page_content stringlengths 12 2.63M | metadata unknown |
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( $\varepsilon_-$ uo $\varepsilon_0$ 1 × $\varepsilon_0$ 1 × $\varepsilon_0$ 1 × $\varepsilon_0$ 1 × $\varepsilon_0$ 2 · $\varepsilon_0$ 3 · $\varepsilon_0$ 3 · $\varepsilon_0$ 4 · $\varepsilon_0$ 4 · $\varepsilon_0$ 5 · $\varepsilon_0$ 5 · $\varepsilon_0$ 6 · $\varepsilon_0$ 7 · $\varepsilon_0$ 8 · $\va... | {
"Header 1": "Objective: Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi energy.",
"token_count": 2296,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
In an n-type semiconductor, electrons are referred to as the majority carrier and holes as the minority carrier. By comparing the relative values of $n_0$ and $p_0$ in the example, it is easy to see how this designation came about. Similarly, in a p-type semiconductor where $p_0 > n_0$ , holes are the majority car... | {
"Header 1": "Objective: Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi energy.",
"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
#### **EXERCISE PROBLEM**
**Ex 4.6** If $n_0 = 1.5 \times 10^{20}$ cm<sup>-3</sup> in silicon at T = 300 K, determine the position of the Fermi level relative to the conduction-band energy $E_c$ . ( $\Lambda \ni 88780 : 0 \equiv {}^{3}\mathcal{F} - {}^{3}\mathcal{F}$ 'su\text{V})
We may use the same general m... | {
"Header 1": "Objective: Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi energy.",
"token_count": 483,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
$[\varepsilon_- \text{uid} \circ_{01} \text{OI} \times \varepsilon \circ_{02} \text{OI} \times \varepsilon \circ_{01} \text{OI} \times \varepsilon \circ_{02} \text{OI} \times \varepsilon \circ_{02} \text{OI} \times \varepsilon \circ_{02} \text{OI} \times \varepsilon \circ_{02} \text{OI} \times \varepsilon \circ_{02} \... | {
"Header 1": "Objective: Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi energy.",
"token_count": 2030,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
When the concentration of electrons in the conduction band exceeds the density of states $N_c$ , the Fermi energy lies within the conduction band. This type of semiconductor is called a degenerate n-type semiconductor.
In a similar way, as the acceptor doping concentration increases in a p-type semiconductor, the di... | {
"Header 1": "Objective: Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi energy.",
"token_count": 2047,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
The opposite of complete ionization occurs at T = 0 K. At absolute zero degrees, all electrons are in their lowest possible energy state; that is, for an n-type semiconductor, each donor state must contain an electron, therefore $n_d = N_d$ or $N_d^+ = 0$ . We must have, then, from Equation (4.50) that $\exp[(E_d... | {
"Header 1": "Objective: Calculate the thermal equilibrium concentrations of electrons and holes for a given Fermi energy.",
"token_count": 472,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
#### **■ Solution**
Find the ratio of holes in the acceptor state to the total number of holes in the valence band plus acceptor state. Taking into account the Boltzmann approximation and assuming the degeneracy factor is g = 4, we write
$$\frac{p_a}{p_0 + p_a} = \frac{1}{1 + \frac{N_v}{4N} \cdot \exp\left[\frac{-(... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1792,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
EXAMPLE 4.9
#### **■ Solution**
(a) From Equation (4.60), the majority carrier electron concentration is
$$n_0 = \frac{10^{16}}{2} + \sqrt{\left(\frac{10^{16}}{2}\right)^2 + (1.5 \times 10^{10})^2} \approx 10^{16} \,\mathrm{cm}^{-3}$$
The minority carrier hole concentration is found to be
$$p_0 = \frac{n_i^... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 2013,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
Suppose $\xi_{\rm c} = 0.01 \times 650$ . Suppose $\xi_{\rm c} = 0.01 \times 650$ . Suppose $\xi_{\rm c} = 0.01 \times 650$ . Suppose $\xi_{\rm c} = 0.01 \times 650$ .
