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Appendix A
Physical Constants
Name Symbol Value Unit Avogadro's constant NAvo 6.02204. 1023 mol 1
Bohr radius TB 5.2917 . 10-11 m Boltzmann's constant k 1.38066. 10-23 WsjK dielectric constant EO 8.85418.10- 12 As V- 1m- 1
electron rest mass rna 9.1095 . 10-31 kg electron volt eV 1.60218.10-19 Ws elementary charge q 1.60218. 10-19 As light velocity in vacuum c 2.99792. 108 m/s permeability in vacuum 110 1.25663. 10-6 Vs A -lm- 1
Planck's constant h 6.62617. 10-34 Ws2
h = hj27r 1.05459. 10-34 Ws2
thermal voltage at 300 K kT/q 2.58522 .10- 2 V wavelength of a Ie V photon ). 1.23986. 10-6 m
Appendix B
Data on Some Indirect Semiconductors (at room temperature)
Si Ge AlP AlAs AISb GaP density (gj cm3 ) 2.328 5.327 2.40 3.7 4.26 4.13 atomsj cm3 or 5.0 4.42 2.46 2.2 1.73 2.48 moleculesj cm3 .1022 .1022 .1022 .1022 .1022 .1022
crystal dia- dia- Zlnc- ZlUC- ZlUC- Zlnc-lattice mond mond blende blende blende blende lattice parameter (nm) 0.543 0.565 0.546 0.5660 0.6135 0.5451 melting point (0 C) 1420 937 2550 1740 1065 1467 thermal conduct-ivity (W jcm°C) 1.5 0.6 0.9 0.91 0.57 0.77 reI. stat. dielect-ric constant 11.9 16.0 9.8 10.1 14.4 11.1 bandgap (e V) 1.12 0.803 2.45 2.163 1.58 2.261 reI. effect. mass electrons me j mo 1.0 1.3 0.15 0.12 0.82 holes mhjmo 0.5 0.3 0.70 0.8 0.98 0.6 intrinsic carrier con-centration (cm -3) 1.5 .1010 2.4 .1013
mobility (cm2 jVs) electrons 1500 3900 60 200 200 110 holes 450 1900 400 75 breakdown field strength (V j cm) ~ 3 . 105 ~ 105 ~ 5 ·1( refractive index at Wgap 3.5 4.2 3.03 3.178 3.4 3.45 type of lU- lU- lU- lU- lU- lU-bandgap direct direct direct direct direct direct
Appendix C
Data on Some Direct Semiconductors (at room temperature)
GaAs GaSb InP InAs InSb density (g/ cm3) 5.32 5.61 4.79 5.67 5.77 atoms/cm3 or 2.22 1.76 2.0 1.8 1.39 molecules/ cm3 .1022 .1022 .1022 .1022 .1022
crystal Zlnc- zmc- zmc- zmc- zmc-lattice blende blende blende blende blende lattice parameter (nm) 0.5653 0.6096 0.5869 0.6058 0.6479 melting point (0C) 1238 712 1058 937 523 thermal conduct-ivity (W /cm°C) 0.46 0.33 0.68 0.27 0.17 reI. stat. dielect-ric constant 13.1 15.7 12.4 14.6 17.7 bandgap (e V) 1.424 0.726 1.351 0.360 0.172 reI. effect. mass electrons me / ma 0.067 0.042 0.077 0.023 0.015 holes mh/ma 0.48 0.44 0.64 0.40 0.40 intrinsic carrier con-centration (cm -3) 1.8 .106 :::::: 1014 1.2 .108 1.2 .1015 5.1017
mobility (cm2/Vs) electrons 8500 2500 4600 27000 77000 holes 400 1420 150 450 1250 breakdown field strength (V / cm) :::::: 4 .105 :::::: 5 .105
refractive index at Wgap 3.655 3.82 3.45 :::::: 3.52 :::::: 4.0 type of bandgap direct direct direct direct direct
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Chapter 11
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Chapter 12
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12.6 Maehnss, J.; Kowalsky, W.; Ebeling, K.J.: Optical waveguide phase modulator in GaInAsP using depletion edge translation. Electron. Lett. 24 (1988) 518-519
12.7 Banyai, L.; Koch, S.W.: A simple theory for the effects of plasma screening on the optical spectra of highly excited semiconductors. Z. Phys. BCondensed Matter 63 (1986) 283-291
12.8 Kowalsky, W.; Ebeling, K.J.: Optically controlled transmission of In GaAsP epilayers. Optics Letters 12 (1987) 1053-1055
12.9 Chemla, D.S.; Miller, D.A.B.: Room-temperature excitonic nonlinear-optical effects in semiconductor quantum-well structures. J. Opt. Soc. Am. B2 (1985) 1155-1173
