Transcript 1. dia - Budapest University of Technology and Economics

Computer simulation of photo induced
phenomena
József Hegedüs
Supervisor:
Prof. Sándor Kugler (Budapest)
thickness change [nm]
Photo-induced expansion in
amorphous Selenium thin-film
Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542
Photo-induced volume change in a-AsSe (expansion) and a-GeSe
(contraction). Solid lines represent the changes in thickness. (A: after
preparation, B: annealed, C: illuminated and D: annealed again.)
a-As2Se3
a-GeSe2
Illuminatio
Illumination
n
Y. Kuzukawa et al.: Journal of Non-Crystalline Solids 227–230 1998 715–718
thickness change [nm]
Photo-induced expansion in
amorphous Arsenic Selenide
Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542
Selenium: model material of
chalcogenide glasses
In Greek mythology
Selenium

Physical properties of Selenium:
 The
building units of Selenium in the condensed
phases are chains and rings
 Basically two-fold coordinated atoms
 Band gap of a-Se: 1.8 eV
 Melting temperature of c-Se: 217 OC
Molecular dynamics simulation:
Verlet algorithm
+
The time step (Δt) usually was 2 femtoseconds.
Molecular dynamics simulation

Atomic interaction is handled by self-consistent
tight-binding model1-4
method1, parameters are fitted to
density functional calculations2-3
 the tight-binding model2-3 describes well the
amorphous structure4
 semiempirical

We control the temperature in the simulations by
rescaling the velocity of each atom
[1]
[2]
[3]
[4]
L. Goodwin, A.J. Skinner, and D. G. Pettifor, Europhys. Lett. 9, 701 (1989)
D. Molina, E. Lomba, G. Kahl, Phys. Rev. B 60, 6372 (1999).
E. Lomba, D. Molina, and M. Alvarez, Phys. Rev. B 61, 9314 (2000)
J. Hegedüs and S. Kugler, J. Phys. Condens. Matter 17 6459 (2005)
Photo-excitation of
Selenium molecules

Systems studied :
 Selenium
ring with 8 atoms
 Selenium chain with 18 atoms

Modeling photo excitation:
 one
electron transfered from HOMO to LUMO
J. Hegedüs, K. Kohary, S. Kugler, & K. Shimakawa, J. Non-Cryst. Solids, 338 557 (2004)
before
excitation
after
excitation
before
excitation
after
excitation
•Photo excitation in amorphous Selenium
thin-films:
1) Structural model preparation
2) Photo-excitation
A structural model of
amorphous Selenium thin-film
open
open
3D PBC
2D PBC
Measuring the thickness of the sample
thickness: difference between Z coordinates of
center of masses of 10 surface atoms
Light excitation
electron-hole
 Electrons
and holes separate after photo
excitation on a subpicosecond timescale due to
the disorder.
 We can neglect the Coulomb attraction
between them.
J. Hegedüs, K. Kohary, D. G. Pettifor, K. Shimakawa, and S. Kugler,
Phys. Rev. Lett, 95 206803 (2005)
Light excitation
 We
electron-hole
study photo-excited electrons and
holes in two separate simulations:
We put one electron to the LUMO
(photo-excited electron)
We remove one electron from the
HOMO (photo-excited hole)
before illumination (effect of photo excited electron)
during illumination (effect of photo excited electron)
Solid line: length of the breaking bond
dotted line: thickness of the sample
Light on
Light off
Thickness of the sample
The photo-induced local expansion is transient.
It can be repeated over and over again.
 Microscopic
structural changes caused by
photo-excited holes
 We remove one electron from the Highest
Occupied Molecular Orbital (HOMO)
Two different kind of bonds: covalent bonds
(black) and weak interchain bonds (gray)
„black” bonds (covalent bonds)
„gray” bonds
(weak interchain
covalent bonds)
Before illumination
During illumination
Transient photo-induced weak
interchain bond formation
Thickness of the sample
Transient photo-induced volume
contraction
Rate equation model
to describe the
macroscopic volume
change
The
macroscopic volume change is
the superposition of several local
volume contractions and expansions
introduce β+ and β- which are the
average volume change caused by one
electron and by one hole
We
 Total
expansion: d+ = β+ ne
 Total
contraction: d- = β- nh
 Number
of electrons (ne) =
number of holes (nh)
 Total
volume change is:
Δ(t) = ( β+ - β-) n(t) = βΔ n(t)
Rate equation for the time development of the
number of photo excited electrons and holes
after switching on the light:
dn(t)/dt = G – C n(t) n(t)
(using: ne(t) = nh(t) = n(t))
Rewritten as an equation for volume change:
dΔ(t)/dt = G’ – C’ Δ2(t)
(using: G’ = G βΔ ; C’ = C/βΔ)
Δ(t) =
1/2
(G’/C’)
1/2
tanh{(G’C’) t}
(Solution)
8
Steady state case: t =
1/2
Δ(t = ) = (G’/C’) = a
8
Only one independent
parameter to fit !!!
Rate equation model with a fitting parameter describes the
experiment in a-Se
light on
J. Hegedüs, K. Kohary, D. G. Pettifor, K. Shimakawa, and S. Kugler,
Phys. Rev. Lett, 95 206803 (2005)
After the light is turned off: G=0
Differential equation for the
volume change:
dΔ(t)/dt = – C’ Δ2(t)
Solution:
8
Δ(t) = a/(aC’t + 1); a = Δ(t = )
Rate equation model with two parameters describes the
experiment in a-Se
light off
Rate equation model
for a-AsSe
J. Hegedüs, K. Kohary, S. Kugler, Journal of Non-Crystalline Solids 352 (2006) 1587
thickness change [nm]
Photo-induced expansion in
amorphous Arsenic Selenide
transient
expansion
metastable
expansion
Y. Ikeda and K. Shimakawa: Journal of Non-Crystalline Solids 338–340 (2004) 539–542
Rate equation model with two independent
parameters describes the experiment in a-AsSe
metastable part
transient part
time[s]
light on
time[s]
light off
J. Hegedüs, K. Kohary, S. Kugler, Journal of Non-Crystalline Solids 352 (2006) 1587
Summary

Photo excited electrons  local volume expansion


Photo excited holes  local volume contraction


weak interchain bond formation
Universal model of the macroscopic photo-induced
volume change.


bond breaking, wave-like structural change
describes: photo induced expansion and contraction
Rate equation models describe the time development in the
experiments:


in a-Se with one independent parameter (transient changes)
in a-AsSe with two independent parameters (transient+metastable
changes)