Constants
[Note: In the following problems, assume T = 300 K and the following parameters unless otherwise stated. For silicon pn junctions: Dn = 25 cm2/s,Dp = 10 cm2/s,τn0 = 5 × 10−7 s, τp0 = 10−7 s. For GaAs pn junctions: Dn = 205 cm2/s,Dp = 9.8 cm2/s,τn0 =
5 × 10−8 s, τp0 = 10−8 s.]
Exercise 6.1
(a) Consider an ideal pn junction diode at T = 300 K operating in the forward-bias region. Calculate the change in diode voltage that will cause a factor of 10 increase in current.
(b)Repeat part (a) for a factor of 100 increase in current.
Exercise 6.2
Consider a GaAs pn junction diode at T = 300 K. The parameters of the device are Nd = 2 × 1016 cm−3,Na = 8 × 1015 cm−3,Dn = 210 cm2/s,Dp = 8 cm2/s,τno = 10−7 s, and τpo = 5 × 10−8 s. Determine the ideal reverse-saturation current density.
Exercise 6.3
Consider an ideal silicon pn junction diode.
(a) What must be the ratio of Nd/Na so that 90 percent of the current in the depletion region is due to the flow of electrons?
(b) Repeat part (a) if 80 percent of the current in the depletion region is due to theflow of holes.
Exercise 6.4
Consider a silicon pn junction diode with an applied reverse-biased voltage of VR = 5 V. The doping concentrations are Na = Nd = 4×1016 cm−3 and the cross-sectional area is A = 10−4 cm2. Assume minority carrier lifetimes of τ0 = τn0 = τp0 = 10−7 s. Calculate the
(a) ideal reverse-saturation current
(b) reverse-biased generation current
(c) the ratio of the generation current to ideal saturation current.
Exercise 6.5
Consider, as shown in Figure, a uniformly doped silicon pn junction at T = 300 K with impurity doping concentrations of Na = Nd = 5×1015 cm−3 and minority carrier lifetimes of τn0 = τp0 = τ0 = 10−7 s. A reverse-biased voltage of VR = 10 V is applied. A light source is incident only on the space charge region, producing an excess carrier generation rate of g′ = 4 × 1019 cm−3 s−1. Calculate the generation current density.
Figure 1: Figure for Problem 6.5
Exercise 6.6
A silicon pn junction at T = 300 K is reverse biased at VR = 8 V. The doping concentrations are Na = 5 ×1016 cm−3 and Nd = 5 × 1015 cm−3. Draw the band diagram of the pn junction, and determine xn,xp,W, and |Emax|. Please provide the process of derivation.
Exercise 6.7
(a) Sketch the energy bands in a zero-biased, reverse-biased, and forward-biased pn junction.
(b) Sketch the steady-state minority carrier concentrations in a forward-biased pn junction.
(c) Sketch the forward-bias I–V characteristics of a pn junction diode showing the effectsof recombination and high-level injection.
