SIXTH FRAMEWORK PROGRAMME

Transcription

Project Training for suitable low cost PV technologies 316488 – KESTCELLS
Deliverable 5.1
Project no. 316488
Project Acronym: KESTCELLS
Project title: Training for sustainable low cost PV technologies: development of kesterite based efficient solar
cells.
Industry-Academia Partnerships and Pathways
Start date of project: 01/09/2012
Duration: 48 months
Project coordinator: Dr. Edgardo Saucedo
Project coordinator organization name: IREC
Project website address: www.kestcells.eu
Deliverable D5.1
Optimisation of thicknesses and optical properties in cell
heterostructure
Delivery date: Month 28 (January 2015)
Dissemination Level:
PU
PU
Public
PP
Restricted to other programme participants (including the Commission Services)
RE
Restricted to a group specified by the consortium (including the Commission Services)
CO
Confidential, only for members of the consortium (including the Commission Services)
Document details:
Workpackage
5: Modelling & design
Partners
AMU
Authors
Dario Cozza
Document ID
D5.1
Release Date
30/12/2014
1
Deliverable D5.1
Content
1
General introduction .......................................................................................................... 3
2
Numerical models and simulation software ..................................................................... 3
2.1
TMM optical model ........................................................................................................................................ 3
2.1.1 Reflection and transmission at the interfaces ............................................................................................. 4
2.1.2 Interface and propagation ........................................................................................................................... 5
2.1.3 Electric field distribution inside the stack .................................................................................................... 6
2.1.4 Power density ............................................................................................................................................. 6
2.1.5 Generation rate profile and photo-current .................................................................................................. 7
2.1.6 Limits of the TMM method .......................................................................................................................... 7
2.2
3
3.1
SCAPS ............................................................................................................................................................ 7
Kesterite Material Parameters ........................................................................................... 8
Designs of Kesterite solar cells: examples from literature ...................................................................... 8
3.2
Material parameters used for the baselines ............................................................................................... 9
3.2.1 Electrical properties .................................................................................................................................. 10
3.2.2 Optical properties ...................................................................................................................................... 10
3.3
4
Baselines validation .................................................................................................................................... 10
Thickness optimization of a CZTSe cell from IREC ...................................................... 12
4.1
New baseline adapted to the IREC cell ..................................................................................................... 12
4.2
Results ......................................................................................................................................................... 13
5
Conclusions/Discussions ................................................................................................ 15
6
ACKNOWLEDGEMENTS .................................................................................................. 15
7
REFERENCES ................................................................................................................... 15
2
Deliverable D5.1
1 General introduction
Workpackage 5 is concerned with the modelling and simulation of kesterite based solar cells with the aim of
designing optimal solar cells configurations and to improve the understanding of the physical mechanisms affecting
the device figures of merit (Voc, Jsc, FF, μ). The full device simulation includes an optical and electrical part that
can be handled separately in order find the origin of efficiency limitations and then to find the device configurations
that optimize these two aspects independently. This deliverable is mostly focussed on the optical part and it
includes the explanation of the employed physical models, discussions about the material parameters used for the
simulations, a case of study and the results about the thickness optimization of a CZTSe cell fabricated at the
laboratory IREC in Barcelona.
Kesterite based solar cells are an interesting alternative to other thin film photovoltaic technologies due to
promising performances combined to earth-abundant elements composition. The most efficient kesterite solar cells
to-date with η=12.6% have been fabricated using the solid solution Cu2ZnSn(S,Se)4 (CZTSSe), which exhibits an
intermediate band gap (Eg) relative to the pure selenide Cu2ZnSnSe4 (CZTSe, Eg ≈ 1.0 eV) and sulfide Cu2ZnSnS4
(CZTS, Eg ≈ 1.5 eV) [1-2]. Despite a rapid progress achieved by different groups in a short time, many aspects are
not well understood yet in terms of material properties and working mechanisms of the device.
Optical and electrical modelling and simulations can be a powerful tool to overcome this gap. In this work, optical
simulation by TMM method [3] and 1-D electrical simulation using the software SCAPS [4] are coupled to obtained
an accurate picture of the behaviour of the device.
The solar cell is modelled as a multilayer stack. For the optical simulation, a wavelength dependent complex index
of refraction ñ = (n + ik) is used to describe each layer and by mean of the TMM method the optical electric field at
any point in the system can be resolved into two components corresponding to the resultant total electric field, one
component propagating in the positive x direction and one in the negative x direction [4]. G(x), the generation rate
profile in the stack computed from the previous calculation is used as an input for the electrical model implemented
in SCAPS, where the same multilayer stack is defined together with all the necessary electrical material properties.
As seen from literature, some material parameters of the kesterite absorbers can have a wide range of different
values depending on the fabrication conditions and process or to the computation method if they are obtained from
ab-initio simulations. As a consequence, in order to perform simulations, there is the obstacle related to the proper
selection of reliable material property values that in this work is addressed in two ways: by analysis and comparison
of the values available from literature and by direct measurements of the parameters, where possible. In this way
two baselines were defined, one for a pure sulphide CZTS layer and one for a pure selenide CZTSe layer. The
pentanary CZTSSe alloy has not been considered at the moment.
