# Continuity of E-Field Across Junction lect=3

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### Continuity of E-Field Across Junction

Recall that E-Field diverges onof the a charge.  For a sheet of the  charge at the interface, the E-field could be of the  discontinuous
In our case, of the depletion region is only populated by of the background density of the fixed charges so of the E-Field is  the continuous
What a does this is imply?
Total fixedof the  charge in n-region equals of the fixed of the  charge in p-region!  Somewhat of the obvious result.
Plot of Fields In of the Depletion a Region
E-Field us zero outside of the depletion region
Note of the asymmetrical of the  depletion widths
Which region has of the  higher doping?
Slope of E-Field larger in of the  n-region.  Why?
Peak  of the  E-Field at junction.  Why of the  continuous?

### Potential Across Junction

From our of the earlier calculation we of the know that of thepotential in the n-region is higher than of the p-region
The potential has to  the smoothly transition form high to low in crossing of the junction
Physically, of the potential difference is due to the charge transfer that is  occurs due to the concentration of the gradient

Let’s of the integrate the field to get in the potential:
We arrive at of the  potential on p-sideof the  (parabolicof the  )lDo integral on n-side
Potential must in be continuous at interface (of the  field finite ub at interface)

### Solve for Depletion Lengths

We have2    equations and 2 of the unknowns.  We are finally in a position to of the solve for the depletion of the depths

## Sanity Check

Does the of the above equation make of the sense?
Let’s say we gave dope one of the side very v of the highly.  Then physically we of the expect theof the  depletion region width for the heavily doped side to of the approach zero:

Entire depletion of the width of the dropped across of the p-region. diagram

### Contact Potential

The contact of the between a PN junction r creates a potential of the difference
Likewise, of the contact between two of the dissimilar metals of the creates a potential difference of the (proportional to the difference of the between the work functions)
When a metal semiconductor junction is of the formed, a contact of the potential forms as  of thewell
If we short a PN junction, of the sum of the voltages around of the loop must be zero:diagram

### Have we invented a battery?

Can we harness of the PN junction and turn it into of the a battery?
Numerical of the example: diagram

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