We have seen that the intrinsic carrier concentration $n_i$ is a very strong function of temperature. As the temperature increases, additional e... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1047,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
[ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_0$ [ $s_-$ uuɔ $s_... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1876,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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( $\varepsilon_-$ wo $\varepsilon_-$ 0 I $\times$ 9 I $\cdot$ 2 $\cdot$ 0 U $\cdot$ $\varepsilon_-$ wo $\varepsilon_+$ 0 I $\cdot$ 9 V I = $\cdot$ 0 U $\cdot$ S I = $\cdot$ 0 U $\cdot$ S I = $\cdot$ 0 U $\cdot$ S I = $\cdot$ 0 U $\cdot$ S I = $\cdot$ 0 U $\cdot$ S I = $\cdot$ 0 U ... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1937,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
( $\varepsilon_{-}$ uso $\varepsilon_{1}$ 01 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × 0 $\varepsilon_{-}$ 101 × ... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 2039,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
If we consider an n-type semiconductor in which $N_d \gg n_i$ , then $n_0 \approx N_d$ , so that
$$E_c - E_F = kT \ln \left( \frac{N_c}{N_d} \right) \tag{4.64}$$
The distance between the bottom of the conduction band and the Fermi energy is a logarithmic function of the donor concentration. As the donor concentra... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1841,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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If we assume that $E_{Fi} \approx E_{\text{midgap}}$ , then from Equation (4.68), the position of the Fermi level at the maximum doping is given by
$$E_{Fi} - E_F = \frac{E_g}{2} - (E_a - E_v) - (E_F - E_a) = kT \ln \left(\frac{N_a}{n_i}\right)$$
or
$$0.56 - 0.045 - 3(0.0259) = 0.437 = (0.0259) \ln \left( \frac{... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1991,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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**effective density of states** The parameter *Nc*, which results from integrating the density of quantum states *gc* (*E* ) times the Fermi function *fF* (*E* ) over the conduction-band energy, and the parameter *N*v, which results from integrating the density of quantum states *g*v(*E* ) times [1 *fF* (*E*)] over t... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 2000,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### **Section 4.3** The Extrinsic Semiconductor
- Silicon at T = 300 K is doped with arsenic atoms such that the concentration of electrons is $n_0 = 7 \times 10^{15}$ cm<sup>-3</sup>. (a) Find $E_c E_F$ . (b) Determine $E_F E_v$ . (c) Calculate $p_0$ . (d) Which carrier is the minority carrier? (e) Find $E_... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 2022,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(c) Additional boron atoms are to be added such that the hole concentration is $4 \times 10^{15}$ cm<sup>-3</sup>. What concentration of boron atoms must be added and what is the new value of $n_0$ ?
- **4.40** The thermal equilibrium hole concentration in silicon at T = 300 K is $p_0 = 2 \times 10^5 \text{ cm}^{-3... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 2004,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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- **4.58** Determine the Fermi energy level with respect to the intrinsic Fermi level for each condition given in Problem 4.34.
- **4.59** Find the Fermi energy level with respect to the valence-band energy for the conditions given in Problem 4.35.
- **4.60** Calculate the position of the Fermi energy level with resp... | {
"Header 1": "EXAMPLE 4.8 Objective: Determine the temperature at which 90 percent of acceptor atoms are ionized. Consider p-type silicon doped with boron at a concentration of $N_a = 10^{16} \\, \\text{cm}^{-3}$ .",
"token_count": 1372,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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I n the previous chapter, we considered the semiconductor in equilibrium and determined electron and hole concentrations in the conduction and valence bands, respectively. A knowledge of the densities of these charged particles is important toward an understanding of the electrical properties of a semiconductor materia... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 2030,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Assume that electron and hole mobilities given in Table 5.1 apply. ( $_{\xi}$ -up $_{\xi 1}$ 0 I × $_{\xi 1}$ 1 8 = $^{v}N$ ·suv)
#### **5.1.2 Mobility Effects**
In the previous section, we defined mobility, which relates the average drift velocity of a carrier to the electric field. Electron and hole mobilitie... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 2031,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(b)
$$N_d = 10^{16} \text{ cm}^{-3} \text{ for } (i) T = 0^{\circ} \text{C} \text{ and } (ii) T = 100^{\circ} \text{C}.$$
#### **■ Solution:**
From Figure 5.2, we find the following:
(a)
$$T = 25^{\circ}\text{C}$$
; (i) $N_d = 10^{16} \text{ cm}^{-3} \Rightarrow \mu_n \cong 1200 \text{ cm}^2/\text{V-s}$ .
(i... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 2032,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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If we choose $N_d = 5 \times 10^{17}$ , then $N_I = 6 \times 10^{17}$ so that $\mu_n \approx 325$ cm<sup>2</sup>/V-s, which gives $\sigma = 20.8$ ( $\Omega$ -cm)<sup>-1</sup>. The doping is bounded between these two values. Further trial and error yields
$$N_d \approx 3.5 \times 10^{17} \, \text{cm}^{-3}$$
and... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 2031,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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The variables are $v_s = 10^7$ cm/s at T = 300 K, $E_{on} = 7 \times 10^3$ V/cm, and $E_{op} = 2 \times 10^4$ V/cm.
