Theinstabilityofterahertz(THz)plasmawavesintwo-dimensional(2D)quantumelectrongasinananometerfieldeffecttransistor(FET)withasymmetricalboundaryconditionshasbeeninvestigated.WeanalyzeTHzplasmawavesoftwopartsofthe2Dquantumelectrongas:gatedandungatedregions.Theresultsshowthattheradiationfrequencyandtheincrement(radiationpower)in2Dungatedquantumelectrongasaremuchhigherthanthatin2Dgatedquantumelectrongas.Thequantumeffectsalwaysenhancetheradiationpowerandenlargetheregionofinstabilityinbothcases.Thisallowsustoconcludethat2Dquantumelectrongasinthetransistorchannelisimportantfortheemissionanddetectionprocessandbothgatedandungatedpartstakepartinthatprocess.