Carrier mobility is one of the most fundamental parameters in semiconductor device modeling, and many mobility models have already been reported. Especially for numerical device simulators, many local models which are functions of impurity concentration and electric field at each local point have been studied. However, concerning their dependence on impurity concentration including carrier screening effects, these models suffer parameter fitting procedure because of their empirical formulation. In such models, carrier screening effects to the Coulomb potential of ionized impurity are not sufficiently considered, although we can find some models which treat the effects as only a small perturbation term. According to the simple theory of Brooks and Herring, carrier screening effects should be included in strong combination with impurity concentration terms and cannot be treated as additional perturbations. Although Brooks-Herring theory is successful, it also suffers from overestimation of the mobility values at concentration higher than 1018 cm-3 which causes some other complicated phenomena. Therefore there have been no models which directly use Brooks-Herring formula. But it is true that such screening effects should be considered when carrier concentration differs from impurity concentration as in the inversion layers of MOSFETs. We have developed a new mobility model for its dependence of impurity and carrier concentration based on the theory of Brooks-Herring. Brooks-Herring theory is based on simple physics of screened Coulomb potential, and therefore makes the model to include effects of free carriers without an artifitial formula. For high doping regime, an additional term has been introduced in Brooks-Herring formula to correct the high doping effects. Except for this term, the model should be most appropriate for including the carrier screening effects upto the concentration of 1018 cm-3. The new model is implimented in a device simulator, and is applied to the evaluation of MOSFETs especially for the universal curves of inversion layer mobility. Moreoever, the applications to the depletion-type MOSFET confirm the validity of the screening effects. The purpose of this paper is to propose the new mobility model and to show its validity through these applications to MOSFETs.

A new mobility model dependent upon electron concentration is presented for studying the screening effect on ionized impurity scattering. By coupling this model with the drift-diffusion and Hartree models, the effects of self-consistent and quasi-equilibrium screening on carrier transport in heavily doped systems are revealed for first time. The transport mechanism is found to be dominated by the electron-concentration-dependent mobility, and transconductance is shown to be determined by effective mobility and changes from degraded to enhanced characteristics with electron concentration modulation.