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PN Junctions Theory Dragica Vasileska Department of Electrical Engineering Arizona State University. PN-Junctions: Introduction to some general concepts Current-Voltage Characteristics of an Ideal PN-junction (Shockley model) Non-Idealities in PN-Junctions AC Analysis and Diode Switching.
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Department of Electrical Engineering
Arizona State University
1. PN-junctions - General Consideration:
(A) Equilibrium analysis of step junctions
(a) Built-in voltage Vbi:
(b) Majority- minority carrier
Solve 1D Poisson equation using depletion charge approximation, subject to the following boundary condi-tions:
Use the continuity of the two solutions at x=0, and charge neutrality, to obtain the expression for the depletion region width W:
The maximum electric field, which occurs at the metallurgical junction, is given by:
(e) Carrier concentration variation:
(f) Depletion layer capacitance:
Consider a p+n, or one-sided junction, for which:
The depletion layer capacitance is calculated using:
(a) Depletion layer width:
(c) Maximum electric field:
(d) Depletion layer capacitance:
Based on accurate numerical simulations, the depletion layer capacitance can be more accurately calculated if Vbi is replaced by the gradient voltage Vg:
No SCR generation/recombination
Reverse saturation current is due to minority carriers being collected over a distance on the order of the diffusion length.
This leads to:
Generated carriers are swept away from the depletion region.
under reverse bias conditions
Zero-bias band diagram:
Forward-bias band diagram:
Reverse-bias band diagram:
Generation of the excess electron-hole
pairs is due to impact ionization.
Expanded view of the
Impact ionization initiated by electrons.
Multiplication factors for
electrons and holes:
Impact ionization initiated by holes.
Breakdown voltage voltage for which the multiplication rates Mn and Mp become infinite. For this purpose, one needs to express Mn and Mp in terms of an and ap:
The breakdown condition does not depend on which
type of carrier initiated the process.
(a) Step p+n-junction
The characteristic time constant is on
the order of the minority carriers lifetime.
Qp(t) = excess hole charge
Valid for p+n diode
To solve exactly this problem and find diode switching time, is a rather difficult task. To simplify the problem, we make the crucial assumption that IR remains constant even beyond t1.
ts switching time
trr reverse recovery time