Calculate the surface potential at the threshold inversion

Question

Consider an NMOS device with the parameters given in Problem 11.10 Plot V, - - versus r,, over the range

Problem 11.10

A 400 Å oxide is grown on p-type silicon with Na = 5 x 10¹⁵ cm-^3. The flat-band voltage is 0.9 V. Calculate the surface potential at the threshold inversion point as well as the threshold voltage assuming negligible oxide charge. Also find the maximum space charge width for this device.