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12.12 Miller, D.A.B.; Chemla, D.S.; Damen, T.C.; Gossard, A.C.; Wiegmann, W.; Wood, T.H.; Burrus, C.A.: Electric field dependence of optical absorption near the band gap of quantum-well structures. Physical Review B 32 (1985) 1043-1060
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Chapter 13
13.1 Sze, S.M.: Semiconductor Devices. Physics and Technology. New York: Wiley & Sons 1985
13.2 Wada, 0.; Hamaguchi, H.; Makiuchi, M.; Kumai, T.; Ito, M.; Nakai, K.; Horimatsu, T.; Sakurai, T.: Monolithic four-channel photodiode/amplifier receiver array integrated on a GaAs substrate. IEEE J. Lightwave Techno!. LT-4 (1986) 1694-1702
13.3 Margalit, S.; Yariv, A.: Integrated Electronic and Photonic Devices. In: Tsang, W.T. (Ed.): Semiconductors and Semimetals, Vo!' 22, Part E, p. 203-263. New York: Academic Press 1985
13.4 Wada, 0.; Sakurai, T.; Nakagami, T.: Recent progress in optoelectronic integrated circuits (OEICs). IEEE J. Quantum Electron. QE-22 (1986) 805-821
13.5 Forrest, S.R.: Monolithic optoelectronic integration: A new component technology for lightwave communications. IEEE J. Lightwave Technol. LT-3 (1985) 1248-1263
13.6 Smith, R.G.; Personick, S.D.: Receiver design for optical fiber communication systems. In: Kressel, H. (Ed.): Topics in Applied Physics, Vol. 39, p. 89-160. Berlin: Springer 1982
13.7 Forrest, S.R.: Optoelectronic integrated circuits. Proceedings IEEE 75 (1987) 1488-1497
13.8 Miura, S.; Hamaguchi, H.; Mikawa, T.; Fujii, T.; Aoki, 0.; Wada, 0.: High-speed GaInAs monolithic PIN/FET receiver. Proceedings Thirteenth European Conference on Optical Communication. Helsinki 1987, pp. 66-69
REFERENCES 521
13.·9 Sakano, S.; Inoue, H.; Nakamura, H.; Katsuyama, T.; Matsumura, H.: In GaAsP /InP monolithic integrated circuit with lasers and an optical switch. Electronics Letters 22 (1986) 594-596
13.10 Razeghi, M.; Maurel, P.; Defour, M.; Omnes, F.; Acher, 0.: MOCVD growth of III- V heterojunctions and superlattices on Si substrates for photonic devices. Proc. Fourteenth European Conference on Optical Communication, Brighto~ 1988, Part 2, p. 74-82. Institution of Electrical Engineers, Exeter 1988
13.11 Matsueda, H.; Hirao, M.; Tanaka, T.P.; Nakamura, M.: Integration of optical devices with electronic circuits for high speed optical communications. In: Proc. 12th Int. Symp. Gallium Arsenide and Related Compounds, Karuizawa, Japan 1985, Inst. Phys., Conf. Ser. No. 79, p. 655-660. Bristol: Adam Hilger 1986
13.12 Shibata, J.; Nakao, I.; Sakai, Y.; Kimura, S.; Hase, N.; Serizawa, H.: Monolithic integration of an InGaAsP /InP laser diode with heterojunction bipolar transistor. Appl. Phys. Lett. 45 (1984) 191-193
List of Important Symbols
Mathematical Symbols <a> Re(a),Im(a) a*
a
average, ensemble average of a real and imaginary parts, respectively, of a, conjugate complex value of a
a = (a"" ay, az )
derivative with respect to time of a, aa/ at vector, Cartesian components
V V t
Va V·a V x a '12 ii i Jv(x) Hm(x) F1/2(X) o(x) Ai(x), Bi(x)
nabla operator transverse nabla operator gradient, grad a divergence, diva curl, curl a Laplace operator L1 tensor imaginary unit Bessel Function of the first kind and v-th order Hermite polynomial of m-th degree Fermi integral Dirac o-function Airy functions
Symbols in Formulae Numbers in parantheses indicate the equations where the symbol first appears
A, L1A area A(z) complex amplitude of a mode (5.1) A21 Einstein coefficient for spontaneous emission (8.8) A magnetic vector potential (8.50) a = ag/an differential gain coefficient (10.8) am, a-m expansion coefficient for forward travelling mode m
B BER B(z)
