Fourier transform infrared spectroscopy (FTIR)

Alexander Hupfer

Michelson Interferometer

• Single Wavelength Source:

• Constructive Interference for: δ = mλ

• Destructive interference for: δ = (2m + 1) λ/2

• Intensity: I(δ) = S cos(2πνδ), ν = 1/λ

δ

Multiple wavelength source

• Ι(δ) = S1cos(2πν1δ) + S2cos(2πν2δ) + S2cos(2πν2δ) + …

• Continuous wavelength source, interferogram:

• Fourier transformation, spectrum:

Resolution

• Because the distance the mirror can travel is limited, the resolution is given by:resolution ~ 1/(2πxmax)

Fourier transform

Advantages of FTIR• All frequencies are measured simultaneously → short

measurement time

• High optical throughput

• Sensitivity, good signal-to-noise-ratio

• Mechanical simplicity (Mirror is only continuously moving part) → long lifetime

• Internal frequency-calibration by laser → no post-calibration necessary, very high accuracy

Limitations of FTIR• Must have a time-varying dipole moment

• Sample must be (partially) transparent to IR

• Free carrier absorption: samples must not be too conductive (for Si: ~1Ωcm)

• Need sufficient absorption length (For Si: ~mm)

• Need conversion factor for good quantitative analysis

• ”Single-beam technique” → Background and sample spectra are measured at different times

• Detection limits typically 1014 - 1015 cm-3

Experimental Setup

Spectrum is influenced by:

• IR source

• Beamsplitter

• Windows / flaps

• Detector

• (mirrors)

Infrared spectrum

IR Sources

• Far Infrared (long wavelength < 400 cm-1): Hg discharge

• Mid Infrared: Globar, black body radiation from 1000 -1600 ºC SiC rod

• Near Infrared: (short wavelength, > 6000 cm-1, < 1.6μm): Quartz Halogen

Beam splitters

• Far infrared: Mylar

• Mid infrared: CaF2, KBr

• Near infrared: Quartz

Windows

• Far infrared (long wavelenght): polyethylene, polypropylene, teflon

• Mid Infrared KBr, CaF2

Detectors

Overview

Molecular vibrations

• Molecular vibrations may absorb IR radiation with a characteristic energy if the bond has a time-varying dipole moment

• Evib - ħω(n+1/2)

• ω = sqrt(k/μ)

Vibration modes of crystals• Crystals:

• Collective vibrational excitations of solids: phonons

• Defects in crystals

• Destroys the translational symmetry of the lattice, altering the normal modes of vibration

• If the frequency of the modified mode lies outside the phonon bands we get a localized vibrational mode (LVM)

• LMVs absorb IR radiation at a characteristic frequency determined by the local atomic configuration

• FTIR of defect LVMs sensitive to chemical and structural nature of the defects

Molecular vibrations - example

• Absorption lines are ‘fingerprints’ for characteristic vibrations:

Anharmonicity• Important if comparing

with ab-initio calculations

• Strongly present in O-H stretch modes, less in O-D

• First approximation: Reduce to 1D potential along normal mode and solve Schrödinger equation numerically

�0.4 �0.3 �0.2 �0.1 0.0 0.1 0.2 0.3 0.4z(A)

�2500

�2000

�1500

�1000

�500

0

V(m

eV)

Isotopes• Substituting hydrogen with deuterium can help identifying defect

• H (μ = 1u) and D (μ= 2u) modes are related by νOH/νOD = sqrt(μOD/μOH) = ~1.41

Defect concentration• T = I/I0 = 10-A

• A: Absorbance

• Tν : Transmittance

• Tν = I/I0 = (1-R) e-αx

• Defect concentration:

• ξ = 1.6 x 1016 cm−1 For interstitial hydrogen in ZnO, S. J. Jokela and M. D. McCluskey, Phys. Rev. B 72, 11320, 2005

• 6.6×1014cm−1 Interstitial H in rutile TiO2 Lavrov et all

x

Demo Time

Lineshapes• For a single vibrational mode a

Lorentzian line shape is expected.

• The width of the line can be connected to the excited state lifetime

• Several reasons can contribute to broadening, e.g. coupling to phonons

Determining bond orientation

• Sometimes it can be helpful to know the bond orientation of a defect

• A IR polarizer can be placed before or after the sample

• I(α) = cos(α-α0)2

• I(α): normalized intensity under angle α α0 : bond angle

Summary• Must have a time-varying dipole moment

• Sample must be (partially) transparent to IR

• Free carrier absorption: samples must not be too conductive (for Si: ~1Ωcm)

• Need sufficient absorption length (For Si: ~mm)

• Need conversion factor for good quantitative analysis

• ”Single-beam technique” → Background and sample spectra are measured at different times

• Detection limits typically 1014 - 1015 cm-3

Summary• Defects in a crystal material may give rise to localized vibrational

modes (LVMs) to absorb IR radiation at a characteristic frequency

• FTIR is a relatively simple, non-destructive tool suitable for studying such LVMs as well a phonon bands, shallow donor or acceptor transitions, free carrier absorption, or other optical properties

• Both qualitative and quantitative (with conversion factors) investigations are possible

• Samples must be thick enough for sufficient absorption an transparent in the IR-range