Analysis of Photocarrier Dynamics at Interfaces in Perovskite Solar

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C: Energy Conversion and Storage; Energy and Charge Transport

Analysis of Photocarrier Dynamics at Interfaces in Perovskite Solar Cells by Time Resolved Photoluminescence Ahmer A. B. Baloch, Fahhad H. Alharbi, Giulia Grancini, Mohammad I. Hossain, Mohammad Khaja Nazeeruddin, and Nouar Tabet J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b07069 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on October 30, 2018

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The Journal of Physical Chemistry

Analysis of Photocarrier Dynamics at Interfaces in Perovskite Solar Cells by Time Resolved Photoluminescence Ahmer A.B. Baloch1, Fahhad H. Alharbi*1,2, Giulia Grancini3, Mohammad I. Hossain2, Md. K. Nazeeruddin3, Nouar Tabet1,2

1

College of Science and Engineering, Hamad bin Khalifa University, Doha, Qatar

2

Qatar Environment and Energy Research Institute, Doha, Qatar

3

Group for Molecular Engineering of Functional Materials, École Polytechnique Fédérale de Lausanne, Valais Wallis, Sion, Switzerland E-mail: [email protected]

Abstract The power-conversion efficiency of perovskite solar cells is drastically affected by photocarrier dynamics at the interfaces. Experimental measurements show a quenching of the photoluminescence (PL) signal from the perovskite layer when it is capped with a hole-transport medium (HTM). Furthermore, time-resolved photoluminescence (TRPL) data show a faster decay of the PL signal in presence of perovskite/HTM interface. The experimental decay is usually fitted using one or two exponential functions with an incomplete physical picture. In this work, an extensive model is used to extract the key physical parameters characterizing carrier dynamics in the bulk and at the interfaces. The decay of the TRPL signal is calculated in presence of both defect assisted

recombination

(SRH)

and

band-to-band

radiative

recombination

where

carrier

extraction/recombination at the interfaces is described by interface recombination velocities. By proper curve fitting of the modeling results and the measured TRPL signal, meaningful optoelectronic parameters governing photophysical processes in mixed halide perovskite thin films and single crystals are extracted. Furthermore, a sensitivity analysis to assess the contribution of these parameters on TRPL kinetics is also performed. Notably, the inclusion of the diffusion, and surface recombination velocity at the interfaces allow to obtain the important physical parameters that govern the TRPL kinetics and improve the conformity of fits to experiments.

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1. Introduction Since their discovery, perovskite solar cells (PSC) unleashed a great deal of enthusiasm in the PV community because of their technological promises and the open questions raised concerning the physical processes occurring in the device. The nature of the gap (direct/indirect)1–3, the values of the carrier mobilities and diffusion length 4–6,the charge transport mechanism 7–11, the role of point defects12,13, and the recombination mechanisms responsible of the carrier losses

