Advanced MOS Devices Homework #3 Due Wednesday, March 2 MOS Capacitor Basics: Depletion Charge Estimate Assume that the depletion region below the gate in a MOSFET is rectangular in cross section and does not extend beyond the gate area (in reality this is not quite the case). a) Given that approximation, estimate the volume of the depletion region below a MOSFET gate of dimension L = 42 nm and W = 5L. Assume the substrate doping density is 5 x 1018 cm-3 p-type, the oxide thickness is 2 nm, and the gate voltage is at threshold. Assume further an ideal device, i.e., VFB = 0. b) Estimate the number of dopant ions in the depletion volume. MOS Capacitor Basics: Surface Potential in Depletion a) For an ideal p-substrate MOS capacitor with dox = 100 Å and NB = 5 x 1016 cm-3, find the surface potential and gate voltage corresponding to weak inversion (i.e., the threshold point). Calculate the depletion region width wT. Make a rough sketch, approximately to scale, of the energy band diagram at threshold. b) Repeat a) for an n-type substrate with the same NB. MOS Capacitor Band Bending The following questions refer to an MOSC with an n-type semiconductor substrate doped at 8 x 1015 cm-3, and an oxide thickness of 200 Å. There is no oxide or interface charge, and no contact potential difference. i) Make a sketch of the energy band diagram for the n-substrate MOSC described above for (a) no applied bias, (b) accumulation, and (c) threshold. In each case, find the surface potential s and the corresponding gate voltage VG. For the accumulation case, assume that the Fermi level at the surface is 0.10 eV below the conduction band edge. Use the “Exact Solution” to Poisson’s equation to calculate the gate voltage at each surface potential. ii) Use the depletion approximation to find the maximum value of the depletion depth, i.e. the depletion depth at threshold. Find the corresponding minimum capacitance. MOS LF CV Calculation Use a computer to plot the low frequency ( = 0) MOSC CV curve vs. VG based on the “exact charge” formulation discussed in class. Choose a suitable number of values for Us over the range UF - 21 < Us < UF + 21. [You might first convince yourself that this range of values for Us corresponds to positioning of the Fermi level at the surface varying from the conduction band edge to the valence band edge.] Produce a plot for an n-substrate MOSC with an oxide thickness of 500 Å and a doping density of 1016 cm-3; repeat for dox = 100 Å and a doping density of 1 x 1017 cm-3. MOS CV Calculations On the website you will find an Excel spreadsheet containing CV data taken from a MOS capacitor (6347CVData.xlsx). There will be three rows representing the gate voltage, 1 MHz capacitance, and Quasi-Static (QS) capacitance. These data were taken on acapacitor with an Al gate of area 2.17 x 10-3 cm2. Plot this data using Excel or any other method you choose. Then do the following. a) Using the 1 MHz data, calculate the oxide thickness, the doping density in the substrate, and the flatband capacitance. b) Find the flatband voltage, and from that calculate the “effective oxide charge” Neff (cm-2) using qAVCNFBoxeff To do this, you will need to calculate the work function difference and subtract it from the flatband voltage to obtain VFB = VFB – ms. c) If the oxide charge distribution (x) is assumed to be constant (in other words, the charge is spread uniformly throughout the oxide), what value and sign must it have to produce the flatband voltage you calculated