Assuming that transistor M₁ and M₂ are identical and have a threshold voltage of 1V, the state of transistors M₁ and M₂ are respectively

Two n-channel MOSFETs, T1 and T2, are identical in all respects except that the width of T2 is double of T1. Both the transistor are biased in the saturation region of operation, but the gate overdrive voltage (V_GS - V_TH) of T2 is double that of T1, where V_GS and V_TH are the gate-to-source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T1 are I_D1 and g_m1 respectively ; the corresponding values of these two parameters for T2 are

A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV, E_c - E_F = 0.9 eV; where E_c and E_F are conduction band minimum and the Fermi energy levels of Si, respectively. Oxide$${\varepsilon _r} = \,\,3.9,\,\,\,{\varepsilon _{0\,\,}}=\,8.85 \times {10^{ - 14}}$$ F/cm, oxide thickness $${t_{ox}} = 0.1\,\mu m$$ and electronic charge q = $$1.6 \times {10^{ - 19}}$$ C. If the measured flat band voltage of the capacitor is –1V, then the magnitude of the fixed charge at the oxide semiconductor interface, in nC/cm², is __________.

The rank of the matrix $$\left[ {\matrix{ 1 & { - 1} & 0 & 0 & 0 \cr 0 & 0 & 1 & { - 1} & 0 \cr 0 & 1 & { - 1} & 0 & 0 \cr { - 1} & 0 & 0 & 0 & 1 \cr 0 & 0 & 0 & 1 & { - 1} \cr } } \right]$$ is __________.