Consider a parallel-plate capacitor having an area of 3225

(a) Compute the electrical conductivity of a cylindrical silicon specimen 7.0 mm (0.28 in.) diameter and 57 mm (2.25 in.) in length in which a current of 0.25 A passes in an axial direction. A voltage of 24 V is measured across two probes that are separated by 45 mm (1.75 in.). (b) Compute the resistance over the entire 57 mm (2.25 in.) of the specimen

An aluminum wire 10 m long must experience a voltage drop of less than 1.0 V when a current of 5 A passes through it. Using the data in Table 18.1, compute the minimum diameter of the wire.

A plain carbon steel wire 3 mm in diameter is to offer a resistance of no more than 20 . Using the data in Table 18.1, compute the maximum wire length.

Demonstrate that the two Ohms law expressions, Equations 18.1 and 18.5, are equivalent.

(a) Using the data in Table 18.1, compute the resistance of an aluminum wire 5 mm (0.20 in.) in diameter and 5 m (200 in.) in length. (b) What would be the current flow if the potential drop across the ends of the wire is 0.04 V? (c) What is the current density? (d) What is the magnitude of the electric field across the ends of the wire?

What is the distinction between electronic and ionic conduction?

How does the electron structure of an isolated atom differ from that of a solid material?

In terms of electron energy band structure, discuss reasons for the difference in electrical conductivity among metals, semiconductors, and insulators.

Briefly state what is meant by the drift velocity and mobility of a free electron.

(a) Calculate the drift velocity of electrons in silicon at room temperature and when the magnitude of the electric field is 500 V/m. (b) Under these circumstances, how long does it take an electron to traverse a 25-mm (1-in.) length of crystal?

At room temperature the electrical conductivity and the electron mobility for aluminum are 3.8 107 (#m)1 and 0.0012 m 2/V#s, respectively. (a) Compute the number of free electrons per cubic meter for aluminum at room temperature. (b) What is the number of free electrons per aluminum atom? Assume a density of 2.7 g/cm3 .

(a) Calculate the number of free electrons per cubic meter for silver, assuming that there are 1.3 free electrons per silver atom. The electrical conductivity and density for Ag are 6.8 107 (#m)1 and 10.5 g/cm3 , respectively. (b) Now, compute the electron mobility for Ag.

From Figure 18.39, estimate the value of A in Equation 18.11 for zinc as an impurity in copper zinc alloys.

(a) Using the data in Figure 18.8, determine the values of r0 and a from Equation 18.10 for pure copper. Take the temperature T to be in degrees Celsius. (b) Determine the value of A in Equation 18.11 for nickel as an impurity in copper, using the data in Figure 18.8. (c) Using the results of parts (a) and (b), estimate the electrical resistivity of copper containing 2.50 at% Ni at 120C.

Determine the electrical conductivity of a CuNi alloy that has a tensile strength of 275 MPa (40,000 psi). See Figure 7.16.

Tin bronze has a composition of 89 wt% Cu and 11 wt% Sn and consists of two phases at room temperature: an a phase, which is copper containing a very small amount of tin in solid solution, and an P phase, which consists of approximately 37 wt% Sn. Compute the roomtemperature conductivity of this alloy given the following data:

A cylindrical metal wire 3 mm (0.12 in.) in diameter is required to carry a current of 12 A with a minimum of 0.01 V drop per foot (300 mm) of wire. Which of the metals and alloys listed in Table 18.1 are possible candidates?

(a) Using the data presented in Figure 18.16, determine the number of free electrons per atom for intrinsic germanium and silicon at room temperature (298 K). The densities for Ge and Si are 5.32 and 2.33 g/cm3 , respectively. (b) Now, explain the difference in these freeelectron-per-atom values.

For intrinsic semiconductors, the intrinsic carrier concentration ni depends on temperature, as follows: ni expa - Eg 2kTb (18.35a) or, taking natural logarithms, lnni - Eg 2kT (18.35b) Thus, a plot of lnni versus 1/T (K)1 should be linear and yield a slope of Eg/2k. Using this information and the data presented in Figure 18.16, determine the band gap energies for silicon and germanium and compare these values with those given in Table 18.3.

Briefly explain the presence of the factor 2 in the denominator of Equation 18.35a.

At room temperature, the electrical conductivity of PbS is 25 (# m)1 , whereas the electron and hole mobilities are 0.06 and 0.02 m2 /V# s, respectively. Compute the intrinsic carrier concentration for PbS at room temperature.

Is it possible for compound semiconductors to exhibit intrinsic behavior? Explain your answer.

