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Electronic structure of transparent conducting oxides (TCO’ s)
Christoph Janowitz Humboldt University Berlin
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TCO-overview Composition space for conventional TCO materials
(ITO, IZO, GIZO) Ginley, Hosono, Paine, Handbook of Transparent Conductors Compound Annual Growth Rate SID.org
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Outline Electronic structure of Ga2O3 and In2O3 single crystals Donors
Character of states at EF Polaronic states Conclusions From Ginley, Hosono,Paine, Handbook of Transparent conductors
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the Czochralski method Institute for crystal growth ( IKZ) Berlin
β- Ga2O3 Crystals grown by the Czochralski method Institute for crystal growth ( IKZ) Berlin Transporting agents: I2+S2 T1 = ºC T2 = 1000 ºC CVT 4 mm 2 mm Sample cut along (100) Z. Galazka et al., Cryst. Res. Technol. 45 pp (2010)
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Crystal structure of β-Ga2O3
From J. Ahman, Acta Cryst. C52, 1336(1996). From E. G. Vı´llora et al., Phy. Rev. B 68, (2003). 4 Ga2O3 per unit cell = 20 atoms
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cleaved (100) surface of β-Ga2O3 crystals
M A The (100) surface of the Brillouin zone G Z b* c* Typical values n = 5.8 x 1017 cm-3 (300K) ρ = (Ω.cm) μ = 239 cm2/Vs
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BEST at BESSYII 2 gratings 7eV < hν < 40eV
C. Janowitz et al., Nucl. Instr. and Methods in Phys. Res A 693, 160 (2012)
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β-Ga2O3 experimental k┴ band structure
𝑘 ⊥ Binding Energy [eV] (Å-1) hν (eV) Symmetric dispersion of emission maxima Γ-point around 30 eV Intensity [a.u.] Binding Energy [eV] Mohamed , Janowitz et al., Appl. Phys. Lett. 97, (2010)
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β-Ga2O3 comparison with DFT calculation
Z Γ A Γ A M Binding Energy [eV] Z M Z Brillouin zone periodicity in the cleavage plane DFT Theory: John Varly, C. Van de Walle, University of California, Santa Barbara
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β-Ga2O3 experimental k|| band structure, indirect band gap
Eg Z G M A No states in the energy gap Eg (direct) is eV The VB width is about 7.37 eV Eg (indirect) is eV VBM near the symmetry point M Valence band width Binding Energy [eV] G M Z b* c* A
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β-Ga2O3 : effect of Sn doping (800ppm Sn), n = 1 x 10 19 cm-3
An emission from the conduction band minimum (CBM) Deep states around eV binding energy CBM -2.0 -1.0 0.0 -4.0 -3.0 Binding Energy [eV] EF Intensity [a.u.] Sn-doped β-G2O3 Undoped β-Ga2O3 Deep states At photon energy of 30 eV (G-point)
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In2O3 single crystals CVT grown In2O3 (HUB) Melt grown In2O3 (IKZ)
Typical properties at 300K In2O3 resistivity 8.5 x 10-3 Ωcm conductivity 120 S/cm mobility 66 cm2/Vs carrier density 1.2 x 1019 cm-3 Z. Galazka et al. Journal of Crystal Growth 363, 349 (2013) IKZ: Institut für Kristallzüchtung Berlin
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In2O3 crystal structure Bixbyite (bcc) unit cell
(80 atoms, a= Å) Bixbyite local Structure New Journal of Physics 13 (2011) melt CVT Laue-picture [111]- und [100]- direction
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Donors, n-type conductivity
Tempering in Oxygen at 1000°C O-vacancies get filled Phys. Status Solidi A, 1–7 (2013) Saturation O on intersites
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In gap states by low energy ARPES
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Deep in gap states by low energy ARPES & STS
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Donors, Theory Oxygen vacancies not primary shallow donor
Defect formation energies for oxygen vacancies too low DFT calculations with hybrid functionals (HF exact exchange) for oxygen rich/poor TCO‘s candidates: Ge, Sn, H J. Varley et al. Appl. Phys. Lett. 97, (2010) Alternative : Intrinsic doping Shallow donors by charge transfer states O2p->Metal-d Resonant photoemission study at O1s and Cu2p thresholds BL: U49/2-PGM2 at BESSY II in Berlin J. Haeberle, M. Richter, Z. Galazka, C. Janowitz, D. Schmeißer; Thin Solid Films 555 (2014) 53.
