HW-230B-4_2010

HW-230B-4_2010 - N s = 0. Take 2 B = 1 V. (a) Choose the...

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ECE 230B, HW-#4, Winter 2010 1. Apply constant-field scaling rules to the long-channel currents, Eq. (3.23) for the linear region, and Eq. (3.28) for the saturation region, and show that they behave as indicated in Table 4.1. 2. Apply constant-field scaling rules to the subthreshold current, Eq. (3.40), and show that instead of decreasing with scaling (1/ κ ), it actually increases with scaling (note that V gs < V t in subthreshold). What if temperature also scales down by the same factor ( T T / )? 3. Apply constant-field scaling rules to the saturation current from the n = 1 velocity saturation model, Eq. (3.79), and the fully saturation-velocity limited current, Eq. (3.81), and show that they behave as indicated in Table 4.1. 4. Consider an n-channel MOSFET with n + polysilicon gate (neglect poly depletion effect). The gate oxide is 7 nm thick, and the p-type body (or substrate) has a retrograde doping as shown in Fig. 4.12 with
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Unformatted text preview: N s = 0. Take 2 B = 1 V. (a) Choose the values of x s and N a such that the maximum depletion width is W dm = 0.1 m and the threshold voltage (at 2 B ) is V t = 0.3 V. (b) Following (a), what is the body effect coefficient, m , and the inverse slope of log sub-threshold current versus gate voltage (long-channel device)? (c) Following (a), how short a channel length can the device be scaled to before short-channel effect becomes severe? 5. Consider a p-type, linear retrograde doping profile of an nMOSFET below. The gate workfunction is that of n+ silicon and the gate oxide thickness is 20 nm. Assume x s = 0.1 m and N a = 10 17 cm-3 . (a) What is the maximum depletion width (take the 2 B value at x = x s )? (b) What is the threshold voltage? (c) What is the inverse slope of log[subthreshold current]? (d) What is the minimum channel length this device can be scaled to? N a x x s N(x)...
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