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We find that
$$J = \left[ A^* T^2 \exp\left(\frac{-e\phi_{Bn}}{kT}\right) \right] \left[ \exp\left(\frac{eV_a}{kT}\right) - 1 \right]$$
(9.23)
where
$$A^* = \frac{4\pi e m_n^* k^2}{h^3} \tag{9.24}$$
The parameter $A^*$ is called the effective Richardson constant for thermionic emission. Equation (9.23) can be... | {
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$$N_a = 10^{18} \text{ cm}^{-3}$$
$N_d = 10^{16} \text{ cm}^{-3}$
$D_p = 10 \text{ cm}^2/\text{s}$ $D_n = 25 \text{ cm}^2/\text{s}$
$\tau_{no} = 10^{-7} \text{ s}$ $\tau_{no} = 10^{-7} \text{ s}$
We can then calculate the following parameters:
$$L_p = 1.0 \times 10^{-3} \text{ cm}$$
$L_n = 1.58 \times 10^{-3}... | {
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We define in this section a specific contact resistance that is used to characterize ohmic contacts.
#### 9.2.1 Ideal Nonrectifying Barrier
We have considered an ideal metal-n-type semiconductor contact in Figure 9.1 for the case when $\phi_m > \phi_s$ . Figure 9.11 shows the same ideal contact for the opposite ca... | {
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Figure 9.15 shows a plot of the theoretical values of $R_c$ as a function of semiconductor doping. For doping concentrations greater than approximately $10^{19}$ cm<sup>-3</sup>, the tunneling process dominates and $R_c$ shows the exponential dependence on $N_d$ . For lower doping concentrations, the $R_c$ v... | {
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The quantized energy levels are shown in Figure 9.20b. Higher energy levels are usually not considered.
Figure 9.20 | (a) Conduction-band edge at N-AlGaAs, n-GaAs heterojunction; (b) triangular well approximation with discrete electron energies.
![](_pag... | {
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The electric flux density D is continuous across the junction, so
$$\epsilon_n E_n(x=0) = \epsilon_P E_P(x=0) \tag{9.42a}$$
which gives
$$N_{dn}x_n = N_{dP}x_P \tag{9.42b}$$
Equation (9.42b) simply states that the net negative charge in the P region is equal to the net positive charge in the n region—the same c... | {
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If the barrier height for electrons is 0.2 eV larger than that for holes, the electron current will be approximately a factor of 10<sup>4</sup> smaller than the hole current, assuming all other parameters are equal. The opposite situation exists for the band diagram shown in Figure 9.23.
The conduction-band edge in F... | {
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For *T* 300 K, determine the theoretical values of (*a*) *-B*0, (*b*) *<sup>n</sup>*, (*c*) *Vbi*, and (*d*) *xn* and Emax at (*i*) *VR* 1 V and (*ii*) *VR* 5 V.
**Figure P9.7** | Figure for Problem 9.7.
- **9.5** Repeat Problem 9.4, parts (*b*) through (*d*), if the experimentally d... | {
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(Take into account the Schottky barrier lowering.)
- **\*9.19** Starting with the basic current equation given by Equation (9.18), derive the relation given by Equation (9.23).
- **9.20** The reverse-saturation current densities in a pn junction diode and a Schottky diode are 1011 A/cm2 and 6 10<sup>8</sup> A/cm2 , res... | {
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#### **Summary and Review**
- \*9.35 (a) Derive an expression for $dV_a/dT$ as a function of current density in a Schottky diode. Assume the minority carrier current is negligible. (b) Compare $dV_a/dT$ for a GaAs Schottky diode to that for a Si Schottky diode. (c) Compare $dV_a/dT$ for a Si Schottky diode to... | {
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he single-junction semiconductor devices that we have considered, including the pn homojunction diode, can be used to produce rectifying current—voltage characteristics and to form electronic switching circuits. The transistor is a multijunction semiconductor device that, in conjunction with other circuit elements, is ... | {
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Figure 10.7a shows the case when a positive voltage is applied to the gate and an accumulation layer of electrons is formed. Figure 10.7b shows the energy bands when a negative voltage is applied to the gate. The conduction and valence bands now bend upward indicating that a space charge region has been induced in the ... | {
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The electron inversion charge density can then be written as
$$n_s = n_{st} \exp\left(\frac{\Delta \phi_s}{V_t}\right) \tag{10.12}$$
Figure 10.12 shows the electron inversion charge density as a function of surface potential for the case when the threshold inversion charge density is $n_{st} = 10^{16} \text{ cm}^{... | {
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This difference again is because the Fermi level is not equal to the conduction-band energy for the n gate and is not equal to the valence-band energy for the p gate. The metal–semiconductor work function difference becomes important in the fl atband and threshold voltage parameters discussed next.
