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- 1. Optical spectroscopy Prof David Lidzey University of Sheffield
- 2. Optical Spectroscopy • Study of the interaction of matter and light (radiated energy). • A key experimental technique use to probe all states of matter (atoms, gas, plasma, solids, liquids etc). • Gives direct information about electronic structure of a system. • Can be used to explore relative composition of a material (i.e. relative concentration of a known compound in solution). • Widely used in industry and quality assurance. • Key technique in semiconductor research.
- 3. Summary Absorption and emission of radiation Transition rates Selection rules for optical transitions Direct vs indirect semiconductors Measurement of absorption Measurement of emission and quantum yield Fluorescence decay lifetime For more information, see “Optical Properties of Solids” by Prof. Mark Fox on which this lecture is loosely based.
- 4. • In quantum systems, we have interaction of a stationary-state (e.g. an atom) with an oscillating state – a photon. • Coupling of the states is strongest when the energy difference between the two states matches the energy of the photon, e.g. • Atoms can either absorb or emit this energy when they jump between states. E2 - E1 = hn E1 E2 hn E1 E2 hn Absorption Emission
- 5. Transition rates • Transition rates (W12) between two states can be calculated using the wavefunction of the initial and final states through Fermi’s golden rule. • Here the M12 is the matrix element for the transition between bands of levels. The matrix element can written as where H is the perturbation that causes the transition (the interaction between the atom and the photon). The strongest interaction process is called the “Electric dipole interaction”. • g(hn) is the photon density of states. This is defined as the number of photon states per unit volume that fall into the energy range E + dE, where E = hn W12 = 2p M12 2 g(hn) M12 = y2 * (r)H(r)ò y1 d3 r
- 6. • Here, the perturbation is expressed by H = -p. e where p is the dipole moment of the electron and e is the electric field applied. Because of this, such transitions are called ‘Electric Dipole’, or ‘Dipole-Allowed’ transitions.
- 7. Selection rules for Electronic transitions. Electric dipole transitions can only happen if a number of rules about initial and final states are obeyed. These are rules about the quantum numbers of the initial and final states. For an electron in a system with quantum numbers l, m, ms, the selection rules are (1)Parity of initial and final states must be different (2) Dm = -1, 0 or +1 (3) Dl = +/- 1 (4) Dms = 0 The photon carries away one unit of angular momentum, so the total angular momentum of the atom must change by one unit in the transition.
- 8. From single emitters to electronic bands. • Atoms in a solid are packed close-together, so outer orbitals interact strongly together. • This broadens discrete levels to bands. Electronic bands retain of atomic character of states. • Transitions between bands allowed if they are allowed by selection rules. • Absorption allowed over continuous range of wavelengths. • Such materials have sizable optical effects, making them useful for device technology. GaAs GaAs crystal structure Interatomic separation E
- 9. Luminescence from a semiconductor Excited states Ground states Inject electrons Inject holes tRtNR Relaxation Rapid relaxation and thermalisation Applies for electrons and holes. Recombination of electrons and holes can result in luminescence. This often different from absorption. Radiative and non-radiative processes compete.
- 10. Quantifying luminescence efficiency Luminescence quantum efficiency (F) can be calculated using tR = radiative rate, tNR = non-radiative rate Have, where A = 1 / tR. If tR << tNR, then F ~ 1.0 and all energy comes out as light. If tR >> tNR, then F ~ 0 and the energy is lost internally as heat. dN dt æ è ç ö ø ÷ total = - N tR - N tNR F = AN N(1 tR +1 tNR ) = 1 1+tR tNR
- 11. Interband Semiconductor Luminescence Direct-gap materials Conduction band Valence band electrons holes hn Eg Photons emitted when electrons at the bottom of the conduction band recombine with holes at the top of the valence band. Since momentum of the photon is negligible compared to that of the electron, e and h have same k-vector. Energy of luminescence close to energy-gap. Examples: GaAs, GaN, GaInP k E
- 12. Generating Photoluminescence • Excite a direct bandgap semiconductor with a photon whose energy is greater than the energy-gap. • Photons are absorbed, raising electrons into the CB and holes into the VB. • Electrons loose energy very quickly by emitting phonons. Each step corresponds to the emission of a phonon (~ 100 fs). Energy and momentum is conserved in this process. • Relaxation process much faster than radiative emission, so electrons collect at bottom of CB before recombining radiatively. electrons holes hn Eg k = 0 E
- 13. Photoluminescence at low carrier density holes k = 0 E E Density of states electrons At low carrier densities, the occupation of electrons and holes have a Boltzmann distribution f (E) µ exp - E kBT æ è ç ö ø ÷ PL emission above energy-gap falls off exponentially due to Boltzmann factor. From “Optical Properties of Solids” by Mark Fox
- 14. Interband Semiconductor absorption Conduction band Valence band hn Eg k E Transitions are possible at a Wide range of energy (wavelengths) from the Valence band to the Conduction band.