14–16

have been the subject of intensive debates. In the standard

configuration, a PSC consists of a thin perovskite absorbing layer sandwiched between an electron transport medium (ETM) and a hole transport medium (HTM). Under light excitation, the photocarriers are generated in the perovskite absorbing layer and diffuse towards the interfaces. Because of the appropriate band alignment at the interfaces, electrons are extracted at the ETM/perovskite interface while holes are extracted at the perovskite /HTM interface17. The carrier extraction at these interfaces occurs within picosecond range after excitation18,19 . The radiative band to band recombination leading to Photoluminescence (PL) occurs in the nanosecond range20–22 . The photocarriers generated close to the interfaces are extracted before contributing to the PL signal leading to the PL quenching. The drastic reduction of PL signal in presence of HTM /perovskite interface has been assigned by many authors to carrier extraction at the selective electrodes22. Time resolved Photoluminescence (TRPL) has been used extensively to investigate the carrier extraction at the interfaces of perovskite solar cells 9,23–26. The contactless nature and its application for both complete and noncomplete device makes it an ideal tool for characterizing limitations in PSC. Careful physical examination of TRPL measurements can provide us with an understanding of the complex attributes of charge dynamics and extraction mechanism in mixed halide PSC. In a typical TRPL experiment, the sample is excited by a very short laser pulse leading to the generation of an initial excess carrier density n(0) which subsequently decays as a result of the recombination and carrier extraction at the interfaces as illustrated by Fig. 1a. Figure 1 shows the TRPL schematic along with conventional curve fitting and charge dynamics fitting method for PL measurements. Conventionally, TRPL curves are analyzed by performing curve-fitting to the PL transients and extracting the associated lifetimes. Due to the complex quasi-exponential shape of the TRPL; one exponent, two exponent and stretched exponential functions for fitting have often been employed as shown in Fig. 1b. The main limitation arising from this method is the extraction of arbitrary life time constants without consistent consideration of the physical processes involved in TRPL decay dynamics. Moreover, as the diffusion and varied recombination pathways in bulk are occurring at comparable time scales, there is a high likelihood that the extracted parameters may be convoluted with other properties. To understand the opto-electronic properties and obtain meaningful insights, charge transport for analyzing PL transients must be taken into consideration. This assists in unraveling the physical factors governing the PL decay under different time scale and conditions. The determination of the PL decay requires solving the continuity equation taking into account the generation, transport, recombination and extraction of the carriers.27,28. In the practical experimental setup, the incident light penetrates into the cell through the transparent glass, FTO and ETM layers and gets absorbed exponentially in the perovskite layer according to Lambert law. Therefore, a diffusion term needs to be included in the continuity 2


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equation which governs the charge dynamics after a pulsed excitation. The effect of doping concentration, intentional or unintentional, must be considered as well to study the collective impact of doping and radiative recombination on TRPL kinetics

8,29

. More importantly, the addition of excitation density, surface

recombination velocity and diffusion provides detailed insight of the complex kinetics occurring at initial PL decay. This can equip us with the true quality of absorbers coupled with HTM or ETM by incorporating the photophysical processes. We describe in this work, such approach along with the boundary conditions and optimization algorithm to consider the carrier extraction and/or recombination at the interfaces. This fundamental work can benefit in understanding the details of the transport and extraction kinetics by dismembering the effect of individual parameters contributing to TRPL in PSC. By coupling this comprehensive model with the experimental measurements, the aim is to go beyond the conventional fitting parameters of life times and extract the parameters with physical significance such as surface recombination/interface recombination velocity ( S L and S R ), monomolecular recombination constant ( k1 ), bi-molecular recombination constant ( k 2 ), mobility (  ) and doping density ( N D ) as shown in Figure 1c. b) Conventional Fitting Methods

CB PL

PL Intensity

a) TRPL measurements

One Exponent

Two Exponent

Stretched Exponent

Time (s)

PL Fitting Parameters Extracted: τ1 , τ2 and b VB

PL Intensity (Normalized)

c) Proposed Carrier Dynamics and Optimization Method PL Intensity (Normalized)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


n  2n  D 2  R1 ( z , t )  R2 ( z , t ) t z d I  k n 2  nN D dz 0 2





Gl a ss Perovs kite Absorber

No



ND

Time (s)

Time (s)

SL

HTM

k1 k 2 μ -

+

SR

Physical Parameters Extracted: SL, SR, k1 , k2, μ and ND Figure 1 a) TRPL signals arising from recombination pathways b) Conventional fitting method of TRPL measurements for fitting constants (in logarithmic scale). PL curves are often fitted by one, two and stretched exponential functions. Here τ1,τ2 and β show lifetimes and stretched constant, respectively. c) The proposed charge dynamics method predicts physical parameters by solving rate equation with appropriate boundary conditions based on the geometry. Here, surface recombination/interface recombination velocity (SL and SR), monomolecular recombination constant (k1), bi-molecular recombination constant (k2), mobility (µ) and doping density (ND) are the physical parameters extracted.

