5. For a long channel \( n \)-MOSFET with \( V_{t}=1 \mathrm{~V} \), calculate the \( V_{g} \) required for an \( I_{d}\left(\right. \) sat.) of 0.1 mA and \( V_{d}( \) sat.) of 5 V . Calculate the small-signal output conductance, \( g \) and the transconductance, \( g_{m}\left(\right. \) sat. ) at \( V_{d}=10 \mathrm{~V} \). Sketch the cross section of this MOSFET and schematically show the inversion charge and depletion charge distributions for \( V_{d}=1 \mathrm{~V}, 5 \mathrm{~V} \) and 10 V . Recalculate the new \( I_{d} \) for \( V_{g}-V_{t}=3 \mathrm{~V} \) and \( V_{d}=4 \mathrm{~V} \).
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To calculate the \( V_{g} \) required for an \( I_{d}\left(\right. \) sat.) of 0.1 mA and \( V_{d}( \) sat.) of 5 V, we can use the saturation current equation for a long channel \( n \)-MOSFET: \[ I_{d} = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{g} - V_{t})^2 Show more…
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(a) Consider an n-channel enhancement mode MOSFET with $(W / L)=10$, $C_{\mathrm{ox}}=6.9 \times 10^{-8} \mathrm{~F} / \mathrm{cm}^{2}$, and $V_{T}=+1 \mathrm{~V}$. Assume a constant mobility of $\mu_{n}=500 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s} .$ Plot $\sqrt{I_{D}}$ versus $V_{G S}$ for $0 \leq V_{G S} \leq 5 \mathrm{~V}$ when the transistor is biased in the saturation region. ( $b$ ) Now assume that the effective mobility in the channel is given by $$ \mu_{\mathrm{eff}}=\mu_{0}\left(\frac{E_{\mathrm{eff}}}{E_{\mathrm{c}}}\right)^{-1 / 3} $$ where $\mu_{0}=1000 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$ and $\mathrm{E}_{c}=2.5 \times 10^{4} \mathrm{~V} / \mathrm{cm} .$ As a first approximation, let $\mathrm{E}_{\mathrm{eff}}=V_{G S} / t_{\mathrm{ox}} .$ Using $\mu_{\mathrm{eff}}$ in place of $\mu_{n}$ in the $\sqrt{I_{D}}$ versus $V_{G S}$ relation, plot $\sqrt{I_{D}}$ versus $V_{G S}$ over the same $V_{G S}$ range as in part $(a) \cdot(c)$ Plot the curves from parts (a) and $(b)$ on the same graph. What can be said about the slopes of the two curves?
An ideal n-channel MOSFET has the following parameters: $V_{T}=0.45 \mathrm{~V}$, $\mu_{n}=425 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}, t_{\text {ox }}=11 \mathrm{~nm}=110 \AA$ A, $W=20 \mu \mathrm{m}$, and $L=1.2 \mu \mathrm{m} .$ (a) Plot $I_{D}$ versus $V_{D S}$ for $0 \leq V_{D S} \leq 3 \mathrm{~V}$ and for $V_{G S}=0,0.6,1.2,1.8$, and $2.4 \mathrm{~V} .$ Indicate on each curve the $V_{D S}(s a t)$ point. (b) Plot $\sqrt{I_{D}(s a t)}$ versus $V_{G S}$ for $0 \leq V_{G S} \leq 2.4 \mathrm{~V}$. (c) Plot $I_{D}$ versus $V_{G S}$ for $0 \leq V_{G S} \leq 2.4 \mathrm{~V}$ and for $V_{D S}=0.1 \mathrm{~V}$.
The parameters of an n-channel enhancement-mode MOSFET are $V_{T}=0.40 \mathrm{~V}$, $t_{\text {ox }}=20 \mathrm{~nm}=200 \AA, L=1.0 \mu \mathrm{m}$, and $W=10 \mu \mathrm{m} .$ (a) Assuming a constant mobility of $\mu_{n}=475 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, calculate $I_{D}$ for $V_{G S}-V_{T}=2.0 \mathrm{~V}$ when biased at $(i) V_{D S}=0.5 \mathrm{~V},(i i) V_{D S}=1.0 \mathrm{~V},($ iii $) V_{D S}=1.25 \mathrm{~V}$, and $(i v) V_{D S}=2.0 \mathrm{~V}$. (b) Consider the piecewise linear model of the carrier velocity versus $V_{D S}$ shown in Figure $\mathrm{P} 11.13$. Calculate $I_{D}$ for the same voltage values given in part $(a) .$ [See Equation ( $11.17) .]$ ( $c$ ) Determine the $V_{D S}$ (sat) values for parts ( $a$ ) and $(b)$.
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