The model has been implemented to study the general impact of electrical and optical properties on the device
performance. By tuning the thickness of the top layers (CdS and ZnO) we can find optimal designs that maximize
the transmission of light to the absorber, maximising also the Jsc of the device.
2 Numerical models and simulation software
2.1
TMM optical model
A Kesterite solar cell is a multilayer stack and at each interface the incident light can be partially transmitted and
partially reflected. If the thickness of the layer is smaller than the coherence length of the incoming light, the
multiple reflections inside the layer and then the superposition of electromagnetic (EM) waves traveling in the
opposite directions generates interference effects and a spatial modulation of the intensity of the EM field along the
full stack. The transfer-matrix method (TMM) is based on the fact that, according to Maxwell's equations, there are
3
Deliverable D5.1
simple continuity conditions for the electric field across boundaries from one medium to the next. If the field is
known at the beginning of a layer, the field at the end of the layer can be derived from a simple matrix operation. A
stack of layers can then be represented as a system matrix, which is the product of the individual layer matrices.
The final step of the method involves converting the system matrix back into reflection and transmission
coefficients. The theory of TMM is described in detail in the book by MacLeod. [5] In the context of thin film organic
solar cells, Pettersson et al. [3] also establish a formalism to know the value of the electric field at a given depth in
the stack. Another example is Monestier et al. [6] where the TMM method was used to optimize the thickness of the
active layer in organic cells based on P3HT: PCBM.
2.1.1
Reflection and transmission at the interfaces
Let’s consider the interface between two layers j and j+1 and a polarized light beam like in the figure 1. Part of the
light is reflected and another part is transmitted to the next layer, and part of it can be absorbed inside the layer. In
both the cases, the state of polarization of the light beam changes. Electromagnetic waves are made of an electric
field and a magnetic field, oscillating on different planes; by convention the "polarization" of light refers to the
polarization of the electric field. Light, which can be approximated as a plane wave in free space or in an isotropic
medium, propagates as a transverse wave. Both the electric and magnetic fields are perpendicular to the wave's
direction of travel. The oscillation of these fields may be in a single direction (linear polarization), or the field may
rotate at the optical frequency (circular or elliptical polarization). In a layer j we can define the two components of
the electric field as Ep,j and Es,j such that the p-component is parallel and the s-component is perpendicular to the
incident plane. [7] In the following we will also use the symbols + and – to indicates respectively the transmitted (
+
E j ) and reflected ( E j ) components of the electric field.
Figure 1: Model of a stack of thin films on a substrate with a light beam traveling through.
At the interface of two homogenous and isotropic mediums, j and j+1, the Snell’s laws can be applied:
𝑵𝒋 𝒔𝒊𝒏𝜽𝒋 = 𝑵𝒋+𝟏 𝒔𝒊𝒏𝜽𝒋+𝟏 ( 1 )
with 𝜃𝑗 the incident angle. The boundary conditions of the Maxwell's theory and the equation of conservation of
energy can be used to establish the Fresnel coefficients for each interface j. [8]
4
Deliverable D5.1
For the perpendicular component s of the field, the reflection and transmission components 𝑟𝑠,𝑗 and 𝑡𝑠,𝑗 can be
expressed as in the following:
𝑬−
𝒔,𝒋
𝒓𝒔,𝒋 =
𝒕𝒔,𝒋 =
𝑬+
𝒔,𝒋
𝑬+
𝒔,𝒋
=
𝑬+
𝒔,𝒋+𝟏
𝜼𝒋+𝟏 −𝜼𝒋
𝜼𝒋+𝟏 +𝜼𝒋
=
𝟐𝜼𝒋+𝟏
𝜼𝒋+𝟏 +𝜼𝒋
(2)
(3)
with 𝜂𝑗 = 𝑁𝑗 𝑐𝑜𝑠𝜃𝑗 . Similarly the component p, parallel to the incident plane, can be expressed as in the following:
𝒓𝒑,𝒋 =
𝑬−
𝒑,𝒋
𝑬+
𝒑,𝒋
=
𝑵𝟐𝒋 𝜼𝒋+𝟏 −𝑵𝟐𝒋+𝟏 𝜼𝒋
𝑵𝟐𝒋 𝜼𝒋+𝟏 +𝑵𝟐𝒋+𝟏 𝜼𝒋
(4)
In the case of transparent substrates, an incident angle 𝜃𝐵 called Brewster angle, such that 𝜃𝐵 =
𝑁1
𝑁0
, can be
computed. At this angle the 𝑟𝑝 component of reflection is zero and the polarization of the reflected beam is linear
and perpendicular to the incident plane. The determination of the Brewster angle is useful for the ellipsometry
measurements because the sensitivity is optimal in the proximity of that. [9]
In the notation of the following parts we will omit the p/s indices for the reflection and transmission coefficients,
using just 𝑟𝑗 and 𝑡𝑗 , since the following laws are valid in both the parallel and perpendicular case.
