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302 CHAPTER 6 Fundamentals of the Metal-Cxide-Semiconductar F = teld-Effect Transistor Problems Q ‘ 2 Consider an aluminum gate—silicon dioxide-p-type silicon MOS structure with: i, = 450 A. The silicon doping is N, = 2 x 10" cm? and the flat-band : is Veo = — 10 ¥V. Determine the fixed oxide charge Qj. d voltage aha An MOS transistor is fabricated on a p-type silicon substrate with Ny = The oxide thickness iS fox = 450 Aand the equivalent fixed oxide chy oh. « » 10! cm=2, Calculate the threshold voltage for (a) in aluminum gate, (b) an n* polysilicon gate, and (c) a p* polysilicon gate. . Repeat Problem 6.8 for an n-type silicon substrate with Ny = 104 em™* i is 400 A oxide is grown on p-type silicon with Ng = 5x 10" em, The flat-band : M Oo 5 yoltage 18 —0.9 V, Calculate the surface potential at the threshold inversion point iy as well as the threshold voltage assuming negligible oxide charge. Also find the maximum space charge with for this device. ¢ Q An MOS transistor with an aluminum gate is fabricated on a p-type silicon substrate. The oxide thickness 18 fox = 499 A and the equivalent fixed oxide charpe is 2), = g x 10! cm=2, The measured threshalst voltage is Vr = +0.80 V. Determine the p-type doping concentration. Repeat Problem 6.14 for an n-type silicon substrate if the measured threshold voltage is Vr = — 1.15 Ve Determine the n-type doping concentration. An Al-silicon dioxide-sitican MOS capacitor has an oxide thickness of 450 hand a doping of Na = 1o'% em. The oxide charge density 1 Cees he flat-band voltage and (b) the threshold voltage. Sketch the electric (a) Calculate (a) t field through the structure at the onset of anversion. ‘ ade i + polysilicon gale is shown in An n-channel depletion m ee : Oo Osh : Figure 6.46b. The n-channel doping 1 Nu Sem 3, and bes perenne is ; te, — 500A. The equivalent fixed oxide charge is Oss = pone ee thickness f- is equal to the maximum ind! charge width. ( space vion at the n-channel-p-substrate junction.) (a) Determine the and (b) calculate the threshold voltage. i ysilicon gate and n-type silicon substrate. ? (d) re P61 | Figure for Problem 6.1. charge re thickness fc, ores : =onsider an MOS capacitor with an nt pol ‘ ii an = 10!* cm let Er — Ee = o.2 eV inthe nt polysilicon. Assume ‘ = and "300 A. Also assume thal x’ (polysiticon) = x (a) Consider n-type silic i ype silicon in an MOS structure. Let 7 = 300K. Determine the the oxide has a thie band diagrams (i) for Ve =O.and (single-crystal silicon), conductor work function difference 63 semiconductor doping so that |" so that |Q',)(max)| = 7.5 x 107-2 Clem? marine the surface potential that can lem*. (by Determine aera at results in the maximum s ; (if) at flat band. (b) Calculate the metal" : ad a space charge width. {c) Calculate the threshold voltage for the ideal case of zero fixed oxide charge Section 6.3 Potential Di i inte! 6.34a), ifferenc . <7, . zero interface Stales. ; : V; fonuee ; é erences in the MOS Capacitor ‘The threshold voltage of 82 n-channel MOSFET is ae a T 6A : oe ie 6.21 to determine @m, unless otherwise stated.] versus temperature OVE the range 200 = i ee the metal-semiconductor work function difference @ms in an MOS nem mH on structure with p-type silicon for the ca i aa perature and 0S eS p case Whe 2 (b)n¢ polysilicon, and i ee hen the gate is (a) aluminum, plot the threshold volt (c) pt polysilicon, Let Na = 6 103 cm—? 6.5 Consider an MOS structure with n-t . fg = OR cm-"- 
