 An abrupt silicon pn junction (N_{a} = 10^{16} cm^{3} and N_{d} = 4 x 10^{16} cm^{3}) is biased with V_{a} = 3 V. Calculate the builtin potential, the depletion layer width and the maximum electric field of the junction.
 An abrupt silicon pn junction consists of a ptype region containing 10^{16} cm^{3} acceptors and an ntype region containing also 10^{16} cm^{3} acceptors in addition to 10^{17} cm^{3} donors.
 Calculate the thermal equilibrium density of electrons and holes in the ptype region as well as both densities in the ntype region.
 Calculate the builtin potential of the pn junction.
 Calculate the builtin potential of the pn junction at 100°C.
 Consider an abrupt silicon pn junction with a builtin potential of 0.62 V.
 What is the potential across the depletion region at an applied voltage, V_{a}, of 0, 0.5 and 2 Volt?
 If the depletion layer is 1 micrometer at V_{a} = 0 Volt, find the maximum electric field in the depletion region.
 Assuming that the net doping density N_{d}  N_{a} is the same in the ntype and ptype region of the diode, carefully sketch the electric field and the potential as a function of position throughout the depletion region. Add numeric values wherever possible.
 An abrupt silicon (n_{i} = 10^{10} cm^{3}) pn junction consists of a ptype region containing 10^{16} cm^{3} acceptors and an ntype region containing 5 x 10^{16} cm^{3} donors.
 Calculate the builtin potential of this pn junction.
 Calculate the total width of the depletion region if the applied voltage, V_{a} equals 0, 0.5 and 2.5 V.
 Calculate maximum electric field in the depletion region at 0, 0.5 and 2.5 V.
 Calculate the potential across the depletion region in the ntype semiconductor at 0, 0.5 and 2.5 V.
 Consider an abrupt pn diode in thermal equilibrium with as many donors in the ntype region as acceptors in the ptype region and a maximum electric field of 13 kV/cm and a total depletion layer width of 1 mm. (assume e_{s}/ e_{0} = 12)
 What is the applied voltage, V_{a}?
 What is the builtin potential of the diode?
 What is the donor density in the ntype region and the acceptor density in the ptype region?
 What is the intrinsic carrier density of the semiconductor if the temperature is 300 K ?
 A silicon (n_{I} = 10^{10} cm^{3}) pn diode with N_{a} = 10^{18} cm^{3} has a capacitance of 10^{8} F/cm^{2} at an applied voltage of 0.5 V. Find the donor density.
 A silicon (n_{i} = 10^{10} cm^{3}) pn diode has a maximum electric field of 10^{6} V/cm and a depletion layer width of 1 mm. The acceptor density in the ptype region is four times larger than the donor density in the ntype region. Calculate both doping densities.
 Consider a symmetric silicon pn diode (N_{a} = N_{d})
 Calculate the builtin potential if N_{a} = 10^{13}, 10^{15} and 10^{17} cm^{3}. Also, calculate the doping densities corresponding to a builtin potential of 0.7 V.
 For the same as in part a), calculate the total depletion layer widths, the capacitance per unit area and the maximum electric field in thermal equilibrium.
 For the same as in part a), calculate the total depletion layer widths, the capacitance per unit area and the maximum electric field in thermal equilibrium.
 Repeat part a) and b) with N_{a} = 3 N_{d}.
 A onesided silicon diode has a breakdown voltage of 1000 V for which the maximum electric field at breakdown is 100 kV/cm. What is the maximum possible doping density in the low doped region, the builtin potential, the depletion layer width and the capacitance per unit area? Assume that bulk potential of the highly doped region is E_{g}/2 (= 0.56 V).
 A silicon pn junction (N_{a} = 10^{16} cm^{3} and N_{d} = 4 x 10^{16} cm^{3}) is biased with V_{a} = 0.6 V. Calculate the ideal diode current assuming that the ntype region is much smaller than the diffusion length with w_{n}^{'} = 1 mm and assuming a "long" ptype region. Use m_{n} = 1000 cm^{2}/Vs and m_{p} = 300 cm^{2}/Vs. The minority carrier lifetime is 10 ms and the diode area is 100 mm by 100 mm.
 Derive equation 4.4.28 from 4.4.14.
 Calculate the relative error when using the "short diode" approximation if L_{n} = 2 w_{p}^{'} and L_{p} = 2 w_{n}^{'}.