2.1.2
Interface and propagation
For each layer j we can define two matrices containing the Fresnel coefficients 𝑟𝑗 and 𝑡𝑗 :
•
•
The Interface matrix 𝑰𝒋 , describing the electric field change at the interface between two mediums j and
j+1:
𝟏
𝑰𝒋 = �
𝒓𝒋
𝒓𝒋
� (5)
𝟏
The propagation matrix 𝑷𝒋 , describing the evolution of the electric field inside the layer j of thickness 𝑑𝑗 .
In the elements of this matrix we can see the Beer-Lambert law with the attenuation coefficient 𝛽𝑗 =
𝑷 𝒋 = �𝒆
−𝒊𝜷𝒋 𝒅𝒋
𝟎 � (6)
𝒆𝒊𝜷𝒋 𝒅𝒋
𝟎
2𝜋
𝜆
𝜂𝑗 :
The evolution of the electric field is given by S, the product of the m-matrices of propagation and of interfaces, with
m equal to the number of layers in the stack:
𝑺 = (∏𝒎
𝒖=𝟏 𝑰𝒖−𝟏 𝑷𝒖 ) ∙ 𝑰𝒎 ( 7 )
The transmitted and the reflected components of the electric field through the full stack then will be equal to:
�
𝑬+
𝑬+
𝟎
𝒎+𝟏
� (8)
−� = 𝑺 � −
𝑬𝟎
𝑬𝒎+𝟏
5
2.1.3
Deliverable D5.1
Electric field distribution inside the stack
We can define de 1D space-dependent electric field along the stack in order to compute its value at any x-position
inside the solar cell. For each layer of the stack the global electric field depends on its incident and reflected
components that are characterized respectively by the matrices 𝑆 + and 𝑆 − . As seen in the figure 1 these two
matrices take into account also the interferences effects due to all the neighbour layers of j. The global matrix S
can be written as in the following:
−
𝑺 = 𝑺+
𝒋 ∙ 𝑷𝒋 ∙ 𝑺𝒋
𝑺=�
𝑺+
𝒋𝟏𝟏
𝑺+
𝒋𝟐𝟏
+
𝑺𝒋𝟏𝟐
+
𝑺𝒋𝟐𝟐
� ∙ 𝑷𝒋 ∙ �
(9)
−
𝑺𝒋𝟏𝟏
−
𝑺𝒋𝟐𝟏
𝑺−
𝒋𝟏𝟐
�
𝑺−
𝒋𝟐𝟐
( 10 )
Considering the previous notation we can write the reflection and transmission coefficients at each interface j as:
𝒓±
𝒋 =
𝒕±
𝒋 =
𝑺±
𝒋𝟐𝟏
( 11 )
𝟏
( 12 )
𝑺±
𝒋𝟏𝟏
𝑺±
𝒋𝟏𝟏
Finally from the equations 9 – 10 we can calculate the position dependent electric field:
𝑬𝒋 (𝒙)
𝑬+
𝟎
2.1.4
=
−𝒊𝜷(𝒅𝒋 −𝒙)
𝒊𝜷(𝒅𝒋 −𝒙)
+𝑺−
𝒋𝟐𝟏 𝒆
−𝒊𝜷(𝒅𝒋 −𝒙)
𝒊𝜷(𝒅𝒋 −𝒙)
−
−
𝑺+
+𝑺+
𝒋𝟏𝟏 𝑺𝒋𝟏𝟏 𝒆
𝒋𝟐𝟏 𝑺𝒋𝟐𝟏 𝒆
𝑺−
𝒋𝟏𝟏 𝒆
( 13 )
Power density
In order to compute the generation rate, which is the number of photons absorbed in the time and volume unity
[1/(𝑚3 ∙ 𝑠)], we must compute first the position dependent power density, also called irradiance. The irradiance is
the temporal average of the Poynting vector 𝑃�⃗. In the case of an electric field propagating along the 𝑥⃗ axis the
irradiance I(x) can be expressed as [10]:
𝟏
𝜺
��⃗ > = 𝐼(𝒙) = 𝒏� 𝟎 |𝑬(𝒙)|𝟐 =
<𝑷
𝟐
𝝁
𝟎
𝟏
𝜺
𝒏�𝝁𝟎 |𝑬(𝟎)|𝟐 𝒆−𝜶𝒙 [𝑾/𝒎𝟐 ]
𝟐
𝟎
( 14 )
Knowing the irradiance at any points of the stack we can compute 𝜙 , the energy absorbed in the volume between
the surface and a position x applying the law of conservation of energy:
𝜹𝑰
𝝓 = −𝒅𝒊𝒗𝑰 = − 𝜹𝒙 [𝑾/𝒎𝟑 ]
𝝓(𝒙) =
𝟏
𝜺
𝜶𝒏�𝝁𝟎 |𝑬(𝒙)|𝟐 [𝑾/𝒎𝟑 ]
𝟐
𝟎
6
( 15 )
( 16 )
Deliverable D5.1
Considering a transparent medium having a refractive index 𝒏𝟎 , the irradiance of the incident light beam is:
𝝓(𝟎) = 𝝓𝟎 =
𝟏
𝟐
𝜺
𝒏𝟎 �𝝁𝟎 |𝑬+ (𝟎)|𝟐 [𝑾/𝒎𝟑 ]
( 17 )
𝟎
In photovoltaics 𝜙0 typically corresponds to the AM1.5 spectrum with the unit [𝑊 ∙ 𝑚−2 ∙ 𝑛𝑚−1 ]. We can now
compute the normalized wavelength and space dependent irradiance for each layer j as in the following:
𝝓𝒋 (𝒙, 𝝀) = 𝝓𝟎 ∙ 𝜶𝒋 (𝝀) ∙ �
2.1.5
𝒏𝒋 (𝝀)
𝒏𝟎
��
𝑬𝒋 (𝒙,𝝀)
𝑬+
𝟎
𝟐
� [𝑾/𝒎𝟑 ]
( 18 )
Generation rate profile and photo-current
The wavelength and space dependent (spectral) generation rate is equal to the ratio between the absorbed energy
inside a layer and the energy of an incident photon ℎ𝜐 :
𝑮𝒂 (𝒙, 𝝀) =
𝝓𝒂 (𝒙,𝝀)
𝒉𝝊
[𝒎−𝟑 𝒔−𝟏 𝒏𝒎]
( 19 )
