# Homework 4 Bipolar Junction Transistor (3 credit points) ```Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
Homework 4
Bipolar Junction Transistor (3 credit points)
BJT under Thermal equilibrium (1 credit point)
A silicon p + np bipolar junction transistor (BJT) is used as an amplifier. The
doping concentration in the emitter, base and collector regions is given by
N AE = 1017 cm −3 , N DB = 1015 cm −3 , N AC = 1014 cm −3 . The BJT is in thermal
equilibrium.
a.)
Calculate and sketch the carrier concentration diagram and the energy
band diagram of the BJT at room temperature. Complete ionization can be
assumed for all three regions of the BJT. Indicate characteristic values like
minority and majority carrier concentrations, width of the space charge
regions, the Fermi level, and build-in voltages.
Parameters: ni=1010 cm-3, kT=25.9meV, εS=11.3 x 8.854 x 10-12 F/m,
q=1.602 x 10-19 As.
b.)
Calculate and schematically sketch the charge density, the electric field
and the potential distribution of the BJT at room temperature. Indicate
characteristic values like the built-in voltages, the maximum electric field and
the width of the space charge regions.
BJT under bias conditions (1 credit point)
In the following the BJT operates in the active mode and the applied voltages
are: VEB=0.5V and VCB=-2V. The Shockley assumptions apply (Uniform
doping in the individual doping regions, abrupt junctions, low-level injection,
no losses due to generation and recombination in the depletion regions).
c.)
Schematically sketch the energy band diagram in the active mode.
Indicate the quasi Fermi levels and the width of the space charge regions.
d.)
The voltage VEB is further increased. As a consequence of the
increased emitter-base voltage more carriers are injected so that the
assumption of low injection does not apply anymore. Calculate the emitterbase voltage VEB level which leads to a transition from low to high injection.
Transport and gain factors (1 credit point)
The BJT is used as a common emitter circuit. The base transport factor is
determined to be αT=0.98. The minority carrier life in the different regions is
given by τ nE = 6 ⋅ 10 −8 s , τ pB = 6 ⋅ 10 −7 s , τ nC = 3 ⋅ 10 −6 s .
Homework 4
Introduction to Electronic Devices, Fall 2006, Dr. D. Knipp
e.)
Calculate the common-emitter current gain.
Note: The influence of the applied voltages on the common-emitter
gain is negligible (Early effect).
Influence of the Impurity concentration on the Mobility and
Diffusivity [Ref. S. Sze, Semiconductor Devices].
Deadline for Submission: 16.11.2006, 8:15 in class
Important Hint: Put the solution in the mailbox of Dr. D. Knipp in
Research I. Solutions in electronic form will not be accepted.