and backward travelling mode -m, respectively (4.102) quantum well thickness (7.138) bit rate (13.16) bit error rate (13.21) complex amplitude of a mode (5.1) Einstein coefficients for stimulated emission and absorption, respectively, (8.7), (8.2)
MATHEMATICAL SYMBOLS 523
f3 B B b, Llb C c D{k) Dc{W)
DCI/{W)
D,,{W) Dph{hw) Dn,Dp
Etm
Ea,Eb EV
Ej,E.,Ec
FM FN{t), Fn{t), F¢{t)
FN{V), Fn{v), F¢(v) F
f{W) fc(W)
f,,{W)
fph{hw)
G 9
phase parameter (3.8) complex magnetic induction (2.6 et seq.) vector ofreal magnetic induction (2.1) width capacitance velocity oflight in vacuum (1.5) density of states in the k-space (7.82) density of states of the electrons in the conduction band (7.88) density of states in the v-th subband of a quantum well (7.139) density of states of the holes in the valence band (7.89) density of states for photons (8.9) diffusion constants for electrons and holes, respectively, (9.10), (9.9) complex dielectric displacement (2.6 et seq.) vector of the real dielectric displacement (2.3) width, thickness complex electric field (2.6) vector of the real electric field (2.1) complex electric field of mode m (4.34) transverse and longitudinal electric field vectors, respectively, (4.36), (4.37) normalized transverse electric field of mode m (4.96) normalized electric fields in waveguides a, b (5.1) electric field vector of supermode v (6.79) electric field amplitude in the film, substrate, cover (3.27) excess noise factor (11.14 7), (11.148) Langevin noise forces for the photon density N, electron density n and phase ¢ (10.145), (10.154), (1O.162) Fourier transforms of FN{t), Fn{t), F¢{t) (10.165), low frequency real electric field vector (5.74), (10.166) occupation probability (7.98) quasi-Fermi distribution for electrons in the conduction band (7.123) quasi-Fermi distribution for electrons in the valence band (7.124) occupation probability for photons in thermodynamic equilibrium (8.13) generation rate (11.48) gain coefficient (lOA)
524
gm
gp gth
gm gij
H I A I
H,H
Hjm,Hjm
H(I/) H H Hm Ht,Hz
Htm
h ilh
hell h(t) Ii = h/27r I Ip i(t) i(//)
in, ip iPh(t) iPh (l/) ith
is
ids
6i'Jv (1/) jn,jp
jo jth ilj(t) il](I/) J
MATHEMATICAL SYMBOLS
gain coefficient of mode m (10.81) maximum gain coefficient (8.103) threshold gain coefficient (10.9) transconductance (13.4) elements of the inverse dielectric tensor (5.88) Hamilton operator (7.9) perturbation part of the Hamilton operator (8.56), (8.73) energy matrix elements (8.66), (8.74) transfer functions (11.63) complex magnetic field (2.6 et seq.) vector of the real magnetic field (2.2) complex magnetic field of mode m (4.34) transverse and longitudinal magnetic field vectors, respectively, (4.36), (4.37) normalized transverse magnetic field of mode m (4.96) film thickness (3.6) film thickness variation (3.51) effective waveguide thickness (3.33) pulse response (11.169) reduced Planck constant (1.2) intensity (2.63) pumping light intensity (8.138) current Fourier transform of i( t) (11.7) dark current (11.75) electron current, hole current (11.112), (11.113) photo current (10.185) Fourier transform of iPh(t) (11.63) laser threshold current (10.51) signal current (11.73) saturation current (11.47) drain-source saturation current (13.3) variation of the noise current (11.28), (11.43) electron and hole current densities, respectively, (9.14), (9.15) saturation current density (9.63) threshold current density (10.44) deviation of the current density from mean value (10.103) Fourier transform of ilj(t) (10.106) complex current density vector (2.6 et seq.) real current density vector (2.2) coupling coefficients (5.35) Boltzmann constant
MATHEMATICAL SYMBOLS 525