We may note that for small electric fields, the drift velocities reduce to
$$v_n \cong \left(\frac{E}{E_{on}}\right) \cdot v_s \tag{5.28a}$$
and
$$v_p \cong \left(\frac{E}{E_{op}}\right) \... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 812,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(a) $\mu_{\rm m} = 1000 \, {\rm cm^2/V} \cdot {\rm g}_{\rm p} = 350 \, {\rm cm^2/V} \cdot {\rm s}_{\rm p} = 350 \, {\rm cm^2/V} \cdot {\rm s}_{\rm p} = 350 \, {\rm cm^2/V} \cdot {\rm s}_{\rm p} = 350 \, {\rm cm^2/V} \cdot {\rm s}_{\rm p} = 350 \, {\rm cm^2/V} \cdot {\rm s}_{\rm p} = 350 \, {\rm cm^2/V} \cdot {\rm s}_{... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 1550,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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[s- $\Lambda_7$ tuo $\xi_69 \approx {}^{u}\eta'(q)$ ; $\xi_7$ tuo $\xi_9 \approx {}^{u}\eta'(q)$ $\xi_7$ tuo $\xi_9 \approx {}^{u}\eta'(q)$ $\xi_7$ tuo $\xi_9 \approx {}^{u}\eta'(q)$ $\xi_7$ tuo $\xi_9 \approx {}^{u}\eta'(q)$ $\xi_7$ tuo $\xi_9 \approx {}^{u}\eta'(q)$ $\xi_7$ tuo $\xi_9 \approx {}^{u}... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 1956,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### **■ Solution**
The diffusion current density is given by
$$J_{n|dif} = eD_n \frac{dn}{dx} \approx eD_n \frac{\Delta n}{\Delta x}$$
= $(1.6 \times 10^{-19})(225) \left(\frac{1 \times 10^{18} - 7 \times 10^{17}}{0.10}\right) = 108 \text{ A/cm}^2$
#### Comment
A significant diffusion current density can ... | {
"Header 1": "**Carrier Transport Phenomena**",
"token_count": 1755,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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EXAMPLE 5.6
Assume that the donor concentration in an n-type semiconductor at $T=300~{\rm K}$ is given by
$$N_d(x) = 10^{16} - 10^{19}x$$
(cm<sup>-3</sup>)
where x is given in cm and ranges between $0 \le x \le 1 \mu m$
#### **■ Solution**
Taking the derivative of the donor concentration, we have
$$\frac... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 2040,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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We can write
$$V_H = + E_H W \tag{5.50}$$
where $E_H$ is assumed positive in the +y direction and $V_H$ is positive with the polarity shown.
In a p-type semiconductor, in which holes are the majority carrier, the Hall voltage will be positive as defined in Figure 5.13. In an n-type semiconductor, in which ele... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 2036,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Is the linear relationship between drift current density and electric field always valid? Why or why not.
- **2.** Define electron and hole mobility. What is the unit of mobility?
- **3.** Explain the temperature dependence of mobility. Why is the carrier mobility a function of the ionized impurity concentrations?
- 4.... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 1965,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(b) If rectangular semiconductor bars are fabricated using the materials in part (a), determine the resistance of each bar if its cross-sectional area is $85 \mu m^2$ and length is $200 \mu m$ .
- **5.16** An n-type silicon material at T = 300 K has a conductivity of $0.25 \, (\Omega \text{-cm})^{-1}$ . (a) What is... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 2000,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Assuming complete ionization, plot the conductivity as a function of $N_d$ over the range $10^{15} \le N_d \le 10^{18}$ cm<sup>-3</sup>. (*b*) Compare the results of part (*a*) to that if the mobility were assumed to be a constant equal to 1350 cm<sup>2</sup>/V-s. (*c*) If an electric field of E = 10 V/cm is applie... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 2034,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(b) Repeat part (a) if $J_n = -20$ A/cm<sup>2</sup>.
#### **Section 5.3 Graded Impurity Distribution**
- Consider an n-type semiconductor at T=300 K in thermal equilibrium (no current). Assume that the donor concentration varies as $N_d(x)=N_{d0}e^{-x/L}$ over the range $0 \le x \le L$ where $N_{d0}=10^{16}$... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 2037,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
"Carrier Mobilities in Silicon Empirically, Related to Doping and Field." *Proc. IEEE* 55 (1967), p. 2192.
- **3.** Dimitrijev, S. *Principles of Semiconductor Devices.* New York: Oxford University, 2006.
- **4.** Kano, K. *Semiconductor Devices*. Upper Saddle River, NJ: Prentice Hall, 1998.
- **\*5.** Lundstrom, M. *F... | {
"Header 1": "Objective: Determine the induced electric field in a semiconductor in thermal equilibrium, given a linear variation in doping concentration.",
"token_count": 674,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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ur discussion of the physics of semiconductors in Chapter 4 was based on thermal equilibrium. When a voltage is applied or a current exists in a semiconductor device, the semiconductor is operating under nonequilibrium conditions. In our discussion of current transport in Chapter 5, we did not address nonequilibrium co... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1979,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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The net rate of change in the electron concentration can be written as
$$\frac{dn(t)}{dt} = \alpha_r \Big[ n_i^2 - n(t)p(t) \Big]$$
(6.7)
where
$$n(t) = n_0 + \delta n(t) \tag{6.8a}$$
and
$$p(t) = p_0 + \delta p(t) \tag{6.8b}$$
The first term, $\alpha_r n_i^2$ , in Equation (6.7) is the thermal-equilibri... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1549,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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$10^{16} \, \text{cm}^{-3} \, \text{s}^{-1}$
$\times$ \$\psi\_{0.1}\$ 10 \cdots 1 \cdots 2 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1 \cdots 1... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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The recombination rate for holes is given by $p/\tau_{pt}$ where $\tau_{pt}$ includes the thermal-equilibrium carrier lifetime and the excess carrier lifetime.
