5.7. PROBLEMS 241
Problem 5.2If a current density of 105 A/cm^2 flows in the interconnect of problem 5.1 to,
calculate the potential drop.
Problem 5.3Use the resistivity of Al and Cu given in table 5.1 and use the Drude model
(chapter 1) to calculate the mobility of electrons in these two materials.
Problem 5.4Discuss why in the analysis of the conductivity of metals we do not consider
hole conductivity.
Problem 5.5Assume the ideal Schottky barrier model with no interface states for an
n-type Si withNd=10^16 cm−^3. The metal work function is 4.5 eV and the Si electron
affinity is 4 eV. Calculate the Schottky barrier height, built-in voltage, and depletion width
at no external bias.
Problem 5.6A Schottky barrier is formed between Al andn-type silicon with a doping of
1016 cm−^3. Calculate the theoretical barrier if there are no surface states. Compare this
with the actual barrier height. Use the data in the text.
Problem 5.7Assume that at the surface of GaAs, 50% of all bonds are “defective” and
lead to a uniform distribution of states in the bandgap. Each defective bond contributes
one bandgap state. What is the two-dimensional density of bandgap states (units of
eV−^1 cm−^2 )? Assume that the neutral levelφois at midgap. Approximately how much
will the Fermi level shift if a total charge density of 1012 cm−^2 is injected into the surface
states? This example gives an idea of “Fermi level pinning”.
Problem 5.8The capacitance of a Pt-n-type GaAs Schottky diode is given by
1
(C(μF))^2
=1. 0 × 105 − 2. 0 × 105 V
The diode area is 0.1 cm^2. Calculate the built-in voltageVbi, the barrier height, and the
doping concentration.
Problem 5.9Calculate the mean thermal speed of electrons in Si and GaAs at 77 K and
300 K.m∗Si=0. 3 mo;m∗GaAs=0. 067 mo.
Problem 5.10 Calculate the saturation current density in an Au Schottky diode made
fromn-type GaAs at 300 K. Use the Schottky barrier height values given in table 5.2.
Problem 5.11 Consider an Aun-type GaAs Schottky diode with 50μm diameter. Plot
the current voltage characteristics for the diode between a reverse voltage of 2 V and a
forward voltage of 0.5 V.
Problem 5.12 Calculate and plot the I-V characteristics of a Schottky barrier diode
betweenWandn-type Si doped at 5× 1016 cm−^3 at 300 K. The junction area is 1 mm^2.
Plot the results from a forward current of 0 to 100 mA.
