# PN Junctions–Lecture 1

## Diffusion (cont)

• The net motion of the gas molecules to of the right chamber was due to the concentration of the gradient
• If each particle of the moves on average of the left or right then eventually of the half will be in the right chamber
• If the moleculesof the  were charged (or electrons), then of the there would be a net of the current flow
• The diffusion of the current flows from high  of theconcentration to low concentration:

Diffusion Equations
Assume that of the mean free path is λ
Find flux of carriers  of thecrossing x=0 plane

• ## Einstein Relation

The thermal of the velocity is given by of the kT ## Total Current and Boundary Conditions

When both driftof the and diffusion are  of the present, the total current of thegiven by the sum:
In resistors, the carrier of the approximately uniform and the of the second term is nearly zero
For currents flowing of the uniformly through an interface (no chargeof the accumulation), the field is discontinous

Carrier Concentration and Potential In thermal equilibrium, there are of the no external fields and we thus expect of the electron and hole current densities to be zero:
Carrier Concentration and Potential (2)
lWe have an equation of the relating the potential to of thecarrier of the concentration
lIf we integrate of the above equation we a have
We define the potential of the  reference to be intrinsic Si Carrier Concentration Versus Potential
The carrier of the concentration is thus of the function of potential
Check that for zero of the potential, we have of the intrinsic carrier concentration of the  (reference).
If we do a similar of the calculation for holes, we arrive at of the similar equation
Note that the law of mass of the  action is upheld The Doping Changes Potential
Due to the log nature of of the potential, the potential of the changes linearly of the  exponential increase of the in doping:
Quick calculation aid: of the  For a p-type concentration of the of 1016 cm-3, the potential is -360 mV
lN-type materials have aof the positive potential with of the respect to intrinsic Si

The Doping Changes Potential
Due to the log nature of the potential, the  of the potential changes linearly of the exponential increase of the  doping:
Quick of the calculation aid:  For a p-type concentration of the 1016 cm-3, the of the potential is -360 mV
N-type of the materials have aof the positive potential with of the respect to intrinsic  of the Si  