#### **10.1.5 Flat... | {
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From conservation of charge, we can write
$$Q'_{mT} + Q'_{ss} = |Q'_{SD}(\text{max})| \tag{10.26}$$
where
$$|Q'_{SD}(\max)| = eN_a x_{dT}$$
(10.27)
**Figure 10.19** | Charge distribution in a MOS capacitor with a p-type substrate at the threshold inversion point.
![](_page_413_... | {
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The threshold voltage for this case can be derived and is given by
$$V_{TP} = \left(-|Q_{SD}'(\max)| - Q_{ss}'\right) \left(\frac{t_{ox}}{\epsilon_{ox}}\right) + \phi_{ms} - 2\phi_{fn}$$
(10.32)
where
$$\phi_{ms} = \phi'_m - \left(\chi' + \frac{E_g}{2e} - \phi_{fn}\right)$$
(10.33a)
$$|Q'_{SD}(\max)| = eN_d x_{... | {
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$(V \ \xi \Omega 1.0 + .enA)$
**TYU 10.5** Consider an n<sup>+</sup> polysilicon gate on silicon dioxide with a p-type silicon substrate doped to $N_a = 3 \times 10^{16} \text{ cm}^{-3}$ . Assume $Q'_{ss} = 5 \times 10^{10} \text{ cm}^{-2}$ . Determine the required oxide thickness such that the threshold voltage ... | {
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#### Solution
The oxide capacitance is
$$C_{ox} = \frac{\epsilon_{ox}}{t_{ox}} = \frac{(3.9)(8.85 \times 10^{-14})}{180 \times 10^{-8}} = 1.9175 \times 10^{-7} \text{ F/cm}^2$$
To find the minimum capacitance, we need to calculate
$$\phi_{fp} = V_t \ln \left( \frac{N_a}{n_i} \right) = (0.0259) \ln \left( \fra... | {
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Since the oxide charge is not a function of gate voltage, the curves
Figure 10.30 | High-frequency capacitance versus gate voltage of a MOS capacitor with a p-type substrate for several values of effective trapped oxide charge.
Figure 10.31 | Schematic d... | {
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Figure 10.38 | $I_D$ versus $V_{DS}$ characteristics for small values of $V_{DS}$ at three $V_{GS}$ voltages.
where $\mu_n$ is the mobility of the electrons in the inversion layer and $|Q'_n|$ is the magnitude of the inversion layer charge per unit area. The inversion laye... | {
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#### \*10.3.3 Current-Voltage Relationship—Mathematical Derivation
In the previous section, we qualitatively discussed the current–voltage characteristics. In this section, we derive the mathematical relation between the drain current, the gate-to-source voltage, and the drain-to-source voltage. Figure 10.43 shows ... | {
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We have
$$\int_{0}^{L} I_{x} dx = -W \mu_{n} C_{\text{ox}} \int_{V_{x}(0)}^{V_{x}(L)} [(V_{GS} - V_{T}) - V_{x}] dV_{x}$$
(10.61)
We are assuming a constant mobility $\mu_n$ . For the n-channel device, the drain current enters the drain terminal and is a constant along the entire channel length. Letting $I_D = -I... | {
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Since Equation (10.69) applies to devices biased in the saturation region, the $V_T$ parameter in this equation may differ from the extrapolated value determined in Figure 10.48a. In general, the nonsaturation current–voltage characteristics will produce the more reliable data.
#### EXAMPLE 10.8
Objective: Determ... | {
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Figure 10.50a shows an n-channel MOSFET and the associated double-subscripted voltage variables. The source-to-substrate pn junction must always be zero or reverse biased, so $V_{SB}$ must always be greater than or equal to zero.
Figure 10.50 | (a) Applied voltages on an n-channel MO... | {
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#### TEST YOUR UNDERSTANDING
- **TYU 10.6** The silicon n-channel MOSFET described in Exercise Problem Ex 10.7 is to be redesigned by changing the *WL* ratio such that *ID* 100 A when the transistor is biased in the saturation regin with *VGS* 1.0 V.
- 1.98) *<sup>L</sup> W* (Ans.