Integrating the spectral generation rate 𝐺𝑎 over all the wavelengths we can obtain the space dependent generation
rate at a generic point x of the stack:
∞
𝑮(𝒙) = ∫𝟎 𝑮(𝒙, 𝝀)𝒅𝝀 [𝒎−𝟑 𝒔−𝟏 ]
( 20 )
Knowing the Generation rate we can compute the generated photo-current 𝐽𝑝ℎ = 𝐽𝑐𝑐 inside the active layer of
thickness 𝑑𝑎 , which can be considered as an upper bound for the final short circuit current Jsc of the device:
𝑱𝒄𝒄 = 𝒆 ∫𝒅 𝑮(𝒙)𝒅𝒙 [𝑨/𝒎𝟐 ]
𝒂
2.1.6
( 21 )
Limits of the TMM method
One limit of the TMM method in its application in the Kesterite/CIGS solar cells domain is the fact that it considers
all the interfaces between the layers as completely flat. Scattering effects that arise from the presence of rough
surfaces are neglected. One visible effect of the presence of roughness, for instance in the optical measurements,
is that the amplitude of the interference fringes due to the thin transparent top layers is attenuated compared to the
case of the simulated flat models, as it will be clear in the sections 3.3 and 4.1. Possible alternatives that take into
account interfaces roughness in the model were discussed in the papers by Winkler et al [1] or in the paper by Krcˇ
et al [14]. The later one proposes a modified TMM method with Fresnel coefficients modified on the basis of
calibrated equations of scalar scattering theory, that are used to determine wavelength-dependent reflectance and
transmittances of specular light. The model accounts for light scattering effects at all rough interfaces in the thinfilm solar cell considering the ratio between specular and diffuse light as well as its angular dispersion.
In the present work no scattering effects were considered yet, they will be implemented later, but the obtained
results can be considered reliable since they approximate the results that could be obtained with the more complex
model explain before.
2.2
SCAPS
SCAPS is a one dimensional solar cell simulation program developed at the department of Electronics and
Information Systems (ELIS) of the University of Gent, Belgium [4]. The electrical simulation is performed by solving
7
Deliverable D5.1
the semiconductor equations with Finite differences numerical methods. The semiconductor equations are a
system of 5 equations including the Poisson equation (electric field), two Carrier Continuity equations and two
Current density equations. In this report we omit a detailed explanation of this system but we only point out the fact
that in the two carrier continuity equations we find the generation rate term G(x), explained in the paragraph
2.1.5 (eq:20), which represents the result of the optical simulation. This is one of the input needed to perform the
electrical simulations. With a software like SCAPS we can set up a solar cell structure with the thickness and
electrical material parameters of each layer we can compute the JV curve, EQE and the figure of merits of the
simulated device.
G(x) (the optical simulation) computed in SCAPS is based on the simple Beer-Lambert law 𝐼𝑥 = 𝐼0 ∙ 𝑒 −𝛼𝑥 , where 𝐼𝑥
is the intensity of the light at a distance x from the surface, 𝐼0 is the intensity of the incoming light at the top surface
level and α is the absorption coefficient. This optical model neglects the n-coefficients of the simulated materials
and the multiple reflections that could take place between the interfaces of each layer in the stack.
