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:‫ספרות עזר‬
.165-168 '‫ עמ‬,‫ מוליכים למחצה והתקנים אלקטרוניים‬,‫לב‬-‫פרופ' אדיר בר‬
P.A. Tipler, Modern Physics, pp 332-342
Mc Kelvey, Solidstate and Semiconductor Physics, pp 461-469
p-n junction, Wikipedia: http://en.wikipedia.org/wiki/PN_junction
Conduction band
Mobile
Electrons
Fixed Ions
EA
EF
Conduction band
EF
ED
+- +- +- +- +- +- +- +- +- +-
Fixed Ions
+- +- +- +- +- +- +- +- +- +-
Valence band
P-type semiconductor
Mobile Holes
Valence band
N-type semiconductor
• The PN junction is the name of the junction that is formed when joining a P-type
semiconductor to an N-type semiconductor.
• Remember: P-type semiconductors are doped with acceptors which when ionized
induced positive mobile charge in the form of extra holes in the material valance
band. In contrast N-type semiconductors are doped with donors which when ionized
induced negative mobile charge in the form of extra electrons in the material
conduction band. Note that In both cases the net space charge (fixed + mobile) will be
zero.
Energy Band diagram of the PN junction under zero bias voltage, V=0.
• At equilibrium the net current (diffusion + drift) of holes and electrons across the
junction is zero.
• The resulting built in voltage in the junction in equilibrium will depends on the
majority and the intrinsic carrier concentrations of the materials:
Vbi   Ei  EF p-side   EF  Ei n-side
 pp0 
 nn0 
kT
kT

ln 
ln 
 

e
n
e
 i 
 ni 
• Note that this internal potential difference cannot be measured with a voltmeter! The
voltmeter measures the difference in the Fermi Energy between two points which is
zero under equilibrium conditions.
• At first , due to the concentration gradient electrons start to defuse from the n-type
material to the p-type material leaving fixed positively charged ions unmasked. Holes
do the opposite and diffuse from the p-type material to the n-type material leaving
negatively charged fixed ions unmasked.
• An area depleted from mobile charge is formed in the junction. The fixed unmasked
ions in this area induce an electric field which opposes the diffusion process. An
equilibrium is reached.
Energy Band diagram of the PN, V>0.
• When the diode forward-bias-voltage is increased, the barrier for electron and hole
diffusion current decreases linearly. Since the carrier concentration decreases
exponentially with energy in both bands, diffusion current increases exponentially as the
barrier is reduced.
Energy Band diagram of the PN, V<0.
• As the reverse-bias-voltage is increased, the barrier for electron and hole diffusion grows
and the diffusion current decreases rapidly to zero, since the fall-off in current is
exponential.
• When the reverse-bias-voltage is increased, the net electric field increases, but drift
current does not change. In this case, drift current is limited not by how fast carriers are
swept across the depletion layer, but rather how often. In equilibrium the drift current is
limited by the number of minority carriers which are thermally generated within a
diffusion length of the junction.
|Idrift| does not change with applied voltage (V), while |Idiff| varies exponentially with
applied voltage,|Idiff| = I0 exp (eV/kT) where I0 is a constant.
The net current I = Idiff – Idrift
At equilibrium, V = 0 and the net current I = 0 we get:
Idiff
V 0
 Idrift
V=0
=I0
At any applied voltage, V:
I  I0 e
since Idrift= I0 at any voltage.
eV
kT
 I drift  I 0 (e
eV
kT
 1)
N
EC
EF
EV
+-
P
+-
• Holes
onserve
the Pas
side
while electrons
on electricity
the N side.from light.
The PNaccumulate
junction can
a photo-voltaic
cellaccumulate
and generate
• The
resulting
potential
difference,
referred
to as
an gap
openwill
circuit,
can be picked
by an
Photons
with energy
greater
then the
material
band
be absorbed
and its up
energy
electrometer.
The voltage
is equal
tothe
theconduction
difference band
in thethere
quasibyFermi
levels
will excite an electron
frommeasured
the valance
band to
creating
an of
the
minority
i.e. electrons
in the
p-type portion
and holes in the n-type portion.
electron
holecarriers,
pair. (excess
energy will
be converted
to heat)
• When
electrodes
arefield
provided
sides,physically
a currentseparates
can flow between
them.
The built
in electric
of theat
PNboth
junction
the created
electron-hole
• Note
thewill
photo
generated
current is oposit in direction to the diode diffusion current
pairs,that
which
otherwise
recombine.
Photo-voltaic cell equivalency circuit:
IL – photo generated current
ID – diode current
RS – serial resistance
RSH – shunt resistance
• Neglecting shunt and serial resistance (RS=0,RSH=∞) the current through the photo-voltaic
eV
cell can be written as:
I  I L  I D  I L  I 0 (e kT  1)
• The open circuit voltage (I=0) is therefore:
VOC 
kT  I L 
ln 1  
e  I0 
• The short circuit current (V=0) will be:
I SC  I L
behavior of a photo-voltaic cell at particular intensities of solar radiation
• Take the I-V characteristic of the PN junction, shift it downward by an amount
corresponding to the light-injected current (I=IL-ID), and flip it, and the result is the
following I-V curve that is often presented for photo-voltaic cells.
• The point at which a curve intersects the vertical axis is the short circuit condition:
V=0, I=ISC
• The point at which a curve intersects the horizontal axis is the open circuit condition:
V=VOC, I=0