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Analysis of the p-n Junction
April 18, 2023
Chapter VI
Calculation of Carrier density and Current Densities
Currents and carrier densities in the neutral regions
Depletion layer width with or without applied bias
With applied bias
Same as Eq (4-48a) in Sze
V
Light passing through a semi-transparent medium follows Bouguer’s (Bouguer-Lambert’s, or Beer’s) Law
• Where b is the light energy passing through the medium per unit area, and is the absorption per unit volume.
xbb s exp
xbdx
dbs exp
dx
db
Currents and carrier densities in the space charge region
Total Current Density
Current from p to n is positive and is opposite to the convention.
No light and no applied bias
No light and no applied bias
No light but with forward bias
No light but with forward bias
P-n Junction under Illumination
Short circuit current: V=0
Under short circuit condition: V=0
In the depletion region, EFn = EFp
Medium has a higher absorption coefficient for short wavelength light
Penetration depth in a semi-transparent medium
• Solution from Electro-magnetic (Maxwell) wave equation in a semi-transparent medium:
)2
exp()](2exp[ kxc
xc
ntiEE
ooyMy
where k is the extinction coefficient for the medium. For light intensity, the decay of light should follow
)4
exp( kxc
IIo
o
continue
Penetration depth of light in a semi-transparent medium can be found when
14
kxco
k4
1
44
kk
cx o
When xp exceeds Ln, emitter is too thick. Part of the region becomes dead layer.
Open circuit voltage
Jm,o is similar to JR in Eq 4-59 in Sze.
pn
i
D
i
p
pom
wqn
N
nDqJ
2
, for NA >> ND
PV cell with a resistive load
Due to reduced band gap at higher T