12. I-V Characteristics of P-N Junction (Diode Characteristics)
【Key Points】
To learn the physical meaning of the I-V rectification characteristics in P-N junction.
I-V characteristics of P-N junction（Diode characteristics）
(a) Analysis by the minority carrier continuity equation （Assumption）No recombination happens in depletion layer.
（Positive bias applied as shown the following figure）
・Derivation of the current by electron diffusion and recombination
１．Apply the positive bias to P-N junction ２．n-side Fermi level goes upward
３．the electron carrier concentration at the depletion layer edge in p-side increases
４．the excess electrons diffuse as a minority carrier in p-side
(ⅰ) Derivation of the minority carrier distribution in p-side
Minority carrier continuity equation:（electron in p-type semiconductor with ｘ＞０）
the electric field , the carrier generation ,
(x=0 positioned the edge of depletion layer) Boundary conditions:
(i-1) Calculate the electron density at the depletion layer edge x=0:
the electron density at depletion layer edge in n-side the electron density at depletion layer edge in p-side
the diffusion potential Therefore,
When external voltage V is applied,
Therefore,
(i-2) The electron density at the edge of p-side：If , (the physical meaning of → the enough length to happen recombination）
→minority carrier distribution（the solution of differential equation）
(minority carrier diffusion length )
is the length that all the minority carrier can be recombined.
Therefore,
(ⅱ) Derivation of the diffusion current
（diffusion current by minority carrier (electron) at p-side）
(ⅲ) Derivation of the current by electron diffusion and recombination Think the amount of decreasing minority carrier recombined
→(Electron current)＝(Diffusion current) +(Recombination current)＝(Diffusion current at x=0)
Total current by electron from n-side to p-side
・Derivation of the current by hole diffusion and recombination from p-side to n-side think as the same manner, then
I-V characteristics in P-N junction
Whole current consists of electron current and hole current.
Reverse saturation current：saturation current by backward bias（V＜0）
Junction capacitance in P-N junction
Fixed charges (ions) are accumulated in the depletion layer, and then capacitance is dependent on voltage.
（differential capacitance per unit area）
Points: Junction capacitance （ ） is proportional to voltage V Higher the impurity density, narrower the width of depletion layer Depletion layer extends in direction to lower impurity density area The charge in depletion layer does not release by the short
(b) Actual I-V characteristics in P-N junction
・Backward bias characteristics
Backward bias causes abruptly increasing the current (Temperature dependent).
→Cause: avalanche effects and tunnel effects
・Recombination in the depletion layer should be considered.
(Total current) = (Diffusion current) ＋ (Recombination current)
(ｎ: ideality factor)
