 A silicon npn bipolar transistor with N_{E} = 10^{18} cm^{3}, N_{B} = 10^{17} cm^{3} and N_{C} = 10^{16} cm^{3}, w_{E} = 1 mm, w_{B} = 0.5 mm , and w_{C} = 4 mm is biased with V_{BE} = 0.6 V and V_{CB} = 0 V. Use m_{n} = 1000 cm^{2}/Vs, m_{p} = 300 cm^{2}/Vs and t_{n} = t_{p} = 100 ns. The emitter area equals 10^{4} cm^{2}.
 Calculate the width of the quasineutral regions in the emitter, base and collector.
Calculate the minoritycarrier diffusion lengths in the emitter, base and collector. Calculate the ratio of the minoritycarrier diffusion length and the quasineutral region width in each region. Calculate the excessminoritycarrier charge density per unit area in the emitter, base and collector. Calculate the emitter current while ignoring the recombination in the depletion region. Calculate the base transit time and the current due to recombination of electrons in the base. Calculate the emitter efficiency and the base transport factor. Calculate the emitter efficiency and the base transport factor. Calculate the transport factor and the current gain assuming there is no recombination in the depletion regions. Calculate the collector capacitance, the majoritycarrier charge density in the base and the Early voltage.
 A silicon npn bipolar transistor has an emitter doping, N_{E} = 2 x10^{18} cm^{3}, an emitter Q.N. width w_{E}' = 1 mm, and a base doping of 2 x 10^{17} cm^{3}. A current gain of 100 and an early voltage of 100 V is desired. Using m_{n} = 1000 cm^{2}/Vs, m_{p} = 300 cm^{2}/Vs and t_{n} = t_{p} = 100 ns, find the corresponding base width and base doping. The emitter area equals 10^{4} cm^{2}.
 Consider a silicon NPN bipolar transistor with a short base region (L_{n} >> w_{B})
 Derive an expression for the minority carrier concentration in the quasineutral region of the base with V_{BC} = 0.
 Assuming that the excess carrier concentrations are equal, find the electric field throughout the quasineutral region in the base for which the hole current density, J_{p}, is zero.
 Find the maximum field if N_{B} = 10^{17} cm^{3}, w_{B} = 0.3 mmm and V_{BE} = 0.6V.
 Consider an npn bipolar transistor with w_{E} = 1 mm, w_{B} = 1 mm,w_{C} = 6 mm, NE = 10^{18} cm^{3}, N_{B} = 10^{16} cm^{3}, N_{C} = 10^{15} cm^{3}, V_{BE} = 0.6 V.
 Calculate the voltage between the collector and the emitter for which the quasineutral region in the base is zero.
 What is the Early voltage of this transistor at a bias voltage, V_{CE}, of 20 V ?
 Explain the conceptual difference between the two voltages. Hint: draw the common emitter IV characteristic of the BJT for V_{BE} = 0.6 V and indicate both voltages on the graph.
 Consider an npn bipolar transistor with w_{E} = 1 mm, w_{B} = 1 mm, w_{C} = 3 mm, N_{E} = 10^{18} cm^{3}, N_{B} = 10^{16} cm^{3}, N_{C} = 10^{15} cm^{3}, V_{BE} = 0.55 V and V_{CE} = 0.1 V.
 Calculate both the majority and minority carrier densities at the edges of the depletion layers at the emitter and collector contacts and at the interfaces between n and ptype regions. No recombination exists in the device except at the emitter and collector contact where the carrier densities equal the thermal equilibrium values. List the numeric values of both carrier types as well as the corresponding positions. Take the origin at the interface between the base and emitter layer, with the emitter to the left of the origin.
 Sketch the majority and minority carrier densities versus position on a semilogarithmic scale ranging from 10^{10} to 10^{19} cm^{3}.
 A silicon npn bipolar transistor has the following doping profile:
N_{d}  N_{a} = NE cos( x/a) for 0 < x a/2
 N_{B} cos(x/a) for a/2 < x < 3 a/2
 NC cos(x/a) for 3 a/2 < x < 2 a
 N_{C} for 2 a < x
Find the width of the quasineutral region in the base. Assume the builtin voltage to be 0.6 V for both diodes. Use N_{E} =10^{18} cm^{3}, N_{B} = 10^{17} cm^{3}, N_{C} = 10^{16} cm^{3}, a = 1 mm, V_{BE} = 0.5 V and V_{BC} = 0 V. Note that the emitter contact is at x = 0.
