Study of the Si/ZnS Multilayer System for Optoelectronic Applications
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km(M + N) = 21, 2
where km is the location of the conduction band minimum of Si in units of 7r/ao (; 0.85, a0 being the bulk lattice constant), and I is an integer. This topological constraint ensures that the [001] and [001] minima (the (001) minima) appear at the superlattice zone center. 367 Mat. Res. Soc. Symp. Proc. Vol. 486 0 1998 Materials Research Society
However, they are not guaranteed to be the lowest minima as the other minima in the k" and ky directions (the (100) minima) do not get zone folded. An additional effect is quantum confinement. An approximate model is to treat the Si electrons in an infinite quantum well with the (001) effective mass as the confinement mass; for the (001) ((100)) valleys, this corresponds to m, (mt). Since mL >> mt, the confinement energy for the (001) valleys is less than for the (100) ones. While the above arguments also apply to the Si/Ge system, the favorable ordering of the valleys is reversed by strain (• 4.2 %) in structures normally considered. This complication due to strain is practically nonexistent for Si/ZnS (strain S0.4 in %); in fact, on a Si substrate, the strain is absent from the Si layer. Directness k-space is, therefore, easily achievable. For efficient radiative recombination, a directness of the transition in real space is also desired. The Si/Ge system is, for the most part, type II, whereby the holes are in the Ge layer and the electrons are in the Si layer. On the other hand, the large band gap of ZnS ensures that Si/ZnS is type I with both holes and electrons in the Si layer. Hence, the radiative recombination would occur mostly in the Si layer and the ZnS acts merely as a high barrier material. Indeed, the Si/ZnS system can be viewed as a generic system for other Si/high-barrier systems. We next consider the wavelength ranges accessible via interband and intersubband transitions. A rough idea can be obtained by examining the band alignment diagram (Fig. 1). The band gaps of Si and ZnS (at room temperature) are 1.12 eV and 3.68 eV, respectively. Si/ZnS
Si/Ge
X 3.7 eV
> 0.34tsm
r A
VBj
I< 1.55A•m
0.51 eV
I> 2.4tm 1.5 eV
83 > 0.83pm
Figure 1: Band edges of the Si/Ge and Si/ZnS systems. The valence band offset is obtained as 1.52 eV from recent measurements of the conduction band offset [6]. The band gaps of Si/ZnS superlattices should, therefore, be bigger than 1.12 eV due to confinement; the corresponding wavelengths would be less than 1.1 Mm. In order to reach the 1.2-1.6/pm range, one would have to make use of intersubband transitions. The situation is simpler in the valence band where the single band offset of 1.5 eV offers a wavelength greater than 0.83 jim. This was, in fact, one of the original motivations to move out of the Si/Ge system since the valence band offset of the latter is much smaller. In the conduction band, the lowest energy valley is the A valley with a barrier height of 3.7eV; the accessible wavelength is thus > 0.34Ajm. Note, however, that the overlap with 368
the r valley (located in ZnS) would strongly influen
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