However it is possible to input an external G(x) into SCAPS, letting the program to perform only the electrical
stimulation of the device. In this way it is possible to perform the optical simulation with other, more accurate,
methods like the TMM and keep using SCAPS for the electrical part of the simulation. Examples of this
methodology will be showed in the paragraph 3.3 and in the section 4.
3 Kesterite Material Parameters
3.1
Designs of Kesterite solar cells: examples from literature
As a reference for the next parts it is useful to keep in mind the designs and relative performances of some relevant
1
examples of kesterite solar cells we can find in literature . In the following tables and graphs, four examples of high
performance solar cells were selected for each case, from the pure sulphide CZTS [11][12] (two examples), the
pure selenide CZTSe [13] and the pentenary solid solution CZTSSe [1].
Table 1
Figure 2
1
* Wang, W., Winkler, M. T., Gunawan, O., Gokmen, T., Todorov, T. K., Zhu, Y., & Mitzi, D. B. Device Characteristics of CZTSSe Thin-Film
Solar Cells with 12.6% Efficiency. Advanced Energy Materials, 2013.
** Kato et al. (2012). Characterization of front and back interfaces on Cu2ZnSnS4 thin-film solar cells. Proceeding of the 27th EU-PVSEC,
2236–2239.
*** Brammertz et al.(2013). Characterization of defects in 9.7% efficient Cu2ZnSnSe4-CdS-ZnO solar cells.
8
Deliverable D5.1
The CZTS solar cell [11], from Solar Frontier, exhibits the higher Voc (~700𝑚𝑉) thanks to the Eg of the material
that is around 1,5eV, and a short circuit current that is around 20 mA/cm2. Contrariwise the CZTSe cell [13], from
IMEC, has a higher Jsc that is slightly lower than 40 mA/cm2 and a Voc around 400mV, since the Eg in this case is
smaller, around 1eV. CZTSSe exhibits intermediate features since with the S/Se ratio it is possible to vary the Eg of
the material from 1,5 to 1 eV. The record CZTSSe solar cell [1], from IBM has a Jsc = 35,2 mA/cm2, Voc = 513,4
mV and the highest conversion efficiency among all the other cases with a value equal to 12,6%.
In the table 2 we can also see the thickness used for the layers of the cells discussed before. For the case of CZTS
cell we report another high efficiency example [12] (from IBM) because the design details of the solar cell from
Solar Frontier [11] are not available.
CZTSSe 12,6%
IBM 2013 [1]
Anti reflecting MgF2
CZTSe 9,7%
IMEC 2013 [13]
CZTS 8,4%
IBM 2013 [12]
CZTS 9,2% [11]
Solar Frontier 2012
110 nm
150 nm
100 nm
?
CONTACTS Ni/Al
2 μm (total)
50nm/1μm
?
?
WINDOW
ITO 50 nm
Al-ZnO 250 nm
Al-ZnO 450 nm
?
i-ZnO
10
120
80
?
CdS
25
50
90÷100
?
ABSORBER
̴ 2μm
̴ 1μm
̴ 600 nm
?
Molybdenum
-
-
-
-
Table 2
It is interesting to notice the difference of thickness for the CdS layer and the window layer (ITO or ZnO) in the
three different designs.
3.2
Material parameters used for the baselines
Two generic baselines were defined in order to model a pure CZTS and a pure CZTSe solar cell. These baselines
are a set of basic input parameters needed to run the models. The difficulty about this task is that in literature we
can find a wide variability in terms of electrical and optical properties related to kesterites and in some cases there
is still some degree of uncertainty about the exact values of some of them. In this work, the material parameters
were selected by statistical comparison of several papers as well as from direct measurements obtained from
characterizations. The models were validated with some preliminary simulations (paragraph 3.3).
Eg
(a)
Figure 3
(b)
p - CZTSe
p - CZTS
n - CdS
n- ZnO
unit
1.05
1.5
2.4
3.3
[eV]
17
18
3
Na or Nd
4.0 1015
2.0 1016
μn
50
50
100
100
[cm /Vs]
μh
12,4
10
25
25
[cm /Vs]
𝜏𝑚𝑖𝑛𝑜𝑟𝑖𝑡𝑦
7
7
3,5
5,5
[ns]
Table 3
9
10
10
[1/cm ]
2
2
Deliverable D5.1
In the following parts we will discuss some details about the parameters of the kesterite layers used in the
baselines and the simulations performed for their validation.
3.2.1
Electrical properties
The values of band gap, dielectric permittivity, the effective masses and the optical constants of the CZTS and
CZTSe layers were obtained from the paper Persson et al [15]. These values were computed with ab-initio
methods simulating perfect kesterite structures (no defects/disorder and no secondary phases). The effective
density of states and thermal velocities were computed from the value of the effective masses found in this paper.
