.

1) can be understood only by including spin and correlation effects. The electronic ground state has A'~s symmetry in double-group notation

of

D4s

('A&s in single group D4s) ^while the lowest excited

states have symmetry

A~„('Aq„)

(allowed for E~ ~c), E„'

('A2„)

(allowed for

Elc),

and A

&„(

Az„)^(dipole forbidden). Since the oscillator strength

of

the E~~ctransition is close toone, it is ascribed to a delocalized exciton, being mainly

of

singlet charac- ter

Az„.

^{The emission} from this state, whose life- time

of r &0.

3)&10 s at

1.

7

K

(Ref. 12) is con- sistent with the oscillator strength

of

^the E~~cab- sorption, is observed with a slight red shift due to reabsorption. The interpretation as a delocalized exciton is supported by photoconductivity' and doping experiments. ' The

Elc

absorption ob- served at the low energetic rise

of

the E~~cabsorp- tion has an oscillator strength

of

the order

of

10

It

is ascribed tothe delocalized triplet exciton E„'

(A2„)^{which is} weakly allowed due to spin-orbit coupling. ^'

At lower energy optical transitions are possible, which can be detected only in emission (mainly

Elc)

with longer lifetime. The red shift

of

this emission against the short-living _E~~cemission de- creases with decreasing

R

over the whole spectral range.

For

Mg[Pt(CN)4] 7H20 at hydrostatic pressure

of

about 13kbar (corresponding to Rbe- tween

3.

05 and

3.

00 A at 295 K)the

Eic

emission vanishes. Moreover, doping experiments prove that this emission is intrinsic and aseries

of

exper- imental facts indicate that the corresponding elec- tronic states are localized to afew planar

[Pt(CN)4] complexes within achain. Some

of

these experimental facts are the following:

(i)A small [Ni(CN)4] impurity concentration quenches selectively the

Elc

^emission. The tem- perature behavior is explained by a phonon-assisted hopping between localized states and the quench- er¹⁴

(ii)The

Elc

emission lifetime is reduced by rare-earth impurities and at low temperatures one observes atwo-component decay. The long-living component equals the intrinsic one and the short- living component is attributed to regions, emitting

0(((eV)

20—

1B

16

c~3(10 dynlcm )

/mo

— 10 0.

8-

- _e

0.6—

14

12 0.2-

2.95 3.00 3.05 3.10 3.15 R(A)

FIG.

2. R-dependent longitudinal input parameters forcalculations ofthe total energy [Eq.^{(2) with Eq. (5)]:}

M~[

— —

_m,

~~+m~)( isthe exciton mass, _D~~ the deformation potential, and e33 the elastic constant. Ris the in-chain metal-metal distance between neighboring [Pt(CN)4]

complexes.

near the impurities. ^'

(iii) A blue shift

of

about 270cm ' (correspond- ing to a [Pt(CN)4] vibration) observed in the

Elc

emission under high magnetic fields is ex- plained by assuming a localized state.^'

(iv) An exchange

of

the crystal water H20 to

D20

strongly increases the

Etc

emission intensity.

This behavior is expected for localized states which are coupled tothe water vibrations.

Owing to the translational _symmetry

of

the crys- tal, even alocalized intrinsic electron state forms an energy band. Emission data from doped materi- al'

'

allow us togive a rough estimate

of

the upper limit for the bandwidth; the intrinsic emis- sion (at 25

K)

^{starts to} decrease at an impurity concentration

x=10,

which means that the characteristic capture time by impurities becomes comparable with the intrinsic recombination life- time

(r=3X

10 sat 25

K). If

one considers only one-dimensional hopping an impurity site is reached after 10 steps (for

x =10 ). '

This gives alower limit for the resting time

ht

at one [Pt(CN)4] unit

of

about

3X10

^' s and, conse- quently, an upper limit

of

the bandwidth

hc=filb

t

of

about 2cm '

(-0.

25 meV). Be- cause

he

is at least afactor

of

10 smaller than the calculated widths

of

conduction and valence bands, '

"

^{there must be a very} efficient intrinsic localization mechanism which most likely is the electron-lattice interaction. Therefore, we interpret the excited electron state responsible for the

Elc

emission as

STE. If

^{there is no} symmetry-lowering lattice distortion, the symmetry classification

of

the

STE

is the same as for the delocalized free ex-

26 DESTABILIZATION OFASELF-TRAPPED EXCITON IN

A. . .

3189 citon,

i.

_{e., it} consists

of

components with symmetry

~2g ^{(~2@) (E~}~c),Eg ('~2@)

(Ej-c),

and

~ i.

^('~2@)

whose separation is larger than for the free exciton, since exchange effects increase due tolocalization.

Though emission from all these localized states has been detected

'

the emission via the E„'state is dominant due toexchange splitting and relaxation.

To

confirm the phenomenological energy-level diagram

of Fig.

^{1 and} the R-dependent kinetic features

of

the different excited electron states, we started from the band model" and considered the effects

of

electron-hole and

of

electron-phonon in- teraction in the case

of

high anisotropy'

'

within acontinuum model. The band calculations" with the input parameters

of Ref.

10yield the energy gap

(Es),

the longitudinal masses

of

electron (m,ii)

and hole (msii), and the deformation potential DII

=EEs/(~/R)

^as a function

of

R (Figs. 2and

3). Of

the dielectric constants, which are required in the calculations

of

the exciton binding energy' Eb, ^e _~I^{has been determined from}

+

y

RE2(R)

with the calculated values for

Es(R).

