Determine the common-emitter current gain

Question

Assignment Task:

We want to simulate a n-p-n BJT with PC1D.

1. Use an n-type Si wafer with an area of 1 mm²,

2. A thickness of 5 μm,

3. A background doping of 1x10¹⁵ cm^-3.

Commonly the base and emitter are formed by diffusion processes.

1. The base diffusion has a Gaussian profile with a depth factor of 0.2 μm and a peak doping of 1x10¹⁸ cm^-3 (1st front diffusion).

2. The emitter diffusion has an erfc profile with a depth factor of 0.1 μm and a peak doping of 1x10²⁰ cm^-3 (2nd front diffusion).

3. Further assume a lifetime of 0.05 μs and surface recombination velocities of 1000 cm/s.

4. Enable all contacts and set the emitter and base internal series resistances to 1x10^-6 Ω and the collector series resistance to 0.1 Ω.

5. The base contact should be at 0.35 μm from the front surface.

Excitation/Simulation:

1. The excitation should be transient with 86 time steps and a time step size of 0.5 s.

2. Set the first time step at t = 0 to 1x10^-9.

3. For the base circuit load the external file (located in the PC1D main folder) ib.vlt and for the collector circuit vce.vlb.

This will create a family of common-emitter curves. The curves for collector current correspond to 0.1, 0.2, 0.3 and 0.4 mA of base current, while the collector-emitter voltage is scanned in a range between 0 and 5 Volts.

Deliverables:

Part 1: Simulate the collector current vs. collector-emitter voltage characteristics. (print this)

Part 2: Determine the common-emitter current gain β. (Show calculations)

Part 3: Determine the emitter efficiency, assuming the base transport factor is unity (1.0). (show calculations)

Part 4: What happens to β if the base diffusion is too deep (depth factor of 0.5 μm). Explain the behavior.

Part 5: What happens to β if the emitter doping is too low (peak doping of 5x1018 cm-3). Explain the behavior.

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