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HW1_Solution

# HW1_Solution - HW#1 Solution Problem#1 Given the table of...

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HW #1 Solution : Problem #1, Given the table of NMOS threshold voltages for measured 250nm devices below find the VT mean, standard deviation, variance, and model the data as a Gaussian function. Find the probability that the threshold voltages will be between 710mV and 690 mV assuming a random Gaussian distribution. The top row shows VT in mV and the bottom row show the frequency of measured occurrence for 1014 samples. n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Vt (mV) 686 688 690 692 694 696 698 700 702 704 706 708 710 712 714 Frequency (ea) 0 5 10 22 54 81 152 163 169 148 94 67 32 11 6 Total1 (Vt × F) 0 3440 6900 1522 4 3747 6 5637 6 10609 6 114100 118638 10419 2 6636 4 4743 6 2272 0 783 2 4284 deviation (Vt - m) -15 -13 -11 -9 -7 -5 -3 -1 1 3 5 7 9 11 13 Total2 (deviation × F) 0 -66 -113 -204 -392 -426 -496 -205 125 406 446 452 280 118 76 (1) Vt mean? μ = (2) Standard Deviation? σ = (3) Variance? (4) Model the data as Gaussian function Gaussian Distribution is g(x) = . So, by inputting value above, g(x) = = (5) Probability between 690 to 710 ? Normalizing by using Z 690 = -2.42, Z 710 = +1.88 Then, by using below Where α =1/ π , β =2 π P(Z 690 Z 710 ) = (1.88) - (-2.42) = 0.97 – 0.01 = 0.96

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Problem #2 a) Consider a 22 nm technology. In that 22 nm technology, an ion implanter sweeps threshold adjustment dopant atoms into the
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HW1_Solution - HW#1 Solution Problem#1 Given the table of...

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