For a silicon crystal doped with phosphorus, what must be

Find values of the intrinsic carrier concentration for silicon at C, C, C, C, and C. At each temperature, what fraction of the atoms is ionized? Recall that a silicon crystal has approximately atoms/cm3.

Calculate the value of for gallium arsenide (GaAs) at T = 300 K. The constant and the bandgap voltage Eg = 1.42 eV.

For a p-type silicon in which the dopant concentration , find the hole and electron concentrations at T = 300 K

For a silicon crystal doped with phosphorus, what must be if at T = 300 K the hole concentration drops below the intrinsic level by a factor of ?

In a phosphorus-doped silicon layer with impurity concentration of , find the hole and electron concentrations at and

A young designer, aiming to develop intuition concerning conducting paths within an integrated circuit, examines the end-to-end resistance of a connecting bar 10 m long, 3 m wide, and 1 m thick, made of various materials. The designer considers:(a) intrinsic silicon (b) n-doped silicon with (c) n-doped silicon with (d) p-doped silicon with (e) aluminum with resistivity of 2.8 .cm Find the resistance in each case. For intrinsic silicon, use the data in Table 3.1. For doped silicon, assume V.s. (Recall that

Contrast the electron and hole drift velocities through a 10-m layer of intrinsic silicon across which a voltage of 5 V is imposed. Let V.s and V.s.

Find the current that flows in a silicon bar of 10-m length having a cross section and having free electron and hole densities of and , respectively, when a 1 V is applied end-to-end. Use V.s and

In a 10-m long bar of donor-doped silicon, what donor concentration is needed to realize a current density of in response to an applied voltage of 1 V. (Note: Although the carrier mobilities change with doping concentration, as a first approximation you may assume to be constant and use the value for intrinsic silicon,

Holes are being steadily injected into a region of ntype silicon (connected to other devices, the details of which are not important for this question). In the steady state, the excess-hole concentration profile shown in Fig. P3.10 is established in the n-type silicon region. Here excess means over and above the thermal-equilibrium concentration (in the absence of hole injection), denoted . If , , , and W = 0.1 m, find the density of the current that will flow in the x direction.

Both the carrier mobility and diffusivity decrease as the doping concentration of silicon is increased. The table below provides a few data points for and versus doping concentration. Use the Einstein relationship to obtain the corresponding values for and .

Calculate the built-in voltage of a junction in which the p and n regions are doped equally with atoms/cm3. Assume . With the terminals left open, what is the width of the depletion region, and how far does it extend into the p and n regions? If the cross-sectional area of the junction is 100 m2, find the magnitude of the charge stored on either side of the junction.

If, for a particular junction, the acceptor concentration is and the donor concentration is , find the junction built-in voltage. Assume ni = . Also, find the width of the depletion region (W) and its extent in each of the p and n regions when the junction terminals are left open. Calculate the magnitude of the charge stored on either side of the junction. Assume that the junction area is 400 m2.

Estimate the total charge stored in a 0.1-m depletion layer on one side of a junction. The doping concentration on that side of the junction is

In a pn junction for which , and the depletion layer exists mostly on the shallowly doped side with W = 0.3 m, find if . Also calculate

By how much does change if or is increased by a factor of 10?

If a 5-V reverse-bias voltage is applied across the junction specified in Problem 3.13, find W and

Show that for a pn junction reverse-biased with a voltage , the depletion-layer width W and the charge stored on either side of the junction, , can be expressed as where and are the values in equilibrium.

In a forward-biased pn junction show that the ratio of the current component due to hole injection across the junction to the component due to electron injection is given by Evaluate this ratio for the case , , m, m, Dp = , and , and hence find and for the case in which the pn junction is conducting a forward current I = 1 mA.

Calculate and the current I for V = 700 mV for a pn junction for which , , A= 200m2, , m, m, , and .

Assuming that the temperature dependence of arises mostly because is proportional to , use the expression for in Eq. (3.2) to determine the factor by which changes as T changes from 300 K to 305 K. This will be approximately the same factor by which changes for a C rise in temperature. What is the factor?

A junction is one in which the doping concentration in the p region is much greater than that in the n region. In such a junction, the forward current is mostly due to hole injection across the junction. Show that For the specific case in which , , m, and m2, find and the voltage V obtained when I = 0.5 mA. Assume operation at 300 K where

A pn junction for which the breakdown voltage is 12 V has a rated (i.e., maximum allowable) power dissipation of 0.25 W. What continuous current in the breakdown region will raise the dissipation to half the rated value? If breakdown occurs for only 10 ms in every 20 ms, what average breakdown current is allowed?

A pn junction for which the breakdown voltage is 12 V has a rated (i.e., maximum allowable) power dissipation of 0.25 W. What continuous current in the breakdown region will raise the dissipation to half the rated value? If breakdown occurs for only 10 ms in every 20 ms, what average breakdown current is allowed?

For a particular junction for which pF, V, and m = 1/3, find at reverse-bias voltages of 1 V and 10 V

The junction capacitance can be thought of as that of a parallel-plate capacitor and thus given by Show that this approach leads to a formula identical to that obtained by combining Eqs. (3.43) and (3.45) [or equivalently, by combining Eqs. (3.47) and (3.48)].

A pn junction operating in the forward-bias region with a current I of 1 mA is found to have a diffusion capacitance of 10 pF. What diffusion capacitance do you expect this junction to have at I = 0.1 mA? What is the mean transit time for this junction?

For the p+n junction specified in Problem 3.22, find and calculate the excess minority carrier charge and the value of the diffusion capacitance at I = 0.2 mA.

A short-base diode is one where the widths of the p and n regions are much smaller than and , respectively. As a result, the excess minority carrier distribution in each region is a straight line rather than the exponentials shown in Fig. 3.12. (a) For the short-base diode, sketch a figure corresponding to Fig. 3.12 and assume as in Fig. 3.12 that . (b) Following a derivation similar to that given in Section 3.5.2, show that if the widths of the p and n regions are denoted and then and , for (c) Also, assuming , , show that where (d) If a designer wishes to limit to 8 pF at I = 1 mA, what should be? Assume . Ln Lp NA  ND Wp Wn I Aqn i 2 Dp Wn xn () ND -----------------------------