If we divide both sides of Equation (6.17) by the differential volume dx dy dz, the net increase in the hole concentration per unit time is
$$\frac{\par... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2028,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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We will impose the condition of charge neutrality: We will assume that the excess electron concentration is just balanced by an equal excess hole concentration at any point in space and time. If this assumption were exactly true, there would be no induced internal electric field to keep the two sets of particles togeth... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2020,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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If we again consider an extrinsic p-type semiconductor under low injection, the concentration of majority carrier holes will be essentially constant, even when excess carriers are present. Then, the probability per unit time of a minority carrier electron encountering a majority carrier hole will be essentially constan... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2009,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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From the charge-neutrality condition, we have that $\delta n = \delta p$ , so the excess electron concentration is given by
$$\delta n(t) = \delta p(t) = \delta p(0)e^{-t/\tau_{p0}} \tag{6.59}$$
#### Comment
The excess electrons and holes recombine at the rate determined by the excess minority carrier hole lif... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2002,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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The solution to Equation (6.63) may then be written as
$$\delta n(x) = \delta n(0)e^{-x/L_n} \qquad x \ge 0 \tag{6.65a}$$
Figure 6.6 | Steady-state generation rate at x = 0.
and
$$\delta n(x) = \delta n(0)e^{+x/L_n} \quad x \le 0 \tag{6.65b}$$
where $\delta n(0)$ is the value... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2037,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### **■ Solution**
The one-dimensional ambipolar transport equation for the minority carrier holes can be written from Equation (6.56) as
$$D_{p} \frac{\partial^{2}(\delta p)}{\partial x^{2}} - \mu_{p} E_{0} \frac{\partial(\delta p)}{\partial x} - \frac{\delta p}{\tau_{p0}} = \frac{\partial(\delta p)}{\partial t... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2013,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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In this example, the excess carriers behave according to the minority carrier hole parameters, which include $D_p$ , $\mu_p$ , and $\tau_{p0}$ . The excess majority carrier electrons are being pulled along by the excess minority carrier holes.
**Figure 6.8** | Excess hole concentrati... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2027,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Using the parameters given in TYU 6.5, calculate the values of $\delta p$ for (a) t=1 $\mu$ s at (i) $1.093 \times 10^{-2}$ cm and (ii) $x=-3.21 \times 10^{-3}$ cm; (b) t=5 $\mu$ s at (i) $x=2.64 \times 10^{-2}$ cm and (ii) $x=1.22 \times 10^{-2}$ cm; (c) t=15 $\mu$ s at (i) $x=6.50 \times 10^{-2}$ cm an... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1938,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Poisson's equation is
$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon} \tag{6.71}$$
The current equation, Ohm's law, is
$$J = \sigma E \tag{6.72}$$
The continuity equation, neglecting the effects of generation and recombination, is
$$\nabla \cdot J = -\frac{\partial \rho}{\partial t} \tag{6.73}$$
![](_page... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1917,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
If we set $t = t_1$ and $t = t_2$ in Equation (6.80) and add the two resulting equations, we may show that the diffusion coefficient is given by
$$D_p = \frac{(\mu_p E_0)^2 (\Delta t)^2}{16t_0}$$
(6.81)
where
$$\Delta t = t_2 - t_1 \tag{6.82}$$
The area S under the curve shown in Figure 6.13 is proportional... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2041,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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We have assumed up to this point that the mean carrier lifetime is simply a parameter of the semiconductor material.
We have been considering an ideal semiconductor in which electronic energy states do not exist within the forbidden-energy bandgap. This ideal effect is present in a perfect single-crystal material wit... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2041,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
Then
$$n_0 \gg p_0$$
, $n_0 \gg \delta p$ , $n_0 \gg n'$ , $n_0 \gg p'$
where $\delta p$ is the excess minority carrier hole concentration. The assumptions of $n_0 \gg n'$ and $n_0 \gg p'$ imply that the trap level energy is near midgap so that n' and p' are not too different from the intrinsic carrier con... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1990,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### **■ Solution**
From Equations (6.106) and (6.107), we have
$$\frac{\delta p_B}{\tau_{p0}} = \frac{\delta p_s}{\tau_{p0s}}$$
so that
$$\delta p_s = \delta p_B \left( \frac{\tau_{p0s}}{\tau_{p0}} \right) = (10^{14}) \left( \frac{10^{-7}}{10^{-6}} \right) = 10^{13} \text{ cm}^{-3}$$
From Equation (6.56), ... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1895,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
(a) (i) \delta p(x) = 8^{i} \tau_{p0} (1 - e^{-x/L_p}), (ii) \delta p(x) = 8^{i} \tau_{p0}; (b) (i) \delta p(0) = 0, (ii) \delta p(0) = 8^{i} \tau_{p0} and \delta p(x) = 0 constant]
```
In the above example, the surface influences the excess carrier concentration to the extent that, even at a distance of $L_p = 31.6... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1979,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
If the generation rate of holes in this differential volume is $g_p = 10^{20}$ cm<sup>-3</sup>-s<sup>-1</sup> and the recombination rate is $2 \times 10^{19}$ cm<sup>-3</sup>-s<sup>-1</sup>, what must be the gradient in the particle current density to maintain a steady-state hole concentration?
