PHOTOVOLTAIC TECHNOLOGIES (ET4377): INSTRUCTION 2 ...

PHOTOVOLTAIC TECHNOLOGIES (ET4377): INSTRUCTION 2
LIGHT MANAGEMENT
Question 1:
Solar simulator spectra and External Quantum Efficiency
P() (10 9 Wm -2 m -1 )
3.0
2.5
2.0
1.5
1.0
0.5
< 800 nm P()=4x10 15 1.2x10 9 [Wm -2 m -1 ]
> 800 nm P()=5.2x10 9 -4x10 15 [Wm -2 m -1 ]
0.0
200 400 600 800 1000 1200 1400
EQE
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
200 400 600 800 1000 1200 1400
Wavelength (x10 -9 m)
Wavelength (x10 -9 m)
Figure 1. Figure 2
The spectral power density of the solar simulator as a The external quantum efficiency of solar cell
function of the wavelength.
A as a function of the wavelength.
Solar simulators are used to study the performance of solar cells in the lab. A solar
simulator is a lamp which has to simulate the solar spectrum under standard test
conditions (STC). In figure 1, the spectral power density of a solar simulator is shown.
The spectral power density of this solar simulator is given by:
300nm 800nm
800nm 1300nm
P( )
4
10
15
P( )
5.2
10
1.2
10
9
4 10
15
9
[Wm
[Wm
2
2
m
m
1
1
]
]
Where the wavelength is expressed in meters.
a) What are the standard test conditions (STC) under which the nominal
performance of solar cells are measured?
b) Calculate the irradiance I of the solar simulator. What are the difference(s)
between the spectrum of the solar simulator and the standard test conditions?
c) What is the photon flux of the solar simulator?
In figure 2, the external quantum efficiency (EQE) as a function of the wavelength of
solar cell A under short circuited (V= 0 V) condition is presented.
d) What is the band gap in eV of the absorber layer of the solar cell A?
e) Calculate the short circuit current density J SC in mA·cm -2 if the solar cell is
measured under the solar simulator.
f) Solar cell B has a different absorber layer in reference to solar cell A. Above the
band gap solar cell B has an EQE=0.70 and remains constant. Solar cell B has a

PHOTOVOLTAIC TECHNOLOGIES (ET4377): INSTRUCTION 2
LIGHT MANAGEMENT
J SC = 17.8 mA·cm -2 under the solar simulator shown in Figure 1. What is the band
gap of this material?
Question 2:
The Rayleigh film
Figure 3
a) Consider the interface between two media with refractive index n=a and n=b
(Figure 3b). What are the Fresnel coefficients R and T expressed in a and b for
irradiance for light with an incident angle of i =0 (perpendicular)?
b) Consider the situation in Fig. 3b. A third medium with refractive index n = x is
placed between the other two media. What are the effective Fresnel coefficients R
and T expressed in a, b and x for irradiance for light with an incident angle of
i =0 (perpendicular)?
c) Proof that the minimum reflection and maximum transmission is obtained for
x ab . Hint: use the function T(x) derived at question 2b. (Which conditions
should be valid to have a maximum for T(x)?)
Question 3:
The AR coating.
Figure 4

PHOTOVOLTAIC TECHNOLOGIES (ET4377): INSTRUCTION 2
LIGHT MANAGEMENT
In Figure 4 the light beam traveling in the z-direction is shown. The interface between
media 1 and 2 is positioned at z=0. The interface between media 2 and 3 is positioned at
z=d. The Fresnel coefficients at the interfaces are t 12 , r 12 , t 23 and r 12 . A light beam
described by:
Ei
(z) E0
cos( t
kz) z 0
is traveling in the z-direction and is incident on the interface at z=0.
a) Give the expression E R
(z a)
for the reflected light beam at z=-a.
b) Give the expression E T
(z b)
for the transmitted light beam at z=b.
c) For which optical thickness is (z a)
minimized?
E R
Question 4: The critical angle
glass
glass
glass
TCO
TCO
TCO
1
•n-a-Si:H
absorber
2
absorber
3
absorber
back reflector
back reflector
back reflector
Figure 5
Consider the thin film silicon solar cells as depicted in Figure 5. The interfaces between
the various layers are not textured but flat. The transparent conductive oxide layer is
Aluminum-doped Zinc-oxide. The back reflector is a magic layer, which reflects all the
light transmitted through the silicon absorber layer under a certain angle r back in to the
cell. The refractive index for Si layer n Si =4.3, transparent conductive oxide n ZnO =1.86,
n glass =1.51 and n Air =1.
a) What is the minimum angle for the refraction at the r to have all light reflected
and the Si-ZnO interface?
b) What is the minimum angle for the refraction at the r to have all light reflected
and the ZnO-glass interface?
c) What is the minimum angle for the refraction at the r to have all light reflected
and the glass-air interface?
d) For which r angles does the light not escape the Si, ZnO and glass?

PHOTOVOLTAIC TECHNOLOGIES (ET4377): INSTRUCTION 2
LIGHT MANAGEMENT
Fresnel coefficient
)
cos(
n
)
cos(
n
)
cos(
n
)
cos(
n
r
i
2
t
1
i
2
t
1
p
)
cos(
n
)
cos(
n
)
cos(
n
)
cos(
n
r
t
2
i
1
t
2
i
1
S
2
t
2
i
1
t
2
i
1
S
)
cos(
n
)
cos(
n
)
cos(
n
)
cos(
n
R
2
i
2
t
1
i
2
t
1
p
)
cos(
n
)
cos(
n
)
cos(
n
)
cos(
n
R
2
2
1
2
1
p
o
i
n
n
n
n
R
0
2
2
1
2
1
p
n
n
n
4n
T
)
n
n
arcsin(
1
2
,critic
i
Snell’s law:
r
i
t
2
i
1 sin
)
(
n
)sin
(
n
Irradiance, photon flux and short current density
d
)
P(
I
hc
)
P(
)
(
0
0
d
hc
)
P(
)d
(
0
0
SC
d
)
EQE(
hc
)
P(
q
)d
)EQE(
(
q
0 V)
(V
J