Download Energy Bands: • The Fermi level: o This is an energy level in the

Energy Bands:
• The Fermi level:
o This is an energy level in the energy gap that represents the point where the
probability of finding an electron is = 0.5 .
o For intrinsic semiconductors, the Fermi level EF, is in the middle of the
energy gap and it is called intrinsic Fermi-level Ei.
Conduction Band
EC
EF = Ei
Energy Gap
EV
Valence Band EV
o For N-type semiconductors, EF is closer to conduction band EC. As a result,
as ND increases Î EF get closer to EC or ϕ F increases.
ϕ F = Fermi potential = (EF - Ei)/q = Vtln(ND/ni) Æ positive
Vt ≈ 0.025 V, Thermal Voltage = constant/T
Conducting Band
EC
EF
Ei
qϕ F
EV
Valence Band
N-type
o For P-type semiconductors, EF is closer to Valence Band EV. As a result, as
NA increases Î EF get closer to Ev.
ϕ F = (EF - Ei)/q =-Vtln(NA/ni) Æ negative
Conducting Band
EC
Ei
qϕ F
EF
EV
Valence Band
P-type
o In the absence of current flaw, the Fermi-level would be continuous and
constant.
• Energy Bands under Bias:
o An applied electric field pushes the bands in its direction, e.g
Electric field Є
EC
EF
EV
o Electrons act like liquid Î accumulate in lowest region in conduction
Band. While holes act like bubbles Î accumulate in highest region in
Valence Band.
o This effect could be used to invert a certain region in a semiconductor by
applying a large enough voltage with the appropriate polarity.
This region is
inverted (EF is
closer to EC than
EV) Æ N-type
Є
Electrons
accumulated
EC
EF
EV
Holes are
depleted
P-Type
Electron
Depletion
EC
EF
EV
Holes
accumulation
Є
This region is
inverted (EF is
closer to EV than
EC) Æ P-type
N-Type
The P-N Junction (Diode):
o The Diode is made by bringing into a contact a p-type semiconductor with an
N-type semiconductor.
o Ferric level will align. As a result, the band will bend around the junction by
q(ϕ FN – ϕ FP). This is called the Build-in potential.
Vbi = ϕ FN – ϕ FP = Vt ln[(NA*ND)/ni2]
ND = net Donor concentration on the N-side
NA = net acceptor concentration on the P-side
Vbi is typically ≈ 0.5 V to 0.8 V
Before:
P
N
EC
Ei
EFP
EC
qϕ FN
qϕ FP
EV
EFN
Ei
EV
After:
P
N
EC
q(ϕ FN – ϕ FP)
EV
EC
EF
EV