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In2O3 electronic structure
a) Brillouin zone b) VB ARPES in normal emission c) Near EF-ARPES d) Intensity map of the gap region, VB and CB In2O2 DFT bandstructure J.E. Medvedeva and C.L. Hettiarachchi PRB 81, (2010) C. Janowitz et al. New Journal of Physics 13 (2011)
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In2O3 electronic structure
Eg1 = eV Dipole forbidden Eg2 = dipole allowed ARPES at 18 eV Allowed and forbidden transitions (Walsh et al., PRL 100, (2008)
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In2O3 effective masses by ARPES
kp direction (normal emission) kN direction (off normal emission) exp. effective masses along the ΓP direction mVB*=(0.27±0.02)m0 and mCB*=(0.18±0.02)m0 Theory: low anisotropy mVB 0,28 mo 0,18 mo < mCB < 0,22 mo J.E. Medvedeva and C.L. Hettiarachchi PRB 81, (2010) exp. effective masses along the ΓN direction mVB*=(0.28±0.05)m0 and mCB*=(0.24±0.02)m0
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Fermi surface Fermi surface cut in ΓM plane
-Near EF state is three dimensional -No surface state -No surface charge accumulation layer state as in thin films (PDC King et al. PRL 101, (2008) V. Scherer, C. Janowitz, A. Krapf, H. Dwelk, D. Braun, and R. Manzke, Appl.Phys.Lett. 100, (2012).
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Methods for the determination of a Fermi level crossing
max [I (EF, k)] method: The criterion for kF can be formulated so: If a band crosses the Fermi-edge then the intensity at EF is exactly at maximum when k = kF [1,2]. [1] Santoni, A.; Terminello, L.; Himpsel, F. & Takahashi, T., Applied Physics A, Springer-Verlag, 52, (1991) [2] S. Legner, S. V. Borisenko, C. Dürr, T. Pichler, M. Knupfer, M. S. Golden, J. Fink, G. Yang, S. Abell, H. Berger, R. Müller, C. Janowitz, and G. Reichardt, Phys. Rev. B 62, 154 (2000) ii) max [∇Iint(k)] method: The basic idea is that by the integrated intensity Iint(k) of an energy distribution curve (EDC) (typically within an energy range between 300 and 800 meV) the occupied, k-resolved density of states of a band n(k) can be equated. Under this condition by applying a sum rule [2,3] it can be derived that k = kF is valid, if Iint(k) has dropped to the half of the maximum value [2,3]. [3] M. Randeria et al., Phys. Rev. Lett. 74, 4951(1995)
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Methods for the determination of a Fermi level crossing
iii) symmetrization method: Here kF is determined by first mirroring every EDC at EF = 0, so Isymm(k, E) = I(k, E) + I(k, -E). For momenta where the occupied states have not yet reached kF the intensity Isymm(k, E) forms a local minimum around EF. The momentum, where this minimum disappears, is kF [4]. [4] J. Mesot et al., Phys. Rev. B 63, (2001)
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Methods for the determination of a Fermi level crossing
iv) the leading edge method: The energetic position of the center of the front flank (tangent) of the single EDC spectrum i.e. the change of the slope is used. The energy position of this inflection point must coincide with the Fermi energy.
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So simply a degenerated semiconductor?
