Quantum Dot Solar Cells Simulation Approach

Quantum Dot Solar Cells:
A Simulation Approach
Ing. Ariel Cedola
GEMyDE, Departamento de Electrotecnia, Facultad de Ingeniería, Universidad Nacional de La Plata
Calle 48 y 116, 1er Piso, La Plata, 1900, Buenos Aires, Argentina
&
Dipartimento di Elettronica e Telecomunicazioni, Politecnico di Torino
Corso Duca degli Abruzzi 24, 10129, Torino, Italia
2014

Ing. Ariel Cedola – UNLP & POLITO

Quantum Dot Solar Cells (QDSC) have gained
attention during the last years as one of the most
feasible semiconductor structures for the
implementation of the intermediate band solar cell
(IBSC) concept.
IBSCs are p-i-n structures with a narrow band of
energy levels within the bandgap of the intrinsic
region.
According to theoretical predictions, based on
idealized considerations, IBSCs maximum
efficiencies could reach values >60%, due to:
• Absorption of low energy photons (processes 1
and 2 in the figure), generation and escape of
extra carriers.
• Increment of cell short-circuit current (Jsc) with
no degradation of open-circuit voltage (Voc).
Intermediate band (IB)
Barrier
Luque A. et. al, Phys. Rev. Lett.,
Vol. 78, N. 26, p. 5014 (1997)

• Semiconductor nanostructures with quantum mechanical properties (e.g. InAs)
¿What are QDs?
• Size: Base 10-60 nm; Height 4-10 nm
• x, y, z confinement (0D DOS)
• Discrete energy levels

• Bandgap and absorption spectrum depend on materials, sizes and shapes
• Non uniformity: absorption spectrum broadening
4 nm
9 nm
8 nm
InAs/GaAs InAs/GaAs GaN QDs

QDs fabrication
• Stranski-Krastanow method
• QDs layer stacking ND = 1010 – 1011 cm-2

EQE

Quantum efficiency of solar cells with embedded QDs layers
Without QDs
QDs (x, ND)
QDs (x, ND)
QDs (x, ND)

InAs/GaAs Quantum Dot Solar Cells (QDSCs)
InAs QDs
layers
p GaAs n GaAs
i GaAs
Energía[eV]
0
-1.5
1.5
x
Energy bands diagram

InAs QDs
layers

 < 900 nm
Efot > EG GaAs
Photogeneration
Recombination

 > 900 nm
Efot < EG GaAs
Photogeneration
Recombination
Escape
Capture
JQD  (EscWLB – CapBWL)

Jolley 2012 Prog. Photovolt.
Guimard 2010 APL Bailey 2011 APL
Yang 2013 SEM&SC
InAs/GaAs QDSCs: Experimental IV curves

QDSCs modeling: State-of-the-art approaches

Our work: Drift-Diffusion + QDs carrier dynamics modeling
 
2
2 i i i i i id a WL WL ES ES GS GS
i
V q
p n N N p n p n p n
x 
   
             

 1 i iWL B B WLn
B B nESC nCAP
i
Jn
R G R R
t q x
 
    
 

 1 i ip WL B B WL
B B pESC pCAP
i
Jp
R G R R
t q x
 

     
 

n n n
V n
J q n qD
x x

 
  
 
p p p
V p
J q p qD
x x

 
  
 
• Poisson equation
• Continuity equations for holes and electrons
Drift-diffusion transport model
i = QDs layer

i i i i i i i
i i
WL B WL WL B WL ES ES WL
nCAP nESC nCAP nESC WL WL
n
R R R R R G
t
   

     

i i i i i i i i i
i i
ES WL ES ES WL ES GS GS ES
nCAP nESC nCAP nESC ES ES
n
R R R R R G
t
   

     

i i i i i
i i
GS ES GS GS ES
nCAP nESC GS GS
n
R R R G
t
 

   

( )
( )
( )( )
1n p ESC
n p ESC
n pn p
R
DOS
  



 
   
 
( )
( )
( ) ( )
1n p CAP
n p CAP
n p n p
R
DOS
  


  
  
 
=WL, ES, GS; =B, WL, ES
• Rate equations for electrons at each energy level at each QD layer
• Escape and capture rates for electrons (holes)
fe(h)i
fe(h)i
QDSCs modeling
i = QDs layer
• Recombination rates

        

ddxffffxG
i
WLiWLiWLiWLii
x
heWLGAMheWLWL 








  0
5.1 ',,exp,,,
        

ddxffffxG
i
ESiESiESiESii
x
heESGAMheESES 








  0
5.1 ',,exp,,,
        

ddxffffxG
i
GSiGSiGSiGSii
x
heGSGAMheGSGS 








  0
5.1 ',,exp,,,
• Photogeneration rates at each QD energy level
0.2 0.4 0.6 0.8 1 1.2 1.4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Wavelength [nm]
AM1.5GSpectralIrradiance[kW/m2/um]
GaAs InAs
IEEE ARGENCON 2014
QDSCs modeling

Results: comparison with experimental measurements
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-0.016
-0.014
-0.012
-0.01
-0.008
-0.006
-0.004
-0.002
0
Tensión [V]
Densidaddecorriente[A/cm2]
Celda de GaAs Ref. [5]
QDSC Ref. [5]
Simulación de la celda de GaAs
Simulación de la QDSC
[5] K. Sablon et al, Strong enhancement of solar cell efficiency due to quantum dots with built in charge,
NanoLetters, vol. 11, pp. 2311-2317 (2011).
Voc=50 mV
Jsc=600 mA/cm2

300 400 500 600 700 800 900 1000 1100 1200
10
0
10
1
10
2
10
3
10
4
10
5
Longitud de onda [nm]
Respuestaespectral[a.u.]
Celda de GaAs Ref. [5]
QDSC Ref. [5]
Simulación de la celda de GaAs
Simulación de la QDSC
[5] K. Sablon et al, Strong enhancement of solar cell efficiency due to quantum dots with built in charge,
NanoLetters, vol. 11, pp. 2311-2317 (2011).
Results: comparison with experimental measurements (cont.)

