Excitonic Effects in the Interband Absorption of Semiconductors

Abstract

Elliott's work on exciton effects a t the direct absorption edge is extended t o include other van Hove singularities and deviations from the effective mass approximation. The sum rule which replaces the /-sum rule in this case is derived. The Koster-Slater and Coulomb interactions are treated as limiting cases. Due t o the electron-hole interaction, the M, and Ml branch-points of c2 are enhanced and sharpened, whilst the M2 and M3 branchpoints are weakened and smoothed out. Only the M, points generate (quasi) discrete levels; no evidence for these is found near the Ml points. For a very prolate MI singularity, certain branch-points appear asymptotically below the critical energy. Die Elliott'sche Arbeit uber Exzitoneneffekte an der Absorptionskante fur direkte Vbergange wird in der Richtung erweitert, daR andere van Hove Singularitaten und Abweichungen von der Niiherung der effektiven Massen eingeschlossen werden. Die Summenregel, die in diesem Falle die f-Summenregel ersetzt, wird hergeleitet, und die Koster-Slaterund Coulomb-Wechselwirkung werden als Grenzfalle behandelt. Wegen der Elektron-Loch-Wechselwirkung werden die kritischen Punkte Mu und MI in ep starker und scharfer, wahrend die Punkte M 2 und M3 abgeschwacht und geglattet werden. Nur die M, Punkte erzeugen (quasi) diskrete Energieniveaus, fiir solche Niveaus wird bei den Ml Punkten kein Hinweis gefunden. Fiir eine sehr gestreckte MI Singularitllt erscheinen asymptotisch kritische Punkte unterhalb der kritischen Energie.

Synthesis of Ge1−xSnx alloys by ion implantation and pulsed laser melting: Towards a group IV direct bandgap material

“…In other words, the decreasing amplitude of these transitions is due to a reduction in the excitonic effect in the structure. Similarly, in other reports, 30,32,33 the authors concluded that the significant change in the transitions at E 1 and E 1 þ D 1 is the most characteristic of an excitonic-induced reduction in their vicinity. For the region around E 2 , because the nature of this transition is more complicated as it is assigned to different regions in the band structure (see Table II), it was not possible to conclude whether the decreased intensity of this transition is due to the reduction in the excitonic effect or not.…”

“…This technique has been used since the 1970s to study the band structure of semiconductors, [30][31][32][33][34] and, with an extended range of photon energy, it is capable of characterising optical transitions beyond the band edge. Based on these optical transitions, the electronic band structure of Ge 1Àx Sn x was studied.…”

Optical properties and electronic density of states

“…Such calc ulation is possible if one truncates the Coulomb interac tion between electron and hole Wannier pac ke ts to extend to a finite number of neighboring cells. The extre me and simplest case of a a·function (KosterSlater) interaction can be solved by hand [31,35] and gives around an MJ criti cal point the shapes of EI' and Ei s hown in figure 11: for an Mi critical point the KosterSlater interaction mixes the Mi one ·electron lin e shape with the Mi+ l • The hi gh energy side of the Ei peak becomes steeper , in agreement with fi gure 10. The line shape observed for th e E I-E, + ~I pea ks in the reflectivity spectru m is composed almost additively of th e Ei and EI' lin e s hape: a t th e energies of these peaks dR/dEi and dR/dEl' are almost equal.…”

“…The exciton interaction is responsible, at most , for small details concerning the observed line shapes. It is generally accepted [31,32] that the exciton interaction suppresses structure in the neighborhood of M3 critical points: the Coulomb attraction with negative reduced masses is equivalent to a repulsion with positive masses. Such a repulsion smooths out critical point structure: no M3 critical point has been conclusively identified in the experimental spectra.…”

“…The solution of the effective mass Experimental evidence for these effects is reported at Hamiltonian with non-positive-definite mass is made this conference in the paper by Kunz et al easier by the fact that the negative mass (along the A We shall now discuss the question of exciton effects direction) has a magnitude much larger (about ten above the fundamental edge of insulators and semicon-times) than the two equal positive masses. It is possible ductors with special emphasis on the zincblende fami-to use the adiabatic approximation [31], i. e., to solve iy. A, mentioned in ,ection 1 the ",0" featme, of the.c 25…”