Abstract
Optical band-to-band absorption can produce an electron and a hole in close proximity which attract each other via Coulomb interaction and can form a hydrogen-like bond state, the exciton. The spectrum of free Wannier–Mott excitons in bulk crystals is described by a Rydberg series with an effective Rydberg constant given by the reduced effective mass and the dielectric constant. A small dielectric constant and large effective mass yield a localized Frenkel exciton resembling an excited atomic state. Excitons increase the absorption slightly below the band edge significantly. The interaction of photons and excitons creates a mixed state, the exciton–polariton, with photon-like and exciton-like dispersion branches. An exciton can bind another exciton or carriers to form molecules or higher associates of excitons. Free charged excitons (trions) and biexcitons have a small binding energy with respect to the exciton state. The binding energy of all excitonic quasiparticles is significantly enhanced in low-dimensional semiconductors. Basic features of confined excitons with strongest transitions between electron and hole states of equal principal quantum numbers remain similar. The three-dimensional confinement of quantum dots allows for forming stable antibinding exciton associates. Excitonic states of quantum dots are a prominent physical basis for the realization of photonic qubits. The exciton emission is deployed for producing single photons on demand with qubits encoded into the polarization or another degree of freedom. Pairs of entangled photons are obtained from the biexciton-exciton cascade. Photons used as flying qubits enable inherently secure data transmission; semiconductor-based quantum optics is a highly active field of research and development.
Karl W. Böer: deceased.
Notes
- 1.
This causes the breakdown of the adiabatic approximation. The error in this approximation is on the order of the fourth root of the mass ratio. For hydrogen this is \( {\left({m}_n/{M}_{\textrm{H}}\right)}^{1/4}\cong 10\% \) and is usually acceptable. For excitons, however, the error is on the order of 1 and is no longer acceptable. This is relevant for the estimation of exciton molecule formation discussed in Sect. 1.4.
- 2.
When a quasi-free charge carrier (electron or hole) moves through a crystal with strong lattice polarization, it is surrounded by a polarization cloud. Carrier plus polarization form a polaron, a quasiparticle with an increased effective mass (see Sect. 1.2 of chapter “Carrier-Transport Equations”).
- 3.
It is, however, influenced by the gradient of an electric field or by strain; see, e.g., Tamor and Wolfe 1980.
- 4.
The ionization energy is also referred to as binding energy or Rydberg energy.
- 5.
\( {\phi}_n(0)\ne 0 \) applies only for S states.
- 6.
Strictly, such transitions cannot occur at k = 0; however, a slight shift because of the finite momentum of the photon permits the optical transition to occur because of a weak electric quadrupole coupling (Elliott 1961). Such transitions can also be observed under a high electric field using modulation spectroscopy (Washington et al. 1977). Dipole-forbidden transitions are easily detected with Raman scattering (Sect. 1.3) or two-photon absorption (for Cu2O, see Uihlein et al. 1981), which follow different selection rules.
- 7.
With a correspondingly large exciton Bohr radius of 1.04 μm for n = 25, compared to ~1 nm for n = 1.
- 8.
The analysis of the measured reflection spectrum as a function of the wavelength and incident angle is rather involved. A relatively simple method for measuring the central part of the exciton–polariton spectrum in transmission through a prismatic crystal was used by Broser et al. (1981) (see Fig. 15).
- 9.
A state close to an actual biexciton state (Sect. 1.4) which immediately decays into other states.
- 10.
Deviations from a pure quadratic dependence are due to the short radiative lifetime for the involved species in direct-bandgap semiconductors, preventing a thermal equilibrium of the population.
- 11.
Still a significant broadening of exciton transitions (of single quantum dots) well above the natural linewidth is observed due to the interaction of the quantum dot with its environment. The interaction with acoustic phonons (deformation potential coupling) and optical phonons (Fröhlich coupling) leads to broad transitions at increased temperature (Rudin et al. 1990); in addition, randomly fluctuating electrical fields of charged defects in the vicinity of the dots lead to a spectral jitter of the transitions on a very short time scale (spectral diffusion) even at low temperature (Türck et al. 2000).
- 12.
We consider only the heavy-hole exciton due to its lower energy in the generally compressively strained epitaxial quantum dots and their larger oscillator strength.
- 13.
Pure states with |M| = 2 are generally not observed in luminescence experiments (in absence of magnetic fields and confinements with reduced symmetry which can mix them with |M| = 1 states), since a j = ± 1 photon cannot induce a radiative transition to the M = 0 ground state.
- 14.
The three triplet states XXT+3, XXT0, and XXT-3, with parallel electron and hole spin are distinguished by the projection of their the total angular momentum (spin + orbital) on the symmetry axis of the quantum dot given by the growth direction.
- 15.
The Bloch sphere is a generalization of the representation of a complex number \( z=x+ iy \) with \( {\left|z\right|}^2={z}^{\ast }z=1 \) as a point in the complex plane on the unit circle: \( {z}^{\ast }z=\left(x- iy\right)\left(x+ iy\right)={x}^2+{y}^2 \).
- 16.
A simple classical example is a code word with three bits: 000 and 111; a (single) bit flip can be corrected by a majority vote: 010→000.
- 17.
- 18.
Meaning g(2)(0) ≪ 0.5, ideally 0; there must actually be only a single photon (and not more) present at a time.