Results: Dependence of I-V curves with number of QD layers and density
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-0.025
-0.02
-0.015
-0.01
-0.005
0
Tensión [V]
Densidaddecorriente[A/cm-2]
ND = 1.2e10 cm-2
ND = 4e10 cm-2
ND = 1e11 cm-2
20x
100x

20 30 40 50 60 70 80 90 100
14.6
14.8
15
15.2
15.4
15.6
15.8
16
16.2
Número de capas de QDs
Eficiencia[%]
ND = 1.2 e10 cm-2
ND = 4e10 cm-2
ND = 1e11 cm-2
Eficiencia de la celda
de GaAs sin QDs
Results: Dependence of the efficiency with the number of QD layers and density

Results: Doping effects
80 nm (NA = 1018 cm-3)
70 nm (NA = 3x1017 cm-3)
600 nm (intr.)
300 nm (ND = 1018 cm-3)
10x
EB-WL
EWL-ES
EES-GS
EB-WL
EWL-ES
EES-GS
1420 meV
Parámetros QDSC-A QDSC-B
Capa p+ GaAs (1018 cm-3) [nm] 80 80
Capa p- GaAs (3x1017 cm-3) [nm] 70 70
Capa i GaAs [nm] 600 600
Capa n+ GaAs (1018 cm-3) [nm] 300 300
ND = Densidad sup. de QDs [cm-2] 6x1010 6x1010
Número de capas de QDs 10 10
Rango de captura de los QDs [nm] 5 5
n: EB-WL, EWL-ES, EES-GS [meV] 140, 62, 70 220, 40, 30
p: EB-WL, EWL-ES, EES-GS [meV] 28, 16, 16 140, 15, 15
n-capWL, n-capES, n-capGS [ps] 0.3, 1, 1 0.3, 1, 1
p-capWL, p-capES, p-capGS [ps] 0.1, 0.1, 0.1 0.1, 0.1, 0.1
rWL, rES, rGS [ns] 1, 1, 1 1, 1, 1

Results: Doping effects (cont.)

Results: Non-linear (additive) behavior & QD dynamics
Full solar spectrum illumination  > 900 nm
K. Sablon et al, NanoLetters, vol. 11, pp. 2311-2317 (2011)

0 0.2 0.4 0.6 0.8
-30
-25
-20
-15
-10
-5
0
X: 0.001
Y: -8.607
Voltage (V)
Currentdensity(mAcm
-2
)
X: 0
Y: -20.74
X: 0
Y: -29.34
h/e follow hole (faster) dynamics
-> linear (additive) behavior
h/e follow electron (slower) dynamics
-> NON linear behavior
Results: Non-linear (additive) behavior & QD dynamics (cont.)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-40
-30
-20
-10
0
10
20
X: 0
Y: -7.09
Voltage (V)
Currentdensity(mAcm
-2
)
X: 0
Y: -20.74
X: 0
Y: -25.3

010E+12
1,000E+12
010E+16
1,000E+16
010E+20
1,000E+20
010E+24
1,000E+24
010E+28
1,000E+28
0 5 10 15 20
Rate[cm-3s-1]
# QD layer
GS
tasa_cap_n_GS
tasa_esc_n_GS
tasa_cap_p_GS
tasa_esc_p_GS
g_sol_qd_gs
tasa_rec_GS
abs(net_cap_n_GS)
abs(net_cap_p_GS)
0 5 10 15 20
GS

100E-12
1,000E-12
001E-08
010E-08
100E-08
1,000E-08
001E-04
010E-04
100E-04
1,000E-04
001E+00
0 5 10 15 20
Ocup. factors
0 5 10 15 20
Ocup. factors
GS
ES
WL
GS
ES
WL

-200E+20
-150E+20
-100E+20
-050E+20
0,000E+00
050E+20
100E+20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
NET ESCAPE
GS->ES ES->WL WL->Barrier
-060E+20
-040E+20
-020E+20
0,000E+00
020E+20
040E+20
060E+20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
NET ESCAPE

Conclusions
• A device-level model including QD intersubband carrier dynamics and transport has been developed
for simulation of QDSCs.
• Preliminary results agree very well with experimental data.
• Effects of doping and non-additive behavior of the QD photocurrent have been investigated.
• QD Photocurrent can be increased with optimal n-uniform doping, althoug the Voc degradation is still
a factor to investigate.
• Non-linearities can be associated to the de-synchronization of QD dynamics

Thankyou for your attention.
ariel.cedola@ing.unlp.edu.ar

Quantum Dot Solar Cells Simulation Approach

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