^{The parame-} ter y ^and the optical constants

e„z — — 2.

5,^E'oz=3.5, and _zoll

e II+1 ^w«e

chose»ndependent

of R

and according toavailable data for

Ba[Pt(CN)4].

4H20.

^' The transverse electron and hole masses m,z

— — 1.

3mo and mq&

— — 1.

75mo, which are not expected todepend on

R,

were chosen to reproduce the experimental binding energy for Ba[Pt(CN)4].

4H20

as obtained from photoconduc- tivity experiments. The R-dependent exciton ener- gies are given in

Fig.

3;they correspond closely to the transition energies

of

the E~~cemission.

The stability

of

delocalized and self-trapped states depends on the total energy

of

the exciton (kinetic energy), the lattice deformation, and the exciton-lattice interaction as afunctional

of

the ex- citon envelope. '

For

an exciton in an anisotropic elastic continuum this _energy is'

.^{2 2}

a, iV,

_u)(

E(ai all)=

2M

' ⁺ _M

2M] Qg Mf) ^Q_[f Qg2 CX~~

—

_Eac

ag &)~

where

M =m, +ms

is the total mass

of

the exciton and

a

is the lattice constant. _n~l and o,j ^character- ize the localization parallel and perpendicular to the chain

of

the exciton-envelope function which is assumed as an anisotropic Gaussian

1/2

g(r

^{) 23y4} _1/2

'~'ll

(eV)

p (kbur)

20 10

{cm')

)(exp —

m (x

+y )+

^z

ll

The elastic deformation-energy parameter

(3)

oo()

^{emission Ellt:}

+++

^emission

Elc

^—20000

band gap&.

f

c33D

i

^4c(

^3DiD

II

+

^2—(

c» + ^c

^&2)D

I I

2 2

4[C33(C11

+

C12 )

—

2C2₁₃

]

(4)

L3

~

2.

0-

LLI

-

₁₆₀₀₀

12000

depends on the elastic constants _c;1and on defor- mation potentials

D.

Comparison

of

optical data for tetracyanoplatinates with different transverse lattice constants but same

R

allows us

to

give an upper limit

of Di &0.

3 eV

«DII

^(see

^Fig.

^2).

Thus assuming C33)~c&3,

Eq.

(4)reduces to

ac 2 C33

where

c33(R).

can be determined from compressibil- ity data (Fig. 2).

The total energy

E(aii, ai) of Eq.

(2)can be visualized in an energy contour diagram as given in the inset

of Fig. 4. It

represents a generalization

of

the total-energy expression for the isotropic con-

R{A}

3.0 3.1

FIG.

3. Comparison between the R dependence of polarized emission for Mg[pt(CN)4] 7H20 (Ref.5) and calculations for the _energy gap, free-exciton energy, and self-trapped exciton energy.

{u)

R-2.95k

(b}^R 3.00A

»0 ^-

_{c)

_R-3.

051}, (d} R 3.10A 50

-

(s) R=3.15

{cm}

-

₁₀₀₀

500

-500

-150-

-1000

-200—

II

-1500

-250-

0

-2000

0.2 OA 0.6 0.⁸

FIG.

4. Total energy ofan exciton in an anisotropic elastic continuum calculated from Eq.(2)[with Eq. (5)]

for different Rvalues with the input parameters ofFig.

2along the path indicated in the _energy contour dia- gram ofthe inset (seealso Ref. 18).

tinuum' tothe case

of

an anisotropic continuum.

The relation with the isotropic case becomes ap- parent by considering the total energy

of Eq.

(2) [with

Eq.

(5}]along the path indicated in the inset

of

Fig.

4.

The total energy

E(a)

shows two types

of

minima: The minimum

E (a =0) =0

represents the delocalized free-exciton state

[P(r) ^=const]

^and

is separated by a potential barrier from the minimum at

a=1,

which corresponds to a

STE

state with a strongly localized envelope. This situ- ation is in agreement with the experimental obser- vation

of

emission from both states.

For

decreas- ing E. the

STE

is destabilized and eventually ceases toexist in accordance with the vanishing

of

the

Ej. c

emission from the localized state (Fig.

3).

The continuum model does not strictly deter- mine the

a

value corresponding toan envelope function, which is localized toabout one lattice constant.

It

turns out that the energy difference between the free exciton and the

STE

at

a =0.

8in

Fig.

⁴is in quantitative agreement with the energy difference between the emission data for E~~cand

Elc

in

Fig. 3.

In conclusion, we interpret optical emission data for the quasi-one-dimensional semiconductor Mg[Pt(CN)4].7H20 under hydrostatic pressure us- ing band calculations and continuum models for free and self-trapped excitons. The quantitative agreement between experimental and theoretical data (Fig.3)gives support tothe interpretation that a self-trapped exciton is destabilized due to the pressure-induced change

of

the intrinsic materi- al parameters.

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of

^{the 1979Toniguchi}

Symposium on Relaxation

of

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R.

Kubo and

E.

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E. E.

Koch,

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(K3[Pt(CN)4]Bra 33H20)^with R

=2.

89A, whose me- tallic properties aredue tothe nonstochiometric Br.

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DESTABILIZATION OFA SELF-TRAPPED EXCITON IN

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