- 15. GaN: Absorption and luminescence Absorption and emission are not the same!From “Optical Properties of Solids” by Mark Fox
- 16. Perovskites can be direct bandgap semiconductors Saidaminov et al Nature Communications 6, 7586 (2015) Mott et al Nature Communications 6 (2015) 7026
- 17. Indirect gap semiconductors Conduction band Valence band electrons holes hn Eg Phonon Conduction band minimum and valence band maximum are at different point in Brillouin zone. Conservation of momentum requires that a phonon is either emitter or absorbed when the photon is emitted. This represents a ‘second-order’ process, giving it a low probability. Radiative lifetime is therefore slow, and competition with non-radiative processes makes luminescence weak. Examples: Si, Ge k E
- 18. Quantifying absorbance Sample Io(l) I(l) d I = I0e-sdN I0 and I are the power per unit area of the radiation incident and transmitted. s is the attenuation cross-section of the absorber N is the number density of the absorbers Absorbance is defined as A = -ln I I0 æ è ç ö ø ÷ = 2.302log10 I I0 æ è ç ö ø ÷ =sdN Very often, when measuring a thin film, we are actually interested in S – the attenuation coefficient, where Units for S are often expressed as cm-1. A = Sd
- 19. Measurement of optical absorption Basic principle - split white light into component wavelengths using a dispersive element (e.g. a grating or prism). Measure how efficiently the different wavelengths are absorbed.
- 20. Components inside an absorption spectrometer Light-source Optical grating on rotating turret Entrance slit Exit slit Sample Detector Scan ‘probe’ wavelength and measure transmitted signal
- 21. Measuring optical absorption using a CCD spectrometer. Shine a white light through a sample Determine the wavelengths transmitted
- 22. Measuring photoluminescence emission This is considerably easier if the sample under test is an efficient emitter (i.e. F ~ 1.0)
- 23. Emission dynamics • Emission from an excited state comes via the process of spontaneous emission • If upper level has a population N at time t, the radiative emission rate is given by • This can be solved to show where tR is the radiative lifetime of the transition. The actual luminescence intensity I(hn) can be dependent on the emission rate, and the relative probability that the upper level is occupied and the lower level is unoccupied. ‘Allowed’ transitions often have radiative lifetimes of ~ 1 ns. dN dt æ è ç ö ø ÷ = -AN N(t) = N(0)exp(-At) = N(0)exp(-t /tR )
- 24. Measuring fluorescence decay lifetime • Sample excited with a very short light-pulse. • Emission recorded as a function of time. • Lasers with pulses 100 fs to 1 ps now commonplace. • Time-resolutions of 100 ps achievable with photomultiplier tubes. Resolutions of 1 ps possible with a ‘streak-camera’. Pulsed laser DetectorSample Mirror Lenses
- 25. Fluorescence dynamics 1 ttotal = 1 trad + 1 tNR I(t) = Aexp(-t /t1)+ Bexp(-t /t2 )+... Gives direct information about carrier relaxation, diffusion and recombination mechanisms. Often a series of processes going on, so practically need to fit decay lifetimes to a series of exponential decay functions.
- 26. Summary • Absorption and PL spectra allow the electronic states within a material to be directly accessed. • The properties of many semiconductor materials have similarities, but also distinct differences, depending on atomic / molecular structure. • Reviewed a number of key techniques of use in routine spectroscopy labs.

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