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 __________.

The values of the integrals $$\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dy} } \right)} dx\,\,$$ and $$\,\,\int\limits_0^1 {\left( {\int\limits_0^1 {{{x - y} \over {{{\left( {x + y} \right)}^3}}}dx} } \right)} dy\,\,$$ are

The minimum value of the function $$f\left( x \right) = {1 \over 3}x\left( {{x^2} - 3} \right)\,\,$$ in the interval $$ - 100 \le x \le $$ $$100$$ occurs at $$x=$$ __________.