SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

6.7. PROBLEMS 299

Figure 6.28: Figure for problem 6.36.

in the quantum well region compared to 1 ns in the rest of the base. The emitter is doped at

5 × 1017 cm−^3. The collector is doped at 5 × 1016 cm−^3. Assume that the elctron mobility

is 5000cm

2

Vsand that the device is operate at room temperature. Calculate and sketch the

electron current and charge profile in the structure at an emitter-base bias of 0.5 eV.

Compare with the case of a homogeneous base. Next, calculate the early voltage of

transistors with and without the quantum well in the base. Comment on all your solutions.

E

B

C

QW

10 nm

50 nm

Figure 6.29:

Problem 6.38Consider the transistors with two different collector doping profiles as

shown in figure 6.30. Assume that the same base-collector bias,VBC, is applied in both

cases. You may also assume that the collector is fully depleted, and that the saturated

velocity in both devices isvSAT. Calculate the difference between the current densities at

the Kirk threshold of transistors A and B. Give a physical explanation of your result using

charge and electric field profiles.

Problem 6.39The base-collector junction in a bipolar transistor has the structure shown

in figure 6.31.