SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

5.7. PROBLEMS 243

quality and can be easily affected by fabrication steps. In ap-ndiode, on the other hand,

the built-in voltage is fixed by doping and is more controllable.

Problem 5.17A metal-i-GaN-n-GaN Schottky junction is shown in the figure 5.14 (a)

below. Fixed positive and negative polarization charges across the GaN create a 2DEG in

this structure. The metal semiconductor barrier heightφBis 0.5 eV. Assume that the

i-GaN layer is 50 nm thick, and that the relative dielectric constant of AlGaN is 10.

1. Draw the equilibrium band diagram. Also draw the band diagram for a reverse bias
   of 10V.


2. Now, a phantom material (see figure 5.14(b)) with a high dielectric constant of 100
   and thickness of 50 nm is inserted between the gate and the GaN layer. Draw the
   band diagram at equilibrium and at a reverse bias of 10 V across the junction.
   Assume that the barrier height on this material is the same as in the case of GaN, and
   that the bands of this material align perfectly with GaN.


3. The tunneling probability across a barrier of the form in figure 5.14 (c) is given by

P=e−

4 π√ 2 md(E^30 /^2 −E^31 /^2 )

2(E 0 −E 1 )h

Use the above expression to estimate the ratio between the tunneling probabilities for

the cases in part (a) and (b) at equilibrium, and when a reverse bias of 10 V is

applied.

i - GaN

n - GaN

Metal

i - GaN

n - GaN

Metal

Phantom

Material

EC

E 1

E 0

A B C

Figure 5.14: Figure for problem 5.17.

• Section 5.4

Problem 5.18 A gold contact is deposited on GaAs doped atNd=5× 20 cm−^3.

Calculate the tunneling probability of the electrons to go into the semiconductor.

Problem 5.19 A metal with a work function of 4.2 V is deposited on ann-type silicon

semiconductor with an electron affinity of 4.0 V. Assume that there are no interface states.

Calculate the doping density for which there is no space charge region at zero applied bias.