Fourier transform infrared spectroscopy...
Transcript of Fourier transform infrared spectroscopy...
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
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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