- **TYU 10.7** The parameters of a... | {
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Likewise, summing currents at the output drain node, we have
$$\frac{V_d}{R_L} + g_m V_{gs} + j\omega C_{gdT} (V_d - V_{gs}) = 0$$
(10.88)
Figure 10.56 | High-frequency smallsignal equivalent circuit of commonsource n-channel MOSFET.
Figure 10.57 | S... | {
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The n-well CMOS process, shown in Figure 10.58b, starts with an optimized p-type substrate that is used to form the n-channel MOSFETs. (The n-channel MOSFETs, in general, have superior characteristics, so this starting point should yield excellent n-channel devices.) The n well is then added, in which the p-channel dev... | {
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#### **REVIEW QUESTIONS**
- **1.** Sketch the energy-band diagrams in a MOS capacitor with an n-type substrate in accumulation, depletion, and inversion modes.
- **2.** Describe what is meant by an inversion layer of charge. Describe how an inversion layer of charge can be formed in a MOS capacitor with a p-type su... | {
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Determine the n-type doping concentration.
- An n<sup>+</sup> polysilicon gate–silicon dioxide–silicon MOS capacitor has an oxide thickness of $t_{ox} = 18$ nm = 180 Å and a doping of $N_a = 10^{15}$ cm<sup>-3</sup>. The oxide charge density is $Q'_{ss} = 6 \times 10^{10}$ cm<sup>-2</sup>. Calculate the (a) flat-... | {
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Consider the defi nition of threshold voltage and show that the inversion charge density goes to zero at the drain terminal at saturation. (Hint: Let *Vx VDS VDS*(sat).)
- 10.33 Consider an n-channel MOSFET with the following parameters: $k'_n = 0.18 \text{ mA/V}^2$ , W/L = 8, and $V_T = 0.4 \text{ V}$ . Determine ... | {
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(b) Plot the following curves on the same graph: $\sqrt{I_D}$ versus $V_G$ for $V_D = 0.1$ V and $V_D = 5$ V over the range $0 \le I_D \le 1$ mA for (i) $R_S = R_D = 0$ and (ii) $R_S = R_D = 1$ k $\Omega$ .
- 10.42 An n-channel MOSFET has the same parameters as given in Problem 10.37. The gate terminal is... | {
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#### **Section 10.4 Frequency Limitations**
- 10.55 Consider an ideal n-channel MOSFET with a width-to-length ratio of (W/L) = 10, an electron mobility of $\mu_n = 400 \text{ cm}^2/\text{V-s}$ , an oxide thickness of $t_{ox} = 475 \text{ Å}$ , and a threshold voltage of $V_T = +0.65 \text{ V}$ . (a) Determine th... | {
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I n this chapter we present additional concepts that are commonly encountered in metal–oxide–semiconductor fi eld-effect transistors (MOSFETs). These concepts include nonideal effects, small device geometry, breakdown, threshold voltage adjustment by ion implantation, and radiation effects. Although there are a multitu... | {
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Neglecting any charges that exist due to current, we can write
$$\frac{d\mathbf{E}}{dx} = \frac{\rho(x)}{\epsilon_s} \tag{11.6}$$
where $\rho(x) = -eN_a$ and is a constant for a uniformly doped substrate. Integrating Equation (11.6) and applying the boundary conditions give the electric field in the space charge ... | {
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If there is a positive fixed oxide charge near the oxide-semiconductor interface, the mobility will be further reduced due to the additional coulomb interaction.