k k ke,kv
L Ln,Lp I, Lll M6 M21,Mev Mn,Mp
mo me,mh N Nm
N tot
LlN(t) LlN(v) NA,ND Ne,Nv
n dnjdW no
nop Lln Lln( t) Llii(v)
neff nf, ns, nc P Pc Pm
PS,PL Pt
Po min
Pm-;.j p
vacuum wave number (2.81) wave vector (2.81) electron wave vectors in the conduction and valence bands, respectively, (8.90), (8.91) length diffusion lengths of electrons and holes, resp., (9.52), (9.53) length transfer matrix of a coupler (6.23) momentum matrix elements (8.89) multiplication factors for electrons and holes, respectively, (11.117), (11.118) rest mass of the electron (7.8) effective mass of an electron and a hole, respectively, (7.55) photon density photon density of mode m (4.70), (10.83) total number of photons in the resonator (10.30) deviation of the photon density from the average value (10.101) Fourier transform of LlN(t) (10.101) densities of acceptors and donors, respectively, (7.110) effective densities of states in the conduction band (7.90) and in the valence band (7.91) density of electrons (2.139) spectral density of electrons (7.99) equilibrium density of electrons (7.129) equilibrium density of electrons in the p-semiconductor (9.56) excess density of electrons (7.129) deviation of electron density from the average value (10.100) Fourier transform of Lln(t) (10.104) intrinsic density of charge carriers (7.115) intrinsic density of charge carriers in the n-and p-semiconductors, respectively, (9.56), (9.57) total number of electrons in the resonator (10.29) density of electrons at the laser threshold (10.37) surface density of electrons (12.45) real refractive index (2.54) effective refractive index (3.4) refractive indices in the film, subtrate, cover power control power (12.39) power of mode m (4.55) signal power, local oscillator power (11.97) test power (12.40) minimum detectable power (11.79) transition rate from m to j (8.81) polarization (5.18), perturbation polarization (5.28)
526
Ppcrt
Po POn .dp
p= ~v Q R R RL R$p
RIN
t U uc(kc, r), uv(kv, r)
unk(r) V Va Vgs VT VD 6VJ(v) VK V v, Va
Vg
Vgm
Vph
W
MATHEMATICAL SYMBOLS
perturbation polarization (5.19) equilibrium density of holes (7.129) equilibrium density of holes in the n-semiconductor (9.57) excess density of holes (7.129) momentum operator (Table 7.1) noise related level separation (13.22) intensity reflection coefficient (2.95), (10.10) resistance load resistance (11.66) total spontaneous recombination (8.37) relative intensity noise (10.185) amplitude reflection coefficient (2.92), (10.1) spectral transition rate for stimulated emission and absorption, respectively, (8.7), (8.2) electrooptic module (5.74) spectral transition rate for spontaneous emission (8.8) posi tion vector (1.1) time-averaged electromagnetic energy flux density (2.48) vector of the electromagnetic energy flux density, Poynting vector (2.45) time-averaged Poynting vector of mode m (4.54) spectral power density (11.15), (10.177) signal-to-noise ratio (11.78) measurement time (10.137) absolute temperature characteristic temperature of laser threshold current (10.260) time (2.1) potential energy (7.8) Bloch functions in the conduction band and the valence band, respectively, (8.90), (8.91) periodical part of the wave function in band n (7.48) voltage applied voltage (9.36) gate-source voltage (13.:0 threshold voltage (13.2) built-in potential (9.4) variation of the noise voltage (11.42) crystal volume (8.90) frequency paramenter (3.7) velocity, saturation velocity group velocity (7.63) group velocity of mode m (4.69) phase velocity (2.55) electron energy
MATHEMATICAL SYMBOLS 527
Wg
W" W"v
W= Wn +Wp
Wm
x,y,z Z t:¥.
