SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

350 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS

width of the p-regionL 2 >> Ln. Calculate the depletion and diffusion capacitances of the

diode. Obtain an expression for the ac resistance.

• Section 7.3

Problem 7.9In the Schottky barrier, the electrons are injected across the barrier with

energies equal to the barrier height. These electrons are very hot. Estimate the

“temperature” of these electrons in a typical Si Schottky barrier with a barrier height ofφb

= 0.6 V. (Electron temperature,Te, is defined by^32 kBTe∼〈Ee〉where〈Ee〉is the average

electron energy.)

Problem 7.10An important consideration in the speed of Schottky barrier diodes is the

time it takes hot electrons (see the previous problem) to lose their energy and achieve

equilibrium thermal energy. In GaAs, electrons lose excess energy exponentially with a

time constant of 1 ps. Consider aW-n-type GaAs Schottky diode withφb=0.8V.How

far will electrons move in the GaAs before they lose 99% of their energy?

• Section 7.4

Problem 7.11Consider an HBT with a base graded from InGaAs to GaAs so that the

bandgap is narrow at the emitter and wide at the collector.

1. Draw the band diagram in the neutral base region of the device.


2. Write down the drift-diffusion equation governing the current in the base region
   assuming no recombination in the base. Assume a forward bias at the base-emitter
   junction and a reverse bias across the base-collector junction. What are the boundary
   conditions for this equation?


3. Solve the differential equation to get the minority charge profile (n(x)versusx)asa
   function of injected current in the base.


4. Sketch (without actually calculating exact values) the minority charge profile with
   and without a reverse grade in the base for the same injected current density. Give
   physical arguments for your result.


5. How will the base transit time vary in these two cases? Why?

• Section 7.5

Problem 7.12In a particular BJT, the base transit time forms 20% of the total delay time

of the charge transport. The base width is 0.5μm and the diffusion constant is

Db=25cm^2 s. Calculate the cutoff frequency for the device.

Problem 7.13A siliconnpnbipolar transistor has a cutoff frequency at 300 K limited by

base transit time. The cutoff frequency is 1 GHz. Estimate the base width if the base

doping is 1016 cm−^3. The minority carrier mobility in the base is 500 cm^2 /V·s.