Figure 11.9 | Schematic of carrier surface scattering effect... | {
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*(From Sze and Ng [22].)*
mean time between collisions or the mean distance between scattering events. In the long-channel device, the channel length *L* is much longer than the mean distance between collisions *l*, so that an average carrier drift velocity exists. As the MOSFET channel length is reduced, the mean di... | {
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#### TEST YOUR UNDERSTANDING
TYU 11.3 An NMOS transistor has the following parameters: $L = 1 \mu m$ , $W = 10 \mu m$ , $t_{ox} = 250 \text{ Å}$ , $N_a = 5 \times 10^{15} \text{ cm}^{-3}$ , and applied voltages of 3 V. If the device is to be scaled using constant-field scaling, determine the new device paramete... | {
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The basic assumption in this analysis is that the bulk charge in the trapezoidal region under the gate is controlled by the gate. The potential difference across the bulk space charge region is 2*f p* at the threshold inversion point, and the built-in potential barrier height of the source and drain junctions is also... | {
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If we neglect short-channel effects, the gate-controlled bulk charge can be written as
$$Q_B = Q_{B0} + \Delta Q_B \tag{11.31}$$
where $Q_B$ is the total bulk charge, $Q_{B0}$ is the ideal bulk charge, and $\Delta Q_B$ is the additional bulk charge at the ends of the channel width. For a uniformly doped p-t... | {
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Figure 11.24a shows the device when avalanche breakdown is just beginning in the space charge region near the drain. We tend to think of the avalanche breakdown suddenly occurring at a particular voltage. However, avalanche breakdown is a gradual process that starts at low current levels and for electric fields somew... | {
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We can then find
$$V_{bi} + V_{DS} = \frac{x_d^2 e N_a}{2\epsilon_s} = \frac{(0.864 \times 10^{-4})^2 (1.6 \times 10^{-19})(10^{16})}{2(11.7)(8.85 \times 10^{-14})}$$
$$= 5.77 \text{ V}$$
The punch-through voltage is then found as
$$V_{DS} = 5.77 - 0.874 = 4.9 \text{ V}$$
#### ■ **Comment**
As the two space c... | {
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**EXAMPLE 11.6**
Consider an n-channel silicon MOSFET with a doping of $N_a = 5 \times 10^{15}$ cm<sup>-3</sup>, an oxide thickness of $t_{ax} = 18$ nm = 180 Å, and an initial flat-band voltage of $V_{FBO} = -1.25$ V. Determine the ion implantation dose such that a threshold voltage of $V_T = +0.4$ V is obt... | {
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[ $_{z-}$ uuɔ $_{11}$ 01 $\times$ $_{z-}$ uuɔ $_{11}$ 01 $\times$ $_{z-}$ uuɔ $_{11}$ 01 $\times$ $_{z-}$ uuɔ $_{z-}$ 1101 $\times$ $_{z-}$ uuɔ $_{z-}$ 1101 $\times$ $_{z-}$ 1101 $\times$ 2018 $\times$ 1101 $\times$ 2018 $\times$ 1101 $\times$ 2019 $\times$ 1101 $\times$ 2019 $\times$ 1101 $\tim... | {
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These charges can exist because the oxide is essentially a perfect dielectric and a net charge density can exist in a dielectric material. Two processes that generate these charges are ionizing radiation and impact ionization in the drain region of a MOSFET operating near avalanche breakdown.
MOS devices are exposed ... | {
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In addition, since the interface states can be charged, they are another source of coulomb interaction with the inversion charge carrier, which means that the inversion carrier mobility is a function of the interface state density through surface-scattering effects. Interface states, then, affect both threshold voltage... | {
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- **snapback** The negative resistance effect during breakdown in a MOSFET caused by the variable current gain in a parasitic bipolar transistor.
- **subthreshold conduction** The process of current conduction in a MOSFET when the transistor is biased below the threshold inversion point.
- **surface scattering** The ... | {
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Using Equation (11.10), plot $\Delta L$ versus $V_{DS}$ over the range $2 \le V_{DS} \le 5$ V for (a) $E_{\text{sat}} = 10^4$ V/cm and $E_{\text{sat}} = 2 \times 10^5$ V/cm.
- Assume that the lateral electric field at the point where the inversion charge pinches off is given by $E_{sat} = V_{DS}(sat)/L$ . (a... | {
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What is the equivalent long-channel threshold voltage?
- An n-channel MOSFET is doped to $N_a = 3 \times 10^{16}$ cm<sup>-3</sup> and has an oxide thickness of $t_{ox} = 20$ nm = 200 Å. The diffused junction radius is $r_j = 0.30$ $\mu$ m. Determine the minimum channel length such that the threshold voltage shif... | {
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Assume the implant is directly adjacent to the oxide-semiconductor interface.
- 11.39 A p-channel MOSFET has a p<sup>+</sup> polysilicon gate, a substrate doping of $N_d = 2 \times 10^{16} \, \mathrm{cm}^{-3}$ , an oxide thickness of $t_{ox} = 18 \, \mathrm{nm} = 180 \, \text{Å}$ , and an oxide trapped charge density... | {
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New York: John Wiley and Sons, 1982.
- **11.** Ning, T. H., P. W. Cook, R. H. Dennard, C. M. Osburn, S. E. Schuster, and H. N. Yu. "1 m MOSFET VLSI Technology: Part IV––Hot Electron Design Constraints." *IEEE Transactions on Electron Devices* ED-26 (April 1979), pp. 346–353.
