Semiconductor Physics and Devices

Donald A. Neamen

Chapter 11

Metal–Oxide–Semiconductor Field-Effect Transistor: Additional Concepts - all with Video Answers

Educators

Chapter Questions

Problem 1

Assume that the subthreshold current of a MOSFET is given by
$$
I_{D}=10^{-15} \exp \left(\frac{V_{G S}}{(2.1) V_{t}}\right)
$$
over the range $0 \leq V_{G S} \leq 1$ volt and where the factor $2.1$ takes into account the effect of interface states. Assume that $10^{6}$ identical transistors on a chip are all biased at the same $V_{G s}$ and at $V_{D D}=5 \mathrm{~V} .(a)$ Calculate the total current that must be supplied to the chip at $V_{G S}=0.5,0.7$, and $0.9 \mathrm{~V} .(b)$ Calculate the total power dissipated in the chip for the same $V_{G S}$ values.

Chai Santi

Chai Santi

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Problem 2

The subthreshold current in a MOSFET is given by $I_{D}=I_{S} \exp \left(V_{G S} / n V_{t}\right)$. Determine the change in applied $V_{G S}$ for a factor of 10 increase in $I_{D}$ for $($ a) $n=1$,
(b) $n=1.5$, and $($ c) $n=2.1$.

Chai Santi

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Problem 3

A silicon n-channel MOSFET has a doping concentration of $N_{a}=2 \times 10^{16} \mathrm{~cm}^{-3}$ and a threshold voltage of $V_{T}=0.40 \mathrm{~V}$. Determine the change in channel length, $\Delta L$, for $(a) V_{G S}=1.0 \mathrm{~V}, V_{D S}=2.0 \mathrm{~V} ;(b) V_{G S}=1.0, V_{D S}=4.0 \mathrm{~V} ;(c) V_{G S}=2.0 \mathrm{~V}$
$V_{D S}=2.0 \mathrm{~V} ;$ and $(d) V_{G S}=2.0, V_{D S}=4.0$

Chai Santi

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Problem 4

Consider the MOSFET described in Problem 11.3.
(a) Determine the minimum channel length so that the incremental change $\Delta L$ is no more than 10 percent of the original length $L$ for applied voltages of $V_{G S}=2 \mathrm{~V}$ and $V_{D S}=3 \mathrm{~V} .(b)$ Repeat part
(a) for $V_{D S}=5 \mathrm{~V}$

Chai Santi

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Problem 5

A silicon MOSFET has parameters $N_{a}=4 \times 10^{16} \mathrm{~cm}^{-3}, t_{a x}=12 \mathrm{~nm}=120 \mathrm{~A}$,
$Q_{s s}^{\prime}=4 \times 10^{10} \mathrm{~cm}^{-2}$, and $\phi_{m s}=-0.5 \mathrm{~V}$. The transistor is biased at $V_{G S}=1.25 \mathrm{~V}$
and $V_{S B}=0 .\left(\right.$ a) Calculate $\Delta L$ for (i) $\Delta V_{D S}=1 \mathrm{~V},($ ii $) \Delta V_{D S}=2 \mathrm{~V}$, and
(iii) $\Delta V_{D S}=4 \mathrm{~V}$. $(b)$ Determine the minimum channel length $L$ such that $\Delta L / L=0.12$ for $V_{G S}=1.25 \mathrm{~V}$ and $\Delta V_{D S}=4 \mathrm{~V}$

Chai Santi

Numerade Educator

Problem 6

The parameters of a silicon MOSFET are $N_{a}=3 \times 10^{16} \mathrm{~cm}^{-3}, V_{T}=0.40 \mathrm{~V}$, $k_{n}^{\prime}=50 \mu \mathrm{A} / \mathrm{V}^{2}, L=0.80 \mu \mathrm{m}$, and $W=15 \mu \mathrm{m} .(a)$ Determine the current $I_{D}^{\prime}$ at
$V_{G S}=1.0 \mathrm{~V}$ for $(i) V_{D S}=2.0 \mathrm{~V}$ and $($ ii $) V_{D S}=4.0 \mathrm{~V} .(b)$ Defining the output resistance as $r_{o}=\left(\Delta I_{D}^{\prime} / \Delta V_{D S}\right)^{-1}$, determine $r_{o}$ for part $(a) .(c)$ Repeat parts $(a)$ and $(b)$ for $V_{G S}=2.0 \mathrm{~V}$

