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ee477_hw2_solutions_nazarian_spring2009_1

# ee477_hw2_solutions_nazarian_spring2009_1 - EE 477L...

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1 EE 477L Homework 2 Solutions Spring ’09 Nazarian ___________________________ Lecture 9:30 Assigned: Friday Feb. 20, 2009 Due: Friday Feb 27, 2009 EEB340 at 11am Show and explain your work clearly and in detail. 1. Some analytical questions: a. Why do we use channel stop implants in MOSFET fabrication technology? Channel stop implants are used to prevent the formation of any unwanted MOS transistor between two neighboring identical diffusions (i.e., btn two n+ or two p+ regions.) The implants would isolate the region so, there won’t be any unwanted channel forming between the regions. b. See the definition of work function energy in page 14 in our Chapter 3 slides and prove the work function difference between semiconductor and gate shown in page 31. Specifically, point out how the electron affinity energies of gate and semiconductor do not appear in the work function difference equation. The work function is defined as the energy required to send an electron from the Fermi energy level to the free space level (E o – E F ). Using this definition the electron affinity- based definition of the work function (i.e., the summation of the electron affinity and the difference between Fermi and Intrinsic Fermi energies) can be avoided. The work function difference between two material, say a metal and a p_type substrate (or better say q Φ GC (G and C denote the Gate and Channel respectively) can hence be the (E o – E F ) G – (E o – E F ) C for which the free space E O is cancelled. The term is then simplified to E FC – E FG where E FC and E FG are the Fermi energy levels of the channel (substrate) and the gate (metal or polysilicon) respectively. c. What is the definition of the threshold voltage V T of an NMOS transistor? Name the four physical components of V T . Threshold voltage is that value for V GS that is needed to invert the channel at the surface of substrate such that the density of the electrons at the surface becomes equal to the density of holes in the substrate. Note that any further increase in V GS would increase the mobile electron concentration. Also note that to invert the channel some certain potential is needed between gate and the substrate. The reference voltage terminal in MOS is however considered as source, and therefore for the cases that body and source are not connected together, a body effect is defined to account for it during threshold voltage calculation. The four physical components of the threshold voltage are: The first voltage component is the work function potential difference between the gate and the channel and the second one is the gate voltage value to change the surface

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2 potential such that from a certain density of holes the channel would get an identical density of electrons. This is hence -2 φ F : - φ F to deplete the channel off of holes and another - φ F to invert it with the same density of electron as it had for holes. The third voltage component is to offset the depletion region charge due to fixed acceptor ions located in the depletion region near the surface. The fourth component is the fixed
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ee477_hw2_solutions_nazarian_spring2009_1 - EE 477L...

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