Final answer:
The mobility (μ) of the material in a FET is calculated using the transconductance, oxide capacitance per unit area, and the transistor's dimensions, resulting in a mobility of 0.5 m2/(V·s) for the given parameters.
Step-by-step explanation:
The mobility (μ) of the charge carriers in a FET can be determined using the transconductance (∂Ip/∂Vgs), gate dimensions, and oxide thickness. Transconductance in the linear region for a FET is given by ∂Ip/∂Vgs = (μ Cox W/L) (Vgs - Vt), where Cox = εox/tox is the oxide capacitance per unit area. We are given ∂Ip/∂Vgs = 1.15 πA/V, W = 2 πm, L = 4 πm, Vgs = 24 V, Vt = 20 V, and tox = 300 nm.
The silicon dioxide (SiO2) dielectric constant (εox) is typically taken as 3.45 × 10−12 F/m. Therefore, Cox = 3.45 × 10−12 F/m / 300 × 10−9 m = 1.15 × 10−4 F/m2. Plugging the known values into the transconductance equation, and solving for μ gives μ = (∂Ip/∂Vgs × L) / (Cox × W × (Vgs - Vt)) = (1.15 × 10−9 A/V × 4 π × 10−6 m) / (1.15 × 10−4 F/m2 × 2 π × 10−6 m × 4 V) = 0.5 m2/(V·s), which is the mobility of the material. This calculation assumes a simple model and does not consider any parasitic effects, high electric field effects or velocity saturation.