- **12.** Ogura, S., P. J. Tsang, W. W. Walk... | {
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he transistor is a multijunction semiconductor device that, in conjunction with other circuit elements, is capable of current gain, voltage gain, and signal power gain. The transistor is therefore referred to as an active device, whereas the diode is passive. The basic transistor action is the control of current at one... | {
"Header 1": "The Bipolar Transistor",
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diffusion of electrons is in the +x direction so that the conventional current is in the -x direction. Considering magnitudes only, Equation (12.1) can be written as
$$i_C = I_S \exp\left(\frac{\nu_{BE}}{V_t}\right) \tag{12.2}$$
The collector current is controlled by the base–emitter voltage; that is, the current... | {
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The term "saturation" as applied to the BJT means that the output current and output voltage do not change as the base–emitter voltage changes. The term "saturation region" as applied to the MOSFET means that the output current does not change (ideally) with a change in the drain-to-source voltage.
*inverse active,* ... | {
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The excess electron concentration is defined as
$$\delta n_B(x) = n_B(x) - n_{B0} \tag{12.10}$$
The general solution to Equation (12.9) can be written as
$$\delta n_B(x) = A \exp\left(\frac{+x}{L_B}\right) + B \exp\left(\frac{-x}{L_B}\right)$$
(12.11)
where $L_B$ is the minority carrier diffusion length in th... | {
"Header 1": "The Bipolar Transistor",
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=
$$(\Delta_{R})_{a}$$
( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ ( $\Delta_{R})_{a}$ (... | {
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The excess minority carrier hole concentrations at the two boundaries are
$$\delta p_E(x'=0) \equiv \delta p_E(0) = C + D$$
(12.19a)
and
$$\delta p_E(x' = x_E) \equiv \delta p_E(x_E) = C \exp\left(\frac{x_E}{L_E}\right) + D \exp\left(\frac{-x_E}{L_E}\right)$$
(12.19b)
Again, the B–E junction is forward biased... | {
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The electron flux that reaches the collector is $J_{nC}^-$ . The majority carrier holes from the base that are injected back into the emitter result in a hole flux denoted by $J_{nE}^+$ . Some electrons and holes
Figure 12.18 | Particle current density or flux components in an npn bip... | {
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We now wish to determine the various transistor current components and each of the gain factors in terms of the electrical and geometrical parameters of the transistor. The results of these derivations show how the various parameters in the transistor influence the electrical properties of the device and point the way ... | {
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In addition, if $\exp{(eV_{BE}/kT)} \gg 1$ , then the base transport factor is approximately
$$\alpha_T \approx \frac{1}{\cosh\left(x_B/L_B\right)} \tag{12.39a}$$
For $x_B \ll L_B$ , we may expand the cosh function in a Taylor series, so that
$$\alpha_T \approx \frac{1}{\cosh(x_B/L_B)} \approx \frac{1}{1 + \fra... | {
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The common-emitter current gain is defined as $\beta_0 = I_C/I_B$ . From Figure 12.8 we see that $I_E = I_B + I_C$ . We can determine the relation between common-emitter and common-base current gains from the KCL equation. We can write
$$\frac{I_E}{I_C} = \frac{I_B}{I_C} + 1$$
Substituting the definitions of curr... | {
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#### EXERCISE PROBLEM
**Ex 12.6** If $J_{r0} = 10^{-8}$ A/cm<sup>2</sup> and $J_{s0} = 10^{-11}$ A/cm<sup>2</sup>, determine the value of $V_{BE}$ such that $\delta = 0.9950$ . ( $\Lambda 07\xi 9.0 = 3^{9}\Lambda \text{ 'suV}$ )
#### **EXAMPLE 12.7**
Objective: Calculate the common-emitter current gain o... | {
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[ $\forall 0.029$ O/s (0.029) Signar (b) (0.029) Signar (b) (0.029) Signar (b) (0.029) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) Signar (c) S... | {
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Objective: Calculate the change in collector current with a change in neutral base width, and estimate the Early voltage.
**EXAMPLE 12.8**
Consider a uniformly doped silicon npn bipolar transistor with the following parameters: $N_B = 5 \times 10^{16} \text{ cm}^{-3}$ , $N_C = 2 \times 10^{15} \text{ cm}^{-3}$ ... | {
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The distance between donor atoms decreases as the concentration of impurity donor atoms increases, and the splitting of the donor level is caused by the interaction of donor atoms with each other. As the doping continues to increase, the donor band widens, becomes skewed, and moves up toward the conduction band, eventu... | {
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To avoid the current crowding effect, these transistors are usually designed with narrow emitter widths and fabricated with an interdigitated design. Figure 12.29 shows the basic geometry. In effect, many narrow emitters are connected in parallel to achieve the required emitter area.
