140b midterm 1 cheatsheet

140b midterm 1 cheatsheet - For C-V Curves: Minimum...

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Unformatted text preview: For C-V Curves: Minimum Capacitance ox C 'min = C ' highf = inv t ox + ox s Maximum Capacitance C ' max = C ' lowf xdT ( F / cm 2 ) 2 = Cox = ox ( F / cm ) t ox inv Flat-band Capacitance ox C 'FB = ( F / cm2 ) kT tox + ox s e eN s a Maximum induced depletion region xdT 4 s Fp = eN a 1/ 2 (cm) Maximum space charge density per unit area of dep. reg. |Q'SD(max)| = eNaxdT (C/cm2) s = 11.7,13.1,16, Si , GaAs , Ge Intrinsic Carrier Concentration (T 300 K) 3 - Eg T ni = * N c * N v * exp kT 300 (cm -3 ) kT = 0.0259 * (T / 300) V Surface Potential For Kn s = -2 Fn or 2 Fp (V ) VFB = -1 Flat-band voltage shift C ox 0 tox xp ( x ) t ox Flat-band Voltage dx VFB = ms - ' QSD p( x) = Q ' ss t ox Q'ss (V ) Cox for triang ular distribution : Substrate Bias Effects x po tox p ( x ) = po t and t difference equations xdx = Q ' ss Metal-semiconductor work function 0 ox ox VT = - Cox = 2e s N a 2 Fp + VSB - 2 Fp Cox VT Cox = + 2 Fp 2e N s a eN a xdT Cox - 2 Fp 2 where, VT = VT (VSB > 0) - VT (VSB = 0) VSB Threshold voltage shift-short Channel Threshold Voltage VT = - - Q ' ss C ox - + ms + 2 Fp = Q ' SD (max) Cox + VFB + 2 Fp + VFB - LFn 2 = VTN = Q ' SD (max) Cox rj 2x 1 + dT - 1 rj L Channel length Modulation VTP = - Q ' SD (max) Cox Q ' ss C ox + ms - 2 Fn = - Q ' SD (max) Cox 2 s + VDS ( sat ) + VDS - Fp + VDS ( sat ) Fp eN a m = 4.28, Al ,5.1, Au ,4.26, silver ,3.20, Al - SiO junction 2 VDS = VDS - VDS ( sat ) ' = 3.25Vfor Si - SiO junction 2 ...
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