Color centers color of crystals To be clear a crystal - no strong ...

<strong>Color</strong> <strong>centers</strong>
<strong>color</strong> <strong>of</strong> <strong><strong>crystal</strong>s</strong>
<strong>To</strong> <strong>be</strong> <strong>clear</strong> a <strong>crystal</strong> - <strong>no</strong> strong electronic or vibronic transitions in visible
spectral range 7400 3600 ( 1.7 3.5 eV )
Some example <strong>of</strong> <strong>color</strong>
1) Perfect diamond <strong>clear</strong>
5.4 eV band gap
irradiation lattice defect ( <strong>color</strong> )
2) CdS yellow orange
2.4 eV band gap blue region is absor<strong>be</strong>d
3) Silicon metallic luster
1.14 eV - <strong>be</strong>low visible range
thin section red
silicon absorption
photon
near gap frequency pho<strong>no</strong>n
4) Ruby dark red - - 0.5% ion substitution
Sapphire blue - - ion substitution
5) Transition elenments containing compounds
<strong>no</strong> energy gap in visible region
even though the compound has
transition element characteristic electronic excited states at visible region
6) Some <strong>crystal</strong> <strong>color</strong>ed by radiation damage
radiation hole or electron trapped in lattice defect have
absorption line in visible region
7) Metallic impurity ppt as fine colloidal particles
glass
gold ppt ruby <strong>color</strong>ed
wave length dependence <strong>of</strong> the scattering cross section <strong>of</strong> the particles

<strong>Color</strong> <strong>centers</strong>
Pure alkali halide transparent throughout the visible region
centered (1) introduction <strong>of</strong> chemical impurity
(2) introduction <strong>of</strong> excess metal ion ( vapor heating )
(3) radiation - X-ray, neutron, electron
(4) electrolysis
<strong>color</strong> centered - lattice defect which absorbs visible light ordinary
lattice vacancy does <strong>no</strong>t <strong>color</strong>
<strong>Color</strong> <strong>centers</strong>
metal
ceramic
alkali halide band gap 9 10 eV
energetic photon hole and electron less energetic photon exciton
exciton mobile uncharged particle higher excited electron + positive hole
self trapped hole : V center
ion vacancy with positive hole ( example center )
Cl - molecule ion

F center
- electron moves cage <strong>of</strong> positively charged octahedrally disposed cation
" inside out " hydrogen atom like atmosphere
1(s) 2(s)-like 2(p)-like
single unpaired electron paramagnetic ( susceptibility measurement )
Electron spin resonance spectra
Optical properties <strong>of</strong> F <strong>centers</strong>
trapped electron in vacancy a particle in an infinitely deep 3D potential well
consider time independent wave function, ψ , Schrődinger equation
ψ ψ
boundary condition
ψ and
( E : total energy
P : potantial energy
K : kinetic energy )

ψ
π
lowest eigen state
π
π π
1st excited state - triply degenerate
ψ , ψ , ψ
π
1s 2p excitation
π
This is crude model
problem boundary condition ψ outside the well ( ESR result shows this
is nit reasonable )
( potential reduction from to finite value )
Relation
Experimental relationship
eV
, do <strong>no</strong>t fit to the relationship
electrons extensive penetration to ions core region A effective is large
F bands are all broad and almost structureless
why !
π

Optical spectroscopic techniques
energy absorption in the band gaps <strong>of</strong> insulators and semiconductors
Insulator - transparent - large energy gap
impurity atoms - selective absorption
intrinsic lattice defect
Sapphire -
broad absorption bands in blue region
colouration <strong>of</strong> ruby
characteristic pink
broad absorption band width - coupling <strong>be</strong>tween electronic motion and lattice
vibration
μ : absorption coefficient
: radiation intensity
μ : thickness
μ
π
: volume concentration <strong>of</strong> defects
: average electric field in medium
:effective field at the defect
: oscillator frequency <strong>of</strong> transition
by solving the above equation ( Smakula )
η
η
μ
η : reflective index
μ : band peak absorption coefficient
: full band width at half peak height
1.29 : Lorentzian band shape
0.89 : Gaussian band shape
can <strong>be</strong> measured if absorption coefficients are measured and oscillator
strength <strong>of</strong> transition is k<strong>no</strong>wn.

Actually it should <strong>be</strong> sharp as in atomic spectra band <strong>be</strong>comes broad as lattice
pho<strong>no</strong>n are excited during transition
Configurational coordinate model
Phisical basis
transition simple model
adiabatic Born-Oppen heimer approximation
electron-pho<strong>no</strong>n interaction
nuclei vibration electron responds ( low mass ) lattice responds only to
average position <strong>of</strong> electrons
radial in phase vibration eigen state sensitive

electronic states and energies <strong>of</strong> defects modulated by lattice vibration when
there is electronic transition, this defect - lattice coupling changes delta function
Frank-condon principle
Electronic transition time is much shorter than atomic vibration period.
Lattice coordination does <strong>no</strong>t change during transition.
Defect-lattice coupling
In specific configurational coordinate (reaction coordinate),
probability <strong>of</strong> any transition ψ
The maximum value <strong>of</strong> ψ occurs at equilibrium position <strong>of</strong>
Q = 0 peak <strong>of</strong> absorption band at 0 K
width <strong>of</strong> peak in n=0, spatial limit <strong>of</strong> line
Temp. increase
function.
different vibrational level different probability distinction

