M. Altarelli

Core excitons in the soft X-ray region: Solid argon

Abstract A theoretical calculation of core excitons is performed for the LII,III soft X-ray threshold of solid argon at ∼ 245 eV. The binding energies and the relative transition amplitudes for the lowest allowed exciton states are computed by formulating the problem in terms of Wannier functions and solving the resulting integral equation in the one-site approximation. The results obtained allow to locate the onset of interband transitions at an energy a few eV above previous theoretical determinations. Therefore, sharp structure previously interpreted in terms of conduction band density of states is attributed to discrete excitonic transitions, as strongly suggested by the close analogy with the atomic absorption spectrum. A comparison with the fundamental excitonic absorption in the vacuum ultra violet region is carried out in terms of the ratio of the electron-hole exchange interaction to the spin-orbit splitting of the hole states.

Far-infrared absorption by excitons in silicon☆

Abstract We report on the first observation of 1s to 2p absorption by excitons in pure silicon. A group of strong lines at 10.2, 11.4 and 12.0 meV is observed along with a continuum extending to higher frequency. A theoretical model for the excitonic absorption accounts well for the observed structure.

Camel's back excitons in GaP

Abstract The influence of the recently proposed camels back structure of the GaP conduction band edge on the exciton spectrum is investigated theoretically. The results are in good agreement with differential absorption data and strongly support a camels back structure, with a 4 meV central hump. The computed exciton binding energy is 18.5 meV, and when combined with recent experimental data, indicates a binding of about 32 meV for the electron-hole liquid.

A new method in the theory of indirect excitons in semiconductors

Abstract A new method for the analysis of indirect excitons in semiconductors is introduced. This approach yields a physical interpretation of the various terms present in the Hamiltonian, and allows an accurate evaluation of the energies of the exciton levels. For Ge, a simpler but equally accurate “axial model” is introduced, which is very suitable for investigating the exciton dispersion, optical lineshapes, and the effect of exciton—exciton interactions and external fields.

Unified theory of exciton and impurity states in semiconductors for an arbitrary magnetic field

Abstract We present a theory for exciton and impurity states in semiconductors, which is valid for all values of the magnetic field. The formalism is based on the introduction of tensor operators and includes the effect of the exchange interaction. Accurate solutions forthe ground state are presented and compared with the results of a previous adiabatic method, which is valid only for very large fields. We show that the present analysis is superior to all previously used methods for all values of the magnetic field.

The direct-indirect transition in In1−xGaxP

Abstract Data (300°K) are presented on laser quality liquid phase epitaxial (LPE) In 1− x Ga x P , grown on lattice-matched {100} GaAs 1− y P y substrates, confirming a theoretical account presented by Altarelli that the direct-indirect transition occurs at x c ≈ 0.74. Photoluminescence data show that crystals ranging in composition from x = 0.52 to x = 0.70, all of which operate as lasers at 77°K, exhibit the same decrease in luminescence intensity from 77 to 300°K, indicating that x c > 0.70 at 300°K. The steep I–V characteristics (at 77 and 300°K) of Zn-diffused diodes prepared on crystals of composition x = 0.70 in contrast to the significantly more resistive behavior of x = 0.74 crystals is consistent also with the assignment x c > 0.70. The Λ band edge (300°K), determined by the photoluminescence data points, intersects the X band edge (300°K) at x c ≈ 0.74. A discussion, in terms of the problems inherent in In 1− x Ga x P crystals growth and quality, is presented to reconcile the difference in the crossover value ( x c ≈ 0.74) reported here on laser crystals and the lower value ( x c ≈ 0.63) of some other recent reports.

Effect of disorder on direct and indirect band gaps of semiconductor alloys

Abstract A simple analysis of the effect of disorder on different band edges of ternary III–V alloys is performed in terms of the symmetry properties of Bloch functions. The effect of disorder on the X 1 conduction band minimum is shown to be strongly dependent on the valence of the alloyed element, in agreement with available experimental data. The implications for indirect gaps and for the calculations of crossover compositions are briefly discussed.

Evaluation of valence band parameters in GaAs from magneto-optical data

Abstract Magneto-optical data for GaAs exciton states in a high magnetic field (115–215 kG) are reported. A recently developed adiabatic theory, which takes into account the degeneracy and anisotropy of the valence bands, is used as a best fitting procedure to provide reliable band parameters. The Luttinger parameter κ is determined to be equal to 1.1.

Pressure experiment determination of the direct-indirect transition in the quarternary In1−xGaxP1−zAsz☆

Abstract Spontaneous and laser emission from In1-xGaxP1-zAsz double heterojunction diodes near the direct-indirect crossover (EΓ = EX, x ≡ xc, z ≡ zc) are studied at 77°K as a function of hydrostatic pressure up to 6 kbar. The pressure coefficients of the spontaneous emission peaks and of the laser modes are ∼- 10.5 × 10-6 eV/bar which is characteristics of the Γ band edge in III–V semiconductors. Laser threshold current is found to rise rapidly as pressure is applied owing to the decreasing Γ-X separation and the resultant carrier transfer to the X minima. Experimental lower limits for the direct-indirect crossover at three points in the In1-xGaxP1-zAsz quaternary system are determined. These three points and the established crossover in GaAs1-yPy (yc ≈ 0.46, 77°K) give for the quaternary crossover (77°K) xc − 0.52zc = 0.72. and the value xc ≈ 0.72 for the limiting case of In1-xGaxP. Band edge bowing effects along the direct-indirect crossover in the In1-xGaxP1-zAsz system are discussed. The highest energy laser (77°K) for this quaternary system is estimated from pressure measurements to be ∼ 2.155 eV (5752 A).

On the splitting of the exciton ground state in silicon

Abstract The exciton ground state in silicon is calculated taking into accoun the effect of the split-off valence band. We show that this effect is very important. The anisotropy splitting of the ground state is found to be 0.32 meV, while a previous analysis, which neglected the split-off band, gave 0.46 meV. The new result is in good agreement with recent experimental data.