- **6.7** Repeat Pro... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2035,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(*b*) Determine the value of excess carrier concentration at (*i*) *t* 0, (*ii*) *t* 2 10<sup>6</sup> s, and (*iii*) *t* . (*c*) Plot the excess carrier concentration as a function of time.
- **6.19** Consider a bar of p-type silicon that is uniformly doped to a value of *Na* 2 1016 cm<sup>3</sup> at *T* 300 K. The... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2031,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
(*b*) Calculate the quasi-Fermi levels for electrons and holes with respect to *EFi*. (*c*) What is the difference (in eV) between E*Fn* and E*F* ?
- **6.31** Consider a p-type silicon semiconductor at *T* 300 K doped at *Na* 5 1015 cm<sup>3</sup> . (*a*) Determine the position of the Fermi level with respect to the in... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 2032,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
The semiconductor is uniformly illuminated for -W < x < 0 producing a constant excess carrier generation rate $G_0'$ . Determine the steady-state excess carrier concentration versus x if the minority carrier lifetime is infinite and if the electric field is zero.
- **6.45** Plot $\delta p(x)$ versus x for various va... | {
"Header 1": "Nonequilibrium Excess Carriers in Semiconductors",
"token_count": 1267,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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p to this point in the text, we have been considering the properties of the semiconductor material. We calculated electron and hole concentrations in thermal equilibrium and determined the position of the Fermi level. We then considered the nonequilibrium condition in which excess electrons and holes are present in the... | {
"Header 1": "The pn Junction",
"token_count": 1873,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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We can define the potential $\phi_{Fp}$ in the p region as
$$e\phi_{Fp} = E_{Fi} - E_F \tag{7.8}$$
Combining Equations (7.7) and (7.8), we find that
$$\phi_{Fp} = +\frac{kT}{e} \ln \left( \frac{N_a}{n_i} \right) \tag{7.9}$$
Finally, the built-in potential barrier for the step junction is found by substituting... | {
"Header 1": "The pn Junction",
"token_count": 2037,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
The constant of integration is then found as
$$C_1' = \frac{eN_a}{2\epsilon_s} x_p^2 \tag{7.20}$$
so that the potential in the p region can now be written as
$$\phi(x) = \frac{eN_a}{2\epsilon_*} (x + x_p)^2 \qquad (-x_p \le x \le 0)$$
(7.21)
The potential in the n region is determined by integrating the electri... | {
"Header 1": "The pn Junction",
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"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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[u2/ $\Lambda_1$ 01 × 9L7 = |xeuu3| 'u2m t905'0 = M 'u2m 69t7'0 = $d^x$ 'u2m 9650'0 = $d^x$ 'u2m 669'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m 6806'0 = $d^x$ 'u2m ... | {
"Header 1": "The pn Junction",
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( $\frac{\text{UU}}{\Lambda} \cdot 01 \times 98 \cdot \xi = \frac{\text{xem}}{3}$ ) $\frac{\text{YW}}{\Omega} \cdot 0 = \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \frac{M}{2} \cdot \... | {
"Header 1": "The pn Junction",
"token_count": 1992,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Equation (7.32) can be rewritten as
$$V_{\text{total}} = V_{bi} + V_R \tag{7.33}$$
where *Vbi* is the same built-in potential barrier we had defi ned in thermal equilibrium.
#### **7.3.1 Space Charge Width and Electric Field**
Figure 7.8 shows a pn junction with an applied reverse-biased voltage *VR.* Also indi... | {
"Header 1": "The pn Junction",
"token_count": 1987,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### EXERCISE PROBLEM
Ex 7.4 The maximum electric field in a reverse-biased GaAs pn junction at T=300 K is to be limited to $|E_{max}|=7.2\times10^4$ V/cm. The doping concentrations are $N_d=5\times10^{15}$ cm<sup>-3</sup> and $N_a=3\times10^{16}$ cm<sup>-3</sup>. Determine the maximum reverse-biased voltage ... | {
"Header 1": "The pn Junction",
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"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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[ $_{z}$ uu $_{z}$ )4 $_{6}$ -01 $_{7}$ 01 $_{7}$ 02 $_{7}$ 03 $_{7}$ 03 $_{7}$ 04 $_{7}$ 07 $_{7}$ 09 $_{7}$ 17 $_{7}$ 18 $_{7}$ 18 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 $_{7}$ 19 ... | {
"Header 1": "The pn Junction",
"token_count": 2035,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Equation (7.47) may be manipulated to give
$$\left(\frac{1}{C'}\right)^2 = \frac{2(V_{bi} + V_R)}{e\epsilon_s N_d} \tag{7.48}$$
which shows that the inverse capacitance squared is a linear function of applied reverse-biased voltage.
