Dear Radhika,

The concept of oscillator strength comes from the classical viewpoint that when an electron is bound to a nuclear framework and possesses perfect oscillating properties that the excitation probability of the electron would have an oscillator strength of unity.

If we consider the molecule as a classical oscillating dipole, the oscillator strength (f) is defined by the integral over the absorption band

f = 4.3 x 10^-9 *integral (ε) dν

Here ε is the extinction coefficient and ν is in wave numbers.

The oscillator strength is also related to the quantum mechanical quantity referred to as the transition dipole moment (er).

f = (8πmeν / 3he^2) |er|^2

I hope this helps.

Best regards,

John

Dear Radhika,

The concept of oscillator strength comes from the classical viewpoint that when an electron is bound to a nuclear framework and possesses perfect oscillating properties that the excitation probability of the electron would have an oscillator strength of unity.

If we consider the molecule as a classical oscillating dipole, the oscillator strength (f) is defined by the integral over the absorption band

f = 4.3 x 10^-9 *integral (ε) dν

Here ε is the extinction coefficient and ν is in wave numbers.

The oscillator strength is also related to the quantum mechanical quantity referred to as the transition dipole moment (er).

f = (8πmeν / 3he^2) |er|^2

I hope this helps.

Best regards,

John

Thank you so much Dr. Gert and Dr. John......

where from this 4.3 x 10(-9) is derived?

(2303/NA)(mc2/πe2) = 4.318 x10-9 in units 1/cm.

Write this as:

(2303/NA)(mc2/π)(ħc/e2)(1/ħc)

mc2 = 0.511 x 106 eV

ħc/e2 = 137 (1/fine structure constant - dimensionless)

ħ = 6.5821 x10-16 eV-s

c = 2.9978 x 108 m/s

NA = 6.022 x 1023

This gives: mc2/πe2 = 1.1295 x1014 in units 1/m

Ln(10)=2.303; comes from absorbance (A) and Beer's law

Ln(I/I0) = -ALn(10)

Therefore, (2303/6.022 x 1023)(1.1295 x 1014 1/m) = 4.318 x10-7 in units 1/m

= 4.318 x10-9 in units 1/cm

This leads to a common form for oscillator strength:

f = 2303(mc2/πe2NA) Integral[ε(ν)dν] = (4.318 x10-9 ) Integral[ε(ν)dν] dimensionless

Dear Dr. Brian,

Thank  you so much for the help.

Hi, there,

There is a paper about the relations between absorption coefficient and oscillator strength. You may find helpful.

http://arxiv.org/ftp/physics/papers/0202/0202029.pdf

Dear Dr. Mahmut,

That was a good paper which explains the relations between absorption coefficient and oscillator strength. Thanks for it.

Michael,

In my derivation ε has units of L/(mol-cm), but 1L = 1000 cm^3, so it works out. Megabarns are used mostly in nuclear science I think, but I never deal with this unit. Perhaps the units I gave for ε in my derivation will help you with the conversions involving megabarn units.

Be aware that the above paper relates to atoms/ions. For definitions in condensed media the effect of the local field is required:

Technical Report A Discussion of Oscillator Strengths and Related Issues

What is the exact significance of increased (decreased) oscillator strength to the photon absorption in say quantum dot based photodetectors?

Can someone help me to get an idea on this topic?

Saranya,

Increased oscillator strength is proportional to the increased probability that a photon will be absorbed.

John

Hi Mr. John E. Hansen,

Thank you for your reply.

However, I do understand that oscillator strength is directly related to photon absorption (absorption coefficient) and is inversely proportional to the carrier lifetime. The oscillator strength is given by transition moment integral that relates to the electronic dipole - allowed transition.

Say, given the case of quantum dot photodetector, how strain deteriorates the oscillator strength i.e. photon absorption? Supposing, you grow multiple stacks of dot layers for some application and as a result, compressive strain results from the dots to the uppermost layer altering the crystallinity of the lattice.

I want to understand this situation. Please explain to me if you have any idea about this?

The color of quantum dots like other nanomaterials is due to

the coherent interaction of the electrons in the conduction band of the quantum dot and the electric field of light. This interaction produces color with a maximum wavelength of absorption, depending on the size of the nanoparticle, its state, and the type of the nanomaterial. In the bulk materials, on the other hand, the oscillator strength is proportional to the extinction coefficient and the change in the dipole moment from the ground to the excited state is proportional to the oscillator strength; thus any change in the shape of the quantum dot by stacking or aggregation would undoubtedly affect the interaction of such material with the electric field of light.

Dear Dr. Saranya,

From what I can understand, you are asking what would happen to the absorption if stacks of quantum dots were to absorb photons? Although the layers/aggregates would not behave like the bulk of the material, definitely, the uppermost layer would be absorbing most of the photons while the lower layers would only be able to absorb photons whose penetration depth is longer than the thickness of the absorbing layer. Therefore, the uppermost layer would absorb most of the high energy photons, while the bottom layers (if they can absorb), will absorb most of the lower energy photons. In practical terms, you would get lower absorbance (at a certain wavelength) with the same amount of quantum dots if you form layers as it is in a solution since most dots in a solution would be able to interact with the photons. I hope this helps.

Is there any relationship between oscillator strength and absorption maximum that can be determined theoretically ??

Send you a paper