15
18
to 10 [1/cm3] but
In the case of the carrier concentrations (Na), different papers reported values from 10
15
16
typically from literature in the best solar cells we find values in the 10 - 10 [1/cm3] range. The value of Na of
CZTS was selected similarly as Katagiri et al.[16], whereas the Na of CZTSe was a value measured at the IM2NP
from a kesterite sample fabricated at IREC (Barcelona). The hole mobility values in the table are an average values
over three different papers in the case of CZTS and five pubblications in the case of CZTSe. Electron mobilitiy
values were assumed considering that in most the semoconductors the ratio 𝜇𝑛 ⁄𝜇𝑝 ~ 3 ÷ 5 .
In terms of CdS-Absorber band alignment many papers agree that CdS-CZTS should have a cliff like band
alignment and CdS-CZTSe should have a spike like alignment (see figures 3.a and 3.b). The values of electron
affinities for the two cases were then chosen in order to have a conduction band offset ∆𝐸𝐶𝐵 = 0.3𝑒𝑉 for the CZTS
(like in Santoni et al [17]) and ∆𝐸𝐶𝐵 = 0.34𝑒𝑉 for the CZTSe (like in Li et al.[18]). The kesterites carrier lifetime
value, which impact the carriers recombinations in the layer, were obtained from Brammertz et al.[13]
3.2.2
455 535
Optical properties
The real and imaginary part of the complex index of
refraction ñ = (n + ik) for the CZTS and CZTSe were
obtained from the paper Persson et al. [15] Knowing k
it is possible to compute the absorption coefficient
(fig.4):
4𝜋𝑘
∙ 106 [𝑚−1 ]
𝛼=
𝜆(𝜇𝑚)
Knowing these optical constants and the thickness of
all the layers of the stack we can perform optical
simulations.
3.3
1.5 eV
1,05eV
Figure 4
Baselines validation
To validate the baseline models, with the optical and electrical material parameters described in the previous
paragraphs, preliminary simulations were performed. The simulated structure is the one showed in the figure 6 and
the same layers thickness was used for both the cases, CZTS and CZTSe. The window layer is Al-ZnO. In the
figures 5.a and 5.b we can respectively see the computed quantum efficiencies and JV curves. The CZTS cell is in
green colour and the CZTSe is in blue. For each case two different types of simulations were performed, one using
the TMM optical method (dashed lines) and one using the inner optical simulation of SCAPS (Beer-Lambert law, as
seen in the paragraph 2.2) with no reflections (full transmission) defined at the front and back contacts (solid lines).
10
(a)
Deliverable D5.1
(b)
Figure 5
From the JV curves (Fig 5.b) we can see that the models are in agreements with the expected trends that were
described in the section 3.1 where we presented some relevant cases of real kesterite cells from literature. The Jsc
is already close to the expected values range whereas the FF and Voc are overestimated. This can be easily
explained by the fact that this baseline models are ideal under many point of views. For instance the recombination
models implemented so far were quite of a basic type, the carrier lifetimes used here for CdS and ZnO layers were
probably too big since their values are related to bulk materials. In the real kesterite solar cells they are most likely
of polycrystalline type so the values of lifetime should considerably drop down: for the simulations of the next
section 4, values in the order of picoseconds are used, as suggested during a discussion in one of the Kestcells
meeting by other colleagues of the consortium.
Another important source of Voc losses is the way the back contact is
modelled: in this basic example the workfunction of the back contact is big
(5.4eV) and it ensures an ideal ohmic contact that is not the case we find in
reality: molybdenum workfunction values should be lower than 5eV.
Moreover here we do not simulate the MoS2/MoSe2 layer that typically forms
between the absorber and the molybdenum back contact. It can have
significant impacts on Voc and FF [19].
Front Contact (Wf = 4,45eV)
WINDOW 370nm
CdS 50 nm
CZTS - CZTSe
From the QE graphs (Fig 5.a) we can appreciate the difference existing
1 um
between the basic Beer-Lambert and the TMM optical simulation. In the
TMM simulations we can see the interference fringes that induce some
peaks of absorption at some wavelengths and minima at other
Back Contact (Wf = 5.4eV)
wavelengths.The position of these peaks and minima is strongly dependent
on the thickness of the top transparent layers. This phenomenon is one of
the bases of the optical optimizations that can be performed on the solar cell
Figure 6
design and that will be discussed in the following section. Compared to real
cases from literature these oscillations, as seen in the figure 5.a, have a quite big amplitude: the reason of this
difference come from the fact that the TMM method used here do not take into account the interfaces roughness,
which in the kesterite solar cells can be on the order of few hundreds of nanometers. More details about this were
explained in the paragraph 2.1.6.
11
Deliverable D5.1
4 Thickness optimization of a CZTSe cell from IREC
4.1
New baseline adapted to the IREC cell
In this section we will deal with an example of optical optimization, in
terms of layers thickness, that was performed in collaboration with the
laboratory IREC in Barcelone. The reference cell is a CZTSe cell
fabricated by PVD – Selenization of sputtered metallic stacks (by IREC).