- 19.
A substitutional nitrogen atom with a vacancy at an adjacent lattice position (Kurtsiefer et al. 2000).
- 20.
There are four (maximally entangled) two-qubit states designated as Bell states. In addition to |Φ+〉 noted in the text these are |Φ-〉 (with “+” replaced by “-” in the sum) and |Ψ+/-〉 with α and β being 0 and 1 in the first and 1 and 0 in the second qubit and the sum built with either “+” or “−”.
- 21.
Optically excited single-photon emission with g(2)(0) = 0.33 at room temperature was achieved using a core-shell GaN/AlGaN nanowire quantum-dot (Holmes et al. 2014).
- 22.
The luminescence of the dark exciton is shown in Fig. 31b.
- 23.
With a π pulse, the system changes, e.g., from “qubit state” |0〉 to |1〉; with 2π, it returns to its initial state.
- 24.
The circularly polarized transitions are a superposition of two cross-polarized linear transitions. The fine-structure splitting is negligible if it is smaller than the radiadive linewidth.
- 25.
Even if the biexciton binding-energy gets zero for larger quantum dots (Fig. 29b), a nonzero fine-structure splitting of such dots leads usually to photon pairs of different energies.
References
Agranovich VM, Mills DL (1982) Surface polaritons. North-Holland, Publ. Co., Amsterdam
Akimoto O, Hanamura E (1972) Excitonic molecule. I. Calculation of the binding energy. J Phys Soc Jpn 33:1537
Akiyama H (1998) One-dimensional excitons in GaAs quantum wires. J Phys Condens Matter 10:3095
Akopian N, Lindner NH, Poem E, Berlatzky Y, Avron J, Gershoni D, Gerardot BD, Petroff PM (2006) Entangled photon pairs from semiconductor quantum dots. Phys Rev Lett 96:130501
Altarelli M, Bachelet G, Del Sole R (1979) Theory of exciton effects in semiconductor surface spectroscopy. J Vac Sci Technol 16:1370
Arakawa Y, Holmes MJ (2020) Progress in quantum-dot single photon sources for quantum information technologies: A broad spectrum overview. Appl Phys Rev 7:021309
Arute F et al (2019) Quantum supremacy using a programmable superconducting processor. Nature 574:505
Astakhov GV, Kochereshko VP, Yakovlev DR, Ossau W, Nürnberger J, Faschinger W, Landwehr G, Wojtowicz T, Karczewski G, Kossut J (2002a) Optical method for the determination of carrier density in modulation-doped quantum wells. Phys Rev B 65:115310
Astakhov GV, Yakovlev DR, Kochereshko VP, Ossau W, Faschinger W, Puls J, Henneberger F, Crooker SA, McCulloch Q, Wolverson D, Gippius NA, Waag A (2002b) Binding energy of charged excitons in ZnSe-based quantum wells. Phys Rev B 65:165335
Bajaj KK, Reynolds DC (1987) An overview of optical characterization of semiconductor structures and alloys. Proc SPIE 0794:2
Baldereschi A, Lipari NO (1973) Spherical model of shallow acceptor states in semiconductors. Phys Rev B 8:2697
Bar-Joseph I (2005) Trions in GaAs quantum wells. Semicond Sci Technol 20:R29
Bassani F, Pastori-Parravicini G (1975) Electronic states and optical transitions in solids. Pergamon Press, Oxford
Bayer M, Ortner G, Stern O, Kuther A, Gorbunov AA, Forchel A, Hawrylak P, Fafard S, Hinzer K, Reinecke TL, Walck SN, Reithmaier JP, Klopf F, Schäfer F (2002) Fine structure of neutral and charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots. Phys Rev B 65:195315
Beinikhes IL, Kogan ShM (1985) Influence of valence band degeneracy on the fundamental optical absorption in direct-gap semiconductors in the region of exciton effects. Sov Phys JETP 62:415
Bennett CH, Brassard G (1984) Proc IEEE Int Conf Computers, Systems and Signal Processing, Bangalore, pp 175–179
Bennett AJ, Pooley MA, Stevenson RM, Ward MB, Patel RB, Boyer de la Giroday A, Sköld N, Farrer I, Nicoll CA, Ritchie DA, Shields AJ (2010) Electric-field-induced coherent coupling of the exciton states in a single quantum dot. Nat Phys 6:947
Bester G, Zunger A (2005) Cylindrically shaped zinc-blende semiconductor quantum dots do not have cylindrical symmetry: Atomistic symmetry, atomic relaxation, and piezoelectric effects. Phys Rev B 71:045318
Birkedal D, Singh J, Lyssenko VG, Erland J, Hvam JM (1996) Binding of quasi-two-dimensional biexcitons. Phys Rev Lett 76:672
Blackwood E, Snelling MJ, Barley RT, Andrews SR,Foxon CTB (1994) Exchange interaction of excitons in GaAs heterostructures. Phys Rev B 50:14246
Bouchiat V, Vion D, Joyez P, Esteve D, Devoret MH (1998) Quantum coherence with a single Cooper pair. Physica Scripta T76:165
