Description

1. Consider a silicon sample at 𝑇 = 300𝐾 that is uniformly doped with acceptor impurity atoms at a concentration of 𝑁𝑎 = 1016𝑐𝑚−3. At 𝑡 = 0, a light source is turned on generating excess carriers uniformly throughout the sample at a rate of 𝑔′ = 8 × 1020𝑐𝑚−3𝑠−1. Assume the minority carrier lifetime is 𝜏𝑛0 = 5 × 10−7𝑠, and assume mobility values of 𝜇𝑛 = 900𝑐𝑚2/𝑉 − 𝑠 and 𝜇𝑝 = 380𝑐𝑚2/𝑉 − 𝑠.
(a) Determine the conductivity of the silicon as a function of time for 𝑡 ≥ 0. (b) What is the value of conductivity at (i) 𝑡 = 0 and (ii) 𝑡 = ∞?

2. A bar of silicon at 𝑇 = 300𝐾 has a length of 𝐿 = 0.05𝑐𝑚 and a cross-sectional area of 𝐴 = 10−5𝑐𝑚2. The semiconductor is uniformly doped with 𝑁𝑑 = 8 × 1015𝑐𝑚−3 and
𝑁𝑎 = 2 × 1015𝑐𝑚−3. A voltage of 10V is applied across the length of the material. For 𝑡 < 0, the semiconductor has been uniformly illuminated with light, producing an excess carrier generation rate of 𝑔′ = 8 × 1020𝑐𝑚−3𝑠−1. The minority carrier lifetime is 𝜏𝑝0 =
5 × 10−7𝑠. At 𝑡 = 0, the light source is turned off.
Determine the current in the semiconductor as a function of time for 𝑡 ≥ 0.

3. A semiconductor is uniformly doped with 1017𝑐𝑚−3 acceptor atoms and has the following properties: 𝐷𝑛 = 27𝑐𝑚2/𝑠, 𝐷𝑝 = 12𝑐𝑚2/𝑠, 𝜏𝑛0 = 5 × 10−7𝑠, and 𝜏𝑝0 = 10−7𝑠. An external source has been turned on for 𝑡 < 0 producing a uniform concentration of excess carriers at a generation rate of 𝑔′ = 1021𝑐𝑚−3𝑠−1. The source turns off at time 𝑡 = 0 and back on at time 𝑡 = 2 × 10−6𝑠.
(a) Derive the expressions for the excess carrier concentration as a function of time for
0 ≤ 𝑡 ≤ ∞.
(b) Determine the value of excess carrier concentration at (i) 𝑡 = 0, (ii) 𝑡 = 2 × 10−6𝑠, and (iii) 𝑡 = ∞.
(c) Plot the excess carrier concentration as a function of time.

4. The 𝑥 = 0 end of an 𝑁𝑎 = 1014𝑐𝑚−3 doped semi-infinite (𝑥 ≥ 0) bar of silicon maintained at 𝑇 = 300𝐾 is attached to a “minority carrier digester” which makes 𝑛𝑝 = 0 at 𝑥 = 0 (𝑛𝑝 is the minority carrier electron concentration in a p-type semiconductor. The electric field is zero.
(a) Determine the thermal-equilibrium values of 𝑛𝑝0 and 𝑝𝑝0.
(b) What is the excess minority carrier concentration at 𝑥 = 0?
(c) Derive the expression for the steady-state excess minority carrier concentration as a function of x.

5. Consider the n-type semiconductor shown below. Illumination produces a constant excess carrier generation rate, , in the region −𝐿 < 𝑥 < +𝐿. Assume that the minority carrier lifetime is infinite and assume that the excess minority carrier hole concentration is zero at 𝑥 = −3𝐿 and at 𝑥 = +3𝐿.
Find the steady-state excess carrier concentration versus x, for the case of low injection and for zero applied electric field.