The absorber layer thickness was estimated to be around 1,8 μm as seen
from the SEM cross-section image in figure 8.b. The CdS buffer layer
has a nominal thickness between 30 and 50 nm and the ITO+i-ZnO
window layer has an overall thickness around 450nm, estimated from the
SEM image. A finer tuning of the thickness was obtained by performing
TMM simulations of a sample of CdS on glass and a ITO-ZnO stack on
glass and comparing the simulations with the measurements of the
corresponding real samples. This preliminary simulation is visible in the
figure 8.a. JV curve and EQE simulations of the baseline model adapted
to the real cell from IREC are visible in the figures 8.d and 8.c
respectively. The final thickness of the layers of the cell baseline,
(a)
(b)
(c)
(d)
Figure 8
12
Figure 7
Deliverable D5.1
summarized in the figure 7, was tweaked in order to get the same interference fringes in the EQE spectrum (Fig
8.c); the reason for the big amplitude of the oscillations in the simulated EQE was already explained in the
paragraph 2.1.6. Two important differences with respect to the general baseline introduced in the paragraph 3.2
are the back contact work function that here is 5eV (previously 5,4eV) and the carrier lifetime in the CdS and the
-3
window layers that in this simulation was set in the range of 10 ns. The window layer, which is actually a stack of
a thin i-ZnO layer plus a thicker ITO layer, here is modelled as a single layer, because the difference can be
considered negligible according to some preliminary simulations (not showed here) and also in agreement with the
paper Winkler et al. that declared the same conclusion. On last remark is about the absorption tail, in the 12001400 nm range, visible in the figure: The absorption of the reference cell goes further in the IR range because of
disorder/defects and maybe secondary phases in the CZTSe that are not considered in the simulated model. The
JV curve in figure 8.d shows that the model baseline defined with the previous assumptions is in good agreement
with the relative measurement performed on the real sample cell from IREC.
4.2
Results
This optimization consists on the maximization of the
light absorbed inside the kesterite layer after traveling
through the Window and the CdS top layers. This was
possible by performing several TMM simulations
varying the thickness of CdS between 0 and 100 nm
and the ITO/ZnO layer between 0 and 600nm. In the
figure 9 we can see the result of the simulation in terms
of total Reflected Photons (top graph) and Photocurrent
absorbed in the CZTSe layer (bottom graph). This
Photocurrent Jcc is the same discussed in the
paragraph 2.1.5 (Eq.21) and it represents an upper
bound for the Jsc that could be achieved by the device.
C
A
B
C
B
A
The point labelled ‘A’ in the figure 9 represents the
baseline configuration that was explained in the
previous paragraph. The points ‘B’ and ‘C’ represent
two possible optimized points. It’s interesting to notice
that the total reflection is lower in ‘C’ than in ‘B’ but the
photocurrent is higher in ‘B’ than in ‘C’. As a
consequence ‘B’ is the point we propose for the
optimization of the cell: we did not consider the area of
the graph with a very thin ITO/ZnO layer because with this configuration, the cell fabrication could be too difficult.
Figure 9
This type of simulations was repeated by including also a 110 nm thick MgF2 anti-reflecting coating above the
window layer, like in figure 11. The result of this second set of simulations is visible in figure 10. From this figure we
can see that the antireflecting coating can reduce the surface reflection of light by about 7-8% (points) and
consequently the Jcc photocurrent at the optimized point ‘B’ rises from 34,6 mA (fig.9) to 37,7 mA (fig.10).
The optimized structure (‘B’) with and without antireflecting coating together with the original IREC baseline
structure were also simulated in SCAPS with the methodology described in the paragraph 2.2 (TMM G(x) +
SCAPS). In the following, the results related to the 3 different cases are summarized in the table 4 and figure 12.
13
Deliverable D5.1
C
A
B
C
B
A
Figure 10
Figure 11
Baseline
Optimized
Optimized + AR
(window 440 nm - CdS 50nm)
(window 300 nm - CdS 40 nm)
(window 300 nm - CdS 40 nm)
Jsc (mA/cm2)
31.81
33.09
35.92
Voc (V)
0.428
0.428
0.428
FF
67.1 %
67.0 %
67.1 %
Efficiency
9.1 %
9.5 %
10.3 %
Model
Table 4
(b)
(a)
Figure 12
14
Deliverable D5.1
5 Conclusions/Discussions
The aim of this deliverable was to set up models of kesterite solar cells (CZTS and CZTSe) in order to perform
simulations and more specifically to perform optical optimizations to maximize the photocurrent of the device. After
the introduction of some models and simulation software tools (section 2) we discussed the set of some general
material parameters used in the models (section 3) and finally we showed an application of these models to
optimize the thickness of the top layers of a real cell fabricated at the IREC laboratory (section 4). With this work we
propose an optimized design that potentially can improve the solar cell with +1,3mA in terms of Jsc and +0,4% of
conversion efficiency without the use of antireflecting coatings. We also expect that a 110nm layer of MgF2 on the
top of the cell could boost this improvement by +4.5mA in terms of Jsc and +1.2% of conversion efficiency
increase.
