Effective mass concept

The effective mass concept addressed here descends from the similarity with the acceleration of a body with mass m* and the acceleration experienced by a free electron (or hole) due to an external force. In general, the thereby obtained effective mass is a tensor and depends on the inverse curvature of the electron energetic states versus electron momentum dispersion (m*)_ij ~ (1/d2E/dk_idk_j). The free-carrier optical response of n- or p-type zincblende III-V materials, for instance, originates from the zincblende G_a-point conduction-band (single-valley, single-band) Bloch electrons, or valence-band holes (single-valley, multiple-band) near the respective Fermi-level location. In particular, m* provides the electron(hole)-momentum-dependent curvature of the conduction(valence) band(s), which are important physical material parameters, to which results from calculation schemes such as kp-methods have to be compared.

AlGaInP

AlGaInP is of highest current technological importance for high-power, high-luminescent solid state light emitters. The physical properties such as the effective mass parameters, phonon modes, and electrical transport properties are influenced by alloying, lattice-mismatch-induced strain and atomic ordering. AlGaInP can be grown lattice matched to GaAs using metal organic vapor phase deposition, and under certain growth conditions spontaneous long range ordering can be avoided. The G_a-point hole and electron effective mass parameters have not yet been determined experimentally for unstrained, disordered AlGaInP, and we have embarked to study these parameters by use of far-infrared magneto-optic ellipsometry. Mueller matrix spectra of a n-GaAs/n-AlGaInP/i-GaAs layer structure are shown in Fig. 2.
Fig. 2.

The spectra are differences between those taken at B = -3T and B = +3T, and reflect the MO-induced birefringence within the differently conductive Te-doped n-GaAs cap layer (approximately 50nm thick) and the n-AlGaInP layer (~1900nm). Modelling of the ellipsometric parameters provides N, m*, and m for both layers independently (T. Hofmann, M. Schubert, C. M. Herzinger, I. Pietzonka, Appl. Phys. Lett. 82, 3463 - 3465 (2003))
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InGaNAs and BGaInAs

The nitrogen and boron diluted InGaAs compounds are promising candidates for NIR absorber materials in multijunction-solar-cell or detector structures, and for active materials in NIR laser diodes. Due to the smaller covalent radii of nitrogen and boron compared with the substituted element, the lattice-mismatch induced strain in InGaAs, when grown on GaAs, can be partially or completely compensated allowing for growth of thick layers. Sufficient n- and p-type doping is a prerequisite for successful fabrication of p-n-junctions. Considerable effort was spent in the last few years concerning growth and optical properties of InGaNAs, less information on systematic doping studies are available, little is known about the physical material properties of BInGaAs. In essence, incorporation of nitrogen in InGaAs causes a dramatic red-shift of the band edge. This effect is explained by nitrogen-induced cluster states within the band gap and perturbed host states within the G_a-point conduction band edge. The perturbed host states overtake the band gap states upon increasing nitrogen concentration accompanied by drastic down shift of their energetic levels. Associated with these amalgamated band gap states is a strong increase of the G_a-point electron effective mass m*. In contrast, boron incorporation in InGaAs has only minor effects on the band edge. A slight increase of the band-gap-energy of BGaAs with increasing boron incorporation was reported. For BGaAs a relatively small and composition independent band gap bowing was predicted.

Fig. 3 depicts selected MO-mueller-matrix difference spectra for three different Si-doped n-type BInGaAs layers deposited by MOCVD on undoped GaAs, for varying silane pressures. With increasing carrier concentration N, the effective mass reduces, and is much larger than expected for unstrained InGaAs (T. Hofmann, G. Leibiger, N. Ashkenov, V. Gottschalch, M. Schubert, Strong increase of the electron effective mass in GaAs incorporating boron and indium, submitted for publication in Phys. Rev.).

Fig. 3.

Collaborators: Osram Opto Semiconductors GmbH Regensburg (Dr. Ines Pietzonka, Dr. Klaus Streubel), Faculty of Chemistry and Mineralogy, University Leipzig (Dr. Volker Gottschalch, Dr. Gunnar Leibiger), University of Nebraska-Lincoln, U.S.A. ( Prof. Dr. J.A. Woollam)

Funding: Deutsche Forschungsgemeinschaft (SCHUH 1338/3-1)