Loading in 2 Seconds...
Loading in 2 Seconds...
PN Junctions Theory Dragica Vasileska Department of Electrical Engineering Arizona State University. PNJunctions: Introduction to some general concepts CurrentVoltage Characteristics of an Ideal PNjunction (Shockley model) NonIdealities in PNJunctions AC Analysis and Diode Switching.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Dragica Vasileska
Department of Electrical Engineering
Arizona State University
pside
1. PNjunctions  General Consideration:
nside
pside
Step junction
Linearlygraded junction
+

qNA
(A) Equilibrium analysis of step junctions
(a) Builtin voltage Vbi:
(b) Majority minority carrier
relationship:
pside
nside
Solve 1D Poisson equation using depletion charge approximation, subject to the following boundary conditions:
pside:
nside:
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:
W
dW
~
V
(f) Depletion layer capacitance:
Consider a p+n, or onesided junction, for which:
The depletion layer capacitance is calculated using:
Reverse
bias
vac
Forward bias
(B) Equilibrium analysis of linearlygraded junction:
(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:
(2) Ideal CurrentVoltage Characteristics:
Spacecharge
region W
Reverse bias
No SCR generation/recombination
Ge
Si
GaAs
V
(d) Origin of the current flow:
Reverse bias:
Forward bias:
Ln
Lp
Reverse saturation current is due to minority carriers being collected over a distance on the order of the diffusion length.
(e) Majority carriers current:
Quasineutrality requires:
This leads to:
(f) Limitations of the Shockley model:
3. NonIdealities in PNjunctions:
Generation lifetime
I (logscale)
V (logscale)
Generated carriers are swept away from the depletion region.
IVcharacteristics
under reverse bias conditions
Recombination lifetime
Exact expression for the recombination current:
Importance of recombination effects:
log(I)
V
Zerobias band diagram:
Forwardbias band diagram:
EFn
EFp
EF
EC
EC
EV
EV
W
W
Tunneling current (obtained by using WKB approximation):
Reversebias band diagram:
EFp
EFn
EC
EV
EFp
EFn
EC
EV
Generation of the excess electronhole
pairs is due to impact ionization.
Expanded view of the
depletion region
Impact ionization initiated by electrons.
Multiplication factors for
electrons and holes:
dx
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+njunction
(4) ACAnalysis and Diode Switching
The characteristic time constant is on
the order of the minority carriers lifetime.
Equivalent circuit model for forward bias:
Qp(t) = excess hole charge
Valid for p+n diode
n
t=0
IF
t increasing
n
t=0
2
1
VF
VR
R
R
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.
Slope almost
constant
t=0
t=ts
ttrr
ts switching time
trr reverse recovery time