Chai Santi

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Problem 7

Consider an n-channel silicon MOSFET. The parameters are $k_{n}^{\prime}=75 \mu \mathrm{A} / \mathrm{V}^{2}$, $W / L=10$, and $V_{T}=0.35 \mathrm{~V}$. The applied drain-to-source voltage is $V_{D S}=1.5 \mathrm{~V}$.
(a) For $V_{G S}=0.8 \mathrm{~V}$, find $(i)$ the ideal drain current, $(i i)$ the drain current if $\lambda=0.02 \mathrm{~V}^{-1}$, and (iii) the output resistance for $\lambda=0.02 \mathrm{~V}^{-1} .(b)$ Repeat part $(a)$ for $V_{G S}=1.25 \mathrm{~V}$.

Chai Santi

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Problem 8

An n-channel MOSFET has a substrate doping concentration of $N_{a}=10^{16} \mathrm{~cm}^{-3}$ and $V_{D s}($ sat $)=2 \mathrm{~V}$. Using Equation (11.10), plot $\Delta L$ versus $V_{D S}$ over the range $2 \leq V_{D S} \leq 5 \mathrm{~V}$ for $(a) \mathrm{E}_{\mathrm{sat}}=10^{4} \mathrm{~V} / \mathrm{cm}$ and $\mathrm{E}_{\mathrm{sat}}=2 \times 10^{5} \mathrm{~V} / \mathrm{cm} .$

Chai Santi

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Problem 9

Assume that the lateral electric field at the point where the inversion charge pinches off is given by $\mathrm{E}_{\text {sat }}=V_{D S}($ sat $) / L$. ( $a$ ) Determine $\mathrm{E}_{\text {sat }}$ for $L=3,1.0,0.50,0.25$, and $0.13 \mu \mathrm{m} .(b)$ For each case given in part $(a)$, estimate the carrier drift velocity.

Chai Santi

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Problem 10

A silicon n-channel MOSFET has the following parameters: $V_{T}=0.45 \mathrm{~V}$, $\mu_{n}=425 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}, t_{a x}=11 \mathrm{~nm}=110 \AA, W=20 \mu \mathrm{m}$, and $L=1.2 \mu \mathrm{m} .$ The
substrate doping is $N_{a}=3 \times 10^{16} \mathrm{~cm}^{-3}$. (a) Using Equations (11.4) and (11.11), calculate the output resistance, $r_{o}=\left(\partial I_{D}^{\prime} / \partial V_{D S}\right)^{-1}$, for $V_{G S}=0.8 \mathrm{~V}$ and $\Delta V_{D S}=2 \mathrm{~V}$.
(b) Repeat part $(a)$ if the channel length is reduced to $L=0.80 \mu \mathrm{m}$.

Chai Santi

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Problem 11

(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?

Chai Santi

Numerade Educator

Problem 12

One model used to describe the variation in electron mobility in an NMOS device is
$$
\mu_{\mathrm{cff}}=\frac{\mu_{0}}{1+\theta\left(V_{G S}-V_{T N}\right)}
$$
where $\theta$ is called the mobility degradation parameter. Assume the following parameters: $C_{\mathrm{ax}}=10^{-8} \mathrm{~F} / \mathrm{cm}^{2},(W / L)=25, \mu_{0}=800 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$, and $V_{T N}=0.5 \mathrm{~V}$. Plot,
on the same graph, $\sqrt{I_{D}}$ versus $V_{G S}$ for the NMOS device biased in the saturation region over the range $0 \leq V_{G S} \leq 3 \mathrm{~V}$ for $\left(\right.$ a) $\theta=0$ (ideal case) and $(b) \theta=0.5 \mathrm{~V}^{-1}$.

Chai Santi

Numerade Educator

Problem 13

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 $(b)$.

Chai Santi

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Problem 14

Consider an NMOS transistor with a threshold voltage of $V_{T N}=0.4 \mathrm{~V}$. Plot, on the same graph, $V_{D s}\left(\right.$ sat) over the range $0 \leq V_{G S} \leq 3 \mathrm{~V}$ for $(a)$ an ideal MOSFET (constant mobility) and (b) a device whose drift velocity is given in Figure P11.13.