Brinkman WF, Rice TM, Bell B (1973) The excitonic molecule. Phys Rev B 8:1570
Broser I, Broser R, Beckmann E, Birkicht E (1981) Thin prism refraction: a new direct method of polariton spectroscopy. Solid State Commun 39:1209
Buckley S, Rivoire K, Vuckovic J (2012) Engineered quantum dot single-photon sources. Rep Prog Phys 75:26503
Bylander J, Robert-Philip I, Abram I (2003) Interference and correlation of two independent photons. Eur Phys J D 22:295
Byrnes T, Kim NY, Yamamoto Y (2014) Exciton–polariton condensates. Nat Phys 10:803
Cavenett BC (1980) Optical detection of exciton resonances in semiconductors. J Phys Soc Jpn 49(Suppl A):611
Cavenett BC (1984) Triplet exciton recombination in amorphous and crystalline semiconductors. J Lumin 31/32:369
Chen Z et al. (2021) Google Quantum AI Exponential suppression of bit or phase errors with cyclic error correction. Nature 595:383
Cho K (1979) Internal structure of excitons. In: Cho K (ed) Excitons. Springer, Berlin, p 15
Christen J, Bimberg D (1990) Line shapes of intersubband and excitonic recombination in quantum wells: Influence of final-state interaction, statistical broadening, and momentum conservation. Phys Rev B 42:7213
Collins RT, Vina L, Wang WI, Mailhiot C, Smith DL (1987) Electronic properties of quantum wells in perturbing fields. Proc SPIE 0792:2
Combescot R (2019) Trion ground-state energy: Simple results. Phys Rev B 100:245201
Compaan A (1975) Surface damage effects on allowed and forbidden phonon Raman scattering in cuprous oxide. Solid State Commun 16:293
Davies JJ, Cox RT, Nicholls JE (1984) Optically detected magnetic resonance of the triplet state of copper-center – donor pairs in CdS. Phys Rev B 30:4516
Davydov VYu, Subashiev AV, Cheng TS, Foxon CT, Goncharuk IN, Smirnov AN, Zolotareva RV, Lundin WV (1997) Surface polariton Raman spectroscopy in cubic GaN epitaxial layers. Mater Sci Forum 264:1371
Dean PJ, Thomas DG (1966) Intrinsic absorption-edge spectrum of gallium phosphide. Phys Rev 150:690
Deng H, Haug H, Yamamoto Y (2010) Exciton-polariton Bose-Einstein condensation. Rev Mod Phys 82:1489
Denisov MM, Makarov VP (1973) Longitudinal and transverse excitons in semiconductors. Phys Status Solidi B 56:9
Denisov VN, Mavrin BN, Podobedov VB (1987) Hyper-Raman scattering by vibrational excitations in crystals, glasses and liquids. Phys Rep 151:1
Dick KA (2008) A review of nanowire growth promoted by alloys and non-alloying elements with emphasis on Au-assisted III-V nanowires. Prog Crystal Growth Character Mater 54:138
Ding F, Singh R, Plumhof JD, Zander T, Krápek V, Chen YH, Benyoucef M, Zwiller V, Dörr K, Bester G, Rastelli A, Schmidt OG (2010) Tuning the exciton binding energies in single self-assembled InGaAs/GaAs quantum dots by piezoelectric-induced biaxial stress. Phys Rev Lett 104:067405
Dingle R, Wiegmann W, Henry CH (1974) Quantum states of confined carriers in very thin AlxGa1-xAs-GaAs-AlxGa1-xAs heterostructures. Phys Rev Lett 33:827
DiVincenzo DP (2000) The physical implementation of quantum computation. Fortschr Phys 48:771
Doherty MW, Manson NB, Delaney P, Jelezko F, Wrachtrup J, Hollenberg LCL (2013) The nitrogen-vacancy colour centre in diamond. Phys Rep 528:1
Ekardt W, Lösch K, Bimberg D (1979) Determination of the analytical and the nonanalytical part of the exchange interaction of InP and GaAs from polariton spectra in intermediate magnetic fields. Phys Rev B 20:3303
Elliott RJ (1961) Symmetry of excitons in Cu2O. Phys Rev 124:340
Ellis DJP, Bennett AJ, Dangel C, Lee JP, Griffiths JP, Mitchell A, Paraiso T-K, Spencer P, Ritchie DA, Shields AJ (2018) Independent indistinguishable quantum light sources on a reconfigurable photonic integrated circuit. Appl Phys Lett 112:211104
Esser A, Zimmermann R, Runge E (2001) Theory of trion spectra in semiconductor nanostructures. Phys Status Solidi B 227:317
Farrow T, See P, Bennett AJ, Ward MB, Atkinson P, Cooper K, Ellis DJP, Unitt DC, Ritchie DA, Shields AJ (2008) Single-photon emitting diode based on a quantum dot in a micro-pillar. Nanotechnology 19:345401
Filinov AV, Riva C, Peeters FM, Lozovik YuE, Bonitz M (2005) Influence of well-width fluctuations on the binding energy of excitons, charged excitons, and biexcitons in GaAs-based quantum wells. Phys Rev B 70:035323
Fischer B, Lagois J (1979) Surface exciton polaritons. In: Cho K (ed) Excitons. Springer, Berlin, p 183
