Lehrstuhl Werkstoffe der Elektrotechnik Exciton spectroscopy in wide bandgap semiconductors Lehrstuhl Werkstoffe der Elektrotechnik (WW6), Universität Erlangen-Nürnberg, Martensstr. 7, 91058 Erlangen Vortrag auf der WET- in 11. 13. Februar 2009
Lehrstuhl Werkstoffe der Elektrotechnik Exciton spectroscopy in wide bandgap semiconductors 1. Exciton theory Wannier-Mott excitons, Frenkel excitons impurity bound excitons 2. Measurement techniques Optical absorption PL/CL, PL-E, TRPL 3. Exciton spectra Features in wide bandgap semiconductors Application to materials science 4. Summary
The exciton concept Exciton: electron-hole pair Attraction by Coulomb forces: 2 e U r 4 r 0 r e and h recombine when they meet, thus * finite lifetime (ps µs range) * e and h must have same group velocity E v k (valid e.g. for k 0) ~ k Exciton: particle of quantum mechanics neutral (no charge) free movement in the lattice effective mass m +m may interact with other particles (e.g. photons) is a boson (integer spin number) ½ r e h Excitons form in 1. Theory WET- semiconductors, insulators and molecular crystals.
Exciton formation energy 1. Theory WET- Treatment analog to hydrogen or positronium: Bohr-Rutherford model one particle orbits around the other particle Formation energy*: n: quantum number (n = 1: ground state) E n e 4 2 2 2 2 32 0 r n me mh me mh reduced mass Energy + Position in the bandgap: free electron and hole: conduction band edge Eg exciton levels in the upper band gap Eg E n E g 0 conduction band valence band... E E E g E E g E E E g 4 g 3 2 1 exciton levels * Formation energies are negative (add a minus sign), but as they are subtracted from the conduction band edge, they are treated positive within this talk.
Exciton formation energy Treatment analog to hydrogen or positronium: Bohr-Rutherford model one particle orbits around the other particle Formation energy: n: quantum number (n = 1: ground state) Eg E n E n e 4 2 2 2 2 32 0 r n Position in the bandgap: free electron and hole: conduction band edge Eg exciton levels in the upper band gap 1. Theory WET-
Wannier-Mott exciton Dielectric medium approach (Wannier-Mott exciton) E n Hydrogen: e 2 2 2 2 32 0 r n Semiconductor: Bohr-Radius 4 m ; 1 e r H Atom ev E1 13, 6 E 1 r n 0,1 m ; 10 e some 10 mev 2 2 n h 0 2 m e r r Cu O (77 K) 2 1. Theory WET- r = 10 100 atomic distances! 1 free exciton E = 2,17 ev; = 10; µ eff 0,7 g E = 100 mev/n² n r [Kittel]
Frenkel exciton Typical exciton formation energies [mev] 1. Theory WET- Frenkel exciton strong bonding to crystal lattice but: wave with translational symmetry may move freely in the lattice! [Kittel] Wannier-Mott and Frenkel excitons: two extremes of the same phenomenon [Kittel]
Frenkel exciton 1. Theory WET- Frenkel exciton models ground state of a potential well collective excitation bound to an atom (like a phonon or a spin wave) + E = 0! Frenkel excitons are observed in Alkali halides Rare gas crystals (organic) molecular crystals Kr (20 K) E E g 11,7 ev 1,5 ev E 1 g E 1 Alkali halide crystals Excitons localized at anions, because anions have deeper excitation levels. [Kittel]
Bound excitons in semiconductors Donor bound exciton (D,X) 0 Acceptor bound exciton (A,X) Exciton is localized on an impurity, (still extends ~10 atomic distances) Binding energy: D 0.1 x impurity ionization energy 0 exciton levels at E 0 g E D 0 Properties of bound excitons bound exciton 3 exciton lifetime ~ E 2 ex D 0 in wide bandgap semiconductors, E n< D0 free excitons vanish at higher temperatures n higher (excited) states exist, but cannot be trated by the Wanier-Mott model anymore Excitons can be bound to any donor or acceptor in the material! excitons bound to ionized impurities may also exist + 1. Theory WET-
Bound excitons in semiconductors Donor bound exciton (D,X) 0 Acceptor bound exciton (A,X) Exciton is localized on an impurity, (still extends ~10 atomic distances) Binding energy: D 0.1 x impurity ionization energy 0 exciton levels at E 0 g E n D 0 higher (excited) states exist, but cannot be trated by the Wanier-Mott model anymore + 1. Theory WET- Wannier Mott Impurity bound Frenkel E1 E1 E1 In semiconductors, only free and impurity bound excitons exist.