Chai Santi

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Problem 15

Apply constant-field scaling to the ideal current-voltage relations in both the saturation and nonsaturation bias regions. (a) How does the drain current scale in each bias region? (b) How does the power dissipation per device scale in each bias region?

Chai Santi

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Problem 16

Consider a MOSFET biased such that carriers are traveling at their saturated velocity in the $\mathrm{n}$ channel. If constant-field scaling is applied to the device, how does the drain current scale?

Chai Santi

Numerade Educator

Problem 17

The initial parameters of an n-channel MOSFET are $k_{n}^{\prime}=0.15 \mathrm{~mA} / \mathrm{V}^{2}, L=1.2 \mu \mathrm{m}$, $W=6.0 \mu \mathrm{m}$, and $V_{T}=0.45 \mathrm{~V}$. The device operates over a voltage range of 0 to $3 \mathrm{~V}$. Assume a constant-field scaling factor of $k=0.65$, but assume the threshold voltage is constant. ( $a$ ) Determine the maximum drain current in the $(i$ ) original device and (ii) scaled device. (b) Determine the maximum power dissipation in the
(i) original device and (ii) scaled device.

Chai Santi

Numerade Educator

Problem 18

Consider an n-channel MOSFET with parameters $N_{a}=5 \times 10^{16} \mathrm{~cm}^{-3}, t_{a x}=12 \mathrm{~nm}=$ $120 \AA$, and $L=0.80 \mu \mathrm{m}$. If $r_{j}=0.25 \mu \mathrm{m}$, determine the threshold voltage shift due to short-channel effects.

Chai Santi

Numerade Educator

Problem 19

The parameters of an n-channel MOSFET are $N_{a}=2 \times 10^{16} \mathrm{~cm}^{-3}, L=0.70 \mu \mathrm{m}$, and $t_{a x}=8 \mathrm{~nm}=80 \AA$. The diffused junction radius is $r_{j}=0.30 \mu \mathrm{m}$. The designed threshold voltage is to be $V_{T}=0.35 \mathrm{~V}$ taking into account the shift due to shortchannel effects. What is the equivalent long-channel threshold voltage?

Chai Santi

Numerade Educator

Problem 20

An n-channel MOSFET is doped to $N_{a}=3 \times 10^{16} \mathrm{~cm}^{-3}$ and has an oxide thickness of $t_{a x}=20 \mathrm{~nm}=200 \AA$. The diffused junction radius is $r_{j}=0.30 \mu \mathrm{m}$. Determine the minimum channel length such that the threshold voltage shift due to shortchannel effects is limited to $\Delta V_{T}=-0.15 \mathrm{~V}$.

Chai Santi

Numerade Educator

Problem 21

The shift in threshold voltage due to short-channel effects given by Equation (11.29) assumed all space charge regions were of equal width. If a drain voltage is applied, this condition is no longer valid. Using the same trapezoidal approximation, show that the threshold voltage shift is given by
$$
\Delta V_{T}=-\frac{e N_{a} x_{d T}}{C_{\text {ox }}} \cdot \frac{r_{j}}{2 L}\left[\left(\sqrt{1+\frac{2 x_{d s}}{r_{j}}}+\alpha^{2}-1\right)+\left(\sqrt{1+\frac{2 x_{\text {dD }}}{r_{j}}}+\beta^{2}-1\right)\right]
$$
where
$$
\alpha^{2}=\frac{x_{d s}^{2}-x_{d T}^{2}}{r_{j}^{2}} \quad \beta^{2}=\frac{x_{d D}^{2}-x_{d T}^{2}}{r_{j}^{2}}
$$
and where $x_{d s}$ and $x_{d D}$ are the source and drain space charge widths, respectively.

Chai Santi

Numerade Educator

Problem 22

The threshold voltage shift due to short channel effects, given by Equation (11.29), has been derived assuming $L$ is large enough so that a trapezoidal charge region can be defined as shown in Figure $11.15 .$ Derive the expression for $\Delta V_{T}$ for the case when $L$ becomes small enough such that the trapezoid becomes a triangle. Assume punch-through does not occur.

