, Annexe c. calcul des éIéments de matrice des différents opérateurs

, 21(r, 0,J)l++n lI

+. , 21(0, 0, B)l -2n[I(J, -1, t) -I(0

, 2I(0, 0, B) _ 2I(1, _1, J)l + 2nlI(3, -1, 1) -I(2,0, 1) -I(1, 1, 1)+ 1, pp.2-3

, 2I(-1, 1, 3) -2I(0, 0, J)l-2mlI, pp.1-1

+. , , pp.1-1

+. and \. , +" (2M, -2s)r.(2Nt _2s')! 3 ?sls' !(Mr -s)!(lr' -s')l(M'-zs -D(F,-E:t;t 71 x I r2

, Bibliographie

M. Abramowitz and I. A. Stegun, Handboolc of Mathematical Functions, 1965.

F. Agullô-rueda, J. A. Brum, E. E. Mendez, and J. M. Hong, Phys. Rev, vol.841, p.1676, 1990.

A. S. Aspnes, Electric-Field Effects on Optical Absorption near Thresholds in Solids, Physical Review, vol.145, issue.2, p.554, 1966.
DOI : 10.1103/PhysRev.145.583

J. V. Atanasoff, The Dielectric Constant of Helium, Physical Review, vol.10, issue.7, p.1232, 1930.
DOI : 10.1007/978-3-662-36445-1

G. Bastard, Waue mechanics applied to semiconductor heterostructures

C. 8. Benoit-À-la-guillaume, J. Debever, and F. Salvan, Radiative Recombination in Highly Excited CdS, Physical Review, vol.9, issue.2, p.567
DOI : 10.1063/1.1754637

F. Bentosella and V. Grecchi, Commun. Math. phy, vol.42, p.169, 1991.

H. A. Bethe and E. Salpeter, in Quantum Mechanics of one - Two -Electron Atoms, 1957.

D. F. Blossey, Wannier Exciton in an Electric Field. I. Optical Absorption by Bound and Continuum States, Physical Review B, vol.7, issue.10, p.3976, 1970.
DOI : 10.1016/0038-1098(69)90714-5

D. F. Blossey, Wannier Exciton in an Electric Field. II. Electroabsorption in Direct-Band-Gap Solids, Physical Review B, vol.23, issue.4, p.1382, 1971.
DOI : 10.1103/PhysRevLett.23.1387

D. F. Blossey and P. Handler, Semiconductors and Semimetals

R. K. Edité and . Willardson, , 1972.

A. I. Bobrysheva, M. V. Grodetskii, and V. T. Zyukov, Binding energy for the surface biexcitonic positive ion, Journal of Physics C: Solid State Physics, vol.16, issue.29, p.5723
DOI : 10.1088/0022-3719/16/29/025

K. W. Bôer, H. J. Hansche, and Y. Kummel, Z.Physik, vol.155, issue.170, 1959.

J. A. Brum and G. Bastard, Phys. Rev, pp.31-3893, 1985.

J. 4. Brum, C. Priester, and G. Allan, Phys. Rev, pp.32-2373, 1985.

H. Buhman, Phys. Rev, vol.851, p.7969, 1995.

J. Callaway, Optical Absorption in an Electric Field, Physical Review, vol.126, issue.2, p.549, 1963.
DOI : 10.1103/PhysRev.126.1386

J. Callaway, Optical Absorption in an Electric Field, Physical Review, vol.117, issue.4A, p.998, 1964.
DOI : 10.1103/PhysRev.117.432

, Bibliographie Quanturn Theory of the Solid State Academic press, 1924.

M. Chester and P. H. , Phys. Rev. Letters, vol.18, p.1, 1964.

K. T. Chung and R. P. Hurst, Phys. Rev, vol.1, issue.2, p.gb, 1966.

J. D. Dow and D. Redfield, Phys. Rev, vol.81, pp.3-8, 1920.

G. Dresselhaus, Effective mass approximation for excitons, Journal of Physics and Chemistry of Solids, vol.1, issue.1-2, p.14
DOI : 10.1016/0022-3697(56)90004-X

F. Dujardin, Thèse d'état, 1992.

F. Dujardin, M. Azaitouni, and B. Stébé, , p.1

C. Duke, Phys. Rev. Lett, vol.16, issue.8lg6b, p.62

C. B. Duke and M. E. Alferieff, Phys. Rev, vol.4, p.8, 1966.

E. Feddi, Thèse de I, 1987.

E. Feddi, F. Dujardin, J. Diouri, A. Elhassani, M. Katih et al., Phys. Stat. Sol (b), vol.201, 1992.

M. Katih, J. Diouri, and E. Feddi, Phys. stat. solid (b), vol.6, p.4, 1998.

G. Finkelstein, Phy. Rev. BEB, pp.1-1

G. Finkelstein, Phy. Rev. BEB IZbgJ, issue.1gg6b

W. Franz, Z. Naturforsch, vol.3, p.484, 1958.

J. Frenkel, Phys. Rev, vol.37, p.1270, 1931.

A. Frova and P. Handler, Phys. Rev. Letters, vol.14, issue.1g6b, p.17

P. Froelich and E. Brândas, Phys. Rev, vol.12, issue.1, 1925.

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series and, prod,ucts, 1965.

N. Harrick, J., Phys. Rev, vol.108, p.1173, 1956.

H. Haug, Koch, s. w., Quanturn Theory of the optical and Electronic Properties of Serniconductors, World Scientif.c, 1990.