Flohrer J, Jahne E, Porsch M (1979) Energy levels of A and B excitons in wurtzite-type semiconductors with account of electron-hole exchange interaction effects. Phys Status Solidi B 91:467
Frenkel JI (1931) On the transformation of light into heat in solids II. Phys Rev 37:1276
Fröhlich H (1954) Electrons in lattice fields. Adv Phys 3:325
Fröhlich D (1981) Aspects of nonlinear spectroscopy. In: Treusch J (ed) Festkörperprobleme. Advances in solid state physics, vol 21. Vieweg, Braunschweig, p 363
García-Cristóbal A, Cantarero A, Trallero-Giner C, Cardona M (1998) Resonant hyper-Raman scattering in semiconductors. Phys Rev B 58:10443
García-Pérez G et al. (2020) IBM Q Experience as a versatile experimental testbed for simulating open quantum systems. npj Quantum Inf 6:1
George GA, Morris GC (1970) The absorption, fluorescence and phosphorescence of single crystals of 1,2,4,5-tetrachlorobenzene and 1,4-dichlorobenzene at low temperatures. Mol Cryst Liq Cryst 11:61
Gerlach B (1974) Bound states in electron-exciton collisions. Phys Status Solidi B 63:459
Germanis S, Atkinson P, Hostein R, Gourdon C, Voliotis V, Lemaître A, Bernard M, Margaillan F, Majrab S, Eble B (2018) Dark-bright exciton coupling in asymmetric quantum dots, Phys Rev B 98:155303
Giblin J, Vietmeyer F, McDonald MP, Kuno M (2011) Single nanowire extinction spectroscopy. Nano Lett 11:3307
Girlanda R, Savasta S, Quattropani A (1994) Theory of exciton-polaritons in semiconductors with nearly degenerate exciton levels. Solid State Commun 90:267
Gisin N, Ribordy G, Tittel W, Zbinden H (2002) Quantum cryptography. Rev Mod Phys 74:145
Gislason HP, Monemar B, Dean PJ, Herbert DC, Depinna S, Cavenett BC, Killoran N (1982) Photoluminescence studies of the 1.911-eV Cu-related complex in GaP. Phys Rev B 26:827
Giustina M, Versteegh MAM, Wengerowsky S, Handsteiner J, Hochrainer A, Phelan K, Steinlechner F, Kofler J, Larsson J-Å, Abellán C, Amaya W, Pruneri V, Mitchell MW, Beyer J, Gerrits T, Lita AE, Shalm LK, Nam SW, Scheidl T, Ursin R, Wittmann B, Zeilinger A (2015) Significant-loophole-free test of Bell’s theorem with entangled photons. Phys Rev Lett 115:250401
Gourley PL, Wolfe JP (1978) Spatial condensation of strain-confined excitons and excitonic molecules into an electron-hole liquid in silicon. Phys Rev Lett 40:526. And: Properties of the electron-hole liquid in Si: zero stress to the high-stress limit. Phys Rev B 24:5970 (1981)
Grosmann M (1963) The effect of perturbations on the excitonic spectrum of cuprous oxide. In: Kuper CG, Whitfield GD (eds) Polarons and excitons. Oliver and Boyd, London, p 373
Grundmann M, Bimberg D (1988) Anisotropy effects on excitonic properties in realistic quantum wells. Phys Rev B 38:13486
Haken H (1963) Theory of excitons II. In: Kuper CG, Whitfield GD (eds) Polarons and excitons. Oliver and Boyd, Edinburgh, p 295
Haken H (1976) Quantum field theory of solids. North Holland Publishing, Amsterdam
Haken H, Nikitine S (eds) (1975) Excitons at high densities. Springer tracts in modern physics. Springer, New York
Hanamura E (1976) Excitonic molecules. In: Seraphin BO (ed) Optical properties of solids. North Holland Publishing, Amsterdam, pp 81–142
Hanamura E, Haug H (1977) Condensation effects of excitons. Phys Rep 33:209
Hanbury Brown R, Twiss RQ (1956) Correlation between photons in two coherent beams of light. Nature 177:27
Heindel T, Thoma A, von Helversen M, Schmidt M, Schlehahn A, Gschrey M, Schnauber P, Schulze J -H, Strittmatter A, Beyer J, Rodt S, Carmele A, Knorr A, Reitzenstein S (2017) A bright triggered twin-photon source in the solid state. Nat Commun 8:14870
Holmes MJ, Choi K, Kako S, Arita M, Arakawa Y (2014) Room-temperature triggered single photon emission from a III-nitride site-controlled nanowire quantum dot. Nano Lett 14:982
Holtkemper M, Quinteiro GF, Reiter DE, Kuhn T (2021) Dark exciton preparation in a quantum dot by a longitudinal light field tuned to higher exciton states. Phys Rev Research 3:013024
Hönerlage B, Lévy R, Grun JB, Klingshirn C, Bohnert K (1985) The dispersion of excitons, polaritons and biexcitons in direct-gap semiconductors. Phys Rep 124:161
Hong CK, Ou ZY, Mandel L (1987) Measurement of subpicosecond time intervals between two photons by interference. Phys Rev Lett 59:2044
