Calculation of the electron wave function in a graded-channel double-heterojunction modulation-doped field-effect transistor

Three double-heterojunction modulation-doped field-effect transistor structures with different channel composition are investigated theoretically. All of these transistors have an In(x)Ga(1-x)As channel sandwiched between two doped Al(0.3)Ga(0.7)As barriers with undoped spacer layers. In one of the structures, x varies from 0 from either heterojunction to 0.15 at the center of the channel quadratically; in the other two, constant values of x of 0 and 0.15 are used. The Poisson and Schroedinger equations are solved self-consistently for the electron wave function in all three cases. The results showed that the two-dimensional electron gas (2DEG) concentration in the channel of the quadratically graded structure is higher than the x = 0 one and slightly lower than the x = 0.15 one, and the mean distance of the 2DEG is closer to the center of the channel for this transistor than the other two. These two effects have important implications on the electron mobility in the channel.