Generación y recombinación. Absorción
Generación y recombinación. Absorción
de la luz. Foto
Light is an electromagnetic wave
An electromagnetic wave is a traveling wave that has time-varying electric and magnetic Fields that are perpendicular to each other and the direction of propagation z.
Energy E / eV
3,0
2,5
2,2
2,05
1,7
UV
IR
1 eV = 1,602
×
10
-19J
1 kT = 0,025 eV (T = 300 K)
1 nm = 10
-9m = 10 Å
410
495
620
700
Wavelength
λ
/ nm
560
Out
Out--put of a solar cell
put of a solar cell
The
The output
output of
of a
a solar
solar cell
cell (photocurrent)
(photocurrent) is
is
determined
determined
by
by
a
a
balance
balance
between
between
photogeneration,
photogeneration,
charge
charge
recombination
recombination
and
and
current
Electrons and holes in intrinsic
Electrons and holes in intrinsic
semiconductor
semiconductor
Generation and Recombination
Generation and Recombination
Generation
Generation:: AnAn electronicelectronic excitationexcitation eventevent increasingincreasing thethe numbernumber of
of freefree carriercarrier availableavailable toto carrycarry chargecharge.. RequiresRequires anan inputinput ofof energy
energy providedprovided byby thethe vibrationalvibrational energyenergy ofof thethe latticelattice (phonons),(phonons), light
light (photons)(photons) oror thethe kinetickinetic energyenergy ofof anotheranother carriercarrier.. ForFor solarsolar cell,
cell, thethe mostmost importantimportant generationgeneration isis photogenerationphotogeneration,, ii..ee.. byby thethe absorption
absorption ofof aa photonphoton..
Recombination: An electronic relaxation event reducing the number of free carriercarrier. Releases energy taken by the same mechanisms to those of generation. For every generation process there is an equivalent recombination process.
Light Absorption
Light Absorption
Para describir las propiedades ópticas de
Para describir las propiedades ópticas de
los sólidos se introduce el
los sólidos se introduce el
índice de
índice de
refracción complejo:
refracción complejo:
ik
n
n
*
=
−
Ecuación
Ecuación de
de una
una onda
onda electromagnética
electromagnética que
que se
se
propaga
propaga en
en una
una substancia
substancia cuyo
cuyo índice
índice de
de
refracción
refracción es
es n*
n* en
en la
la dirección
dirección x
x::
)
*
(
c
x
n
t
i
o
e
E
E
ω
ω
−
=
x
k
nx
ω
ω
c
x
k
c
nx
t
i
o
e
e
E
E
ω
ω
ω
−
−
=
(
)
i)Nos muestra una onda plana de frecuencia ω que se
propaga con la velocidad c/n y cuya amplitud se amortigua exponencialmente a lo largo de la dirección de propagación. ii) Fase afectada por parte real de n*.
c
x
k
e
I
ω
2
−
∝
En la práctica se mide la intensidad I de la luz:
2
E
I
→
∝
x
e
I
I
=
(
0
)
−
α
ω
k
2
α: coeficiente de absorción. Probabilidad de la absorción de un fotón
por una muestra de espesor unidad. α-1 puede considerarse como la
longitud media del recorrido libre del fotón en la substancia (profundidad de penetración).
x
e
I
I
=
(
0
)
−
α
α
ω
=
c
k
2
Absorción de la luz.
Absorción de la luz.
La
La
absorción
absorción
de
de
la
la
luz
luz
se
se
debe
debe
fundamentalmente
fundamentalmente a
a la
la acción
acción de
de los
los
mecanismos
mecanismos siguientes
siguientes::
Intrínseca
Intrínseca o
o fundamental
fundamental..
Intrínseca
Intrínseca o
o fundamental
fundamental..
Excitónica
Excitónica..
Por
Por portadores
portadores de
de carga
carga libre
libre..
Por
Por impurezas
impurezas..
El
El espectro
espectro de
de absorción
absorción completo
completo del
del
sólido
sólido se
se compone
compone de
de los
los espectros
espectros de
de
absorción
absorción relacionados
relacionados con
con la
la acción
acción de
de
los
los distintos
distintos mecanismos
mecanismos..
los
los distintos
distintos mecanismos
mecanismos..
