PHYS2170 Lecture Notes - Lecture 15: Depletion Region, Electric Potential, Indium Phosphide
4 Aug 2019
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PHYS2170 – Week 11 Lecture 1
Bringing p-type and n-type Si Together
The Depletion Region
- Expect the electron and hole concentrations change
gradually from high to low density
- Approximation
o The transition region is completely depleted of
mobile carriers (depletion region)
o Can assume ideal charge densities
o -xp and xn = widths of depletion regions in p- and n-
type materials respectively
- The net charge of the whole region is neutral
o Area of -ve == area of +ve
Calculating the Internal Field
- Poisson’s equation relates the charge density to the
electric potential produced
- Charge conservation leads to
- Poisson’s equation for -xp to 0
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- Integrate to get internal field in p-type
Calculating “built-in” Voltage
- Total potential
difference
o The potential at barrier region
- Total width of the
depletion region
- If NA ≫ ND then:
p-n Junction in Contact
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Band Bending
- From the simple model, there is a quadratic dependence of
the potential energy in the transition region
o Although more complex models give different
results, the variation is always monotonic
- The energy difference between
the bands is eU0, called the built-
in voltage (inbuilt potential),
also named Vb
- The electric field names a barrier of Vbi volts to electron
diffusion from n- to p-
- Holes lose U as they move with the field from n to p
- Electrons lose U as they move from p to n
- Electrons on the n-side have lower U than electrons on the p-side
- The CB edge is lower on the n-side compared to the p-side
Electron Flows
- There will be an electron flow from left to right proportional to the number of electrons in the p-type
- The electrons in the n-type material are numerous and while most sit at the bottom of the conduction
band, a significant number have sufficient energy to cross to the p-side