Hopfield JJ, Thomas DG (1963) Theoretical and experimental effects of spatial dispersion on the optical properties of crystals. Phys Rev 132:563
Hudson AJ, Stevenson RM, Bennett AJ, Young RJ, Nicoll CA, Atkinson P, Cooper K, Ritchie DA, Shields AJ (2007) Coherence of an entangled exciton–photon state. Phys Rev Lett 99:266802
Ishii R, Funato M, Kawakami Y (2020) Long-range electron-hole exchange interaction in aluminum nitride. Phys Rev B 102:155202
Kabler MN (1964) Low-temperature recombination luminescence in alkali halide crystals. Phys Rev 136:A1296
Kalra R, Laucht A, Hill CD, Morello A (2014) Robust two-qubit gates for donors in silicon controlled by hyperfine interactions. Phys Rev X 4:021044
Kamtekar KT, Monkman AP, Bryce MR (2010) Recent advances in white organic light-emitting materials and devices (WOLEDs). Adv Mater 22:572
Kane BE (1998) A silicon-based nuclear spin quantum computer. Nature 393:133
Kato Y, Yu CI, Goto T (1970) The effect of exchange interaction on the exciton bands in CuCl-CuBr solid solutions. J Phys Soc Jpn 28:104
Kazimierczuk T, Fröhlich D, Scheel S, Stolz H, Bayer M (2014) Giant Rydberg excitons in the copper oxide Cu2O. Nature 514:343
Kittel C (1963) Quantum theory of solids. Wiley, New York, p 131
Kittel C (1966) Introduction to solid state physics. Wiley, New York
Knill E, Laflamme R, Milburn GJ (2001) A scheme for efficient quantum computation with linear optics. Nature 409:46
Knox RS (1984) Introduction to exciton physics. In: DiBartolo B, Danko J (eds) Collective excitations in solids. Plenum Press, New York, p 183
Köhler A, Bässler H (2015) Electronic processes in organic semiconductors. Wiley-VCH, Weinheim
Koteles ES, Jagannath C, Lee J, Vassell MO (1987) Uniaxial stress as a probe of valence subband mixing in semiconductor quantum wells. Proc SPIE 0792:168
Kudlek G, Presser N, Pohl UW, Gutowski J, Lilja J, Kuusisto E, Imai K, Pessa M, Hingerl K, Sitter A (1992) Exciton complexes in ZnSe layers: a tool for probing the strain distribution. J Cryst Growth 117:309
Kulakovskii VD, Lysenko VG, Timofeev VB (1985) Excitonic molecules in semiconductors. Sov Phys Usp 28:735
Kurizki G, Bertet P, Kubo Y, Mølmer K, Petrosyan D, Rabl P, Schmiedmayer J (2015) Quantum technologies with hybrid systems. Proc Natl Acad Sci 112:3866
Kurtsiefer C, Mayer S, Zarda P, Weinfurter H (2000) Stable solid-state source of single photons. Phys Rev Lett 85:290
Lambrecht WRL, Rodina AV, Limpijumnong S, Segall B, Meyer BK (2002) Valence-band ordering and magneto-optic exciton fine structure in ZnO. Phys Rev B 65:075207
Lampert MA (1958) Mobile and immobile effective-mass-particle complexes in nonmetallic solids. Phys Rev Lett 1:450
Landau LD (1933) Electron motion in crystal lattices. Phys Z Sowjetunion 3:664
Li S, Luo J, Liu J, Tang J (2019) Self-trapped excitons in all-inorganic halide perovskites: fundamentals, status, and potential applications. J Phys Chem Lett 10:1999
Liu J, Su R, Wei Y, Yao-Silva B, Yu Y, Iles-Smith J, Srinivasan K, Rastelli A, Li J, Wang X (2019) A solid-state source of strongly entangled photon pairs with high brightness and indistinguishability. Nat Nanotechnol 14:586
Lo HK, Curty M, Tamaki K (2014) Secure quantum key distribution. Nat Photon 8:595
Loudon R (1963) Theory of first-order Raman effect in crystals. Proc R Soc Lond A275:218
Lounis B, Orrit M (2005) Single-photon sources. Rep Prog Phys 68:1129
MacFarlane GG, McLean TP, Quarrington JE, Roberts V (1957) Fine structure in the absorption-edge spectrum of Ge. Phys Rev 108:1377
Mahan GD, Hopfield JJ (1964) Piezoelectric polaron effects in CdS. Phys Rev Lett 12:241
McCallum JC, Johnson BC, Botzem T (2021) Donor-based qubits for quantum computing in silicon. Appl Phys Rev 8:031314
McLean TP (1963) Excitons in germanium. In: Kuper CG, Whitfield GD (eds) Polarons and excitons. Oliver and Boyd, London, p 367
Mikhnenko OV, Blom PWM, Nguyen T-Q (2015) Exciton diffusion in organic semiconductors. Energy Environ Sci 8:1867
Miller RC, Kleinman DA (1985) Excitons in GaAs quantum wells. J Lumin 30:520
Miller DAB, Chemla DS, Damen TC, Gossard AC, Wiegmann W, Wood TH, Burrus CA (1985) Electric field dependence of optical absorption near the band gap of quantum-well structures. Phys Rev B 32:1043
Moskalenko SA (1958) The theory of Mott exciton in alkali-halide crystals. Zh Opt Spektrosk (USSR) 5:147
