q2_fall05

# q2_fall05 - Fall 2005 6.012 Microelectronic Devices and...

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Unformatted text preview: Fall 2005 6.012 Microelectronic Devices and Circuits Prof. J. A. del Alamo November 16, 2005 ­ Quiz #2 problem grade Name: Recitation: total General guidelines (please read carefully before starting): • Make sure to write your name on the space designated above. • Open book : you can use any material you wish. • All answers should be given in the space provided. Please do not turn in any extra material. If you need more space, use the back of the page. • You have 120 minutes to complete your quiz. • Make reasonable approximations and state them , i.e. quasi­neutrality, depletion approxima­ tion, etc. • Partial credit will be given for setting up problems without calculations. NO credit will be given for answers without reasons. • Use the symbols utilized in class for the various physical parameters, i.e. µ n , I D , E , etc. • Every numerical answer must have the proper units next to it. Points will be subtracted for answers without units or with wrong units. • Use φ = 0 at n o = p o = n i as potential reference. • Use the following fundamental constants and physical parameters for silicon and silicon dioxide at room temperature: n i = 1 × 10 10 cm − 3 kT /q = 0 . 025 V q = 1 . 60 × 10 − 19 C s = 1 . 05 × 10 − 12 F/cm ox = 3 . 45 × 10 − 13 F/cm 1 2 3 4 1. (30 points) Below is an n + ­ polysilicon­gate MOSFET. The substrate doping is N a = 10 17 cm − 3 and the insulator thickness is 5 nm . The gate length L = 0 . 25 µm while the gate width is W = 2 . 5 µm . The inversion layer mobility for the MOSFET is µ N = 250 cm 2 /V · s . A capacitance voltage curve of the n + poly­silicon gate MOSFET was taken by connecting the source, drain and body terminals together. A voltage was applied between the gate and the body. With the device biased as follows: V BS = 0 V , V DS = 0 . 1 V , V GS = 1 . 11 V , answer the following questions: (1a) (5 points) Calculate the sheet charge density at the drain end of the device, Q n ( y = L ) (numerical answer expected). (1b) (5 points) Calculate the electron drift velocity at the drain end of the device, v n ( y = L ) (numerical answer expected)....
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q2_fall05 - Fall 2005 6.012 Microelectronic Devices and...

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