Fi... | {
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A larger punch-through voltage will also require a larger collector width in order to avoid premature breakdown in this region.
#### **EXERCISE PROBLEM**
Ex 12.10 The metallurgical base width of a silicon npn bipolar transistor is $x_{B0} = 0.80 \mu \text{m}$ . The base and collector doping concentrations are $N_... | {
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$(\forall \mathcal{H} \ 0 \in \mathcal{I} \nabla \cdot \text{SuV})$
- **TYU 12.9** (a) If, because of fabrication tolerances, the neutral base width for a set of transistors varies over the range of $0.800 \le x_B \le 1.00 \ \mu\text{m}$ , determine the variation in the base transport factor $\alpha_T$ . Assume $L_... | {
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Combining Equations (12.64) and (12.70), we have
$$-(I_B + I_C) = \alpha_R I_{CS} \left[ \exp\left(\frac{eV_{BC}}{kT}\right) - 1 \right] - I_{ES} \left[ \exp\left(\frac{eV_{BE}}{kT}\right) - 1 \right]$$
(12.73)
If we solve for $[\exp(eV_{BC}/kT) - 1]$ from Equation (12.73), and substitute the resulting expressi... | {
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The Gummel–Poon model can also take into account nonideal effects, such as the Early effect and high-level injection. As the B–C voltage changes, the neutral base width changes so that the base Gummel number $Q_B$ changes. The change in $Q_B$ with B–C voltage then makes the electron current density given by Equat... | {
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C_n = 1.75 pF)$$
#### 12.6 | FREQUENCY LIMITATIONS
The hybrid-pi equivalent circuit, developed in the last section, introduces frequency effects through the capacitor–resistor circuits. We now discuss the various physical factors in the bipolar transistor affecting the frequency limitations of the device and then d... | {
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Comparing Equations (12.104) and (12.102), the beta cutoff frequency is related to the cutoff frequency by
$$f_{\beta} \cong \frac{f_T}{\beta_0} \tag{12.105}$$
Figure 12.42 shows a Bode plot of the common-emitter current gain as a function of frequency and shows the relative values of the beta and cutoff frequenc... | {
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#### **12.7.2 The Schottky-Clamped Transistor**
One method frequently employed to reduce the storage time and increase the switching speed is the use of a Schottky-clamped transistor. This is a normal npn bipolar device with a Schottky diode connected between base and collector, as shown in Figure 12.45a. The circu... | {
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For a bandgap narrowing of 100 meV, the Early voltage is increased by approximately a factor of 12. Incorporating Ge into the base region can increase the Early voltage by a large factor.
Base Transit Time and Emitter-Base Charging Time Effects The decrease in bandgap energy from the base-emitter junction to the base... | {
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cutoff frequency The frequency at which the magnitude of the common-emitter current gain is unity.
early effect Another term for base width modulation.
early voltage The value of voltage (magnitude) at the intercept on the voltage axis obtained by extrapolating the $I_C$ versus $V_{CE}$ curves to zero current... | {
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(ii) At what value of $I_C$ does $V_{CB} = 0$ ? (b) Repeat part (a) for $R_C = 10$ k $\Omega$ .
#### **Section 12.2 Minority Carrier Distribution**
- A uniformly doped silicon npn bipolar transistor at T=300 K is biased in the forward-active mode. The doping concentrations are $N_E=8\times10^{17}$ cm<sup>-3<... | {
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Determine (a) $V_{BC}$ , (b) $V_{CE}(sat)$ , (c) the #/cm<sup>2</sup> of excess minority carrier electrons in the base region, and (d) the #/cm<sup>2</sup> of excess minority carrier holes in the long collector. Let $L_C = 35$ $\mu$ m.
