A transistor structure includes a first undoped, silicon-containing channel layer, a buried germanium channel, and a second undoped, silicon-containing channel layer. The first and second channel layers may contain SiGe or, alternatively, Si only. Another transistor structure includes a first channel layer, a buried germanium channel, and a second, undoped channel layer containing silicon and germanium over the buried channel. A further transistor structure includes a first channel layer, a buried germanium channel, and a second channel layer containing compositionally graded SiGe over the buried channel. A still further transistor structure includes a first silicon layer, an undoped or homogeneously doped buried channel containing silicon and germanium, and a second silicon layer over the buried channel.