Semiconductor Physics and
Devices
Lecture 9
Contact Potential
ETE - 301
Priyanti Paul Tumpa, Dept. of ETE, CUET 1
Contact Potential
• The potential difference between two types of material is called Contact
Potential.
• Let us consider separate regions of p and n type semiconductor material are
brought together to form a junction.
• The n material has a large concentration of electrons and few holes, whereas the
converse is true for p material.
• Upon joining two regions, diffusion of carriers will take place because of large
carrier concentration gradient at the junction.
• The holes will diffuse from p side to n side and electrons will diffuse from n to p.
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Contact Potential
• As there is an opposing
electric field, Ex in the
junction, there will be no
diffusion current there.
• A region of positive
space charge will be
developed near the n side
of the junction and
negative space charge near
p side.
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Contact Potential
• No net current can flow across the junction at equilibrium, the drift current due to E
field will cancel the diffusion current.
• The electric field appears in some region W about the junction, and the equilibrium
potential difference across W is Vo.
• As E = -dV(x)/dx, we assume electric fields are zero in the neutral regions
outside W.
• Thus there is a constant potential Vn in the neutral n material and a constant Vp in
the neutral p material.
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Contact Potential
• So potential difference, Vo = Vn –Vp.
• W is called transition region and potential difference Vo is called Contact potential.
• Contact potential is necessary to maintain equilibrium at the junction.
• The contact potential separates the bands. The valance and conduction energy bands
are at higher on the p side of the junction than on the n side by the amount qVo.
• The separation of the bands required to make the Fermi level constant throughout
the device.
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Relation between Contact Potential and Doping Concentration:
• We know the drift and diffusion current of holes just cancle at equilibrium:
• This equation can be rearranged to obtain
.
• Electric field is the gradient of potential. E = -dV(x)/dx;
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Relation between Contact Potential and Doping Concentration:
Taking integration of potential from Vp to Vn and hole concentration from Pp
to Pn,
If the junction is made of Na acceptor on p side and donor Nd on n side, then
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Example: An abrupt Si p-n junction has 𝑵𝒂 = 1018 𝑐𝑚−3 on one side
and Nd = 5*1015 𝑐𝑚−3 on the other side.
a) Calculate the fermi level positions at 300k in the p and n regions.
b) Draw an equilibrium band diagram for the junction and determine the
contact potential Vo from the diagram.
c) Compare the results of part (b) with Vo as calculated from the
equation.
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Equilibrium Fermi Levels
The Fermi level must be constant throughout the device at equilibrium.
As we know,
Which can be reduce to
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Equilibrium Fermi Levels
• The energy bands on either side of the
junction are separated by the contact
potential Vo times the electronic charge q;
• Thus energy difference Evp –Evn = qVo
• At Equilibrium,
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Space Charge at a Junction
• Within the transition region, electrons and holes transit from one side of t he
junction to another side.
• Some electrons are diffused from n to p, and some are swept by the electric
field from p to n. So very few carriers are within the transition region at any
given time.
• In the transition region, space charge are due to uncompensated donor and
acceptor ions.
• The charge density on n side is due is just q times the concentration of donor
ions Nd, the negative charge density on the p side is –q times the concentration
of acceptor Na.
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Space Charge at a
Junction
• At junction, charges on either
side is equal, the transition
region may be extended to the p
and n regions unequally.
• Like, if p side is more lightly
doped than n side (Na < Nd),
then space charge region must
extend farther into p material
than n material.
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Space Charge at a Junction
• The total uncompensated charge on either side of the junction is
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Space Charge at a Junction
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Space Charge at a Junction
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Space Charge at a Junction
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Space Charge at a Junction
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Example 5.2 (self)
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