**Figure 7.10** | S... | {
"Header 1": "The pn Junction",
"token_count": 895,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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( $\varepsilon$ -wo $\varepsilon$ 101 × 70' $\varepsilon$ = $\varepsilon$ 101 × $\varepsilon$ 10' $\varepsilon$ = $\varepsilon$ 101 × $\varepsilon$ 10' $\varepsilon$ = $\varepsilon$ 101 × $\varepsilon$ 10' $\varepsilon$ 20' S = $\varepsilon$ 101 × $\varepsilon$ 10' S = $\varepsilon$ 10' S = $\varepsilon$ ... | {
"Header 1": "The pn Junction",
"token_count": 2045,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Determine $x_n, x_p$ , W, and $|E_{max}|$ . (b) Repeat part (a) for a reverse-biased voltage of $V_R = 12$ V. $[\text{uu} > / \Lambda_S 01 \times \gamma_S C C] = |x_S \text{uu}| / \text{uu} > / \Lambda_S 01 \times \text{uu}| / \text{uu} > / \Lambda_S 01 \times \text{uu}| / \text{uu} > / \Lambda_S 01 \times \text{u... | {
"Header 1": "The pn Junction",
"token_count": 2006,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
If we assume that a reverse-biased electron current $I_{n0}$ enters the depletion region at x = 0 as shown in Figure 7.13, the electron current $I_n$ will increase with distance through the depletion region due to the avalanche process. At x = W, the electron current may be written as
$$I_n(W) = M_n I_{n0} (7.4... | {
"Header 1": "The pn Junction",
"token_count": 2020,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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The space charge density can be written as
$$\rho(x) = eax \tag{7.62}$$
where a is the gradient of the net impurity concentration.
The electric field and potential in the space charge region can be determined from Poisson's equation. We can write
$$\frac{d\mathbf{E}}{dx} = \frac{\rho(x)}{\epsilon_s} = \frac{eax... | {
"Header 1": "The pn Junction",
"token_count": 1985,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### 7.6 I SUMMARY
- A uniformly doped pn junction is initially considered, in which one region of a semiconductor is uniformly doped with acceptor impurities and the adjacent region is uniformly doped with donor impurities.
- A space charge region, or depletion region, is formed on either side of the metallurgical... | {
"Header 1": "The pn Junction",
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"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(d) Determine $x_n, x_p$ , and the peak electric field for this junction.
- **7.5** Repeat problem 7.4 for the case when the doping concentrations are $N_a = N_d = 2 \times 10^{16} \text{ cm}^{-3}$ .
- **7.6** A silicon pn junction in thermal equilibrium at T = 300 K is doped such that $E_F E_{Fi} = 0.365$ eV in th... | {
"Header 1": "The pn Junction",
"token_count": 2007,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
(a) Determine the change in built-in potential barrier if the doping concentration in the p region increases by a factor of 3.
(b) Determine the ratio of junction capacitance when the acceptor doping is 3N<sub>a</sub> compared to that when the acceptor doping is N<sub>a</sub>. (c) Why does the junction capacitance incr... | {
"Header 1": "The pn Junction",
"token_count": 2030,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
Determine (*a*) the doping in the other region of the pn junction and (*b*) the cross-sectional area. (*c*) The reverse-biased voltage is changed and the capacitance is found to be 0.80 pF. What is the value of *VR*?
- **7.32** Examine how the capacitance *C* and the function (1*/C* ) vary with reverse-biased voltage *... | {
"Header 1": "The pn Junction",
"token_count": 2027,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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New York: Holt, Rinehart & Winston, 1986.
- **6.** Neudeck, G. W. *The PN Junction Diode*. Vol. 2 of the *Modular Series on Solid State Devices,* 2nd ed. Reading, MA: Addison-Wesley, 1989.
- **\*7.** Ng, K. K. *Complete Guide to Semiconductor Devices*. New York: McGraw-Hill, 1995.
- **8.** Pierret, R. F. *Semiconductor... | {
"Header 1": "The pn Junction",
"token_count": 513,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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I n the last chapter, we discussed the electrostatics of the pn junction in thermal equilibrium and under reverse bias. We determined the built-in potential barrier at thermal equilibrium and calculated the electric fi eld in the space charge region. We also considered the junction capacitance.