Chai Santi

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Problem 23

Consider the short-channel effect. Plot $V_{T}-V_{F B}$ versus $L$ as shown in Figure $11.16$ over the range $0.5 \leq L \leq 6 \mu \mathrm{m}$. Use the parameters given in the figure and assume $V_{S B}=0 .$

Chai Santi

Numerade Educator

Problem 24

Repeat Problem $11.23$ at $N_{a}=10^{16}$ and $10^{17} \mathrm{~cm}^{-3}$ for $V_{S B}=0,2,4$, and $6 \mathrm{~V}$.

Chai Santi

Numerade Educator

Problem 25

Equation (11.29) describes the shift in threshold voltage due to short channel effects. If constant-field scaling is applied, what is the scaling factor in $\Delta V_{T} ?$

Chai Santi

Numerade Educator

Problem 26

An n-channel MOSFET has parameters of $N_{a}=3 \times 10^{16} \mathrm{~cm}^{-3}, W=2.2 \mu \mathrm{m}$, and $t_{a x}=8 \mathrm{~nm}=80 \AA$. Neglecting short-channel effects, calculate the shift in threshold voltage due to narrow-channel effects. Assume the fitting parameter is $\xi=\pi / 2$.

Chai Santi

Numerade Educator

Problem 27

Consider an n-channel MOSFET with $N_{a}=10^{16} \mathrm{~cm}^{-3}$ and $t_{a x}=12 \mathrm{~nm}=120 \AA$. The depletion region at each end of the channel can be approximated by a triangular region, as shown in Figure P11.27. Assume both the lateral and vertical depletion widths are equal to $x_{d T}$. The threshold voltage shift due to narrow-channel effects is to be limited to $\Delta V_{T}=+0.045 \mathrm{~V}$. Determine the minimum channel width $W$. Neglect short-channel effects.

Chai Santi

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Problem 28

Consider the narrow-channel effect. Use the transistor parameters described in Example 11.4. Plot $V_{T}-V_{F B}$ over the range $0.5 \leq W \leq 5 \mu \mathrm{m}$ for a long-channel device.

Chai Santi

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Problem 29

Equation (11.35) describes the shift in threshold voltage due to narrow-channel effects. If constant-field scaling is applied, what is the scaling factor in $\Delta V_{T}$ ?

Chai Santi

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Problem 30

(a) A MOS device has a silicon dioxide insulator with a thickness of $t_{a x}=20 \mathrm{~nm}=200 \AA$.
(i) Determine the ideal breakdown voltage. (ii) If a safety factor of 3 is required, determine the maximum safe gate voltage that may be applied. $(b)$ Repeat part
(a) for an oxide thickness of $t_{a x}=8 \mathrm{~nm}=80 \AA$.

Chai Santi

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Problem 31

(a) In a power MOSFET, a maximum gate voltage of $8 \mathrm{~V}$ is to be applied. Determine the minimum oxide thickness necessary if a safety factor of 3 is specified.
(b) Repeat part $(a)$ if the maximum gate voltage is $12 \mathrm{~V}$.

Chai Santi

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Problem 32

The snapback breakdown condition is defined to be when $\alpha M=1$, where $\alpha$ is the common base current gain and $M$ is the multiplication constant given by Equation $(11.40)$. Let $m=3$ and let $V_{B D}=15 \mathrm{~V}$. The common base current gain is a very strong function of junction current $I_{D}$. Assume $\alpha$ is described by the relation
$$
\alpha=(0.18) \log _{10}\left(\frac{I_{D}}{3 \times 10^{-9}}\right)
$$
where $I_{D}$ is given in amperes. Plot the curve of $I_{D}$ versus $V_{C E}$ which satisfies the snapback condition over the range $10^{-8} \leq I_{D} \leq 10^{-3} \mathrm{~A} .$ (Use a log scale for the current.)

Chai Santi

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Problem 33

Near punch-through occurs when the two depletion regions are within approximately six Debye lengths of each other. The extrinsic Debye length $L_{D}$ is defined as
$$
L_{D}=\left[\frac{\epsilon_{s}(k T / e)}{e N_{a}}\right]^{1 / 2}
$$
Consider the n-channel MOSFET in Example 11.5. Calculate the near punchthrough voltage. How does this voltage compare to the ideal punch-through voltage determined in the example?