- An npn silicon bipolar transistor at T=300 K has uniform dopings of $N_E=10^... | {
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(*b*) Calculate the emitter injection effi ciency, , for *NBNE* 0.01, 0.10, 1.0, and 10. Assuming that *<sup>T</sup>* and are unity, determine for each case. (*c*) Considering the results of parts (*a*) and (*b*), what conclusions can be made concerning when the base transport factor or when the emitter injection effi ... | {
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The uniform dopings are $N_E = 10^{18} \text{ cm}^{-3}$ , $N_B = 5 \times 10^{16} \text{ cm}^{-3}$ , and $N_C = 10^{15} \text{ cm}^{-3}$ . Other parameters are $D_E = 10 \text{ cm}^2/\text{s}$ , $D_B = 25 \text{ cm}^2/\text{s}$ , $\tau_{E0} = 10^{-8} \text{ s}$ , and $\tau_{B0} = 10^{-7} \text{ s}$ . Determine t... | {
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Neglecting the B–E space charge width and assuming $x_B \ll L_B$ , (a) determine the change in neutral base width as $V_{BC}$ changes from 1 to 5 V, (b) find the corresponding change in collector current, (c) estimate the Early voltage, and (d) find the output resistance.
- 12.40 Consider a uniformly doped silicon n... | {
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Show that, when a collector–emitter voltage is applied, we have
$$I_C \equiv I_{CEO} = I_{CS} \frac{(1 - \alpha_F \alpha_R)}{(1 - \alpha_F)}$$
- 12.53 The parameters in the Ebers-Moll model are $\alpha_F = 0.9920$ , $I_{ES} = 5 \times 10^{-14}$ A, and $I_{CS} = 10^{-13}$ A. Let T = 300 K. Plot $I_C$ versus ... | {
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Upper Saddle River, NJ: Pearson Prentice Hall, 2006.
- **18.** Sze, S. M. *High-Speed Semiconductor Devices.* New York: John Wiley & Sons, 1990.
- **19.** \_\_\_\_\_\_\_\_. and K. K. Ng. *Physics of Semiconductor Devices,* 3rd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2007.
- **20.** Tiwari, S., S. L. Wright, and A. W.... | {
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he Junction Field-Effect Transistor (JFET) is a separate class of fi eld-effect transistors. The MOSFET has been considered in Chapters 10 and 11. In this chapter, we cover the physics and properties of the JFET. Although we have discussed the MOS and bipolar transistors in previous chapters, the material in this chapt... | {
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If we assume that *L* - *L,* then the electric fi eld in the n-channel region remains unchanged from the *VDS*(sat) case; the drain current will remain constant as *VDS* changes. Once the carriers are in the drain region,
**Figure 13.5** | Expanded view of the space charge region in th... | {
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**n-channel pn JFET** Figure 13.10a shows a simplified one-sided n-channel pn JFET. The metallurgical channel thickness between the $p^+$ gate region and the substrate is a, and the induced depletion region width for the one-sided $p^+$ n junction is h. Assume the drain-to-source voltage is zero. If we assume the ab... | {
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The built-in potential barrier is
$$V_{bi} = V_t \ln \left( \frac{N_a N_d}{n_i^2} \right) = (0.0259) \ln \left[ \frac{(2 \times 10^{16})(10^{18})}{(1.5 \times 10^{10})^2} \right] = 0.832 \text{ V}$$
From Equation (13.8), the internal pinchoff voltage must be
$$V_{p0} = V_{bi} + V_p = 0.832 + 2.25 = 3.08 \text{ V}... | {
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The derivation of the ideal current–voltage relation of the JFET is somewhat tedious, and the resulting equations are cumbersome in hand calculations. Before we go through this derivation, consider the following expression, which is a good approximation
to the I-V characteristics when the JFET is biased in the satura... | {
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We may also note, from Equation (13.33), that the channel conductance is modulated or controlled by the gate voltage. This channel conductance modulation is the basis of the field-effect phenomenon.
We have shown that the drain becomes pinched off, for the n-channel JFET, when
$$V_{DS} = V_{DS}(\text{sat}) = V_{p0}... | {
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The transconductance in the saturation region is then found to be
$$g_{ms} = \frac{\partial I_{D1}(\text{sat})}{\partial V_{GS}} = \frac{3I_{P1}}{V_{p0}} \left( 1 - \sqrt{\frac{V_{bi} - V_{GS}}{V_{p0}}} \right) = G_{01} \left( 1 - \sqrt{\frac{V_{bi} - V_{GS}}{V_{p0}}} \right)$$
(13.41a)
Using the current–voltage ap... | {
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#### **■ Solution**
The built-in potential barrier is
$$V_{bi} = V_t \ln \left( \frac{N_a N_d}{n_i^2} \right) = (0.0259) \ln \left[ \frac{(10^{18})(3 \times 10^{15})}{(1.8 \times 10^6)^2} \right] = 1.25 \text{ V}$$
The internal pinchoff voltage is
$$V_{p0} = \frac{ea^2 N_d}{2\epsilon_s} = \frac{(1.6 \times 10... | {
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Calculate the conduction parameter $k_n$ and the current $I_{D1}$ (sat) for $V_{GS} = 0.50 \text{ V}$ .