In this chapter, we co... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 1971,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Substituting Equations (8.2) and (8.3) into Equation (8.1), we obtain
$$n_{p0} = n_{n0} \exp\left(\frac{-eV_{bi}}{kT}\right) \tag{8.4}$$
This equation relates the minority carrier electron concentration on the p side of the junction to the majority carrier electron concentration on the n side of the junction in the... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 1678,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Does low injection still apply? [sə $\delta$ ' $_{\epsilon}$ -uvo $_{\epsilon 1}$ 01 $\times$ 76'8 = ("uv) $_{\epsilon}$ 01 $\times$ $_{\epsilon}$ 01 $\times$ $_{\epsilon}$ 5' $\in$ = ("uv) $_{\epsilon}$ 101 $\times$ $_{\epsilon}$ 5' $\in$ = ("uv) $_{\epsilon}$ 101 $\times$ $_{\epsilon}$ 6' $\in... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 2037,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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In the n region for $x > x_n$ , we have that E = 0 and g' = 0. If we also assume steady state so $\partial (\delta p_n)/\partial t = 0$ , then Equation (8.8) reduces to
$$\frac{d^{2}(\delta p_{n})}{dx^{2}} - \frac{\delta p_{n}}{L_{p}^{2}} = 0 \qquad (x > x_{n})$$
(8.9)
where $L_p^2 = D_p \tau_{p0}$ . For the sam... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 1875,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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We can calculate the minority carrier hole diffusion current density at $x = x_n$ from the relation
$$J_{p}(x_{n}) = -eD_{p} \frac{dp_{n}(x)}{dx} \Big|_{x=x_{n}}$$
(8.20)
Since we are assuming uniformly doped regions, the thermal-equilibrium carrier concentration is constant, so the hole diffusion current densi... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 1616,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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( $\tau_{po} = 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-1} \times 10^{-... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 1680,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### **■ Solution**
The electron diffusion current density is given by Equation (8.24) as
$$J_n = \frac{eD_n n_{p0}}{L_n} \left[ \exp\left(\frac{eV_a}{kT}\right) - 1 \right] = e\sqrt{\frac{D_n}{\tau_{n0}}} \cdot \frac{n_i^2}{N_a} \left[ \exp\left(\frac{eV_a}{kT}\right) - 1 \right]$$
Substituting the numbers, we... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 2042,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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As temperature increases, less forward-bias voltage is required to obtain the same diode current. If the voltage is held constant, the diode current will increase as temperature increases. The change in forward-bias current with temperature is less sensitive than the reverse-saturation current.
Objective: Determine t... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 2021,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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[Yu \$7.7 (3) \$\forall V \text{m } 60.7 (q) \$\forall V \text{m } \$\forall V \text{S} \text{T} \text{O} (p) \$\forall V \text{suV}]
- TYU 8.3 Consider the silicon pn junction diode described in TYU 8.2. The p region is long and the n region is short with $W_n = 2 \mu \text{m}$ . (a) Calculate the electron and hole c... | {
"Header 1": "**The pn Junction Diode**",
"token_count": 209,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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In the derivation of the ideal current–voltage relationship, we assumed low injection and neglected any effects occurring within the space charge region. High-level injection and other current components generated within the space charge region cause the *I–V* relationship to deviate from the ideal expression. The addi... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
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"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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(a) 1.677
$$\times$$
10<sup>-17</sup> A/cm<sup>2</sup>; (b) 6.166 $\times$ 10<sup>-10</sup> A/cm<sup>2</sup>; (c) 3.68 $\times$ 10<sup>7</sup>
**Forward-Bias Recombination Current** For the reverse-biased pn junction, electrons and holes are essentially completely swept out of the space charge region so that $n ... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 2035,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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In general, the diode current–voltage relationship may be written as
$$I = I_s \left[ \exp\left(\frac{eV_a}{nkT}\right) - 1 \right]$$
(8.59)
where the parameter n is called the *ideality factor*. For a large forward-bias voltage, $n \approx 1$ when diffusion dominates, and for low forward-bias voltage, $n \app... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
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Now, as the ac voltage increases during its positive half cycle, the concentration of holes at *x* 0 will increase and reach a peak value at *t t*1, which corresponds to the peak value of the ac voltage. When the ac voltage is on its negative half cycle, the total voltage across the junction decreases so that the con... | {
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$$D_{p} \frac{d^{2} p_{1}(x)}{dx^{2}} - \frac{p_{1}(x)}{\tau_{p0}} - j\omega p_{1}(x) = 0$$
(8.79)
Noting that $L_p^2 = D_p \tau_{p0}$ , Equation (8.79) may be rewritten in the form
$$\frac{d^2p_1(x)}{dx^2} - \frac{(1+j\omega\tau_{p0})}{L_p^2}p_1(x) = 0$$
(8.80)
or
$$\frac{d^2p_1(x)}{dx^2} - C_p^2 p_1(x) = 0... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 1625,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Then we may write
$$\sqrt{1 + j\omega \tau_{p0}} \approx 1 + \frac{j\omega \tau_{p0}}{2} \tag{8.100a}$$
and
$$\sqrt{1+j\omega\tau_{n0}} \approx 1 + \frac{j\omega\tau_{n0}}{2} \tag{8.100b}$$
Substituting Equations (8.100a) and (8.100b) into the admittance Equation (8.98), we obtain
$$Y = \left(\frac{1}{V_t}\ri... | {
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[Au 0:LI = ${}^p$ 2 '73 9:VI = ${}^p$ 4 (9) 'Au 0:V6'0 = ${}^p$ 2 '73 £97 = ${}^p$ 4 (p) 'suV]
**TYU 8.6** A silicon pn junction diode at T = 300 K has the same parameters as those described in Ex 8.7. The neutral n-region and neutral p-region lengths are 0.01 cm. Estimate the series resistance of the diode (ne... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 2008,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Recall the degenerately doped semiconductors we discussed in Chapter 4: the Fermi level is in the conduction band of a degenerately doped n-type material and in the valence band of a degenerately doped p-type material. Then, even at *T* 0 K, electrons will exist in the conduction band of the n-type material, and hole... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 2044,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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#### **REVIEW QUESTIONS**
- 1. Sketch the energy bands in a zero-biased, reverse-biased, and forward-biased pn junction.
