Gain Spectrum for the In₄Se₃Crystal with a Non-Standard Dispersion Law of Charge Carriers

Abstract

Based upon the ab initio band structure calculations results and the density of states function of the orthorhombic In4Se3 crystal as well as the experimental data concerning its radiative recombination, it was shown that the Bernard-Durafour condition is fulfilled for this crystal. The absorption coefficient α that exhibits a negative value in the given energy range and for the given concentrations of non-equilibrium charge carriers, was calculated. 71.20.Nr, 72.40.+w, 78.20.Ci 1. Crystalline structure and energy spectrum of the In 4 Se 3 crystalRecently, a growing interest to some layered indium selenides [1][2][3] has occurred due to their non-standard dispersion laws for charge carriers and the possibility to create InSe-In 4 Se 3 heterostructures [4]. The layered In 4 Se 3 semiconductor belongs to the orthorhombic system and its symmetry is described by the D 12 2h (P nnm) space group. It is a direct-band-gap material with the smallest energy gap in the Γ point of the Brillouin zone (BZ). The dispersion laws for electrons and holes exhibit a low--energy non-parabolicity due to the presence of the four--power terms of the wave vector k. A consequence of this fact is a peak-like density of states function [5]. These peculiarities were observed for the first time in calculations of the band structure of In 4 Se 3 crystal by the semiempirical pseudopotential method [6], confirmed both by the ab initio band structure calculations [1] in the framework of density functional theory (DFT), and experimentally [2,3]. Such a placement of the band extrema favors the radiative recombination of charge carriers, which is the subject of theoretical investigation of this paper. The experimental investigation on the radiative recombination of In 4 Se 3 were reported in [7]. In this case, a generation of charge carriers took place by means of the electron beam of the density j ∈ (0.2-5.0) A/cm 2 , with the energy of a single electron W ∈ (65-70) × 10 3 eV at T = 90 K, in the spontaneous and stimulated regimes. These experimental investigations were performed before the band structure of In 4 Se 3 has been investigated. Generation and recombination of charge carriers in the In 4 Se 3 crystalThe theory of emission and absorption of a two-level system can be applied to a semiconductor [8], when assumed that the number of transitions per time unit from the ground state 1, being a chosen energy level in the valence band, to an excited state 2 in the conduction band, can be given as: ν abs 12, where B 12 is the Einstein coefficient [9] describing a transition probability, f 1 , f 2 are the Fermi-Dirac distribution functions, g 1 , g 2 are the density of states functions for the considered levels in the valence and conduction bands, Z(E 12 ) is the density of photons. The number of transitions per time unit connected with a stimulated and spontaneous radiation can be described as: ν stim 21 where n is a refraction coefficient. , which implies the Bernard-Durafour condition:, where E f 2 and E f 1 are the quasi-Fermi levels of the no...

Structural Aspect of Formation of a Nanosystem of In/In$_{4}$Se$_{3}$ (100)

“…It is well known [5,9] that crystal structure of In 4 Se 3 is dominated by multivalent clusters of indium atoms in positions In1, In2, In3, i.e., (In3) 5+ bonded with selenium in the layer-packet (see Fig. 4, a) and elevated In atoms in position In4 (In + ions), which are very weakly connected to the rest of the atoms and form an infinite one-dimensional chain along c-axis direction [001].…”

Electronic structure and optical properties of the heterostructures on the basis of the In₄Se₃ and In₄Te₃ crystals

“…Нові дослідження для кристалів In4Se3 і In4Te3, які останнім часом з'являються у літературі, наприклад, виявлені унікальні термоелектричні властивості [1], явище оптичного підсилення [2], створення гетероструктур [3,4], і т.д., свідчать про надзвичайний інтерес до даних сполук як перспективних матеріалів для сучасної оптоелектроніки, наноелектроніки та термоелектрики. Особлива будова цих кристалів дозволяє отримувати в умовах надвисокого вакууму досконалі поверхні сколювання з борознистим рельєфом [5,6], завдяки чому розширюються їхні потенційні можливості для виготовлення приладів нанометрових розмірів.…”