Chai Santi

Numerade Educator

Problem 34

The near punch-through voltage (see Problem 11.33) of an n-channel MOSFET is to be no less than $V_{D S}=5 \mathrm{~V}$. The source and drain regions are doped $N_{d}=10^{19} \mathrm{~cm}^{-3}$, and the channel region is doped $N_{a}=3 \times 10^{16} \mathrm{~cm}^{-3} .$ The source and body are at ground potential. Determine the minimum channel length.

James Kiss

Numerade Educator

Problem 35

Repeat Problem $11.34$ if a source-substrate voltage $V_{S B}=2 \mathrm{~V}$ is applied.

Chai Santi

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Problem 36

The threshold voltage of an $\mathrm{n}$ -channel MOSFET, with an oxide thickness of $t_{\alpha x}=12 \mathrm{~nm}=120 \AA$, needs to be shifted in the positive direction by $0.80 \mathrm{~V}$. Determine the type of ion implant and the implant dose required.

Chai Santi

Numerade Educator

Problem 37

The threshold voltage of a p-channel MOSFET, with an oxide thickness of $t_{o x}=18 \mathrm{~nm}=180 \AA$, needs to be shifted in the negative direction by $0.60 \mathrm{~V}$ Determine the type of ion implant and the implant dose required.

Chai Santi

Numerade Educator

Problem 38

An n-channel MOSFET has an $\mathrm{n}^{+}$ polysilicon gate, a substrate doping of $N_{a}=6 \times 10^{15} \mathrm{~cm}^{-3}$, an oxide thickness of $t_{\alpha x}=15 \mathrm{~nm}=150 \AA$, and an oxide
trapped charge density of $Q_{x s}^{\prime}=5 \times 10^{10} \mathrm{~cm}^{-2} .(a)$ Determine the threshold voltage.
(b) The required threshold voltage is $V_{T}=+0.50 \mathrm{~V}$. Determine the type and ion implant density necessary to achieve this specification. Assume the implant is directly adjacent to the oxide-semiconductor interface.

Chai Santi

Numerade Educator

Problem 39

A p-channel MOSFET has a p $^{+}$ polysilicon gate, a substrate doping of $N_{d}=2 \times 10^{16} \mathrm{~cm}^{-3}$, an oxide thickness of $t_{\alpha x}=18 \mathrm{~nm}=180 \AA$, and an oxide
trapped charge density of $Q_{s s}^{\prime}=10^{11} \mathrm{~cm}^{-2}$. (a) Calculate the threshold voltage.
( $b$ ) The required threshold voltage is $V_{T}=-0.40 \mathrm{~V}$. Determine the type and ion implant density necessary to achieve this specification. Assume the implant is directly adjacent to the oxide-semiconductor interface.

Chai Santi

Numerade Educator

Problem 40

Consider an n-channel MOSFET with a substrate doping of $N_{a}=4 \times 10^{15} \mathrm{~cm}^{-3}$, an oxide thickness of $t_{a x}=8 \mathrm{~nm}=80 \AA$, and an initial flat-band voltage of $V_{F B}=-1.25 \mathrm{~V} .(a)$ Determine the threshold voltage. $(b)$ For an enhancement-mode device, the required threshold voltage is $V_{T}=+0.40 \mathrm{~V}$. Determine the type and ion implant density that is necessary to achieve this specification. ( $c$ ) Repeat part $(b)$ for a depletion-mode device with a required threshold voltage of $V_{T}=-0.40 \mathrm{~V}$.

Chai Santi

Numerade Educator

Problem 41

The channel of a device with $t_{\mathrm{ax}}=500 \mathrm{~A}$ and a p-type substrate with $N_{a}=10^{14} \mathrm{~cm}^{-3}$ is implanted with acceptors using an effective dose of $D_{I}=10^{12} \mathrm{~cm}^{-2}$. The implant is approximated as a step function with $x_{I}=0.2 \mu \mathrm{m} .$ Calculate the shift in threshold voltage due to back bias effects for $V_{S B}=1.3$, and 5 volts.

