Theory of Free‐Carrier Infrared Absorption in GaAs

Abstract

Free-carrier infrared absorption spectra in GaAs are calculated for carrier scattering on ionized impurities and phonons due to Coulomb, Frohlich, and deformation potential interaction. Starting from the Kubo formula and applying the diagram technique the interactions of electrons with electrons, phonons, and ionized impurities are taken into account in the random phase approximation (RPA). The obtained absorption spectra exhibit coupled plasmon-phonon peaks which collapse for vanishing electron-LO phonon interaction. By taking into account only plasmon and screening effects of the electron gas the calculated absorption spectra show plasmon bands in the case of carrier-ionized impurity scattering and both, a LO phonon emission edge and weak plasmon-LO phonon combination peaks in the case of carrier-LO phonon scattering. The scattering of electrons by acoustic phonons is not influenced by plasmons. The dependences of various carrier scattering mechanisms on frequency, temperature, and material parameters are determined for n-GaAs.Die Infrarotabsorptionsspektren freier Ladungstrager in Ga As werden fur Ladungstragerstreuung an ionisierten Storstellen und Phononen bei Berucksichtigung von Coulomb-, Frohlich-und Deformationspotentialwechselwirkung berechnet. Ausgehend von der Kubo-Formel werden unter Benutzung der Diagrammtechnik die Wechselwirkungen der Ladungstrager untereinander sowie mit Phononen und ionisierten Storstellen in der RPA-Naherung behandelt. Die erhaltenen Absorptionsspektren zeigen gekoppelte Plasmon-Phonon-Banden, die fur verschwindende Elektron-LOPhonon-Wechselwirkung zerfallen. Werden nur die Plasmon-und Abschirmeffekte des Elektronengases beriicksichtigt, zeigen die Absorptionsspektren im Fall der Ladungstragerstreuung an ionisierten Storstellen Plasmonbanden und im Fall der Ladungstragerstreuung an LO-Phononen sowohl eine LO-Phononenemissionskante als auch schwache Plasmon-Phonon-Kombinationsbanden. Die Streuung von Elektronen an akustischen Phononen wird durch Plasmonen nicht beeinflu&. Die Abhangigkeit der verschiedenen Ladungstragerstreumechanismen von der Frequenz, Temperatur und den Materialparametern wird fur n-GaAs bestimmt.

Effect of free-carrier absorption on the threshold current density of GaAs∕(Al,Ga)As quantum-cascade lasers

“…For the determination of the FCA coefficient ␣ FC ͑ , n͒, we have measured transmittance spectra at room temperature and at 77 K. In contrast to the reflectance spectra, the absorption coefficient is essentially determined by the imaginary part of the DF ⑀, i.e., Im͕⑀͖, which depends on the dominant scattering mechanism of the free carriers. For scattering of free carriers on acoustical (ac) and longitudinal optical phonons (op) as well as ionized impurities (imp), the following relation is approximately valid in the high-frequency limit, 4,5 i.e., ប Ͼ E F , where E F denotes the Fermi energy of the free carriers, and / ␥ ӷ 1…”

“…Using the values given for the coefficients c i in Ref. 5 and the values of n determined from the reflectance spectra, the absorption spectra of the n-type GaAs samples for n between 4 ϫ 10 16 and 4 ϫ 10 18 cm −3 and wave numbers between 800 and 1500 cm −1 can be well described by…”

Ionized‐Impurity‐Mediated Free‐Carrier Absorption in n‐GaAs Slabs

“…The conductivity of the system is calculated from (8) to (ll), (14), and (15). For that purpose, the current-current Green function n(t) is represented in the interaction picture with the interaction Hamiltonian H,i and a second-order perturbation expansion of the corresponding 8-matrix is carried out (see, e.g., [4]). The leading term of the resulting configuration-averaged impurity-potential correlation function is given bv where (...), denotes the configuration average and ni the impurity concentration.…”

“…to (26) together with (22), (5), (6), and (17) one obtains finally with A comparison with (20) yields our final result for the high-frequency conductivity of non-interacting electrons scattered on ionized impurities, I n the limit d -. co the +sum in (29) can be replaced by an q,-integral and one arrives a t the expression for the bulk conductivity as given in [4] (equation (34)).…”

“…This free-carrier absorption process was thoroughly investigated in n-GaAs both experimentally and theoretically [l to 41. The theoretical results suggest that in the presence of ionized-impurity scattering a remarkable structure occurs near the free-carrier plasma frequency which results from impuritymediated plasmon scattering [5,4]. By measuring both the transmission and reflectivity of n-GaAs slabs Szuszkiewicz et al [6] very recently delivered the first experimental evidence of such a plasmon peak.…”