- 2. Write the boundary conditions for the excess minority carriers in a pn junction (a) under forward bias and (b) under reverse bias.
- 3. Sketch the steady-state minority carrier concentration... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 2042,
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The ratio of electron current to total current is to be 0.10 and the maximum current density is to be no more than 20 A /cm2 *.* Use the semiconductor parameters given in Example 8.2.
- **8.13** An ideal silicon pn junction at *T* 300 K is under forward bias. The minority carrier lifetimes are *<sup>n</sup>*<sup>0</s... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 2034,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
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Assume that $E_g = 1.12$ eV as well as the diffusion coefficients and lifetimes are independent of temperature. The ratio of the magnitude of forward- to reverse-biased currents is to be no less than $2 \times 10^4$ with forward- and reverse-biased voltages of 0.50 V, and the maximum reverse-biased current is to be... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 2009,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
- **8.35** Consider, as shown in Figure P8.35, a uniformly doped silicon pn junction at *T* 300 K with impurity doping concentrations of *Na Nd* 5 1015 cm<sup>3</sup> and minority carrier lifetimes of *<sup>n</sup>*<sup>0</sup> *<sup>p</sup>*<sup>0</sup> <sup>0</sup> 10<sup>7</sup> s. A reverse-biased voltage of *VR*... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 1998,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
If the total current density is the same in each diode under forward bias, discuss the expected relative values of electron and hole current densities.
- **\*8.53** A silicon p n junction diode is to be designed to have a breakdown voltage of at least 60 V and to have a forward-bias current of *ID* 50 mA while still op... | {
"Header 1": "8.2 | GENERATION-RECOMBINATION CURRENTS AND HIGH-INJECTION LEVELS",
"token_count": 806,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
I n the preceding two chapters, we have considered the pn junction and assumed that the semiconductor material was the same throughout the structure. This type of junction is referred to as a *homojunction.* We developed the electrostatics of the junction and derived the current–voltage relationship. In this chapter, w... | {
"Header 1": "**Metal–Semiconductor and Semiconductor Heterojunctions**",
"token_count": 2001,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
For the uniformly doped semiconductor, we have
$$W = x_n = \left[\frac{2\epsilon_s(V_{bi} + V_R)}{eN_d}\right]^{1/2}$$
(9.7)
where $V_R$ is the magnitude of the applied reverse-biased voltage. We are again assuming an abrupt junction approximation.
Objective: Determine the theoretical barrier height, built-in p... | {
"Header 1": "**Metal–Semiconductor and Semiconductor Heterojunctions**",
"token_count": 791,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
$(\text{w}_0/\Lambda_0 \text{I} \times \text{t}_0 \text{I}) \times \text{t}_0 \text{I} \times \text{t}_0 = \text{t}_0 \times \text{t}_0 \times \text{t}_0 = \text{t}_0 \times \text{t}_0 \times \text{t}_0 = \text{t}_0 \times \text{t}_0 \times \text{t}_0 = \text{t}_0 \times \text{t}_0 \times \text{t}_0 = \text{t}_0 \time... | {
"Header 1": "**Metal–Semiconductor and Semiconductor Heterojunctions**",
"token_count": 1838,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
From Equation (9.9), we can write
$$\frac{d(1/C')^2}{dV_R} \approx \frac{\Delta(1/C')^2}{\Delta V_R} = \frac{2}{e\epsilon_s N_d}$$
Then, from the figure, we have
$$\frac{\Delta(1/C')^2}{\Delta V_R} \approx 4.4 \times 10^{13}$$
so that
$$N_d = \frac{2}{(1.6 \times 10^{-19})(11.7)(8.85 \times 10^{-14})(4.4 \tim... | {
"Header 1": "**Metal–Semiconductor and Semiconductor Heterojunctions**",
"token_count": 924,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
[ $_{c}$ tm $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ H $_{-0}$ ... | {
"Header 1": "**Metal–Semiconductor and Semiconductor Heterojunctions**",
"token_count": 1939,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
#### **■ Solution**
The Schottky barrier lowering is given by Equation (9.15), which in this case yields
$$\Delta \phi = \sqrt{\frac{eE}{4\pi\epsilon_s}} = \sqrt{\frac{(1.6 \times 10^{-19})(6.8 \times 10^4)}{4\pi (13.1)(8.85 \times 10^{-14})}} = 0.0273 \text{ V}$$
The position of the maximum barrier height is ... | {
"Header 1": "**Metal–Semiconductor and Semiconductor Heterojunctions**",
"token_count": 1986,
"source_pdf": "datasets/websources/Physics_v1/Physics/Neamen.pdf"
} |
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