[Yul $SZSCO = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{1/2}I^2 = (188)^{... | {
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Calculate the pinchoff current $I_{P1}$ and the maximum drain current $I_{D1}$ (sat) for $V_{GS} = 0$ . [Yw 957:0 = (185)]<sup>1</sup>Q1 'Yw 659:0 = $1^d I$ 'swY]
#### \*13.3 | NONIDEAL EFFECTS
As with any semiconductor device, there are nonideal effects that will change the ideal device characteristics. In a... | {
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This saturation effect occurs at a drain voltage smaller than the $V_{DS}(\text{sat})$ value determined previously. Both $I_{DS}(\text{sat})$ and $V_{DS}(\text{sat})$ will be smaller than previously calculated.
Figure 13.16 shows normalized plots of $I_D$ versus $V_{DS}$ . Figure 13.16a is for the case of a ... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 2013,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
We have,
when the output is short-circuited,
$$I_i = j\omega \left( C_{gs} + C_{gd} \right) V_{gs} \tag{13.62}$$
If we let $C_G = C_{gs} + C_{gd}$ , then at the cutoff frequency
$$|I_i| = 2\pi f_T C_G V_{gs} = g_m V_{gs} \tag{13.63}$$
or
$$f_T = \frac{g_m}{2\pi C_g} \tag{13.64}$$
From Equation (13.41b), ... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 2019,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
(From Shur [13].)
separation between the carriers and ionized donors increases further the electron mobility, since there is even less coulomb interaction. One disadvantage of this graded heterojunction is that the electron density in the potential well tends to be smaller than in the abrupt junction.
The molecul... | {
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"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 1963,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
If we assume a constant mobility, then for low $V_{DS}$ values, we have
$$I_{D} = \frac{\epsilon_{N} \mu W}{2L(d + \Delta d)} \left[ 2(V_{g} - V_{\text{off}}) V_{DS} - V_{DS}^{2} \right]$$
(13.74)
The form of this equation is the same as that for the pn JFET or MESFET operating in the nonsaturation region. If ... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 1924,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
#### **REVIEW QUESTIONS**
- **1.** Sketch the cross section of a p-channel pn JFET and indicate voltage polarities for device operation.
- **2.** Sketch cross sections of a p-channel pn JFET showing the depletion regions when biased in the nonsaturation region and in the saturation region.
- **3.** What is the mech... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 2027,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
Normalize this transconductance to millisiemens per unit width, or mS /mm.
- **13.15** (*a*) Calculate the maximum transconductance for the transistor described in Problem 13.13 (*b*) Determine the maximum transconductance if the channel length is reduced to 2 m.
- **13.16** The Schottky barrier height, *Bn*, of a meta... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 2004,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
(d) If the electron mobility is a constant and equal to $\mu_n = 1000 \text{ cm}^2/\text{V-s}$ , calculate $I_{D1}(\text{sat})$ if velocity saturation did not occur.
- \*13.30 (a) Repeat Problem 13.29 if $L = 1 \mu m$ and all other parameters remain the same. (b) If velocity saturation occurs, does the relation $... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 2039,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
B. "Subthreshold Conduction in Uniformly Doped Epitaxial GaAs MESFETs." *IEEE Transactions on Electron Devices* 36, no. 7 (July 1989), pp. 1264–1273.
- **3.** Dimitrijev, S. *Principles of Semiconductor Devices*. New York: Oxford University Press, 2006.
- **4.** Drummond, T. J., W. T. Masselink, and H. Morkoc. "Modulat... | {
"Header 1": "**The Junction Field-Effect Transistor**",
"Header 2": "13.2.2 Ideal DC Current-Voltage Relationship—Depletion Mode JFET",
"token_count": 902,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
n previous chapters, we have considered the basic physics of transistors that are used to amplify or switch electrical signals. Semiconductor devices can be designed to convert optical energy into electrical energy, and to convert electrical signals into optical signals. These devices are used in broadband communicatio... | {
"Header 1": "**Optical Devices**",
"token_count": 2041,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
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