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# Answer to Question #207531 in Mechanical Engineering for UUID

Question #207531

An Al-silicon dioxide-silicon MOS capacitor has an oxide thickness of 450 Å and a doping of NA 10¹5 cm³. The fixed oxide charge density is 3 x 10¹¹1 cm². Calculate (a) the flat-band voltage and (b) the threshold voltage.

1
2021-06-24T11:53:02-0400

Part a

\phi_{FP}=-(0.0259) \ln(\frac{10^{15}}{15*10^{10}})

\phi_{ms}=\phi_m'-(x'+\frac{E_s}{2e}+|\phi_{FP}|)=3.20-(3.25+0.56+0.288)=-0.898 V

C_{ox}=\frac{\varepsilon_{ox}}{t_{ox}}=\frac{3.9*8.8510^{-14}}{450*10^{-8}}=9.67*10^{-8}F/cm^2

v_{FB}=\phi_{ms}-\frac{\phi_{ss}}{C_{ox}}=-0.898-\frac{3*10^{11}*1.6*10^{-19}}{9.67*10^{-8}}=-1.52 V

Part b

V_T=\frac{|Q'_{SD}(max)|}{C_{ox}}+2|\phi_{FP}|+V_{FB}

V_{dT}=[\frac{4*11.7*8.85*10^{-14}*0.288}{1.6*10^{-19}*10^{15}}]^{0.5}=0.863 \mu m

|Q'_{SD}(max)|=1.6*10^{-19}*10^{15}*0.863*10^{-4}=1.38*10^{-8}c/cm^2

V_T=\frac{1.38*10^{-8}}{7.67*10^{-8}}+2*0.288-1.52 = -0.764 V

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