Yonghe Zhang ionocovalent theory applications (15). I. Method
American Huilin Institute http://www.amhuilin.com/
Marcel et al.  established a relation between the Zhang Lewis acid strength of the dopant element and its scattering cross section:
LSn4+/LGe4+ ～ QGe4+/QSn4+
“In fact, we have recently shown(2,3,4) that the ideal doping cation must have a low electronegativity and a small ionic radius (r) associated with high effective nuclear charge (Z*). Indeed , such a cation having high value of Z*/r2 will polarize the electron cloud of oxygen 2p6 valence band more strongly, thereby screening its charge so as to weaken it as a scattering center. Moreover, a low electrronegativity for the dopant cation accounts for a weak interaction between the conduction band electrons and the dopant cation. Zhang  established an empirical equation relating the Lewis acid strength of the cation, L its electronegtativity, and the Z*/r2 value as
L = Z*/r2 – 7.7X + 8.0 (1)
Under such a circumstance, a high L value of the doping cation necessarily means a reduced scattering effect (and thereby a reduced scattering cross section) of the doping cation with regard to the conduction band electrons. Therefore, when the factor dominating the mobility is the scattering of electrons from the ionized donor centers, higher (lower) mobilities will occur for semiconductors doped with donor elements having higher (lower) L values [2,3,4]. Following this guideline, it appeared that the use of Ge4+ as a doping element in ITO (partially or totally substituted to Sn4+) could induce an enhancement in the mobility since 
L Ge4+ = 3.06 > L Sn4+ = 1.62 (2)
Consequently , we can obtain the following expression after simple transformation
Q Ge4+/Q Sn4+ = 0.55 (3)
It is interesting to note that for similarly heavily doped ITO and IGO (such as f and k) the value obtained above is close to the ratio calculated based on the Lewis acid strengths . Using relation (2) we get
L Sn4+/L Ge4+ = 0.53 (4)
This result confirms the expected close relation between the scattering cross section of the dopant ion and its Lewis acid strength. It appears that when the factor dominating the mobility is the scattering of electrons from the ionized donor centers, L roughly varies inversely as Q.
We note here that the concepts we have put forward also apply for other degenerate oxides having a predominant ionic-bond character as we have recently investigated.”
 C. Marcel, J. Salardenne, S. Y. Huuang, G. Campet, and J. Portier, Active and Passive Elec.Comp.1997, Vol. 19, 217-223
 S. J. Wen, G. Campet, J. Portier and J. Goodenough Mat.Science and Eng.,1992, B. 14, 115.
 G. Campet, S. D. Han, S. J.Wen, J. P. Manaud, J. Portier, Y. Xu and J. Salardenne, Mat. Sci. and Eng., B (accepted for publication 1995).
 S. J. Wen, doctoral thesis, University of Bordeaux I, 1992.
 Y. Zhang. Inorg. Chem., 1982, 21, 3886，3889.