For each of the following pairs of semiconductors, decide which has the smaller band gap energy, Eg, and then cite the reason for your choice. (a) C (diamond) and Ge (b) AlP and InAs (c) GaAs and ZnSe (d) ZnSe and CdTe (e) CdS and NaCl

Define the following terms as they pertain to semiconducting materials: intrinsic, extrinsic, compound, elemental. Provide an example of each.

An n-type semiconductor is known to have an electron concentration of 5  1017 m3 . If the electron drift velocity is 350 m/s in an electric field of 1000 V/m, calculate the conductivity of this material.

(a) In your own words, explain how donor impurities in semiconductors give rise to free electrons in numbers in excess of those generated by valence bandconduction band excitations. (b) Also, explain how acceptor impurities give rise to holes in numbers in excess of those generated by valence bandconduction band excitations.

(a) Explain why no hole is generated by the electron excitation involving a donor impurity atom. (b) Explain why no free electron is generated by the electron excitation involving an acceptor impurity atom.

Predict whether each of the following elements will act as a donor or an acceptor when added to the indicated semiconducting material. Assume that the impurity elements are substitutional.

(a) The room-temperature electrical conductivity of a silicon specimen is 500 (#m)1 . The hole concentration is known to be 2.0  1022 m3 . Using the electron and hole mobilities for silicon in Table 18.3, compute the electron concentration. (b) On the basis of the result in part (a), is the specimen intrinsic, n-type extrinsic, or p-type extrinsic? Why? 1

Germanium to which 1024 m3 As atoms have been added is an extrinsic semiconductor at room temperature, and virtually all the As atoms may be thought of as being ionized (i.e., one charge carrier exists for each As atom). (a) Is this material n-type or p-type? (b) Calculate the electrical conductivity of this material, assuming electron and hole mobilities of 0.1 and 0.05 m2 /V#s, respectively.

The following electrical characteristics have been determined for both intrinsic and p-type extrinsic gallium antimonide (GaSb) at room temperature: S(# m) 1 n(m3 ) p(m3 ) Intrinsic 8.9  104 8.7  1023 8.7  1023 Extrinsic 2.3  105 7.6  1022 1.0  1025 (p-type) Calculate electron and hole mobilities. Th

Calculate the conductivity of intrinsic silicon at 80C.

At temperatures near room temperature, the temperature dependence of the conductivity for intrinsic germanium is found to be given by s = CT -3>2 expa - Eg 2kTb (18.36) where C is a temperature-independent constant and T is in Kelvins. Using Equation 18.36, calculate the intrinsic electrical conductivity of germanium at 175C

Using Equation 18.36 and the results of Problem 18.33, determine the temperature at which the electrical conductivity of intrinsic germanium is 40 (#m)1 .

Estimate the temperature at which GaAs has an electrical conductivity of 1.6  103 (#m)1 , assuming the temperature dependence for s of Equation 18.36. The data shown in Table 18.3 may prove helpful. 1

Compare the temperature dependence of the conductivity for metals and intrinsic semiconductors. Briefly explain the difference in behavior.

Calculate the room-temperature electrical conductivity of silicon that has been doped with 1023 m3 of arsenic atoms.

Calculate the room-temperature electrical conductivity of silicon that has been doped with 2  1024 m3 of boron atoms.

Estimate the electrical conductivity at 75C of silicon that has been doped with 1022 m3 of phosphorus atoms.

Estimate the electrical conductivity at 135C of silicon that has been doped with 1024 m3 of aluminum atoms.

A hypothetical metal is known to have an electrical resistivity of 3.3  108 (#m). A current of 25 A is passed through a specimen of this metal 15 mm thick. When a magnetic field of 0.95 tesla is simultaneously imposed in a direction perpendicular to that of the current, a Hall voltage of 2.4  107 V is measured. Compute the following: (a) the electron mobility for this metal (b) the number of free electrons per cubic meter 18

A metal alloy is known to have electrical conductivity and electron mobility values of 1.2  107 (#m)1 and 0.0050 m2 /V#s, respectively. A current of 40 A is passed through a specimen of this alloy that is 35 mm thick. What magnetic field would need to be imposed to yield a Hall voltage of 3.5  107 V?

Briefly describe electron and hole motions in a pn junction for forward and reverse biases; then explain how these lead to rectification.

How is the energy in the reaction described by Equation 18.21 dissipated?

What are the two functions that a transistor may perform in an electronic circuit?

State the differences in operation and application for junction transistors and MOSFETs.