As we saw in the paragraph 4.1 (figure 8.d) the behaviour of the IREC baseline model is close to the one of the real
cell but some differences are still present. These differences rise from the fact that several of the input parameters
used in the model were not obtained from specific characterizations performed on layers related to the reference
cell. For the next future we plan improve the reference baseline by performing more characterizations to extract
opto-electronic parameters related to this cell. In this way we should be able to improve the matching between the
simulated model and the real cell, increasing also the reliability of the final results and opening the way to
performing also other type of analysis and studies on the cell.
6 Acknowledgements
Kesterite samples preparation by Markus Neuschitzer (IREC) who is gratefully acknowledged.
7 References
1. Wang, W., Winkler, M. T., Gunawan, O., Gokmen, T., Todorov, T. K., Zhu, Y., & Mitzi, D. B. Device
Characteristics of CZTSSe Thin-Film Solar Cells with 12.6% Efficiency. Advanced Energy Materials, 2013.
2. Winkler, M. T., Wang, W., Gunawan, O., Hovel, H. J., Todorov, T. K., & Mitzi, D. B. Optical designs that
improve the efficiency of Cu2ZnSn(S,Se)4 solar cells. Energy & Environmental Science. 2014.
3. Pettersson, L. A. A., Roman, L. S., & Ingana, O. Modeling photocurrent action spectra of photovoltaic
devices based on organic thin films, J. Appl. Phys, 86(1), 487–496,1999.
4. Burgelman, M., Nollet, P., and Degrave, S., “Modelling polycrystalline semiconductor solar cells” Thin Solid
Films 361-362, 527–532, 2000.
5. H. A. MacLeod. Thin-Film Optical Filters. 4 edition (2010).
6. Florent Monestier, Jean-Jacques Simon, Philippe Torchio, Ludovic Escoubas, François Flory, Sandrine
Bailly, Remi de Bettignies, Stephane Guillerez, and Christophe Defranoux. Modeling the short-circuit
current density of polymer solar cells based on P3HT :PCBM blend. Solar Energy Materials and Solar Cells
91(5), 405–410 (2007).
7. Jean M. Bennett. Polarization. In Michael Bass, editor, Handbook of Optics - Vol. IV, chapter 12, pages
12.3–12.31. Optical Society of America, 3 edition (2009).
8. Michel Ney. Bases de l ’ électromagnétisme. Techniques de l’ingénieur e1020, 1–20 (2004).
9. Hiroyuki Fujiwara. Spectroscopic Ellipsometry. Principles and Applications. John Wiley & Sons, Ltd (2007).
10. William Tropf J. Properties of crystals and Glasses. In Michael Bass, editor, Handbook of Optics - Vol. IV,
chapter 2, pages 2.1–2.93. Optical Society of America, 3 edition (2009).
11. Kato et al. (2012). Characterization of front and back interfaces on Cu2ZnSnS4 thin-film solar cells.
Proceeding of the 27th EU-PVSEC, 2236–2239.
15
Deliverable D5.1
12. Shin, B., Gunawan, O., Zhu, Y., Bojarczuk, N. A., Chey, S. J. and Guha, S. (2013), Thin film solar cell with
8.4% power conversion efficiency using an earth-abundant Cu2ZnSnS4 absorber. Prog. Photovolt: Res.
Appl., 21: 72–76.
13. Brammertz, G., Buffière, M., Oueslati, S., ElAnzeery, H., Ben Messaoud, K., Sahayaraj, S., … Poortmans,
J. (2013). Characterization of defects in 9.7% efficient Cu2ZnSnSe4-CdS-ZnO solar cells. Applied Physics
Letters, 103(16), 163904.
14. Krc, J., & Smole, F. (2003). Potential of light trapping in microcrystalline silicon solar cells with textured
substrates. Progress in Photovoltaics, 11(7), 429–436. doi:10.1002/pip.506
15. Persson, C. (2010) Journal of Applied Physics, 107(5), 053710
16. Katagiri H, 2005, THIN SOLID FILMS, V480, P426, DOI 10.1016/j.tsf.2004.11.024
17. Santoni, a, Biccari, F., Malerba, C., Valentini, M., Chierchia, R., & Mittiga, a. (2013). Valence band offset at
the CdS/Cu 2 ZnSnS 4 interface probed by x-ray photoelectron spectroscopy. Journal of Physics D:
Applied Physics, 46(17), 175101.
18. Li, J., Wei, M., Du, Q., Liu, W., Jiang, G., & Zhu, C. (2013). The band alignment at CdS/Cu 2 ZnSnSe 4
heterojunction interface. Surface and Interface Analysis, 45(2), 682–684.
19. Chelvanathan, P., & Hossain, M. (2012). Effects of Transition Metal Dichalcogenide Molybdenum Disulfide
Layer Formation in Copper–Zinc–Tin–Sulfur Solar Cells from Numerical Analysis.
16

SIXTH FRAMEWORK PROGRAMME

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