Consideration of doping profiles in MOSFET mobility modeling

Abstract

I I53 -ANALYTICAL 0 B.E.M. E h. . i 8 eo Distance across chip (cm.) Fig. 5. Thermal profile over the chip surface. The chip and package lateral dimensions are the same: 50 mil X 50 mil.using both the BEM and the corresponding analytical solutions. It was shown that the agreement between BEM and the analytical solutions is excellent. The most appealing feature of BEM is the simplicity and ease of data preparation coupled with the fact that it admits discontinuous shape functions for its (boundary) elements. This provides the engineer an invaluable tool for determining the regions in the device model where the mesh needs further refinement. As to the accuracy of the method, it must be pointed out that the method models the boundary value problem exactly within the domain. Errors are introduced only because we are not able to perform the integrations in closed form but must resort to brute force numerical techniques.

Calculation of the average interface field in inversion layers using zero-temperature Green’s function formalism

“…Again, the values for this parameter are found to be model dependent. Krustick and White 43 have found such behavior in their experimental studies.…”

1/fγ DRAIN CURRENT NOISE MODEL IN ULTRATHIN OXIDE MOSFETS

“…where W is the effective channel width, µ n (y) is the electron mobility in the surface inversion layer along the channel direction y, Q n (y) is the electron charge density per unit area, V(y) is the potential distribution along the channel, V gs ' is the internal gate-source voltage, V ds ' is the internal drain-source voltage, V FB is the flat band voltage, ψ s is the surface inversion potential, C ox is the gate oxide capacitance per unit area, ζ is a bulk charge parameter which describes the dependence of the effective field on the doping profile [15], Q b (y) is the silicon bulk charge, N sub is the substrate doping density, n i is the intrinsic carrier density, v th =kT/q is the thermal voltage, and q is the electron charge. Putting (9d) into (9c) and expanding the threshold voltage around V ds ' = 0, we obtain …”

“…The effective mobility µ n,eff in ultrathin oxide MOSFETs is described by [12] ( ) ( ) 2 (15) where k bulk = 0.5k ' bulk , α 1 = α 0 + 2Rα 1 µ n0 C ox (W/L), and α 2 are the quadratic degradation parameters. The ratio R 0 = δ∆Q n / δ∆Q T depends on the bias and on the spatial location of the trapping center within the oxide layer and is given by [17].…”

“…Finally, the parasitic resistance R and the mobility degradation parameter α 0 can be obtained from plots of α 0 vs V gs -V T0 for several values of V ds . Figure 2 (d) is plotted substituting the extracted parameters into (15). By plotting the constant values in high gate voltage regions as a function of V ds and applying a least squares fit, R = 6 Ω and α 0 = 0.01 V -1 are obtained.…”

Experimental determination of the effective mobility in NMOSFETs: a comparative study

“…Usually, as per the original work of Sabnis and Clemens [14], the mobility is plotted versus an eective electric ®eld instead of a surface electric ®eld, provided that the former is the mean electric ®eld that electrons see in the channel [15,16]. However, this electric ®eld is not always accurately calculated, which could lead to a slightly dierent functional dependence of the eective mobility on it.…”