t:¥H
13 f3a,f3o f3l,f3&,f3c
13m 13; = 131 + 6131 p . r r
energies of the acceptor and donor levels, respectively, (7.112) Fermi energy (7.98) quasi-Fermi energies in the conduction and valence bands, respectively, (7.123), (7.124) electron energy at the lower edge of the conduction band (7.86) electron energy at the edge of the lI-th subband in the conduction band of a quantum well (7.134) bandgap energy electron energy at the upper edge ofthe valence band (7.89) electron energy at the edge of the lI-th subband in the valence band of a quantum well (7.135) energy difference (1.2) band discontinuity in the conduction band and the valence band, respectively, (9.1) exciton energy (12.48) width of the avalanche zone (11.117) spot size, minimal radius of a mode (3.87) depletion layer width in the n- and p-semiconductors, respectively, (9.29), (9.30) total depletion layer width (9.31) electromagnetic energy density of the mode m (4.56) Cartesian position coordinates wave impedance (2.58) intensity absorption coefficient (2.53) intrinsic loss (10.4) decay coefficient of mode m in z-direction (4.35) absorption coefficient of mode m through mirror losses (10.126) transverse decay coefficients in the substrate, cover (3.16) (3.18) ionization coefficient for electrons and holes, respectively, (11.108) Henry factor (10.132) propagation constant, phase (2.53) propagation constant in the waveguide of modes a, b (5.1) transverse propagation constants in the film, substrate, cover (3.16), (3.17), (3.18) transverse propagation constants in the film in x- and y-direction (4.3) propagation constant of mode m in z-direction (4.34) perturbed propagation constant in the waveguide I (6.99) spontaneous emission factor (10.17) confinement factor (10.22) complex propagation constant in z-direction (2.51)
528
E - I ." E = E - ZE
EO
LlEij
"I "I TJd, "Ii
:"'1m
ij = n + iK e tJ "'ab, ICba, IC
K
A A Am LlAFP LlAc Jl Jlo Jln, Jlp V
Vr V/t
Llv 6VFP 6Vlaser p P 0-
r
ifJ
ifJT E , ifJT M
Ll¢(t) Ll~(v) <p
MATHEMATICAL SYMBOLS
damping constant with small signal modulation (10.113) half phase deviation (5.2) relative dielectric constant (2.14) complex relative dielectric constant (after (2.18)) dielectric constant of vacuum (2.12) element of the dielectric tensor (5.29) quantum efficiency (11.45) conversion efficiency (10.55) differential and internal quantum efficiencies, respectively, (10.52), (10.51) coupling efficiency for mode m (4.119) complex refractive index (2.59) angle of incidence (2.98) phase angle (2.66) coupling factor (5.2) extinction coefficient (2.59) period of a perturbation (3.51), lattice period (10.120) vacuum wavelength (1.5) wavelength of mode m (10.7) wavelength separation between neighboring modes (10.12) spectral width of spontaneous emission (10.91) relative permeability (2.15) perbeability of a vacuum (2.13) mobility of electrons and holes, respectively, (9.13) modulation frequency (6.57) resonance frequency for small signal modulation (10.112) cut-off frequency (6.58) measurement bandwidth (10.180), frequency interval (11.28) linewidth in the passive resonator (10.210) laser linewidth (10.209) complex charge density (2.6 et seq.) real charge density (2.3) conductivity (2.17) photon lifetime in the resonator (10.20) photon lifetime for mode m (10.83) intraband relaxation time (2.137) lifetimes for spontaneous recombination (8042) and emission (10.19), respectively photon lifetimes due to output and intrinsic losses, resp., (lOA) scalar potential (8.51) half phase shift in total internal reflection (2.119), (2.134) phase shift (6.58), phase change (10.128) Fourier transform of Ll¢(t) (10.167) incidence angle in the yz-plane
MATHEMATICAL SYMBOLS
W
wB Llw(t) Llw(1I ) Llwpp
position- and time-dependent wave function of a particle (7.1) position-dependent wave function of a particle (7.10) electron wave functions in the conduction band and the valence band (8.90), (8.91) angular frequency of a sound wave (5.56) angular frequency of light (1.2) Bragg angular frequency (10.232) angular frequency change (10.128) Fourier transform of Llw(t) (10.190) angular frequency separation of neighboring modes (10.13)
529
Subject Index
