One of the most important parameters for the design and analysis of heterojunction and QW electronic and optoelectronic devices is the heterojunction band offset. The band offset is a consequence of the difference between the band-gap energies of two semiconductors. As shown in Figure 9.1, the energy difference is distributed between a CB offset DE c and a VB offset DE v . In a type I (straddling lineup), we obtainwhile for type II (broken-gap and staggered lineups) the relationship is given bywhere DE g ¼ jE g1 À E g2 j is the band-gap energy difference.Since the temperature variations of the band-gap energies are very similar among various semiconductors [1], the band offsets and offset ratio can usually be assumed to be independent of temperature.
Group-IV Semiconductor Heterostructure System
(a) CSi/SiThe C x Si 1Àx /Si heterostructure shows a biaxial tensile strain in the alloy layer. The biaxial strain or stress in the coherently strained QW layers splits the LH and HH bands so that the LH band is highest in C x Si 1Àx layer. Similarly, for C x Si 1Àx layers with smaller x compositions, the lowest CB is at the X (D) band. Brunner et al.[2] measured near-band-edge emission from pseudomorphic C x Si 1Àx /Si QW structures with x up to $2 at%. They found a linear decrease in the PL emission peak with increasing x, which is about 30% larger than the expected band-gap reduction induced by strain. This might indicate that incorporation of C reduces the intrinsic band-gap energy. The trend for decreasing C x Si 1Àx band-gap energy was also proposed by detailed binding calculations [3].The band-offset values for C x Si 1Àx /Si heterostructure have been determined experimentally by several authors [4,5]. Houghton et al.[4] confirmed a type-I alignment in C x Si 1Àx /Si with x ¼ 0.5 À 1.7 at% and also observed an elastic-strain-induced transition from type I to type II in
Properties of Semiconductor Alloys: Group-IV, III-V and II-VI Semiconductors Sadao AdachiC x Si 1Àx /Si QWs. The band-offset ratio obtained by these authors is DE c : DE v ¼ 65 : 35 with E g (Si) ! E g (C x Si 1Àx ). Williams et al. [5] also obtained a band-offset ratio of about 70 : 30 for x ¼ 0.5 À 1.7 at%. The corresponding band lineup is shown schematically in Figure 9.2(a). An ab initio calculation confirms the offset ratio of 70 : 30 [6].
(b) SiGe/SiPrevious studies on the band alignment of the Si x Ge 1Àx /Si heterostructure suggest type-I [7,8] or type-II behavior [9-12]. By employing a wafer bending technique, Thewalt et al. [11] observed both type-I and type-II behaviors respectively, in PL of an UHV-CVD-grown Si 0.7 Ge 0.3 /Si(100) QW at high and low laser powers. They concluded that a determination of type-I alignment [7,8] is a result of the band-bending effects due to high excitation. More recently, Cheng et al. [12] made PL measurements on UHV-CVD-grown and MBE-grown Si x Ge 1Àx /Si MQWs and concluded that the band alignment was type II with DE c ¼ 0.3DE g and DE v ¼ 1.3DE g , as shown in Figure 9.2(b). (c) CSiGe/Si Patel et al. [18] o...