The elementary model of a degenerate semiconductor describes the bandwidth below the Fermi energy. The electron concentration n in the conduction band is given by NC effective density of states in the conduction band, EC - conduction band minimum energy and EF the Fermi energy. at 300K an energy minimum below the Fermi energy (ΔE = EF – EC) of ΔE = eV for n=1.8·1018 cm-3 and ΔE = eV for n=1.3·1019 cm-3. More elaborated model including CB nonparabolicity (M. Feneberg, priv. com.) M. Feneberg et al. PHYSICAL REVIEW B 93, (2016)
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Comparison to experimental values
State is blurred Doping independend ΔΕ = 280meV – (500meV)
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Polaronic gas in Anastase TiO2
body centered tetragonal d not s „large polaron quasiparticle“ intermediate between localized small polaron and free electron
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ARPES on Anatase TiO2, ne ~ 3.5 x 10 19 cm-1
shallow QP band at 40meV renormalisation m*/m ~ 1,7 Replicas at ~ 100 meV 3-dim Franck Condon Electron coupled to vibrational mode: zero phonon peak + vibronic satellites Raman spectroscopy (PRB 55, 7014 (1997)): LO Eu phonon mode at 108 meV Satellites disappear at high doping (3,5 x 1020cm-3)
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Polaron band in In2O3 ? (different material (electronic structure, phonon spectrum))
no one to one correspondence with In2O3 -> no renormalisation observed -> no substructure observed -> In2O3 with several phonons between 37 meV and 62 meV by Raman (White&Keramidas, Spectr. Chim. Acta A, 28, 501 (1972) and by absorption 31,4meV-38,6 meV , (Irmscher et al., Phys.Stat.Sol A 211,54 (2014) „Multiphonon Generation during Photodissociation of Slow Landau-Pekar Polarons“ E.N. Myasnikov et al., J. Exp. Theo. Phys. 102, 480 (2006) strong electron phonon interaction - Fröhlich Hamiltonian (large polaron) - longitudinal polarization interactions - polarisation field quantized - Single polaron can photodissociate to one or many phonons - Polaron band forms after decay of a single polaron
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Halfwidth of polaron band
For the effective carrier mass of m* = (1-3) me the halfwidth of the polaronband can be estimated to 3.4 Ep < ħΩ1/2 < 5.6 Ep with Ep the polaron energy. Assuming that the polaron energies are proportional to the phonon energies and by using the phonon energies between 37meV and 62 meV 111meV < ħΩ1/2 < 347 meV Compares to experimental value of 280+ meV from photoemission spectroscopy. V. Scherer, C. Janowitz, Z. Galazka, M. Nazarzadehmoafi, R. Manzke, EPL, 113 (2016) 26003
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Summary Valence bands well described by DFT
(band dispersions, effective masses…) Classical degenerate semiconductor model possibly not sufficient No two dim. states like charge accumulation layers on UHV cleaved single crystals Incorporation of electron phonon interaction (polarons)
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Thank you Collaborators Valentina Scherer Zbigniew Galazka John Varley
Mansour Mohamed Leibniz-Institut für Kristallzüchtung Department of Materials, University of California, Santa Barbara Assiut university, Egypt BESSY II EES group Thank you
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Landau Pekar Feynman Cardona (bandgap)
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Some estimates for Fröhlich polarons
Fröhlich coupling constant α ∝= 𝑒 2 ℎ𝑐 √ 𝑚𝑏 𝑐 2 2ℎ𝜔𝐿𝑂 ∙( 1 𝜀∞ - 1 ε𝑜 ) ε0 Static dielectric constant ε∞ High freq. Diel. Constant mb bandstructure effective mass ωLO phonon frequency (α ~ x total number of phonons in cloud around electron, => Polaron effects α >1) Polaron effective mass m* =~ mb (1+ α/6) for α<<1; m* ≈ mb 0.02 α4 for α >>1 („Feynman approx“. J.T. Devreese „Polarons“ Digital Encycl. Of Appl. Phys. Ed. GL Trigg, Wiley) μ ~ exp Θ/T; Θ Debeye Temperature. better: μ ~ F(α) exp Θ/T ( J.T. Devreese „Polarons“ Digital Encycl. Of Appl. Phys. Ed. G.L. Trigg, Wiley, C. Kittel, Quantum Theory of solids Wiley 1987))
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Kristallzüchtung, XRD CVT from melt In2O3 Kristalle gezüchtet aus Schmelze Z. Galazka et al., Journal of Crystal Growth ,362, 349 – 352 (2013) XRD-Ergebnisse von den Kristallen aus beiden Züchtungsarten zeigen eine Einkristallphase
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Transporteigenschaften
Ladungsträgerdichte von Kristallen aus CVT überschreitet den kritischen Wert des Mott-Kriteriums (nc=2,7·1018cm-3) Eine Entartung liegt vor Kristalle aus der Schmelze unterscheiden sich stark untereinander, so dass Mott-Kriterium nicht immer erfüllt ist n-Leitung 219K Transporteigenschaften bei Raumtemperatur Proben aus CVT Proben aus Schmelze Spezifischer Widerstand 8,5 mΩ·cm 182 mΩ·cm Leitfähigkeit 117 S/m 5,5 S/m Mobilität 66 cm2/V·s 164 cm2/V·s Ladungsträgerdichte 1,3·1019 cm-3 2,1·1017cm-3 150 K 10% Änderung 200 K 70 cm2/V·s V. Scherer et al., Appl.Phys.Lett. 100, (2012).
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Charge accumulation in thin films
P.D.C. King et al. PRL 101, (2008) (Here undoped is 1019cm-3) charge accumulation layer Strong band bending charge accumulation only near surface Band bending changes with doping
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