absorption 42, 44, 225 - coefficient 28, 44, 230, 401 - edge displacement 456 - for direct transitions 247 - in quantum wells 254 - modulator 481 - spectrum 236 - zone 423 -,fundamental 236 -, tunnel-assisted 454 acceptor density 210 -level 205 Airy differential equation 455 - function 455,479 AIGaAs 13, 42, 45 AIGalnP 14 amplification, photo conduction 444 amplitude modulation 335 anisotropic medium 125 anti-reflection layer 400 astigmatism 327 asymmetry parameter 53 attenuation by bends 69 - due to scattering 69 Auger recombination 217, 382 avalanche breakdown voltage 412, 419 - diode, design of 432 - multiplication 419 - - in periodic pn-structures 441 - -, dynamics of 424 - photodiode 418, 432 A vogadro constant 8 band filling in modulators 426, 464 - - in quantum wells 470 - structure 186, 187 - - of GaAs 189 - - oflnP 192
band structure of Si 192 band-band transition 215, 244 band-impurity transition 265 bandgap 13 -, temperature dependence 15 bandtails 269 bandwidth, avalanche diode 426 -, modulator 159 bar state 151, 157 beam radius 73, 379 beat 168 - frequency 388 Bessel function 64 bistability 483 bit error rate 497, 504 - rate 496 Bloch wave 244 Bloch's theorem 185, 187 Bohr radius 204 Boltzmann distribution 208, 288 - statistics 414 Bose-Einstein distribution 229, 394 boundary conditions 30 Bragg reflection 67, 122 - reflector 359, 369 breakdown 419 Brewster angle 40 Brillouin zone 186, 188 buffer layer 481 built-in potential 279 capacitance of a pn-junction 295 -, parasitic 494 carrier confinement 299 - density in the neutral region 289 - - in the space charge region 289 - generation, optical 465 - multiplication 423
INDEX
carrier, free 45 cathodoluminescence 228 Cauchy principal value 21 causality 21 channel noise 495 characteristic equation 51, 186 chirp 368, 382 coherent superposition 410 collision time 424 complete ionization 210 compound semiconductor 1, 12 conduction band 11, 190 confinement factor 309 continuity equation 19 control power of directional coupler
160 conversion efficiency 317 correlation of Langevin forces 347 Coulomb force 204 - potential 274 - -, screened 274 coupler, directional 143 coupling between waveguides 370 - coefficient 118 - constant 109, 117, 148 - efficiency 104 -length 110 - matrix 165 - of modes 109, 114 -, codirectional 110 -, contradirectional 111 cross state 151, 157 cross-section variations 105 crystal 2 - density 20 - direction 4 - lattice model, one-dimensional 184 - momentum 195 - - conservation 244 - plane 4 - structure 2 current flow across a pn-junction 285 - multiplication 420 - noise source, equivalent 392 cut-off frequency 55
531
cut-off frequency of a modulator 159 dark current 389, 406, 414 DBR laser diode 359 de Broglie wavelength 219 Debye length 274 decision level 497 degeneracy 209, 212 - factor 210 delay time 338 density of states for a parabolic band
201 - - - for photons 229 - - - in k-space 200 - - - on energy scale 200 - - -, effective 202 depletion edge translation 462 -layer 285 - - width 284, 286, 412 detailed equilibrium 229, 281 detection sensitivity 406, 496 - - for digital signals 496 detector, photo capacitive 441 DFB laser diode 360 diamond lattice 6 dielectric constant 20 - tensor 126, 133 diffraction 63 diffusion constant 280 - current 280 - length 291, 405 - time 405 - zone 294 diode capacitance 404, 413 dipole moment 43 directional coupler 143 - - driving power 160 - - filter 153 - - modulator 154 - - travelling wave modulator 162 - - with carrier injection 460 - - with phase reversal 156 - -, dynamics 158 - -, multi-channel 168 - -, switched 154 - -, symmetric 147
532
dispersion relation 26 donor density 210 -level 204 Doppler effect 124 double heterostructure 296 drift current 280 - time 401 dynamics, quantum limit of 482 effective index method 84 - mass approximation 197 - - theorem 250 EH wave 76 eigenvalue equation 57 Einstein coefficient 227-229 - - for spontaneous emission 446 - relation 281 electroabsorption 453 - modulator 458 electroluminescence 228 electron affinity 277 - density 207 - gas, one-dimensional 222 - -, two-dimensional 218,279 - lifetime 234, 308, 339 - momentum 195 -motion 195 - number fluctuation 346, 350 -, free 182 electron-hole pair generation 418 - - - for variable bandgap 435 electrons, rate equation for 308 electro optic effect 125, 127 - module 128 - tensor 127, 133 electrorefraction 458 emission 225 - factor, spontaneous 308, 331 - rate, spontaneous 308 - spectrum 327, 331,340,342 -, spontaneous 225, 344 -, stimulated 225 endface coupling 102 energy band 9, 187 - - diagram for a pn-heterojunction
286
energy conservation law 25 - density 24, 91 - flux 24, 91 - flux density 25 - gap 10, 11 - level of impurities 203 - matrix element 240, 242 -, modal 91 ensemble average 391 epitaxial layer 12 - -, strained 507 equation, characteristic 51, 186 equilibrium, perturbed 213 -, detailed 229, 281 etalon, active 365 excess carrier density 217 - noise factor 429
