Chapter 5: Problems
Chapter 5: Review Questions
Chapter 5 print file in PDF format
  1. A silicon npn bipolar transistor with NE = 1018 cm-3, NB = 1017 cm-3 and NC = 1016 cm-3, wE = 1 mm, wB = 0.5 mm , and wC = 4 mm is biased with VBE = 0.6 V and VCB = 0 V. Use mn = 1000 cm2/V-s, mp = 300 cm2/V-s and tn = tp = 100 ns. The emitter area equals 10-4 cm2.
    1. Calculate the width of the quasi-neutral regions in the emitter, base and collector.
    2. Calculate the minority-carrier diffusion lengths in the emitter, base and collector. Calculate the ratio of the minority-carrier diffusion length and the quasi-neutral region width in each region.
    3. Calculate the excess-minority-carrier charge density per unit area in the emitter, base and collector.
    4. Calculate the emitter current while ignoring the recombination in the depletion region.
    5. Calculate the base transit time and the current due to recombination of electrons in the base.
    6. Calculate the emitter efficiency and the base transport factor.
    7. Calculate the emitter efficiency and the base transport factor.
    8. Calculate the transport factor and the current gain assuming there is no recombination in the depletion regions.
    9. Calculate the collector capacitance, the majority-carrier charge density in the base and the Early voltage.

  2. A silicon npn bipolar transistor has an emitter doping, NE = 2 x1018 cm-3, an emitter Q.N. width wE' = 1 mm, and a base doping of 2 x 1017 cm-3. A current gain of 100 and an early voltage of 100 V is desired. Using mn = 1000 cm2/V-s, mp = 300 cm2/V-s and tn = tp = 100 ns, find the corresponding base width and base doping. The emitter area equals 10-4 cm2.

  3. Consider a silicon NPN bipolar transistor with a short base region (Ln >> wB)
    1. Derive an expression for the minority carrier concentration in the quasi-neutral region of the base with VBC = 0.
    2. Assuming that the excess carrier concentrations are equal, find the electric field throughout the quasi-neutral region in the base for which the hole current density, Jp, is zero.
    3. Find the maximum field if NB = 1017 cm-3, wB = 0.3 mmm and VBE = 0.6V.

  4. Consider an npn bipolar transistor with wE = 1 mm, wB = 1 mm,wC = 6 mm, NE = 1018 cm-3, NB = 1016 cm-3, NC = 1015 cm-3, VBE = 0.6 V.
    1. Calculate the voltage between the collector and the emitter for which the quasi-neutral region in the base is zero.
    2. What is the Early voltage of this transistor at a bias voltage, VCE, of 20 V ?
    3. Explain the conceptual difference between the two voltages. Hint: draw the common emitter I-V characteristic of the BJT for VBE = 0.6 V and indicate both voltages on the graph.

  5. Consider an npn bipolar transistor with wE = 1 mm, wB = 1 mm, wC = 3 mm, NE = 1018 cm-3, NB = 1016 cm-3, NC = 1015 cm-3, VBE = 0.55 V and VCE = 0.1 V.
    1. 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 p-type 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.
    2. Sketch the majority and minority carrier densities versus position on a semi-logarithmic scale ranging from 1010 to 1019 cm-3.

  6. A silicon npn bipolar transistor has the following doping profile:
    Nd - Na =
    • NE cos( x/a) for 0 < x a/2
    • NB cos(x/a) for a/2 < x < 3 a/2
    • NC cos(x/a) for 3 a/2 < x < 2 a
    • NC for 2 a < x

    Find the width of the quasi-neutral region in the base. Assume the built-in voltage to be 0.6 V for both diodes. Use NE =1018 cm-3, NB = 1017 cm-3, NC = 1016 cm-3, a = 1 mm, VBE = 0.5 V and VBC = 0 V. Note that the emitter contact is at x = 0.

  7. 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 aR, aF, IES and ICS of the Ebers-Moll model and find out whether the reciprocity theorem is valid under those conditions. Plot the Gummel plot (IC and IB versus VBE on a semi-logarithmic scale) for NE = 1019 cm-3, NB = 1017 cm-3, NC = 1016 cm-3 and wE = 0.3mm, wB = 0.2 mm, wC = 1 mm. The area of the emitter is 10-6 cm-2 and VCE = -2V. Hint: remember that the quasi-neutral regions depend on the applied voltages.

  8. Derive the minority carrier density in the uniformly doped base of an npn bipolar transistor (including recombination) as a function of x, VBE and VBC . Find an expression for the electron current at both edges of the quasi-neutral region In(0) and In(wB') and show that:
    • In(0) - In(wB') = Qn,B/tn for any tn
    • and I(0) = Qn,B/tr for tn >> tr = wB'2/2Dn and VBC < 0, where tr is the base transit time and tn is the minority carrier life time.

  9. An npn silicon bipolar transistor has a current gain of 100 when operated in the forward active mode of operation with VBE = 0.6 V and VBC = 0 V. Transistor parameters are NE = 1018 cm-3, NB = 1016 cm-3, NC = 1015 cm-3, wE = 1 mm, mn = 1000 cm2/V-s, mp = 300 cm2/V-s. Assume there is no recombination in the transistor except at the contacts. (ni = 1010 cm-3, es/e0 = 11.9)
    Calculate the quasi-neutral width of the base, wB'.

  10. A silicon npn bipolar transistor with area 10-2cm2 has the following doping concentrations in the emitter, base and collector: NE = 1018cm-3, NB = NC = 1017cm-3.
    1. At a bias of VBE = 0.7 V and VCE = 0.5V, calculate the total number of excess electrons in the base region and the recombination current in the base (tn = 100ns). Assume the width of the quasi-neutral region in the base to be 0.8 mm. The diffusion length in the emitter is 100 mm.
    2. Calculate the hole current from the base into the emitter.
    3. Calculate the voltage VBE for which the hybrid-pi small signal parameter Cse equals the junction capacitance, Cj, of the base-to-collector diode assuming this diode has a depletion layer width of 0.4mm.

  11. A silicon pnp transistor (NE = NB = NC = 1017 cm-3 and area = 10-4 cm2) is biased with VEB = 0.7 V and VCB = 0 V. Use mp = 300 cm2/V-s.
    1. Ignoring recombination, find the total excess charge in the base region if the quasi-neutral region width in the base equals 1mm.
    2. Ignoring recombination find the total current due to diffusion of holes in the base region.
    3. 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.

  12. 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 wE. Is the current gain larger or smaller than for a transistor with a long emitter width?

  13. A silicon npn transistor with NE = 1018 cm-3, NB = 1017 cm-3 and NC = 1016 cm-3, has a quasi-neutral region width of 1 mm for VCB = 0 V and a collector current of 1 mA.
    1. What voltage must be applied between the collector and the emitter (while keeping VEB constant) to double the collector current (IC = 2 mA). Ignore recombination in the base region. (This effect is also referred to as base-narrowing)
    2. Calculate the corresponding base-emitter voltage and the width of the base region using mn = 1000 cm2/V-s, mp = 300 cm2/V-s and an emitter area of 10-4 cm2