Optical absorption 2. Measurement techniques WET- GaAs, 21 K h h E E g g E 1 fundamental absorption (generation of e and h) excitonic absorption (generation of free excitons) [Kittel]
Recombinative luminescence Optical emission due to optical or electron excitation at (radiative recombination spectroscopy) h E g Photoluminescence (PL) fixed incident photon energy, variable energy detection PL excitation (PLE) altering incident energy fixed detection energy time resolved PL (TRPL) pulsed excitation, measure rise and decay of a fixed detection energy 2. Measurement techniques WET- [www.ifkp.tu-berlin.de]
Recombinative luminescence Optical emission due to optical or electron excitation at (radiative recombination spectroscopy) h E g 2. Measurement techniques WET- Photoluminescence (PL) fixed incident photon energy, variable energy detection PL excitation (PLE) altering incident energy fixed detection energy time resolved PL (TRPL) pulsed excitation, measure rise and decay of a fixed detection energy most excited electrons and holes will relax into ground states before recombination excite at energies of higher states and detect ground state luminescence evaluate exciton lifetimes and different decay channels
Temperature dependence 3. Exciton spectra WET- Bound excitons (at Eg En D 0 ) dominate tow temperature spectra Free excitons (at Eg E n ) dominate high temperature spectra Excitons at higher states are only visible in high-quality material at very low temperatures E < D n 0 AlN 293 K Increasing temperatures... lead to peak broadening shift the bandgap according to E T E 0 g g 2 T T AlN: D0 30 mev E 49 mev 1 10 K [Prinz07]
Valence band splitting 3. Exciton spectra WET- Crystal field splitting cr due to crystal symmetry Spin-orbit splitting so due to electron-atom interaction Different endpoints of electron-hole recombination leads to different transitions of free/bound excitons. The same happens if the symmetry is lowered by strain (heteroepitaxy, strained layers). Selection rules: Intensities depend on polarisation of the incident light. AlN (schematic) [Li 2003]
Valence band splitting 3. Exciton spectra WET- Crystal field splitting cr due to crystal symmetry Spin-orbit splitting so due to electron-atom interaction Different endpoints of electron-hole recombination leads to different transitions of free/bound excitons. X A X B X C The same happens if the symmetry is lowered by strain (heteroepitaxy, strained layers). Selection rules: Intensities depend on polarisation of the incident light. AlN (schematic) [Li 2003]
Valence band splitting 3. Exciton spectra WET- Crystal field splitting cr due to crystal symmetry Spin-orbit splitting so due to electron-atom interaction Different endpoints of electron-hole recombination leads to different transitions of free/bound excitons. 0 (D,X A) 0 (D,X B) 0 (D,X ) C The same happens if the symmetry is lowered by strain (heteroepitaxy, strained layers). Selection rules: Intensities depend on polarisation of the incident light. AlN (schematic) [Li 2003]
Valence band splitting 3. Exciton spectra WET- Crystal field splitting cr due to crystal symmetry Spin-orbit splitting so due to electron-atom interaction Different endpoints of electron-hole recombination leads to different transitions of free/bound excitons. The same happens if the symmetry is lowered by strain (heteroepitaxy, strained layers). Selection rules: Intensities depend on polarisation of the incident light. AlN (schematic) [Ibach-Lüth]