 A silicon pn junction (N_{a} = 10^{15} cm^{3}, w_{p} = 1 mm and N_{d} = 4 x 10^{16} cm^{3}, w_{n} = 1 mm) is biased with V_{a} = 0.5 V. Use m_{n} = 1000 cm^{2}/Vs and m_{p} = 300 cm^{2}/Vs. The minority carrier lifetime is 10 ms and the diode area is 100 mm by 100 mm.
 Calculate the builtin potential of the diode.
 Calculate the depletion layer widths, x_{n} and x_{p}, and the widths of the quasineutral regions.
 Compare the width of the quasineutral regions with the minoritycarrier diffusionlengths and decide whether to use the "long" or "short" diode approximation. Calculate the current through the diode.
 Compare the result of part c) with the current obtained by using the general solution (equation 4.4.24)
 Using the approximation chosen in part c) calculate the ratio of the electron current to the hole current traversing the depletion region.
 An abrupt silicon pn diode consists of a ptype region containing 10^{18} cm^{3} acceptors and an ntype region containing 10^{15} cm^{3} donors.
 Calculate the breakdown field in the ntype region.
 Using the breakdown field from part a), calculate the breakdown voltage of the diode.
 What is the depletion layer width at breakdown?
 Discuss edge effects and specify the minimum junction depth needed to avoid these effects.
 A 1 cm^{2} solar cell consists of a ptype region containing 10^{18} cm^{3} acceptors and an ntype region containing 10^{15} cm^{3} donors. w_{p}^{'} = 0.1 mm and w_{n} >> L_{p}. Use m_{n} = 1000 cm^{2}/Vs and m_{p} = 300 cm^{2}/Vs. The minority carrier lifetime is 10 ms . The diode is illuminated with sun light, yielding a photocurrent density of 30 mA/cm^{2}.
 Calculate the open circuit voltage and shortcircuit current of the solar cell.
 Calculate the maximum power generated by the call and the corresponding voltage and current.
 Calculate the fill factor of the solar cell.
 Calculate the fill factor for the same cell when it is illuminated by a concentrator so that the photocurrent density equals 300 A/cm^{2}.
 A semiconductor device made of silicon has, under thermal equilibrium, an Mshaped electric field distribution as shown in the figure below.
 Find the total potential across the semiconductor as a function of E_{max} with a = 0.1 mm.
 Find the total potential across the semiconductor as a function of E_{max} with a = 0.1 mm.
 Find E_{max} and the builtin voltage f_{i}.
 Plot N_{d}  N_{a} for a > x > a and indicate numeric values. Specify whether the different regions are ptype or ntype.
 Design an abrupt silicon pn diode with a capacitance per unit area of 10 nF/cm^{2} in thermal equilibrium and a maximum electric field of 10^{5} V/cm at a reverse bias of 10 Volt. Provide values of the acceptor and donor density, the builtin potential and the depletion layer width in thermal equilibrium and at a reverse bias of 10 Volt.
 A silicon pn junction consists of a halfsphere with onemicron radius and a doping density of 10^{18} cm^{3} embedded in an ntype substrate with a donor density of 10^{16} cm^{3}. Breakdown occurs in the diode when the maximum field reaches 6x10^{5} V/cm. Calculate the breakdown voltage. Justify any assumptions you make.
 Calculate the builtin voltage for a silicon pn junction with N_{a} = N_{d} = 10^{15} cm^{3} at T = 500 K. Do not assume the electron and hole concentration to equal the donor or acceptor concentration.
 Derive the minority electron density in a silicon pn junction at the edge of the depletion region as a function of the acceptor density and the applied voltage. State the approximations made. Calculate the minority electron density for N_{a} = 10^{17} cm^{3}, N_{d} = 10^{16} cm^{3} and V_{a} = 2 V.
 An abrupt silicon pn diode has a maximum electric field of 10^{6} V/cm and a depletion layer width of 10 mm. The acceptor density in the ptype region is three times larger than the donor density in the ntype region. Calculate both doping densities.
 A onesided abrupt silicon pn junction with N_{a} = 10^{18} cm^{3} and N_{d} = 10^{15} cm^{3} is biased with V_{a} = 0.7 V. Calculate the ideal diode current using the following parameters: w_{p}^{'} = w_{n}^{'} = 100 mm, m_{n} = 500 cm^{2}/Vs and m_{p} = 300 cm^{2}/Vs. The minority carrier lifetime is 1 ms and the diode area is 100 mm by 100 mm. Use either the "long" or "short" diode equation and justify your choice.