Half width,
ν
After excitation
ν
ν
lattice relaxation by emitting pho<strong>no</strong>n to vibration level.
relative position <strong>of</strong> emission band and absorption band position Stokes shift
larger num<strong>be</strong>r <strong>of</strong> pho<strong>no</strong>ns excited in a transition, larger the Stokes shift
Weaker coupling ( fewer pho<strong>no</strong>ns ), overlap <strong>be</strong>tween the lowest vibrational states
n=m=0

at high temperature, excitation in F band raises F center electron into the
conduction band
- F center luminescence decreases (photoconducting)
measurement <strong>of</strong> temperature dependence
life time <strong>of</strong> fluorescence - nature <strong>of</strong> the excited 2p-state
photoconductivity
τ : mean life time <strong>of</strong> electron in excited state (microsecond order at low
temperature)
ionization probability :
τ
τ τ τ τ
τ τ τ
τ
τ
: quantum efficiency for luminescence
Δ
τ τ

2p level <strong>of</strong> F center is 0.16 eV <strong>be</strong>low the bottom <strong>of</strong> conduction band
radiative life time <strong>of</strong> F center : 0.58×10 -6 sec.
(spin memory effect - de-excitation
)
relaxation spin
Excited states <strong>of</strong> F center
1s 2p
1s np is also expected
n 3
K, L1, L2 , L3 bands were also observed in short wave length
oscillator strength f, F_center ( 1 )
K-bands ( 0.1 )
L-bads ( 0.01 )
K-band is both asymmetric in shape and insensitive to temperature

Pertur<strong>be</strong>d F <strong>centers</strong>
optical properties <strong>of</strong> F center - complete isotropic
perturbation
broken
(slight change)
uniaxial stress, electric field F center symmetry can <strong>be</strong>
FA - center - stronger perturbation 6 nearest neighbor cation
ion
1 akali
usual octahedral symmetry tetrahedral symmetry
<strong>crystal</strong> <strong>be</strong> irradiated with F band light at photoconversion temperature
ν anion vacancy
if the <strong>crystal</strong> is held at this temperature for some time, center formed
center concentration

cation impurity concentration, num<strong>be</strong>r <strong>of</strong>
center/anion pair
Firstly center/anion pair formation cation impurity diffusion
1s ground state - spherically symmetry (<strong>no</strong> effect <strong>of</strong> impurity atom)
2p excited state - 3 2p state degenerate
2 2p state degenerate (Fig. 4.10 b )
XY plane polarized

<strong>color</strong> <strong>of</strong> Luby, Emerald and Sapphire
: corundum, α-alumina or sapphire
bond : 60% ionic, 40% covalent
completely full or empty shells present in
all electrons are paired <strong>of</strong>f <strong>color</strong>less
structure
Oxygen ion diameter 2.8
aluminum ion diameter 1.1
located in distorted octahedral site

ion location slightly lower than halfway <strong>be</strong>tween oxygen layers
ion surrounded by 6 negatively charged oxgyen electrostatic field
(=<strong>crystal</strong> field)
bond is <strong>no</strong>t purely ionic
Consider as ligand field
= electric charge (<strong>crystal</strong>line field) and specific bonding characteristics with
ligands effect
example - Luby
substitute ( size 1.2 )

lo<strong>be</strong>s protrude toward surrounding octahedron corner oxygen
ion(-)
negative-negative overlap repulsive high energy state ( level)
lo<strong>be</strong>s protrude halfway <strong>be</strong>tween the ligands lower energy

than set
( level )
Since overall energy does <strong>no</strong>t change, energy splitting upward and downward are
inversely proportional to the num<strong>be</strong>r <strong>of</strong> equal energy levels
energy splitting due to ligand field
Tetragonal distortion : two oxygen ions in z direction are more removed each
other dz 2 <strong>be</strong>comes lower energy dzz and dyz <strong>be</strong>cones lower energy
ground level : : zero energy

: very little change with strength <strong>of</strong> field
: very much change with strength <strong>of</strong> field
0 K absorption band will <strong>be</strong> very sharp
higher temperature ion vibraion broad band absorption
Emerald
"emerald green"
The same structure and the same impurity ?
Emerald
In pure state <strong>color</strong>less shappire (goshenite)
overall bonding <strong>be</strong>comes weaker less
stronger ligand field (consider oxygen slightly lower effective charge)
Ruby and Neodymium lasers
green, U.V., violet radiation to ruby emission <strong>of</strong> red right

Laser
"optically pumped" by light source ligand field type materials by light source
"direct electrical excitaion" gas laser semiconductor laser

4f lanthanide Nd
Nd laser
Nd in CaWO4
Nd in Y3Al5O12 garnet
Nd in silicate glass