The assumptions of conventional effectivemass theory, especially the one of continuity of the envelope function a t an abrupt interface, are reviewed aitically so lhat the need for a fresh approach bemmes apparenL A new envelope-function melhod, developed ty h e author over the past few years, is reviewed. This new method is based on both a generalization and a novel application to microstructures of the htlinger-Kohn envelope-hnction expansion. The differences between lhis new method and h e conventional envelope-function method are emphasized. An altemative derivation of the new envelope-function equations, which are exact, to that already published is provided. A new and improved derivation of lhe author's effective-mass equation is given, in which the differences in lhe wnecenlre eigenstates of the constituent nyslals are laken into account. This derivation h valid for abrupt interfaces and relies only on the slow variation of lhe envelope fundion(s). Unambiguous bundary conditions lhat automatically " e w e probabilily current are derived, The muse of the kinks i n the conventional effective-mass envelope function, at abrupt effective-mass changes, i s identified. The formal resuits are mtensively illustrated with a numerical example. A plot of lhe author's m e t envelope funclion shows that i t has a soft kink at an effective-mass discontinuity. This soft kink is also seen in the aact wavefunction. I t is this feature which is approximated in mnventional models by the effective-mass-related kink. The reasons why conventional effective-mass theory works so well tecome clear. The distinction between Luttinger-Kohn and WnnierSlaler envelope functions is highlighted. It is demonstrated that the author's generalization and new application of the Luttinger-Kohn envelope-function expansion can also be carried out tor the WnnierSlater case. However, it is found that the derivation of effective-mass equations for the generalized MnnierSlater envelope functions is not as straightfomard as for the Lutlinger-Kohn case. Some problems uncovered recently in y i n g to extend effectivemass lheoly lo the non-parabolic regime are resolved.

We acknowledge support of this work by the DFG within SFB 287.

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Optical fibers have revolutionized the telecommunications industry to such an extent that the network capacity available today was unthinkable 20 years ago. Even so, with the advent of the datawave, and the exponential increase of network traffic predicted to continue indefinitely, the generation of bandwidth remains a challenge. One of the major limitations to the implementation of future high-capacity, ultra-broadband optical networks is the expansion of the fiber bandwidth beyond that available from the current state-of-the-art signal amplification device-the erbium-doped fiber amplifier (EDFA). Although there is currently a large effort to expand the flat-gain bandwidth of the EDFA, most of these efforts involve sophisticated engineering, exotic glass fibers, or multicomponent cascaded systems. In a radically different approach, we are attempting to use the unique properties of semiconductor nanocrystals, or quantum dots, as "designer atoms" in order to produce an ultra-broadband optical amplifier with complete coverage of the telecommunications wavelengths. In this paper we review the synthesis of thiol-stabilized mercury chalcogenide nanocrystals via an aqueous colloidal route, which demonstrate extremely intense photoluminescence all the way across the spectral region of interest, i.e., from 1000 to over 1700 nm.

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