Mott NF (1938) Conduction in polar crystals. II. The conduction band and ultra-violet absorption of alkali-halide crystals. Trans Faraday Soc 34:500
Muhonen JT, Dehollain JP, Laucht A, Hudson FE, Sekiguchi T, Itoh KM, Jamieson DN, McCallum JC, Dzurak AS, Morello A (2014) Storing quantum information for 30 s in a nanoelectronic device. Nat Nanotechnol 9:986
Muljarov EA, Zhukov EA, Dneprovskii VS, Masumoto Y (2000) Dielectrically enhanced excitons in semiconductor-insulator quantum wires: theory and experiment. Phys Rev B 62:7420
Müller AS, Avlasevich YS, Müllen K, Bardeen CJ (2006) Evidence for exciton fission and fusion in a covalently linked tetracene dimer. Chem Phys Lett 421:518
Müller M, Bounouar S, Jöns KD, Glässl M, Michler P (2014) On-demand generation of indistinguishable polarization-entangled photon pairs. Nat Photon 8:224
Najafov H, Lee B, Zhou Q, Feldman LC, Podzorov V (2010) Observation of long-range exciton diffusion in highly ordered organic semiconductors. Nat Mater 9:938
Nielsen MA (2004) Optical quantum computation using cluster states. Phys Rev Lett 93:040503
Ogawa T, Takagahara T (1991) Optical absorption and Sommerfeld factors of one-dimensional semiconductors: an exact treatment of excitonic effects. Phys Rev B 44:8138
Ollivier H, Maillette de Buy Wenniger I, Thomas S, Wein SC, Harouri A, Coppola G, Hilaire P, Millet C, Lemaître A, Sagnes I, Krebs O, Lanco L, Loredo JC, Antón C, Somaschi N, Senellart P (2020) ACS Photonics 7:1050
Orieux A, Versteegh MAM, Jöns KD, Ducci S (2017) Semiconductor devices for entangled photon pair generation: a review. Rep Prog Phys 80:076001
Paik H, Schuster DI, Bishop LS, Kirchmair G, Catelani G, Sears AP, Johnson BR, Reagor MJ, Frunzio L, Glazman LI, Girvin SM, Devoret MH, Schoelkopf RJ (2011) Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys Rev Lett 107:240501
Peruzzo A, McClean J, Shadbolt P, Yung M-H, Zhou X-Q, Love PJ, Aspuru-Guzik A, O’Brien JL (2014) A variational eigenvalue solver on a photonic quantum processor. Nat Commun 5:4213
Phillips RT, Lovering DJ, Denton GJ, Smith GW (1992) Biexciton creation and recombination in a GaAs quantum well. Phys Rev B 45:4308
Ploog K, Döhler GH (1983) Compositional and doping superlattices in III-V semiconductors. Adv Phys 32:285
Poem E, Kodriano Y, Tradonsky C, Lindner NH, Gerardot BD, Petroff PM, Gershoni D (2010) Accessing the dark exciton with light. Nature Physics 6:993
Pohl UW (2008) InAs/GaAs quantum dots with multimodal size distribution. In: Wang ZM (ed) Self-assembled quantum dots. Springer, New York, p 43
Pohl UW (2020) Epitaxy of Semiconductors – Physics and fabrication of heterostructures, 2nd edn. Springer, Cham
Pohl UW, Strittmatter A, Schliwa A, Lehmann M. Niermann T, Heindel T, Reitzenstein S, Kantner M, Bandelow U, Koprucki T, Wünsche H-J (2020) Stressor-induced site control of quantum dots for single-photon sources. In Kneissl M, Knorr A, Reitzenstein S, Hoffmann A (eds) Semiconductor nanophotonics. Springer Nature, Cham, pp 52–90
Pope M, Swenberg CE (1982) Electronic processes in organic crystals. Oxford University Press, Oxford, UK
Raussendorf R, Briegel HJ (2001) A one-way quantum computer. Phys Rev Lett 86:5188
Reynolds DC, Collins TC (1981) Excitons: their properties and uses. Academic Press, New York
Robert A, Barkoutsos PK, Woerner S, Tavernelli I (2021) Resource-efficient quantum algorithm for protein folding. npj Quantum Inf 7:38
Rodina AV, Dietrich M, Göldner A, Eckey L, Hoffmann A, Efros AL, Rosen M, Meyer BK (2001) Free excitons in wurtzite GaN. Phys Rev B 64:115204
Rodt S, Schliwa A, Pötschke K, Guffarth F, Bimberg D (2005) Correlation of structural and few-particle properties of self-organized InAs∕GaAs quantum dots. Phys Rev B 71:155325
Rodt S, Reitzenstein S, Heindel T (2020) Deterministically fabricated solid-state quantum-light sources. J Phys Condens Matter 32:153003
Rössler U (1979) Fine structure, lineshape, and dispersion of Wannier excitons. In: Treusch J (ed) Festkörperprobleme. Advances in solid state physics, vol 19. Vieweg, Braunschweig, p 77
Rudin S, Reinecke TL, Segall B (1990) Temperature-dependent exciton linewidths in semiconductors. Phys Rev B 42:11218
