Semiconductor nanomembrane (NM) is a thin-film semiconductor layer which can be released from its donor wafer. Typical thickness ranges from several tens of nanometer to hundreds nanometer. In recent years, the semiconductor NMs have been drawing more interest due to their unique material properties and versatile applications. One of the most popular NM is a Si NM released from Si-On-Insulator (SOI) using a hydrofluoric acid (HF) undercut process. Because a buried oxide layer (BOX, SiO2) has a large etching selectivity against the Si in HF, the Si NM can be easily detached from the SOI and transferred to any types of substrates using a Polydimethylsiloxane (PDMS) stamp. Several advantages that make it suitable for high performance electronic and optoelectronic devices are single crystallinity, high flexibility, reliable transfer methods, and compatibility with Si based fabrication techniques. Other types of NMs are Ge NM, GaAs NM, and GaN NM. In this thesis, novel electronic and optoelectronic applications, including tunable biaxial compressive strained Si NM, resonant tunneling diodes, Ge on insulator (GeOI), and flexible Ge NM metal-semiconductor-metal (MSM) photodiodes, are designed and implemented.