Chai Santi

Numerade Educator

Problem 42

A MOSFET has the following parameters: $\mathrm{n}^{+}$ poly gate, $t_{\mathrm{ox}}=80 \mathrm{~A}, N_{d}=10^{17} \mathrm{~cm}^{-3}$, and $Q_{i s}^{\prime}=5 \times 10^{10} \mathrm{~cm}^{-2} .(a)$ What is the threshold voltage of this MOSFET? Is the device enhancement- or depletion-mode? $(b)$ What type of implant and dose are required such that $V_{T}=0 ?$

Chai Santi

Numerade Educator

Problem 43

One rad (Si) produces on the average $8 \times 10^{12}$ electron-hole pairs $/ \mathrm{cm}^{3}$ in silicon dioxide. ${ }^{1}$ Assume that a pulse of ionizing radiation with a total dose of $10^{5} \mathrm{rads}(\mathrm{Si})$ is incident on an MOS device with a $750 \AA$ oxide. Assume that there is no electronhole recombination and that the electrons are swept out through the gate terminal. If 10 percent of the generated holes are trapped at the oxide-semiconductor interface, calculate the threshold voltage shift.

Chai Santi

Numerade Educator

Problem 44

Reconsider Problem $11.43$. If the threshold voltage shift is to be no more than $\Delta V_{T}=-0.50 \mathrm{~V}$, calculate the maximum percentage of holes that can be trapped.

Chai Santi

Numerade Educator

Problem 45

Show that, for the simple model for radiation-induced hole trapping we have considered, the threshold voltage shift is proportional to $\Delta V_{T} \propto-t_{\mathrm{ax}}^{2} .$ Thin oxides are one requirement for radiation-tolerant MOS devices.

Chai Santi

Numerade Educator

Problem 46

Design a silicon n-channel MOSFET with a polysilicon gate to have a threshold voltage of $V_{T}=+0.30 \mathrm{~V}$. The oxide thickness is to be $t_{a x}=12 \mathrm{~nm}=120 \AA$ and the channel length is to be $L=0.80 \mu \mathrm{m} .$ Assume $Q_{k s}^{\prime}=0 .$ It is desired to have a drain current of $I_{D}=80 \mu \mathrm{A}$ at $V_{G S}=1.25 \mathrm{~V}$ and $V_{D S}=0.25 \mathrm{~V}$. Determine the substrate doping concentration, channel width, and type of gate required. Specify any possible ion implantation process and take short channel effects into account.

Chai Santi

Numerade Educator

Problem 47

A particular process produces an n-channel MOSFET with the following properties:
$$
\begin{array}{ll}
t_{\mathrm{ox}}=325 \AA & L=0.8 \mu \mathrm{m} \\
N_{a}=10^{16} \mathrm{~cm}^{3} & W=20 \mu \mathrm{m} \\
\mathrm{n}^{+} \text {polysilicon gate } & r_{j}=0.35 \mu \mathrm{m} \\
Q_{s}^{\prime}=10^{11} \mathrm{~cm}^{-2} &
\end{array}
$$
The desired threshold voltage is $V_{T}=0.35 \mathrm{~V}$ at $T=300 \mathrm{~K}$. Design an additional process to achieve this objective by using ion implantation, which produces a step function profile that is $0.35 \mu \mathrm{m}$ deep.

Chai Santi

Numerade Educator

Problem 48

A CMOS inverter is to be designed in which both the $\mathrm{n}$ -channel and p-channel devices have the same magnitude of doping concentration equal to $10^{16} \mathrm{~cm}^{-3}$, equal oxide thickness of $t_{\mathrm{ox}}=150 \AA$, equal oxide trapped charge of $Q_{s s}^{\prime}=+8 \times 10^{10} \mathrm{~cm}^{-2}$. The gate of the $\mathrm{n}$ channel is $\mathrm{p}^{+}$ poly and the gate of the $\mathrm{p}$ channel is $\mathrm{n}^{+}$ poly. Determine the type of ion implant and the implant dose in each device such that the final threshold voltages are $V_{T N}=+0.5 \mathrm{~V}$ and $V_{T P}=-0.5 \mathrm{~V}$.

Chai Santi

Numerade Educator