A study has been made of how the growth temperature affects the electron mobility in InAlAs/InGaAs transistor structures lattice-matched with InP substrates. The structures were grown by molecular beam epitaxy without changes in the deposition conditions during the growth. It was found that the optimum growth temperature, corresponding to the highest mobility measured at room temperature, is about 540 degrees C, well above the temperature 500 degrees C, which is ordinarily used for these materials. The increase in mobility with increasing deposition temperature stems from an improvement in the quality of the InAlAs, while the segregation of In during the growth of InGaAs has no significant effect on the tendencies for the mobility to change. The point corresponding to the maximum mobility agrees well with the temperature at which intense desorption of In begins during the growth of the InGaAs. Accordingly, the decrease in mobility with a further increase in the growth temperature is probably due to a decrease in the In content in the channel. The results found show that high mobilities [up to 9800 cm(2)/(V . s) at a 2D-electron concentration of 2.9 X 10(12) cm(-2)] can be achieved by optimizing the growth temperature in device structures without changes in the deposition conditions during the growth. (C) 1995 American Institute of Physics.