INDEX
- - from avalanche multiplication 427
- - in a photomultiplier 438 excitation by current 263 - -light 263 exciton 472 - resonance 257,473 - - suppression 474 -, bound 472 expansion coefficient 101, 115 expectation value 176 extinction coefficient 28, 44 Fabry-Perot resonator 303 far field distribution 372 - - intensity 373 Faraday's law 24 feedback, optoelectronic 483 Fermi distribution 207 - energy 207 - level 279 FET 487 field correlation 355 - distribution 56, 78 - effect transistor 487 - expansion 99 - strength, electric 19 - -, magnetic 19 -, longitudinal 89
INDEX
field, transverse 89 film lens 84 - prism 84 - wave 51,58 filter 112 -, tunable 158 focused wave 103 Fourier transform 334 Franz-Keldysh effect 453 frequency fluctuation 349 - modulation 341 - noise 353 - parameter 53 - shift 124 fundamental absorption 42 gain 232 - bandwidth product 426,448 - coefficient 249, 253 - -, differential 253, 305, 336 - guiding 323 - in quantum boxes 260 - in quantum wells 254, 258 - in quantum wires 260 - spectrum 249 -, temperature-dependent 261 gate leakage current 492, 503 Gaussian probability function 356 generation rate 399 - recombination noise 448 Golden Rule 242 graded index film 71 group velocity 91, 94 guard ring 433 Gunn effect 190 Hamilton operator 177, 237 HE wave 76 heat dissipation 470 height function 63 Helmholtz equation 23 Henry factor 343, 354 Hermite function 72 heterodyne detection 385, 410 - transmission 368 heterojunction 277 hole 11, 198
hole density 207 - gas, two-dimensional 279 - motion 198 -, heavy 190 -, light 192 impedance 27, 28 - transformation 366 impurity band 205, 212 - density 210 - ionization energy 275 - level 203 - photo conduction 443 -, shallow 205 index ellipsoid 127 - guiding 319 indicatrix 126 InGaAsP 15, 42, 45
533
injection of charge carriers 290, 293 integration, on silicon 506 -, optoelectronic 487 intensity 28 - noise 352 - profile in the laser resonator 318 interconnects, optical 507 interface deformation 62 - scattering 68 interference function 373 intraband relaxation 214, 252 - transition 42 intrinsic photo conduction 445 ionization 418 - coefficient 418 - field, classical 480 - for variable bandgap 434 - in superlattice structures 435 - ratio 426 isolator, optical 505 isotype heterojunction 296 Kerr effect 125, 459 Kramers-Kronig relation 22, 458 Kronig-Penney model 184 Lambert-Beer's law 231 Langevin force 346 Laplace operator 23, 24 large signal modulation 337
534
laser diode 303 - - modulator integration 504 - - with distributed feedback 360 - - with mushroom structure 322 - -, array 369 --, BH 319 - -, coupled 365 - -, CSP 321 --, DBR359 - -, DCPBH 320 - -, gain guided 325 - -, GRINSCH 380 - -, index guided 319 --, MCRW 321 - -, oxide stripe 323 - -, surface emitting 375 - -, tunable 368 - FET integration 490 - output power 315, 318, 328 lattice matching 12, 14 - parameter 3, 10 -, crystal 2 leakage current 300 level separation, noise related 497 lifetime, carrier density dependent 446 light-current characteristics 328 limit of dynamics 482 line broadening, homogeneous 329 - -, inhomogeneous 329 linewidth of the emission 357 local oscillator 410 loss, intrinsic 305, 314 majority carrier 290, 293 mass action law 211 -, effective 190 -, reduced 247 matrix element 244 - -, energy dependent 262 - -, estimation 250 Maxwell's equations 19 MESFET 487 micro cleaving 492 microresonator 476 Mie scattering 62 Miller indices 5
minority carrier 290, 294 mirror loss 340
INDEX
mixed compound semiconductor 1, 11 mobility 214, 281 mode 88,95 - conversion 66 - coupling 109, 114 - expansion 100 - power 102 - separation 306 modulation of laser diode 333 modulator with quantum well
structure 475 -, electrooptic 154 -, optically controlled 464 -, optoelectronic 453 -, two-dimensional 476, 483 monitor diode 491 multi-mode oscillation 339 multiplication factor 419, 422, 433 - -, optimal 431 - zone 423 nabla operator 19 neutral region 293, 294 Newton's equation 196 noise equivalent circuit 396 - factor of an FET 499 - in laser diode 343 - l/v 358, 501 - power spectrum 350, 388 - related level separation 497 normalization 98 occupation probability 207 Ohm's law 21 operator 176 orthogonality 97 orthonormal basis 100 oscillator, harmonic 43 oxide stripe laser diode 323 packing density 4 penetration depth 38, 400 periodic boundary condition 183, 200 - pn-structure 439 - potential 185 permeability 20
INDEX
