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