Linear non-hysteretic gating of a very high density 2DEG in an undoped   metal-semiconductor-metal sandwich structure
  Modulation doped GaAs-AlGaAs quantum well based structures are usually used to achieve very high mobility 2-dimensional electron (or hole) gases. Usually high mobilities ($>10^{7}{\rm{cm}^{2}\rm{V}^{-1}\rm{s}^{-1}}$) are achieved at high densities. A loss of linear gateability is often associated with the highest mobilites, on account of a some residual hopping or parallel conduction in the doped regions. We have developed a method of using fully undoped GaAs-AlGaAs quantum wells, where densities $\approx{6\times10^{11}\rm{cm}^{-2}}$ can be achieved while maintaining fully linear and non-hysteretic gateability. We use these devices to understand the possible mobility limiting mechanisms at very high densities. 
K. Das Gupta, A. F. Croxall, W.Y. Mak, H. E. Beere, C. A. Nicoll, I.   Farrer, F. Sfigakis, and D. A. Ritchie
cond-mat.mes-hall cond-mat.str-el