A rectangular slab of silicon is doped with 1022 m-3 Boron (B) atoms. The intrinsic carrier concentration ni in silicon

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A rectangular slab
of silicon is doped with 1022 m-3 Boron (B)
atoms. The intrinsic carrier concentration ni in
silicon at 300K is 1.5x1016 m-3 and it varies
with temperature as T3/2exp(-Eg/2kT),
where Eg=1.1eV is the bandgap energy, T is the
absolute temperature in K and k is Boltzmann’s constant.
The silicon slab is 6 μm long with a rectangular cross section of 2
μm 2 (1 μm x 2 μm). Assume kT=0.026 eV and
kT/q=0.026 V. Assume that the electron mobility is
μe=0.04 m2/Vs and that the hole
mobility is μh=0.02 m2/Vs.
v)Calculate the
resistance of the slab described above at 300K and 360K
If 5x1022 m-3 Gallium
(Ga) atoms were added to this
sample calculate the majority and minority carrier
concentration 300 K and state the type of carrier
(electron or hole). State whether the same is n-type, p-type or
fully compensated. (4 marks)
(vi) Calculate the current density and the current through the
original sample of question i)Evaluate the majority and minority
carrier concentrations at 300 K and state the type of carrier
(electrons or holes) Is this silicon p-type or n-type? if 5 V is
dropped along the length of this silicon slab at 300 K. Which type
of carrier: electron or hole contributes most of the total current?
(5 marks)
vii) Calculate the Fermi Level, EF, of the original sample of
question i) relative to the valence band edge EV. (4 marks)