We note in Section 12.5 (Figure 12.20) that in FeO (wstite), the iron ions can exist in both Fe2 and Fe3 states. The number of each of these ion types depends on temperature and the ambient oxygen pressure. Furthermore, we also note that in order to retain electroneutrality, one Fe2 vacancy is created for every two Fe3 ions that are formed; consequently, in order to reflect the existence of these vacancies, the formula for wstite is often represented as Fe(1x)O, where x is some small fraction less than unity. In this nonstoichiometric Fe(1x)O material, conduction is electronic and, in fact, it behaves as a p-type semiconductorthat is, the Fe3 ions act as electron acceptors, and it is relatively easy to excite an electron from the valence band into an Fe3 acceptor state with the formation of a hole. Determine the electrical conductivity of a specimen of wstite with a hole mobility of 1.0  105 m2 /V#s, and for which the value of x is 0.040. Assume that the acceptor states are saturated (i.e., one hole exists for every Fe3 ion). Wstite has the sodium chloride crystal structure with a unit cell edge length of 0.437 nm. 1

At temperatures between 540C (813 K) and 727C (1000 K), the activation energy and preexponential for the diffusion coefficient of Na in NaCl are 173,000 J/mol and 4.0  104 m2 /s, respectively. Compute the mobility for an Na ion at 600C (873 K).

A parallel-plate capacitor using a dielectric material having an Pr of 2.2 has a plate spacing of 2 mm (0.08 in.). If another material having a dielectric constant of 3.7 is used and the capacitance is to be unchanged, what must the new spacing be between the plates?

A parallel-plate capacitor with dimensions of 38 mm by 65 mm (11 2 in. by 21 2 in.) and a plate separation of 1.3 mm (0.05 in.) must have a minimum capacitance of 70 pF (7 1011 F) when an ac potential of 1000 V is applied at a frequency of 1 MHz. Which of the materials listed in Table 18.5 are possible candidates? Why?

Consider a parallel-plate capacitor having an area of 3225 mm2 (5 in.2 ), a plate separation of 1 mm (0.04 in.), and a material having a dielectric constant of 3.5 positioned between the plates. (a) What is the capacitance of this capacitor? (b) Compute the electric field that must be applied for 2 108 C to be stored on each plate.

In your own words, explain the mechanism by which charge-storing capacity is increased by the insertion of a dielectric material within the plates of a capacitor.

For CaO, the ionic radii for Ca2 and O2 ions are 0.100 and 0.140 nm, respectively. If an externally applied electric field produces a 5% expansion of the lattice, compute the dipole moment for each Ca2O2pair. Assume that this material is completely unpolarized in the absence of an electric field. 1

The polarization P of a dielectric material positioned within a parallel-plate capacitor is to be 4.0 106 C/m2 . (a) What must be the dielectric constant if an electric field of 105 V/m is applied? (b) What will be the dielectric displacement D?

A charge of 2.0 1010 C is to be stored on each plate of a parallel-plate capacitor having an area of 650 mm2 (1.0 in.2 ) and a plate separation of 4.0 mm (0.16 in.). (a) What voltage is required if a material having a dielectric constant of 3.5 is positioned within the plates? (b) What voltage would be required if a vacuum were used? (c) What are the capacitances for parts (a) and (b)? (d) Compute the dielectric displacement for part (a). (e) Compute the polarization for part (a).

(a) For each of the three types of polarization, briefly describe the mechanism by which dipoles are induced and/or oriented by the action of an applied electric field.(b) For gaseous argon, solid LiF, liquid H2O, and solid Si, what kind(s) of polarization is (are) possible? Why?

(a) Compute the magnitude of the dipole moment associated with each unit cell of BaTiO3, as illustrated in Figure 18.35. (b) Compute the maximum polarization possible for this material.

The dielectric constant for a sodalime glass measured at very high frequencies (on the order of 1015 Hz) is approximately 2.3. What fraction of the dielectric constant at relatively low frequencies (1 MHz) is attributed to ionic polarization? Neglect any orientation polarization contributions.

Briefly explain why the ferroelectric behavior of BaTiO3 ceases above its ferroelectric Curie temperature.

For an intrinsic semiconductor whose electrical conductivity is dependent on temperature per Equation 18.36, generate a spreadsheet that allows the user to determine the temperature at which the electrical conductivity is some specified value, given values of the constant C and the band gap energy Eg

A 90 wt% Cu10 wt% Ni alloy is known to have an electrical resistivity of 1.90 107 #m at room temperature (25C). Calculate the composition of a coppernickel alloy that gives a room-temperature resistivity of 2.5 107 #m. The room-temperature resistivity of pure copper may be determined from the data in Table 18.1; assume that copper and nickel form a solid solution. 18

Using information contained in Figures 18.8 and 18.39, determine the electrical conductivity of an 85 wt% Cu15 wt% Zn alloy at 100C (150F).

Is it possible to alloy copper with nickel to achieve a minimum yield strength of 130 MPa (19,000 psi) and yet maintain an electrical conductivity of 4.0 106 (#m)1 ? If not, why? If so, what concentration of nickel is required? See Figure 7.16b.