Sasaki M, Fujiwara M, Ishizuka H, Klaus W, Wakui K, Takeoka M, Miki S, Yamashita T, Wang Z, Tanaka A, Yoshino K, Nambu Y, Takahashi S, Tajima A, Tomita A, Domeki T, Hasegawa T, Sakai Y, Kobayashi H, Asai T, Shimizu K, Tokura T, Tsurumaru T, Matsui M, Honjo T, Tamaki K, Takesue H, Tokura Y, Dynes JF, Dixon AR, Sharpe AW, Yuan ZL, Shields AJ, Uchikoga S, Legré M, Robyr S, Trinkler P, Monat L, Page JB, Ribordy G, Poppe A, Allacher A, Maurhart O, Länger T, Peev M, Zeilinger A (2011) Field test of quantum key distribution in the Tokyo QKD Network. Opt Express 19:10387
Schliwa A, Winkelnkemper M, Bimberg D (2007) Impact of size, shape, and composition on piezoelectric effects and electronic properties of In(Ga)As/GaAs quantum dots. Phys Rev B 76:205324
Schwartz I, Schmidgall ER, Gantz L, Cogan D, Bordo E, Don Y, Zieliński M, Gershoni D (2015) Deterministic writing and control of the dark exciton spin using single short optical pulses. Phys Rev X 5:011009
Schwartz I, Cogan D, Schmidgall ER, Gantz L, Don Y, Zieliński M, Gershoni D (2015b) Deterministic coherent writing of a long-lived semiconductor spin qubit using one ultrafast optical pulse. Phys Rev B 92:201201
Seguin R, Schliwa A, Rodt S, Pötschke K, Pohl UW, Bimberg D (2005) Size-dependent exciton fine-structure splitting in self-organized InAs/GaAs quantum dots. Phys Rev Lett 95:257402
Shields AJ, Pepper M, Ritchie DA, Simmons MY (1995a) Influence of excess electrons and magnetic fields on Mott-Wannier excitons in GaAs quantum wells. Adv Phys 44:47
Shields AJ, Osborne JL, Simmons MY, Pepper M, Ritchie DA (1995b) Magneto-optical spectroscopy of positively charged excitons in GaAs quantum wells. Phys Rev B 52:R5523
Shinada M, Sugano S (1966) Interband optical transitions in extremely anisotropic semiconductors. I. Bound and unbound exciton absorption. J Phys Soc Jpn 21:1936
Shinar J (ed) (2004) Organic light-emitting devices: a survey. Springer, New York
Singh J (1984) The dynamics of excitons. In: Ehrenreich H, Turnbull D (eds) Solid state physics, vol 38. Academic Press, Orlando/New York, p 295
Singh R, Bester G (2010) Lower bound for the excitonic fine structure splitting in self-assembled quantum dots. Phys Rev Lett 104:196803
Singh J, Birkedal D, Lyssenko VG, Hvam JM (1996) Binding energy of two-dimensional biexcitons. Phys Rev B 53:15909
Slussarenko S, Pryde GJ (2019) Photonic quantum information processing: A concise review. Appl Phys Rev 6:041303
Solovyev VV, Kukushkin IV (2009) Measurement of binding energy of negatively charged excitons in GaAs/Al0.3Ga0.7As quantum wells. Phys Rev B 79:233306
Someya T, Akiyama H, Sakaki H (1996) Enhanced binding energy of one-dimensional excitons in quantum wires. Phys Rev Lett 76:2965
Song KS, Williams RT (1993) Self-trapped excitons. Springer series in solid-state sciences, vol 105. Springer, Berlin
Stébé B, Ainane A (1989) Ground state energy and optical absorption of excitonic trions in two dimensional semiconductors. Superlattice Microstruct 5:545
Stievater TH, Li X, Steel DG, Gammon D, Katzer DS, Park D, Piermarocchi C, Sham LJ (2001) Rabi oscillations of excitons in single quantum dots. Phys Rev Lett 87:133603
Tamor MA, Wolfe JP (1980) Drift and diffusion of free excitons in Si. Phys Rev Lett 44:1703
Thewalt MLW, Rostworowski JA (1978) Biexcitons in Si. Solid State Commun 25:991
Thoma A, Schnauber P, Böhm J, Gschrey M, Schulze JH, Strittmatter A, Rodt S, Heindel T, Reitzenstein S (2017) Two-photon interference from remote deterministic quantum dot microlenses. Appl Phys Lett 110: 011104
Thomas GA, Rice TM (1977) Trions, molecules and excitons above the Mott density in Ge. Solid State Commun 23:359
Thomas GA, Timofeev VB (1980) A review of N = 1 to ∞ particle complexes in semiconductors. In: Moss TS, Balkanski M (eds) Handbook on semiconductors, vol 2. North Holland Publishing, Amsterdam, p 45
Tomiki T (1969) Optical constants and exciton states in KCl single crystals III. The spectra of conductivity and of energy loss. J Phys Soc Jpn 26:738
Toyozawa Y (1980) Electrons, holes, and excitons in deformable lattice. In: Kubo R, Hanamura I (eds) Excitons. Springer, Berlin
Türck V, Rodt S, Stier O, Heitz R, Engelhardt R, Pohl UW, Bimberg D, Steingrüber R (2000) Effect of random field fluctuations on excitonic transitions of individual CdSe quantum dots. Phys Rev B 61:9944
Ueta M, Nishina Y (eds) (1976) Physics of highly excited states in solids. Lecture notes in physics, vol 57. Springer, New York
Uihlein C, Fröhlich D, Kenklies R (1981) Investigation of exciton fine structure in Cu2O. Phys Rev B 23:2731