Phonon interaction 3. Exciton spectra WET- Phonon-assisted recombination Emission of (different) phonons lowers the transition energy single/multi-phonon replica TA = 46, 51 mev LA = 77 mev TO = 95, 96 mev LO = 104, 107 mev 6H-SiC, 10 K (almost) no zero-phonon lines of free excitons in indirect semiconductors (conservation of momentum) for bound excitons k 0 is partly relaxed by localisation (Heisenberg uncertanity) 6H-SiC: D0 16, 30, 32 mev E 30 mev 1 (P, R, S of Nitrogen donor) [Peppermüller]
Complex spectra 3. Exciton spectra WET- Recombination luminescence in ZnO A: free exciton transitions (to A valence band) 0 I 0 I 3: (D,X A ) different donor bound excitons 0 I I : (A,X A) different acceptor bound excitons 5 Use PLE to detect excited states of the I acceptor bound exciton... 6a 11 [Gutowski & Hofmann]
3. Exciton spectra Complex spectra WET- Recombination luminescence in ZnO A: free exciton transitions (to A valence band) 0 I 0 I 3: (D,X A ) different donor bound excitons 0 I I : (A,X A) different acceptor bound excitons 5 Use PLE to detect excited states of the I acceptor bound exciton... 6a 11 PLE on I 6a in ZnO 0 3 0 I 6a I 6a : (A,X A) higher vibronic/rotational states 1 4 0 I 6aB I 6aB: (A,X B) ground state (fourfold degenerated) (energy difference A B 5 mev) a e 0 I 6a I 6a : (A,X )* higher excited states A [Gutowski & Hofmann]
Applications to materials science Strain induced by heteroepitaxy bandgap changes (similar to temperature dependence): compressive strain bandgap increases valence band crossing (under tensile strain, light holes go up, heavy holes go down) 3. Exciton spectra WET- 1.8 K tensile strain in GaN unstrained compressive strain [Teisseire]
Applications to materials science Strain induced by heteroepitaxy 3. Exciton spectra WET- Position depends on strain.* High linewidth depends on strain fields (lattice plane bending, variations in composition) low exciton lifetime (defects, low structural quality) * may also be influenced by charge carrier density (polaron approach) tensile strain in GaN unstrained compressive strain 1.8 K [Teisseire]
Applications to materials science Strain induced by heteroepitaxy bandgap changes (similar to temperature dependence): compressive strain bandgap increases valence band crossing (under tensile strain, light holes go up, heavy holes go down) 3. Exciton spectra WET- 1.8 K tensile strain in GaN unstrained compressive strain [Teisseire]
Applications to materials science Strain induced by heteroepitaxy PLE reveals higher state donor bound excitons 3. Exciton spectra WET- tensile strain in GaN unstrained compressive strain energy difference between ground and n-th excited state of the (D, X) 0
Applications to materials science Strain induced by heteroepitaxy PLE reveals higher state donor bound excitons 3. Exciton spectra WET- tensile strain in GaN unstrained compressive strain (D,X )* 0 B (D,X )* 0 A energy difference between ground and n-th excited state of the (D, X) 0 Result: Valence band crossing in GaN at 3.459 ev
Applications to materials science Evaluating crystalline quality 3. Exciton spectra WET- AlN, 10 K [Prinz07] AlN epilayer on SiC [Taniyasu] AlN bulk crystals [WET] [Feneberg, priv. comm.]
Summary Excitons are particles forming the emission ground state in electron hole recombination Frenkel excitons in alkali halides and molecular crystals Wannier-Mott free and impurity bound excitons in semiconductors Exciton detection by optical absorption and radiative luminescence zoo of recombination lines Use in materials science evaluate structural quality and defects (exciton lifetime) evaluate strain state and strain field (position shift) evaluate homogeneity (luminescence maps) 4. Summary WET-