 A capacitance measurement of a one sided p^{+}n diode resulted in the following plot of 1/C^{2} versus the applied voltage. Calculate and plot the doping profile N_{d} as a function of the distance from the metallurgical interface. The diode are is 10^{4} cm^{2} and the relative dielectric constant of the semiconductor is 12. If the electron and hole masses equal the free electron mass, m_{0}, what is the bandgap of the semiconductor?
 A "long" abrupt pn diode consists of a ptype region with a four times higher resistivity than the ntype region, while the depletion layer width in the ptype region is twice that in the ntype region. What is the ratio of the maximum electron current to the maximum hole current? Assume the minority carrier lifetime to be the same in both regions
 For a silicon pn diode find the maximum builtin voltage at 300K, assuming nondegenerate material. Repeat at 300^{o}C.
 An n^{+}np^{+} diode has the following field distribution:
 Calculate the voltage applied to the diode.
 Plot then charge distribution throughout the depletion region at that bias voltage.
 Calculate the donor density in the middle region.
 A onesided p^{+}n diode has an ntype region width w_{n} which is much larger than the hole diffusion length L_{p}. Derive an expression for the current I(V_{a}) through the diode, taking into account the modulation of the depletion region due to the applied voltage. Ignore the injection of electrons into the ptype region.
 An abrupt pn diode consists of a ptype region containing 10^{16} cm^{3} shallow acceptors and an ntype region containing also 10^{16} cm^{3} shallow acceptors in addition to 10^{17} cm^{3} shallow donors.
 Calculate the thermal equilibrium density of electrons and holes in the ptype region as well as both densities in the ntype region.
 Calculate the builtin potential of the pn diode.
 Calculate the builtin potential of the pn diode at 100^{o}C.
 same as 4.3
 Consider a onesided silicon p^{+}n junction with V_{a} = 0.6 Volt, N_{d} = 10^{15} cm^{3}, t_{n} = t_{p} = 10 ms.
 Calculate the electron and hole density at the edge of the ntype quasineutrral region.
 Calculate the hole current density at the edge of the ntype quasineutral region and 10 microns away from that edge in to quasineutral region. Assume the quasineutral region to be "long".
 An abrupt pn diode has a builtin potential of 0.75 Volt and a depletion layer width of 1 micron at a forward bias of 0.5 Volt. What is the width of the depletion layer at a reverse bias voltage of 1 Volt?
 An abrupt pn diode has a builtin potential of 0.7 V and an ntype region doped with 10^{16} cm^{3} shallow donors. Calculate the acceptor density, N_{a}, in the ptype region, the depletion layer width in both regions, x_{n} and x_{p}, and the maximum electric field, E_{max}, if the diode is in thermal equilibrium.
 Consider an abrupt silicon pin diode with N_{a} = N_{d} = 10^{17} cm^{3} and a 2 micron wide intrinsic region. V_{a} = 0 Volt.
 Calculate the electric field using the full depletion approximation.
 Calculate n(x) and p(x) in the intrinsic material from n = n_{i} exp[(E_{F}  E_{i})/kT] and p = n_{i} exp[(E_{i}  E_{F}kT]
 Calculate J_{n}(x) in the intrinsic material
 Does the drift current equal the diffusion current in the intrinsic material? Why? Is the full depletion approximation valid? Why?
 The field distribution of an abrupt silicon pn diode is shown below. The electron density at x = a = 0.1 mm equals 10^{17} cm^{3}. Calculate the electron density at x = a = 0.1 mm. The maximum electric field equals E_{max} = 1.5 x 10^{5} V/cm. Note that the diode is not in thermal equilibrium.
 An abrupt silicon pn diode is uniformly doped with a donor density, N_{d} = 10^{17} cm^{3}, in the ntype and an unknown acceptor density in the ptype region. The depletion layer width in the ntype region is three times the depletion layer width in the ptype region and the maximum electric field in the junction is 10^{5} V/cm. Find the acceptor density, the builtin potential, the applied voltage and the corresponding junction capacitance per unit area.
 A silicon pn with a saturation current of 10^{10} A is used as a solar cell. The diode is illuminated with sunlight, yielding a photocurrent of 1 mA. Find the maximum power, which can be generated by this diode. Calculate the corresponding voltage and current.
