Fitting of Diverging Thermoelectric Power in a Strongly Interacting 2D Electron System of Si-MOSFETs

The diverging-effective mass (DEM) in a metallic system is evidence of strong correlation between fermions in strongly correlated systems. The identification of the DEM still remains to be revealed The effective mass, m*$=$m$_{\mathrm{o}}$/(1-$\rho^{4})$ [1] where $\rho $ is band filling helps clarify the diverging thermoelectric power, S, measured in inhomogeneous Si-MOSFET systems [2]. As a carrier density n$_{\mathrm{s}}$ decreases, S increases rapidly This is regarded as the metal-insulator transition (MIT) near n$_{\mathrm{c}}\approx $79x10$^{-1}$cm$^{-2}$, where n$_{\mathrm{c}}$ is about 0.02{\%} to n$_{\mathrm{Si}}\approx $3.4x10$^{-14}$cm$^{-2}$ in Si. This can be solved in assuming that $\rho =$n$_{\mathrm{c}}$/n$_{\mathrm{s}}$ increases as n$_{\mathrm{s}}$ decreases. n$_{\mathrm{c}}$ is an excited(doped) carrier density in the semiconductor induced by gate and can be also regarded as a metallic carrier density, that is, n$_{\mathrm{c}}\equiv $n$_{\mathrm{seminon}}=$n$_{\mathrm{metal}}$. n$_{\mathrm{s}}$ is given as n$_{\mathrm{tot}}\equiv $n$_{\mathrm{s}}=$n$_{\mathrm{c}}+$n$_{\mathrm{seminon}}$ where n$_{\mathrm{seminon}}$ is a carrier density in a nonmetallic phase. The carrier density measured by Hall effect is the sum of carriers both induced by gate field and generated by MIT. Moreover, a larger metallic phase is not made due to a conducting path in the field-effect structure after a metallic phase is formed. Thus, increasing n$_{\mathrm{s}}$ indicates increasing n$_{\mathrm{non}}$; this corresponds to an over-doping to increase inhomogeneity. It's fitting is given from S$=(\alpha \pi ^{3}$k$^{2}_{\mathrm{B}}$T/3e)(1/E$_{\mathrm{F}})$ $=(\alpha $8$\pi ^{3}$k$^{2}_{\mathrm{B}}$T/3h$^{2})$(m*/e*n$_{\mathrm{c}})$ $=$S$_{\mathrm{o}}$(1/$\rho )$(1/(1-$\rho^{\mathrm{4}}))$, where e*$=\rho $e [1], $\rho =$n$_{\mathrm{c}}$/n$_{\mathrm{s}}$, T$=$0.8K, m*$=$m$_{\mathrm{o}}$/(1-$\rho^{4})$ [1], $\alpha =$0.6, and S$_{\mathrm{o}}=(\alpha $8$\pi ^{3}$k$^{2}_{\mathrm{B}}$T/3h$^{2})$(m$_{\mathrm{o}}$/en$_{\mathrm{c}})$ $\approx $12.36 are used. The data S [2] are closely fitted by m* [1] Physica C 341-348(2000)259. [2] Phys. Rev. Lett. 109 (2012) 096405.