 For a pnp bipolar transistor with a "short" emitter and base, derive a general expression for the emitter, collector and base current, which is valid under low and high injection. Ignore recombination in the depletion regions. Identify the parameters a_{R}, a_{F}, I_{ES} and I_{CS} of the EbersMoll model and find out whether the reciprocity theorem is valid under those conditions. Plot the Gummel plot (I_{C} and I_{B} versus V_{BE} on a semilogarithmic scale) for N_{E} = 10^{19} cm^{3}, N_{B} = 10^{17} cm^{3}, N_{C} = 10^{16} cm^{3} and w_{E} = 0.3mm, w_{B} = 0.2 mm, w_{C} = 1 mm. The area of the emitter is 10^{6} cm^{2} and V_{CE} = 2V. Hint: remember that the quasineutral regions depend on the applied voltages.
 Derive the minority carrier density in the uniformly doped base of an npn bipolar transistor (including recombination) as a function of x, V_{BE} and V_{BC} . Find an expression for the electron current at both edges of the quasineutral region In(0) and In(w_{B}') and show that:
 I_{n}(0)  I_{n}(w_{B}') = Q_{n,B}/t_{n} for any t_{n}
 and I(0) = Q_{n,B}/t_{r} for t_{n} >> t_{r} = w_{B}'^{2}/2D_{n} and V_{BC} < 0, where t_{r} is the base transit time and t_{n} is the minority carrier life time.
 An npn silicon bipolar transistor has a current gain of 100 when operated in the forward active mode of operation with V_{BE} = 0.6 V and V_{BC} = 0 V. Transistor parameters are N_{E} = 10^{18} cm^{3}, N_{B} = 10^{16} cm^{3}, N_{C} = 10^{15} cm^{3}, w_{E} = 1 mm, m_{n} = 1000 cm^{2}/Vs, m_{p} = 300 cm^{2}/Vs. Assume there is no recombination in the transistor except at the contacts. (n_{i} = 10^{10} cm^{3}, e_{s}/e_{0} = 11.9)
Calculate the quasineutral width of the base, w_{B}'.
 A silicon npn bipolar transistor with area 10^{2}cm^{2} has the following doping concentrations in the emitter, base and collector: N_{E} = 10^{18}cm^{3}, N_{B} = N_{C} = 10^{17}cm^{3}.
 At a bias of V_{BE} = 0.7 V and V_{CE} = 0.5V, calculate the total number of excess electrons in the base region and the recombination current in the base (t_{n} = 100ns). Assume the width of the quasineutral region in the base to be 0.8 mm. The diffusion length in the emitter is 100 mm.
 Calculate the hole current from the base into the emitter.
 Calculate the voltage V_{BE} for which the hybridpi small signal parameter C_{se} equals the junction capacitance, C_{j}, of the basetocollector diode assuming this diode has a depletion layer width of 0.4mm.
 A silicon pnp transistor (N_{E} = N_{B} = N_{C} = 10^{17} cm^{3} and area = 10^{4} cm^{2}) is biased with V_{EB} = 0.7 V and V_{CB} = 0 V. Use m_{p} = 300 cm^{2}/Vs.
 Ignoring recombination, find the total excess charge in the base region if the quasineutral region width in the base equals 1mm.
 Ignoring recombination find the total current due to diffusion of holes in the base region.
 Calculate the transit time of the holes through the base and show that the current multiplied with the transit time equals the total excess charge in the base region.
 Derive expressions for the emitter efficiency and the dc current gain of a pnp bipolar transistor (operating in the active region) with a short emitter width w_{E}. Is the current gain larger or smaller than for a transistor with a long emitter width?
 A silicon npn transistor with N_{E} = 10^{18} cm^{3}, N_{B} = 10^{17} cm^{3} and N_{C} = 10^{16} cm^{3}, has a quasineutral region width of 1 mm for V_{CB} = 0 V and a collector current of 1 mA.
 What voltage must be applied between the collector and the emitter (while keeping V_{EB} constant) to double the collector current (I_{C} = 2 mA). Ignore recombination in the base region. (This effect is also referred to as basenarrowing)
 Calculate the corresponding baseemitter voltage and the width of the base region using m_{n} = 1000 cm^{2}/Vs, m_{p} = 300 cm^{2}/Vs and an emitter area of 10^{4} cm^{2}
