# Chapter 7: MOS Field-Effect-Transistors     ## Problems Consider an n-type MOSFET, which consists of a 10 nm thick oxide (er = 3.9) and has a gate length of 1 micron, a gate width of 20 micron and a threshold voltage of 1.5 Volt. Calculate the resistance of the MOSFET in the linear region as measured between source and drain when applying a gate-source voltage of 3 Volt. What should the gate-source voltage be to double the resistance? The surface mobility of the electrons is 300 cm2/V-sec. Consider an n-type MOSFET with an oxide thickness tox = 20 nm (er = 3.9) and a gate length, L = 1 micron, a gate width, W = 10 micron and a threshold voltage, VT = 1 Volt. Calculate the capacitance per unit area of the oxide, COX, and from it the capacitance of the gate, CG. Calculate the drain current, ID, at a gate-source voltage, VGS = 3 Volt and a drain-source voltage, VDS = 0.05 Volt. The surface mobility of the electrons mn = 300 cm2/V-sec. Use the linear model of the MOSFET. A MOSFET (L = 1 mm, tox = 15 nm, VT = 1 V and mn = 300 cm2/V-sec) must provide a current of 20 mA at a drain-source voltage of 0.5 Volt and a gate-source voltage of 5 Volt. How wide should the gate be? A MOSFET (L = 1 mm, tox = 10 nm, VT = 1 V and mn = 300 cm2/V-sec) is to be used as 50 W terminating resistor when applying a gate-source voltage, VGS = 5 Volt. How wide should the gate be? The capacitance of an n-type silicon MOSFET is 1 pF. Provided that the oxide thickness is 50 nm and the gatelength is 1 micron, what is the resistance of the MOSFET in the linear regime when biased at a gate voltage which is 5 Volt larger than the threshold voltage? Use a reasonable value for the surface mobility knowing that the bulk mobility equals 1400 cm2/V-sec. Consider a p-channel silicon MOSFET with an aluminum gate.Draw the energy band diagram of the MOS structure for VG = VFB. Indicate the workfunction of the metal and the semiconductor, as well as the electron affinity.Draw the field distribution for VG = VT (onset of inversion).Calculate the depletion layer width and the field in the oxide at the onset of inversion. (Nd = 1016 cm-3, tox = 100 nm, VFB = -0.5V) Calculate the depletion region width within a p-type bulk silicon MOS capacitor with Nd = 1017 cm-3, at the onset of inversion. A silicon p-substrate (Na = 1016 cm-3) MOSFET with tox = 0.1 mm, eox/e0 = 3.9 and a negative interface charge per unit area of -10-8 C/cm2, has a threshold voltage which is 1 Volt smaller than desired. By what value should one change the oxide thickness to obtain the desired threshold voltage? Should one increase or decrease the oxide thickness? A silicon MOSFET (nI = 1010 cm-3, es/e0 = 11.9 and eox/e0 = 3.9) is scaled by reducing all dimensions by a factor of 2 and by increasing the doping density of the substrate by a factor of 4.Calculate the ratio of the following parameters of the scaled device relative to that of the original device: (make approximations if necessary)The transconductance at VGS - VT = 1 V.The gate capacitanceThe transit frequency at VGS - VT = 1 V. (Assume that CDS = 0)The threshold shift when increasing the reverse bias of the source-bulk diode from 1 Volt to 3 Volt.The breakdown voltage of the oxide assuming the breakdown field to be constant.The breakdown voltage of the drain-to-bulk p-n diode assuming the breakdown field to be constant. A silicon p-substrate (Na = 1016 cm-3) MOSFET with tox = 0.1 mm, eox/e0 = 3.9 and VFB = -0.2 V, has a threshold voltage which is 1 Volt smaller than desired. By what value should one change the oxide thickness, tox, to obtain the desired threshold voltage? Should one increase or decrease the oxide thickness?