∑
=
i
i
(
)
)
(
λ
α
λ
α
Absorción intrínseca o
Absorción intrínseca o
fundamental
fundamental
Optical absorption generates electron hole pairs. Energetic electrons must loose their excess energy to lattice vibrations until their average energy is (3/2)kT in the conduction band.
Absorción
Absorción en
en semiconductores
semiconductores con
con
band
The absorption coefficient α depends on the photon energy hυ and hence
on the wavelength.
Density of states increases from band edges and usually exhibits peaks and troughs.
Generally α increases with the photon energy greater than Eg because
more energetic photons can excite electrons from populated regions of the VB to numerous available states deep in the CB.
g(E): number of states per unit energy per unit volume. g(E): number of states per unit energy per unit volume.
We assume that the VB states are filled and that the CB states are empty We assume that the VB states are filled and that the CB states are empty We assume that the VB states are filled and that the CB states are empty We assume that the VB states are filled and that the CB states are empty (n<<N
(n<<Ncc).).
The photon absorption process increases when there are more VB states The photon absorption process increases when there are more VB states available as more electrons can be excited. We also needed available CB available as more electrons can be excited. We also needed available CB states into which the electrons can be excited, otherwise the electrons states into which the electrons can be excited, otherwise the electrons cannot find empty states to fill.
cannot find empty states to fill.
The probability of photon absorption depends on both the density of The probability of photon absorption depends on both the density of VB states and the density of CB states.
VB states and the density of CB states.
For photons of energy h For photons of energy hνν
A
A=E=Egg, the absorption can only occur from E, the absorption can only occur from EVV to Eto ECC
where the VB and CB densities of states are low and thus the absorption where the VB and CB densities of states are low and thus the absorption coefficient is small.
Coeficiente de absorción para
Coeficiente de absorción para
semiconductores con band
semiconductores con band--gap
gap
directo.
directo.
2
/
1
)
(
)
(
h
ν
≅
A
h
ν
−
E
g
α
A=cte.=2x10
4[cm
-1.eV
-1/2]
Absorción
Absorción en
en semiconductores
semiconductores con
con
band
Dependencia espectral del “
Dependencia espectral del “
α
α
” para
” para
las transiciones indirectas.
las transiciones indirectas.
2
)
(
)
(
h
≅
B
h
−
E
g
±
h
Ω
r
r
r
ω
ω
α
(
h
ω
)
≅
B
(
h
ω
−
E
g
±
h
Ω
)
α
Direct vs. indirect semiconductors
Direct vs. indirect semiconductors
The
The indirectindirect bandgapbandgap ofof SiSi makesmakes
optical
optical absorptionabsorption inefficientinefficient duedue to
to thethe requirementrequirement ofof phononphonon emission/scattering
emission/scattering withwith photonsphotons in
in orderorder toto conserveconserve crystalcrystal momentum
Photon flux.
Photon flux.
The
The
photon flux
photon flux
is a quantity useful in solar cell
is a quantity useful in solar cell
calculations: it is defined as the number of photons
calculations: it is defined as the number of photons
crossing a unit area perpendicular to the light beam per
crossing a unit area perpendicular to the light beam per
second.
second.
If we let
If we let
I(E)
I(E)
denote the intensity of the light in W/cm
denote the intensity of the light in W/cm
22then we have:
then we have:
then we have:
then we have:
av
hc
E
b
E
E
b
E
I
λ
)
(
)
(
)
(
=
=
Photon flux calculation
Photon flux calculation
Photogeneration rate
Photogeneration rate
If
If we
we can
can assume
assume that
that all
all photons
photons are
are absorbed
absorbed
to
to generate
generate free
free carriers,
carriers, then
then the
the rate
rate of
of carrier
carrier
generation,
generation, per
per unit
unit volume,
volume, at
at a
a depth
depth x
x below
below
the
the surface
surface is
is given
given by
by::
Where I is the photon flux at x.
Notice that is the number and not the energy of photons which determines the photogeneration rate.
