Description

In the following problems 1-5, if not stated,
For silicon pn junctions: 𝐷𝑛 = 25𝑐𝑚2/𝑠, 𝐷𝑝 = 10𝑐𝑚2/𝑠, 𝜏𝑛0 = 5 × 10−7𝑠, 𝜏𝑝0 = 10−7𝑠. For GaAs pn junctions: 𝐷𝑛 = 205𝑐𝑚2/𝑠, 𝐷𝑝 = 9.8𝑐𝑚2/𝑠, 𝜏𝑛0 = 5 × 10−8𝑠, 𝜏𝑝0 = 10−8𝑠.

1. Consider an ideal silicon pn junction diode.

2. An ideal silicon pn junction at 𝑇 = 300𝐾 is under zero bias. The minority carrier lifetimes are 𝜏𝑛0 = 10−6𝑠, and 𝜏𝑝0 = 10−7𝑠. The doping concentration in the n region is
𝑁𝑑 = 1016𝑐𝑚−3.
Plot the ratio of hole current to the total current crossing the space charge region as the p region doping concentration varies over the range 1015 ≤ 𝑁𝑎 ≤ 1018𝑐𝑚−3. (Use a log scale for the doping concentrations.)

3. Consider a silicon pn junction diode with an applied reverse-biased voltage of 𝑉𝑅 = 5𝑉.
The doping concentrations are 𝑁𝑑 = 𝑁𝑎 = 4 × 1016𝑐𝑚−3 and the cross-sectional area is
𝐴 = 10−4𝑐𝑚2. Assume minority carrier lifetimes of 𝜏0 = 𝜏𝑛0 = 𝜏𝑝0 = 10−7𝑠. Calculate
(a) the ideal reverse-saturation current,
(b) the reverse-biased generation current,
(c) the ratio of the generation current to ideal saturation current.

4. Consider a GaAs pn junction diode with a cross-sectional area of 𝐴 = 2 × 10−4𝑐𝑚2 and doping concentrations of 𝑁𝑑 = 𝑁𝑎 = 7 × 1016𝑐𝑚−3. The electron and hole mobility values are 𝜇𝑛 = 5500𝑐𝑚2/𝑉 − 𝑠 and 𝜇𝑝 = 220𝑐𝑚2/𝑉 − 𝑠, respectively, and the lifetime values are 𝜏0 = 𝜏𝑛0 = 𝜏𝑝0 = 2 × 10−8𝑠.
Calculate the ideal diode current at a
(a) reverse-biased voltage of 𝑉𝑅 = 3𝑉
(b) forward-bias voltage of 𝑉𝑎 = 0.6𝑉
(c) forward-bias voltage of 𝑉𝑎 = 0.8𝑉
(d) forward-bias voltage of 𝑉𝑎 = 1𝑉

5. Consider a GaAs pn diode at 𝑇 = 300𝐾 with 𝑁𝑑 = 𝑁𝑎 = 1017𝑐𝑚−3 and with a crosssectional area of 𝐴 = 5 × 10−3𝑐𝑚2. The minority carrier mobilities are 𝜇𝑛 =
3500𝑐𝑚2/𝑉 − 𝑠 and 𝜇𝑝 = 220𝑐𝑚2/𝑉 − 𝑠. The electron-hole lifetimes are 𝜏0 = 𝜏𝑛0 =
𝜏𝑝0 = 10−8𝑠.
Plot the diode forward-bias current include including recombination current between diode voltages of 0.1 ≤ 𝑉𝐷 ≤ 1𝑉. Compare this plot to that for an ideal diode.

6. For a uniformly doped 𝑛++𝑝+𝑛 bipolar transistor in the thermal equilibrium, (a) Sketch the energy-band diagram.
(b) Sketch the electric field through the device.
(c) Repeat parts (a) and (b) for the transistor biased in the forward-active region.

7. A uniformly doped silicon npn bipolar transistor at 𝑇 = 300𝐾 is biased in the forwardactive mode. The doping concentrations are 𝑁𝐸 = 8 × 1017𝑐𝑚−3, 𝑁𝐵 = 1016𝑐𝑚−3, and
𝑁 = 1015𝑐𝑚−3.
Find the thermal-equilibrium values 𝑝𝐸0, 𝑛𝐵0, and 𝑝𝐶0.
(b) Calculate the values of 𝑛𝐵 at 𝑥 = 0 and 𝑝𝐸 at 𝑥′ = 0 for 𝑉𝐵𝐸 = 0.64𝑉.
(c) Sketch the minority carrier concentrations through the device and label each curve.

8. (a) The following currents are measured in a uniformly doped npn bipolar transistor.
𝐼𝑛𝐸 = 0.50𝑚𝐴, 𝐼𝑛𝐶 = 0.495𝑚𝐴, 𝐼𝑝𝐸 = 3.5𝜇𝐴, 𝐼𝑅 = 5𝜇𝐴, 𝐼𝐺 = 0.5𝜇𝐴, 𝐼𝑝𝑐0 = 0.5𝜇𝐴 Determine the following current gain parameters: 𝛾, 𝛼𝑇, 𝛿, 𝛼, 𝛽 (see next page).
(b) If the required value of common-emitter current gain is 𝛽 = 120, determine new values of 𝐼𝑛𝐶, 𝐼𝑝𝐸 and 𝐼𝑅 to meet this specification assuming 𝛾 = 𝛼𝑇 = 𝛿.

9. The emitter in a BJT is often made very thin to achieve high operating speed. In this problem, we investigate the effect of emitter width on current gain. Consider the emitter injection efficiency given by

Assume that 𝑁𝐸 = 100𝑁𝐵, 𝐷𝐸 = 𝐷𝐵, 𝐿𝐸 = 𝐿𝐵. Also let 𝑥𝐵 = 0.1𝐿𝐵.
Plot the emitter injection efficiency for 0.01𝐿𝐸 ≤ 𝑥𝐸 ≤ 10𝐿𝐸.
From these results, discuss the effect of emitter width on the current gain.