Open Circuited pn Junction
Semiconductor Devices and Circuits
(ECE 181302)
16th August 2023
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• Holes diffuse from the p region, they uncover
negatively charged acceptor atoms.
• Electrons diffuse from the n region, positively
charged donor atoms are left behind.
• The net positive and negative charges in the n
and p regions induce an electric field in the
region near the metallurgical junction, in the
direction from the positive to the negative
charge, or from the n to the p region.
• The net positively and negatively charged regions
are referred to as the space charge region (SCR).
• Essentially all electrons and holes are swept out
of the SCR by the electric field.
• Since the SCR is depleted of any mobile charge,
this region is also referred to as the depletion
region.
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Diffusion Current ID in the pn Junction
• The two diffusion current components due to diffusion of holes and electrons add
together to form the diffusion current ID, whose direction is from the p side to the n side.
• However, uncovered charges on both sides of the depletion region establishes an electric
field E across the region and hence a potential difference V0 results across the depletion
region, with the n side at a positive voltage relative to the p side.
• Electric field E opposes further diffusion of holes into the n region and electrons into the
p region.
• Voltage drop V0 across the depletion region acts as a barrier that has to be overcome for
holes to diffuse into the n region and electrons to diffuse into the p region.
• The barrier voltage V0 limits the carrier diffusion process.
• The larger the barrier voltage, the smaller the number of carriers that will be able to
overcome the barrier, and hence the lower the magnitude of diffusion current.
• Diffusion current ID depends strongly on the voltage drop V0 across the depletion region.
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V0 = - E W
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Drift Current IS in the pn Junction
• Thermally generated holes in the n material that reach the edge of the depletion region
experience the electric field E in the depletion region that sweeps the holes across into
the p side.
• Similarly, thermally generated minority electrons in the p material at the edge of the
depletion region are swept by the electric field E in the depletion region across to the n
side.
• The two drift current components—electrons moved by drift from p to n and holes
moved by drift from n to p—add together to form the drift current IS, whose direction is
from the n side to the p side of the junction.
• Drift current is determined by the number of minority carriers that make it to the edge of
the depletion region and get swept across by E.
• Under open-circuit conditions no external current exists; i.e. the two opposite currents ID
and IS across the junction must be equal in magnitude.
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Junction Barrier Voltage
• With no external voltage applied, the barrier voltage V0 across the pn junction is given
by
• where NA and ND are the doping concentrations of the p side and n side of the junction,
respectively.
• V0 also known as junction built-in voltage depends both on doping concentrations and
on temperature.
• Where VT = kT/q. The parameter VT is known as the thermal voltage.
• At room temperature, T = 300 K and VT = 25.9 mV.
• Typically, for silicon at room temperature, V0 is in the range of 0.6 V to 0.9 V.
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Charge Stored in the
Depletion Region
• NA > N D
• Width of the depletion layer will not be the same
on the two sides.
• Depletion layer will extend deeper into the more
lightly doped material.
• Width of the depletion region in the p side: xp is
smaller than in the n side by xn.
• Magnitude of the charge on the n side of the
junction is
• Magnitude of the charge on the p side of the
junction is
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Width of the Depletion Region
• By the charge equality condition;
or
• The width W of the depletion layer is:
and
• Charge stored on either side of the depletion region expressed in terms of W is:
also expressed as
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Open Circuited
pn Junction
V
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(V0 = - E W)
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References/Books:
• G. Streetman, and S. K. Banerjee, “Solid State Electronic Devices,” 7th edition,
Pearson, 2014.
• D. Neamen, D. Biswas, "Semiconductor Physics and Devices," McGraw-Hill
Education.
• S. M. Sze and K. N. Kwok, “Physics of Semiconductor Devices,” 3rd edition, John
Wiley &Sons, 2006.
• A.S. Sedra and K.C. Smith, “Microelectronic Circuits”, Saunder's College
Publishing, 1991.
• Robert L. Boylestad and Louis Nashelsky, “Electronic Devices and Circuit Theory”,
7th edition, Prentice Hall.
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