Unrau W, Quandt D, Schulze J-H, Heindel T, Germann TD, Hitzemann O, Strittmatter A, Reitzenstein S, Pohl UW, Bimberg D (2012) Electrically driven single photon source based on a site-controlled quantum dot with self-aligned current injection. Appl Phys Lett 101:211119
Vogl P (1976) Microscopic theory of electron-phonon interaction in insulators or semiconductors. Phys Rev B 13:694
Vouilloz F, Oberli DY, Dupertuis M-A, Gustafsson A, Reinhardt F, Kapon E (1997) Polarization anisotropy and valence band mixing in semiconductor quantum wires. Phys Rev Lett 78:1580
Vouilloz F, Oberli DY, Dupertuis M-A, Gustafsson A, Reinhardt F, Kapon E (1998) Effect of lateral confinement on valence-band mixing and polarization anisotropy in quantum wires. Phys Rev B 57:12378
Wagner MR, Callsen G, Reparaz JS, Kirste R, Hoffmann A, Rodina AV, Schleife A, Bechstedt F, Phillips MR (2013) Effects of strain on the valence band structure and exciton-polariton energies in ZnO. Phys Rev B 88:235210
Wang X-L, Voliotis V (2006) Epitaxial growth and optical properties of semiconductor quantum wires. J Appl Phys 99:121301
Wang Y, Dolde F, Biamonte J, Babbush R, Bergholm V, Yang S, Jakobi I, Neumann P, Aspuru-Guzik A, Whitfield JD, Wrachtrup J (2015) Quantum simulation of helium hydride cation in a solid-state spin register. ACS Nano 9:7769
Wang X-L, Chen L-K, Li W, Huang H-L, Liu C, Chen C, Luo Y-H, Su Z-E, Wu D, Li Z-D, Lu H, Hu Y, Jiang X, Peng C-Z, Li L, Liu N-L, Chen Y-A, Lu C-Y, Pan J-W (2016) Experimental ten-photon entanglement. Phys Rev Lett 117:210502
Wannier GH (1937) The structure of electronic excitation levels in insulating crystals. Phys Rev 52:191
Washington MA, Genack AZ, Cummins HZ, Bruce RH, Compaan A, Forman RA (1977) Spectroscopy of excited yellow exciton states in Cu2O by forbidden resonant Raman scattering. Phys Rev B 15:2145
Weisbuch C, Benisty H, Houdré R (2000) Overview of fundamentals and applications of electrons, excitons and photons in confined structures. J Lumin 85:271
Wendin G (2017) Quantum information processing with superconducting circuits: a review. Rep Prog Phys 80:106001
Wicksted J, Matsushita M, Cummins HZ, Shigenari T, Lu XZ (1984) Resonant Brillouin scattering in CdS. I. Experiment. Phys Rev B 29:3350
Wootters WK, Zurek WH (1982) A single quantum cannot be cloned. Nature 299:802
Yamada Y, Sakashita T, Watanabe H, Kugimiya H, Nakamura S, Taguchi T (2000) Optical properties of biexcitons in ZnS. Phys Rev B 61:8363
Yu PY (1979) Study of excitons and exciton-phonon interactions by resonant Raman and Brillouin spectroscopies. In: Cho K (ed) Excitons. Springer, Berlin, p 211
Yu PW, Reynolds DC, Bajaj KK, Litton CW, Klem J, Huang D, Morkoc H (1987) Observation of monolayer fluctuations in the excited states of GaAs-AlxGa1−xAs multiple-quantum-well. Solid State Commun 62:41
Zhang J, Wildmann JS, Ding F, Trotta R, Huo Y, Zallo E, Huber D, Rastelli A, Schmidt OG (2015) High yield and ultrafast sources of electrically triggered entangled-photon pairs based on strain-tunable quantum dots. Nature Commun 6:10067
Zieliński M (2021) Dark-bright excitons mixing in alloyed InGaAs self-assembled quantum dots. Phys Rev B 103:155418
Zieliński M, Don Y, Gershoni D (2015) Atomistic theory of dark excitons in self-assembled quantum dots of reduced symmetry. Phys Rev B 91:085403
Zieliński M, Gołasa K, Molas MR, Goryca M, Kazimierczuk T, Smoleński T, Golnik A, Kossacki P, Nicolet AAL, Potemski M, Wasilewski ZR, Babiński A (2015) Excitonic complexes in natural InAs/GaAs quantum dots. Phys Rev B 91:085303
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this entry
Cite this entry
Böer, K.W., Pohl, U.W. (2022). Excitons. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-06540-3_14-4
Download citation
DOI: https://doi.org/10.1007/978-3-319-06540-3_14-4
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06540-3
Online ISBN: 978-3-319-06540-3
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics
Publish with us
Chapter history
-
Latest
Excitons- Published:
- 24 September 2022
DOI: https://doi.org/10.1007/978-3-319-06540-3_14-4
-
Excitons
- Published:
- 26 March 2020
DOI: https://doi.org/10.1007/978-3-319-06540-3_14-3
-
Excitons
- Published:
- 27 September 2017
DOI: https://doi.org/10.1007/978-3-319-06540-3_14-2
-
Original
Excitons- Published:
- 17 December 2015
DOI: https://doi.org/10.1007/978-3-319-06540-3_14-1