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All important theories of impurity resistivity in three dimensions each give one of two results. All results are obtained without any implicit inclusion of electron-electron scattering. The electron-electron scattering has an indirect effect on the impurity resistivity in that it affects the distribution function for the carriers. Result number one is found in the limit of no electron-electron scattering while the second result is found from theories where the basic assumption is that the electrons are thermalized in their centre-of-mass system, i.e. very strong electron-electron scattering. Thus the two results can be viewed as the upper and lower limits of the result of a more elaborate theory including electron-electron scattering. In the present work the authors study the corresponding upper and lower limits for impurity scattering in a two-dimensional system. Numerical results for general temperatures are presented for delta -doped GaAs. Analytical expressions are given for the low- and high-temperature limits of the resistivity.

All important theories of impurity resistivity each give one of two results. These two results coincide for zero temperature but differ for higher temperatures. The electron-electron scattering does not give a direct contribution to the resistivity. However, it has a indirect effect. It affects the occupation numbers of the electron states and thereby modifies the impurity scattering. The two results discussed are both obtained in the absence of explicit electron-electron scattering. The solution of the Boltzmann equation in absence of electron-electron scattering gives one of two results. In the limit of strong electron-electron scattering the second result is obtained; strong electron-electron interaction leads to full thermalisation in the centre-of-mass system of the carriers. Thus the two results are the extreme limits of the results from the Boltzmann equation for varying strength of the electron-electron scattering. The authors make a realistic estimate of the electron-electron scattering-rate and calculate the Boltzmann result for doped GaAs.

For most theories of impurity resistivity the lowest-order results are the same for zero temperature, but for finite temperatures there are two different results. The fact that the Boltzmann results and the results from force-balance type theories disagree for finite temperatures has recently led to increased theoretical activity. In the present work the authors study how the newly proposed generalized Drude approach of Sernelius (1989) and the dynamical theory of Farvacque (1989) compare with other theories. They use the full temperature-dependent random-phase approximation screening in their numerical calculations, but also present results with the generalized temperature-dependent Thomas-Fermi screening. The authors furthermore give some analytical results where this is possible. They show that inclusion of electron-electron scattering in the solution to the Boltzmann equation brings the result closer to that from the force-balance type theories; very strong electron-electron scattering results in perfect agreement. Numerical results are presented for doped GaAs.