perturbation polarization 114, 134, 136 - theory, time-dependent 239 -, scalar 117 phase matching 139 - modulation 95 - noise 353 - velocity 27, 93 photo conduction, dynamics 447 -, intrinsic 445 photo conductor 443 photo current 387 photodiode 396 photoluminescence 228 photon density 93 - -, stationary 312, 330 - lifetime 308, 329 - number fluctuation 344, 350 photons, rate equation for 308 pin-FET receiver 501 - SEED 505 pin-photo diode 398, 401, 402, 411 Planck's constant 9 - radiation law 229 plasma effect in modulator 461 - frequency 44 pn-junction 279, 285 -, with current flow 285 Pockels effect 125, 127 Poisson distribution 391, 409 - equation 282 polarization 43 potential at a pn-junction 283 - well of infinite depth 181 - -, rectangular 178 -, scalar 237 power spectrum of a noise signal 350,
388 - splitter 149 -, minimum detectable 407, 431 -, transported 80, 91 Poynting theorem 25 - vector 24, 25 preamplifier noise 501 principal axis system 126 propagation constant 26
535
pulse response, photo conductor 447 - -, photo current 402, 413 pumping current modulation 339 quantum box 223 - efficiency 397, 400, 413 - -, differential 316 - -, internal 316 - limit of dynamics 482 - - of optical detection 409, 411 - noise limit 500 - well 218 - - laser diode 378 - wire 222 - -laser 382 quasi-Fermi distribution 215 - energy 214, 217 - level at pn-junction 293 radiation characteristics 369 - loss 69, 313 - mode 49,60 radiative transition 237 random variable 390 rate equations 306 - - for several modes 329 - - with confinement factor 311 - - with noise 346 - -, multi-mode 329 - -, small signal approximation 333 Rayleigh scattering 62 receiver noise 496 - sensitivity 499 reciprocity theorem 96 - - with sources 115 recombination rate 233 rectangular waveguide 77, 81 reflection 32 - coefficient 33 - - of a filter 113 -law 35 reflector, dielectric 475 refraction law 35 refractive index 26, 45 - -, effective 50 relaxation oscillation 337, 341 residuallinewidth 358
536
resistor noise, thermal 393 resonance condition for modes 305 - frequency 335 resonator, coupled 365 ridge waveguide 84 RIN 352 Roosbroeck-Shockley relation 232, 248 saturation current density 293 - - of an FET 488 - drift velocity 402, 413, 418 - power 331 scattering by surface gratings 121 - by ultrasonic waves 123 - length of electrons 219 - of photons by phonons 124 Schottky barrier height 492, 503 - gate 487 - photo diode 416,502 Schrodinger equation 177 - -, time-dependent 177 - -, time-independent 178 screening 272 - length 270, 273 SEED 482 self control 482 semiconductor 1 -, degenerate 209 -, direct 13, 190 -, indirect 13, 193 -, intrinsic 207 sensitivity 499 Shockley-Read mechanism 216 shot noise 391, 406 - - limit 409, 411 - - - of a receiver 500 Si crystal 10 side mode power 331 - - saturation 331 - - suppression 331, 341, 342, 360 signal processing, parallel 470 signal-to-noise ratio 406 - - for avalanche diode 430 - - for photoconduction 450 solid state photomultiplier 437 source distribution 116
space charge region 280 spot radius, complex 325 squeezed state 409
INDEX
staircase avalanche photo diode 438 Stark effect 477 - -, optical 484 - -, quantum confined 480 stochastic process 388 strip waveguide 75 subband 219 substrate mode 49,59 superinjection 301 superlattice photo detector 437 supermode 164, 170, 370 surface emitter 375 - state density 493 synchronization 119 taper 105 TE wave 43 TE-TM mode conversion 125, 133, 137 temperature, characteristic 382 thermal generation of carriers 414 threshold carrier density 314 - condition for laser oscillation 305 - current analysis 377 - - density 314 - gain 305 - - with confinement factor 313 - voltage of an FET 488 time constant 404, 413, 418 TM wave 39 total internal reflection 36, 41 transconductance 488, 496 transfer characteristics 335 - function 403 - - for photoconduction 447 -length 143 transimpedance amplifier 501 transit time 402, 413, 418, 448 transition rate 225 - -, modal 307 transmission 32 - coefficient 33 - control, optical 467 - modulator 466
INDEX
transmission modulator, dynamics 469 transparency density 253, 305 trap process 216 travelling wave modulator 162 tunnel current 415 tunneling of electrons 453 uncertainty relation 176,482 unit cell 3 vacuum level 277 valence band 11, 190 variance of a variable 176 variation theorem 92 vector potential 237 Vegard's law 12, 14 vertical cavity laser diode 375
video detection 409 wave equation 22 - function 175 - guiding 49 -, evanescent 65, 89 -, plane 26 waveguide 49 - angle 104 - bend 104 - transition 102 -, strip loaded 86 waveguiding layer 379 Wiener-Chintchin theorem 351 work function 277 zincblende lattice 6
537
