Hosono: Mobility from a Curve

Read the actual measurement distinctions

The 2004 abstract reports a film Hall mobility separately from transistor saturation mobilities.

The 2010 technical discussion explains saturation-style extraction from square-root drain current versus gate voltage. It warns that drain-bias conditions and residual nonlinearity affect the parameters deduced from a fit.

This is a physical measurement question, not a contest between isolated headline numbers. A material film and a complete transistor are different objects; a fitted parameter is also conditional on the representation used.

Sources for this section: [1] · [2]

Original curve and two fitting windows

Invent gate voltages V=[1,2,3,4,5] volts and corresponding y=√I values [0,1,2,3.2,4.4] in √µA. Stipulate an appropriate saturation-style bias and fixed geometry for this purely numerical fixture. Fit a straight line through V=1 and 3, then a separate line through V=3 and 5.

For each fit, find slope m and the voltage-axis intercept V₀. Define an original dimensionless proxy M=(m/m₀)², where m₀=1 √µA/V. Compare the proxies. This normalization is supplied by the exercise; it is not a calibrated mobility in cm²/(V s) and is not a reconstruction of a historical transistor.

Sources for this section: [2]

Reference answer: the window matters

The first line has m=(2−0)/(3−1)=1 √µA/V and V₀=1 V. The second has m=(4.4−2)/(5−3)=1.2 √µA/V. Using y=m(V−V₀) at V=3 gives V₀=3−2/1.2=4/3 V.

The proxies are 1 and 1.44. The second is 44% larger, although the invented points belong to the same supplied curve. A single global straight line cannot pass through every point: the high-window line predicts y=0.8 at V=2, but the supplied value is 1.

Changing the fitting window therefore changes the reported summary of this nonlinear fixture. It does not demonstrate that a material has become 44% better or identify a true, window-independent device constant. Those claims would require a justified physical model, calibration and suitable observations.

Sources for this section: [2]

What to preserve in a technical comparison

A reproducible comparison should retain which sample was measured, what voltage range and representation were used, and what operating conditions justified that representation.

The historical discussion supplies a concrete reason for asking those questions. The original fixture exposes the algebraic effect of changing the window. Neither the fixture nor an abstract alone reproduces the complete device experiment.

Sources for this section: [2] · [1]