Neamen

368 C H A P T E R 9 Metal–Semiconductor and Semiconductor Heterojunctions

(ii) the voltage across each diode. (b) Repeat part (a) for the case when the diodes are
connected in parallel.

9.23 A Schottky diode and a pn junction diode have cross-sectional areas of
A ϭ 7 ϫ 10Ϫ4 cm2. The reverse-saturation current densities at T ϭ 300 K of the
Schottky diode and pn junction are 4 ϫ 10Ϫ8 A/cm2 and 3 ϫ 10Ϫ12 A/cm2, respec-
tively. A forward-bias current of 0.8 mA is required in each diode. (a) Determine the
forward-bias voltage required across each diode. (b) If the voltage from part (a) is
maintained across each diode, determine the current in each diode if the temperature
is increased to 400 K. (Take into account the temperature dependence of the reverse-
saturation currents. Assume Eg ϭ 1.12 eV for the pn junction diode and ␾B0 ϭ 0.82 V
for the Schottky diode.)

9.24 Compare the current–voltage characteristics of a Schottky barrier diode and a pn junc-
tion diode. Use the results of Example 9.5 and assume diode areas of 5 ϫ 10Ϫ4 cm2.
Plot the current–voltage characteristics on a linear scale over a current range of
0 Յ ID Յ 10 mA.

Section 9.2 Metal–Semiconductor Ohmic Contacts

9.25 The contact resistance of an ohmic contact is Rc ϭ 10Ϫ4 ⍀-cm2. Determine the junction
resistance if the cross-sectional area is (a) 10Ϫ3 cm2, (b) 10Ϫ4 cm2, and (c) 10Ϫ5 cm2.

9.26 (a) The contact resistance of an ohmic contact is Rc ϭ 5 ϫ 10Ϫ5 ⍀-cm2. The cross-
sectional area of the junction is 10Ϫ5 cm2. Determine the voltage across the junction
if the current is (i) I ϭ 1 mA and (ii) I ϭ 100 ␮A. (b) Repeat part (a) if the cross-
sectional area is 10Ϫ6 cm2.

9.27 An ohmic contact between a metal and silicon may be formed that has a very low
barrier height. (a) Determine the value of ␾Bn that will produce a contact resistance
of Rc ϭ 5 ϫ 10Ϫ5 ⍀-cm2 at T ϭ 300 K. (b) Repeat part (a) for a contact resistance of
Rc ϭ 5 ϫ 10Ϫ6 ⍀-cm2.

9.28 A metal, with a work function ␾m ϭ 4.2 V, is deposited on an n-type silicon semicon-
ductor with ␹s ϭ 4.0 V and Eg ϭ 1.12 eV. Assume no interface states exist at the junc-
tion. Let T ϭ 300 K. (a) Sketch the energy-band diagram for zero bias for the case
when no space charge region exists at the junction. (b) Determine Nd so that the con-
dition in part (a) is satisfied. (c) What is the potential barrier height seen by electrons
in the metal moving into the semiconductor?

9.29 Consider the energy-band diagram of a silicon Schottky junction under zero bias
shown in Figure P9.29. Let ␾B0 ϭ 0.7 V and T ϭ 300 K. Determine the doping
required so that xd ϭ 50 Å at the point where the potential is ␾B0͞2 below the peak
value. (Neglect the barrier lowering effect.)

9.30 A metal–semiconductor junction is formed between a metal with a work function of
4.3 eV and p-type silicon with an electron affinity of 4.0 eV. The acceptor doping
concentration in the silicon is Na ϭ 5 ϫ 1016 cmϪ3. Assume T ϭ 300 K. (a) Sketch the
thermal equilibrium energy-band diagram. (b) Determine the height of the Schottky
barrier. (c) Sketch the energy-band diagram with an applied reverse-biased voltage of
VR ϭ 3 V. (d) Sketch the energy-band diagram with an applied forward-bias voltage of
Va ϭ 0.25 V.

9.31 (a) Consider a metal–semiconductor junction formed between a metal with a
work function of 4.65 eV and Ge with an electron affinity of 4.13 eV. The doping