Specify a donor impurity type and concentration (in weight percent) that will produce an ntype silicon material having a room-temperature electrical conductivity of 200 (#m)1 .

One integrated circuit design calls for diffusing boron into very highpurity silicon at an elevated temperature. It is necessary that at a distance 0.2 m from the surface of the silicon wafer, the room-temperature electrical conductivity be 1000 (#m)1 . The concentration of B at the surface of the Si is maintained at a constant level of 1.0  1025 m3 ; furthermore, it is assumed that the concentration of B in the original Si material is negligible, and that at room temperature, the boron atoms are saturated. Specify the temperature at which this diffusion heat treatment is to take place if the treatment time is to be 1 h. The diffusion coefficient for the diffusion of B in Si is a function of temperature as D(m2 >s) = 2.4 * 10-4 expa - 347,000 J>mol RT b S

One of the procedures in the production of integrated circuits is the formation of a thin insulating layer of SiO2 on the surface of chips (see Figure 18.26). This is accomplished by oxidizing the surface of the silicon by subjecting it to an oxidizing atmosphere (i.e., gaseous oxygen or water vapor) at an elevated temperature. The rate of growth of the oxide film is parabolic that is, the thickness of the oxide layer (x) is a function of time (t) according to the following equation: x2 = Bt (18.37) Here, the parameter B is dependent on both temperature and the oxidizing atmosphere. (a) For an atmosphere of O2 at a pressure of 1 atm, the temperature dependence of B (in units of m2 /h) is as follows: B = 800 expa - 1.24 eV kT b (18.38a) where k is Boltzmanns constant (8.62  105 eV/atom) and T is in K. Calculate the time required to grow an oxide layer (in an atmosphere of O2) that is 100 nm thick at both 700C and 1000C.(b) In an atmosphere of H2O (1 atm pressure), the expression for B (again, in units of m2 /h) is B = 215 expa - 0.70 eV kT b (18.38b) Calculate the time required to grow an oxide layer that is 100 nm thick (in an atmosphere of H2O) at both 700C and 1000C, and compare these times with those computed in part (a).

The base semiconducting material used in virtually all modern integrated circuits is silicon. However, silicon has some limitations and restrictions. Write an essay comparing the properties and applications (and/or potential applications) of silicon and gallium arsenide.

Problem 18.47 noted that FeO (wstite) may behave as a semiconductor by virtue of the transformation of Fe2 to Fe3 and the creation of Fe2 vacancies; the maintenance of electroneutrality requires that for every two Fe3 ions, one vacancy is formed. The existence of these vacancies is reflected in the chemical formula of this nonstoichiometric wstite as Fe(1x)O, where x is a small number having a value less than unity. The degree of nonstoichiometry (i.e., the value of x) may be varied by changing temperature and oxygen partial pressure. Compute the value of x required to produce an Fe(1x) O material having a p-type electrical conductivity of 1200 (#m)1 ; assume that the hole mobility is 1.0  105 m2 /V# s, the crystal structure for FeO is sodium chloride (with a unit cell edge length of 0.437 nm), and the acceptor states are saturated. FUN

For a metal that has an electrical conductivity of 6.1  107 (#m)1 , what is the resistance of a wire that is 4.3 mm in diameter and 8.1 m long? (A) 3.93  105 (B) 2.29  103 (C) 9.14  103 (D) 1.46  1011 18.2FE

What is the typical electrical conductivity value/range for semiconducting materials? (A) 107 (#m )1 (B) 1020 to 107 (#m)1 (C) 106 to 104 (#m)1 (D) 1020 to 1010 (#m)1

A two-phase metal alloy is known to be composed of a and b phases that have mass fractions of 0.64 and 0.36, respectively. Using the roomtemperature electrical resistivity and the following density data, calculate the electrical resistivity of this alloy at room temperature. Phase Resistivity (#m) Density (g/cm3 ) a 1.9  108 8.26 b 5.6  107 8.60 (A) 2.09  107 #m (B) 2.14  107 #m (C) 3.70  107 #m (D) 5.90  107 #m 18.4FE Fo

For an n-type semiconductor, where is the Fermi level located? (A) In the valence band (B) In the band gap just above the top of valence band C) In the middle of the band gap (D) In the band gap just below the bottom of the conduction band

The room-temperature electrical conductivity of a semiconductor specimen is 2.8  104 (#m)1 . If the electron concentration is 2.9  1022 m3 and electron and hole mobilities are 0.14 and 0.023 m2 /V#s, respectively, calculate the hole concentration. (A) 1.24  1024 m3 (B) 7.42  1024 m3 (C) 7.60  1024 m3 (D) 7.78  1024 m3