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Unformatted text preview: ECE 230B, HW-#4, Winter 2010 1. Apply constant-field scaling rules to the long-channel currents, Eq. (3.19) for the linear region, and Eq. (3.23) for the saturation region, and show that they behave as indicated in Table 4.1. Solution: Under the scaling transformation, W → W / κ , L → L / κ , t ox → t ox / κ , V ds → V ds / κ , V g → V g / κ , and V t → V t / κ , Eq. (3.19) becomes I C W L V V V I ds eff ox g t ds ds →- = μ κ κ κ κ κ κ κ ( ) / / ; and Eq. (3.23) becomes I C W L m V V I ds eff ox g t ds →- = μ κ κ κ κ κ κ ( ) / / 1 2 2 . Note that both m = 1 + 3 t ox / W dm and μ eff which is a function of E eff given by Eq. (3.49) are nearly invariant under constant field scaling. 2. Apply constant-field scaling rules to the subthreshold current, Eq. (3.36), and show that instead of decreasing with scaling (1/ κ ), it actually increases with scaling (note that V g < V t in subthreshold). What if temperature also scales down by the same factor ( T → T / κ )?...
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- Threshold voltage, constant-field scaling rules