J. R. Haynes, Phys. Rev. Letters, vol.4, p.86, 1966.

M. Hosoda, J. Appl. Phys, vol.80, p.94, 1996.

Y. Ishida and S. Hiyama, Pap. Inst. phys and chem. Res. Tokyo LSZ, issue.1e28

E. O. R52-kane, Zener tunneling in semiconductors, Journal of Physics and Chemistry of Solids, vol.12, issue.2, p.181, 1959.
DOI : 10.1016/0022-3697(60)90035-4

L. V. Keldysh, [translation: Soviet Phys, Theoret. Phys. (U.S.S.R), vol.34, issue.7, pp.1138-788, 1953.

K. Kheng, Phys. Rev. Lett, vol.71, pp.1-1752, 1993.

C. Kittel, Introduction ù la physique de l'état solide

R. W. Koss and L. M. Lambert, Phy. Rev, vol.5, p.7479, 1972.

M. Lampert, Mobile and Immobile Effective-Mass-Particle Complexes in Nonmetallic Solids, Physical Review Letters, vol.1, issue.12, p.450, 1958.
DOI : 10.1016/0022-3697(56)90004-X

L. Landau and E. Lifchitz, Mécanique quantique êdition MIR, 1966.

F. L. Lederman and J. D. Dow, Phys. Rev, vol.813, p.1633, 1976.

P. Lelong and G. Bastard, Solid. State. Com, vol.98, pp.9-819, 1996.

S. Le-goff, Thèse d'Université de Metz, 1992.

J. M. Lévy-leblond, Possibility of Exciton Binding to Ionized Impurities in Semiconductors, Physical Review, vol.139, issue.3, p.1526, 1969.
DOI : 10.1103/PhysRev.139.A1991

E. E. Mendez, F. Agullô-rueda, and J. M. Hong, Phys. Rev. lett, vol.6023, issue.re88, p.2426

A. A. Miller, Phys. Rev, vol.832, p.1043, 1985.

T. S. Moss, Phys, vol.32, p.2136, 1962.

G. Munschy and . Stébé, Phys. Stat. Sol. (b), vol.8, issue.21, p.3, 1974.

G. Munschy and B. Stébé, Non-adiabatic calculation of the binding energy of the excitonic molecule ion, physica status solidi (b), vol.78, issue.1, p.135, 1975.
DOI : 10.1002/pssb.2220720114

S. Nikitine, Optical Properties of Solids, Nudelman et Mitra eilitions Pleunurn press, 1969.

J. R. Packard, D. A. Campbell, W. C. Tait, and J. App, Phys, vol.38, issue.1e67, p.5255

P. Pavlov and . Khokhlov, , 1989.

C. L. Pekeris, States of Helium, Physical Review, vol.115, issue.5, p.1216, 1959.
DOI : 10.1103/PhysRev.115.366

C. M. Penchina, Phonon-Assisted Optical Absorption in an Electric Field, Physical Review, vol.108, issue.3A, p.924, 1965.
DOI : 10.1103/PhysRev.108.1384

T. Ohyama, Internal Stark Effect on Impurity States in Germanium, physica status solidi (b), vol.41, issue.1, p.373, 1980.
DOI : 10.1139/p63-183

H. I. Ralph, J. Phys. C. Ser, vol.2, p.378, 1968.

A. Schmeller, W. Hansen, and J. P. Kotthaus, Franz???Keldysh effect in a two???dimensional system, Applied Physics Letters, vol.63, issue.3, p.330
DOI : 10.1063/1.110352

B. O. Seraphin and N. Bottka, Franz-Keldysh Effect of the Refractive Index in Semiconductors, Physical Review, vol.6, issue.2A, p.560, 1965.
DOI : 10.1063/1.1754202

B. Shields and A. J. , Phys. Rev. Bb2, pp.1-049

A. J. Shields, Phys. Rev. BE2, issue.1g95c, pp.7-8

A. J. Shieids, Phys. Rev. BEb, issue.1gg7, p.1313

W. Shockley, Phys. Rev. Lett. Zg, vol.4, issue.IgT2

B. Stébé and G. Munschy, solid. state. commun. rz, pp.10-11, 1925.

. Stébé, Thése d'état (I}TT)

B. Stébé, T. Sauder, and M. Certier, solid. state. commun

B. Stébé and A. Ainane, , p.4

. Tharmalingam, Phys. Rev. IBO, p.2204

A. Thilagam, Phys. Rev, vol.812, issue.1gg7, p.7804

D. G. Thomas and T. M. Rice, solid. state. commun, vol.28, p.3

G. H. Wannier, Phys. Rev, vol.2, issue.1gg7, p.191

G. H. Wannier, Elementsof solidstateTheory. cambridge univ. press

G. H. Wannier, Phys. Rev, vol.112, p.432, 1960.

G. H. Wannier and D. R. Fredkin, phys. Rev, vol.2, 1910.

D. P. Wang, C. T. Chen, T. M. Hsu, and J. Appr, , pp.9-71, 1996.

F. C. Weinstein, J. D. Dow, and L. , B. y., phys. Rev, vol.4, p.502, 1921.

R. Williams, Phys. Rev, vol.112, p.1487, 1960.

R. Williams, Physical Review, vol.22, issue.2, p.442, 1962.
DOI : 10.1103/PhysRev.106.703

Y. Yacoby, Phys. Rev, pp.140-263, 1965.

Y. Yacoby, Bulk Measurement of the Franz-Keldysh Effect in Si, Physical Review, vol.130, issue.2, p.445, 1966.
DOI : 10.1103/PhysRev.130.914

J. Zak, Phys. Rev. Lett. ZO, vol.4, 1963.