Polarizability of Donors in Polar Semiconductors. Effect of a Weak Magnetic Field

Abstract

The electrical pohrizability t.cnsor of shallow donors in polar semiconductors is calculated in the presence of a wcak rnagnctic field. A variational t.rcatment of the donor is developed in the framework of the effective-mass theory, including the effects of interaction between the charge carriers and the longitudinal-optical (LO) phonons within the static approximation. The effective-mass Hamiltoriian of the donor a.llows for central-cell corrections by means of a phenomenological impurity potent.ia.1. The results are compmcd with previous theoretical work and experiment. in the cam of donor impurities in Si. I t is shown t.hat the donor polarizability depends strongly on the form chosen for the model impurity potential and undergoes a 30 to 50% dccrcase due to the electron-(LO)phonon i n k a c t i o n in the CBSC of impurities in 111-V and 11-VI compounds, respectively.Der elekt.rische Polarisa,tionstcnsor fhchcr Ilonatorcn in polaren Hableitern wird fur den Pall schwacher Msgnetfelder bercchnet. Ein Variationsverfahrcn fiir dcn Donator wird unter Benutznng der Effcktivmassentheoric cntwickelt, wobei die Wechselwirkung zwischen dcn geladcncn 'l'eilchen nnd den longitudinalen-optisehcn (LO)-Phononen einbegriffcn ist und die statischo Niiherung bcnutzt wird. Der Effektivmassen-Hamiltonoperator ent.halt ein phanomenologisches Potential, welchcs den ,,central cell"-Effekt bcrucksichtigt. Die Ergebiiisse werden mit vorhcrgehcnden theorctischen Hcrcchnungcn und Expcrimenten im Fallc von Donatoren in Si verglichen. Hs mird bewiescn, daS die Polarisierbarlrcit wesent.lich von der Form des Storstellenpotentials abhangt und cine Verminderung yon 30 bis 50% durch die Elektron-(L0)I'hononen-Wcchselwirkung im Falle der 111-V-bcziehungsweise 11-Vl-Halbleitcrn erfahrt.

Shallow Donor Binding Energies in Semiconductors in a Magnetic Field

“…The polarizability of the donors in polar. seniiconductors in a magnetic field has been computed in [6]. These authors conclude that the choice of the model potential is important and the contribution from electron-lattice coupling is large (30 to 50%).…”

Polaron and Finite-Barrier Effects on Polarizability of Shallow Donors in Quantum Well Wires

“…The results are presented in reduced atomic units (a.u*) which correspond to a length unit of the e¡ective Bohr radius a* and an energy of the e¡ective Rydberg R*. We have considered the case of ZnSe/ZnCdTe QWW structure, we have used: m à 0:16m e and e 0 9:42 [23] (R à 24:53 meV, a à 31:15 Ð). For the comparison with the literature, we choose the case of GaAs/GaAlAs QWW which the parameters used are: m à 0:067m e and e 0 12:5 [3] (R à 5:83 meV and a à 98:7 Ð).…”

“…A comparison with our previous work [1] (In¢nite-barrier case) and the numerical results and discussions are presented in Section 3. For application, we will use QWW made out of ZnSe (ZnSe/ZnCdSe) a 0 0:448 [23] and a QWW made of GaAs a 0 0:067 (GaAs/GaAlAs) [13] for comparison with the literature.…”

Polaron and Form Effects on the Polarizabilities of Shallow Donors in Quantum Well Wires

“…The polarizability values are calculated using the following parameters: m* 0.16m e , e 0 9.42 suitable for wires made out of ZnSe [23]. The effective Rydberg Ry * 24X53 meV and the effective Bohr radius a * 31X15 # e define the relevant energy and length scale, respectively.…”

“…This paper is organized as follows: In Section 2 we present the general formalism, we deduce the expressions for the donor binding energy and polarizability of shallow polaron donors as a function of the wire width. The numerical results and discussions are presented in Section 3 with an application to a wire made out of ZnSe (a 0 0.448) [23].…”