3



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2. Time Resolved Photoluminescence modeling Let us consider the case of a perovskite layer deposited on a glass substrate and covered by a thin HTM layer as displayed in Fig. 2 a) and 2b). The continuity equation in the perovskite layer can be written on the following form:

n  2n  D 2  R1 ( z, t )  R2 ( z, t ) t z where

(1)

n is the minority excess carrier density, D is the carrier diffusion constant, z is the distance from the

origin taken at the location of the interface glass/perovskite, R1 is the recombination constant associated to Shockley Read Hall (SRH) recombination, and R2 is the recombination rate associated with the band to band recombination (bimolecular process). The Auger recombination is negligible under the normal working condition of solar cells (below an excess carrier density of 1017cm-3 )23. The end of the excitation laser pulse is taken as the time origin (i.e. at t  0 ). The SRH recombination rate is a function of the photocarrier density, the energy level of the trap ( Et ), its cross section  and density N t 30 . R1 

 n0  n  p0  p   ni2 E E  n0  n    p0  p   2ni cosh  i t   kT 

 vth Nt

Where n0 and p0 are the equilibrium carrier densities of electrons and holes respectively,

(2)

n and p are the

densities of photogenerated carriers  n  p  , Ei is the mid gap and Et is the trap energy level. Under low injection level conditions, the photocarrier density

n is much lower than the equilibrium density of

the majority carriers, R1 can be expressed as linear function of the photocarrier density n  z , t  R1 ( z, t )  k1n( z, t )

where k1 is the SRH recombination frequency. For k1 

(3)

n -type absorber, k1 is given by:  vth Nt

n  E  Et  1  2 i cosh  i  n  kT 

(4)

R2 is given by: R2 (z, t) = k2 éë(n0 + n)(p0 + p) - ni2 ùû

(5)

where k 2 is the band-to-band recombination constant which is a characteristics of the material. It is clear from Eq. 2 that R1 has some radiative part as in Eq. (5). 4


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Assuming


n -type absorber and considering the low injection condition, n  p

n0  ND , the term R2

becomes also a linear function of the photocarrier density: R2 ( z, t )  k2 N Dn

(6)

Therefore Eq. (1) can be rewritten under low injection conditions as follows:

n  2n  D 2   k1  k2 N D  n t z

(7)

Notice that the term k 2 N D is non negligible only if the absorbing layer is highly doped (for typical values of

k1  107 s-1 and k2  1010 cm3s-1 , N D  1017 cm-3). Therefore, under low injection level conditions, and low doping concentration, the decay of the photogenerated carriers is mainly controlled by the SRH recombination rate k1 . Under high injection levels, Eq. (1) takes the following form

n  2n  D 2   k1  k2 N D  n  k2n 2 t z

(8)

where k1 is given by

k1 

Note that the variation of k1

Ei  Et

 vth Nt  n  E  E  2 1  i cosh  i t    kT    n

(9)

on the injection level depends upon the level of the trap. For deep level, that is

kT , k1 is half of its value under low injection conditions, that is k1 

 vth Nt

(10)

2

However, for shallow levels, k1 increases as the density of photocarriers

n increases.

As shallow level contributes very little to the recombination process under low injection levels, we will consider only the deep levels in our analysis. Therefore, in the presence of deep levels, Eq. (1) can be rewritten in the following form for all injection levels:

n  2n  D 2   k1  k2 N D  n  k2n 2 t z Where the constant k1 varies from k1 to

(11)

k1 as the injection is increased from low to high levels. 2

Considering the experimental configuration shown in Fig. 2, the photoluminescence signal is then obtained by integrating the radiative terms over the absorber as follows

5



d





I PL   k2 n 2  nN D dz

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(12)

0

In order to obtain the PL signal decay versus time, we need to specify the boundary conditions of the problem and determine the function n  z , t  by solving Eq. (11). These boundary conditions can be expressed at the ends of the absorbing materials by introducing a surface /interface recombination velocity, S . The inclusion of surface recombination velocity along with diffusion term provides an accurate assessment of the complicated kinetics at the initial PL signal. In the case of an absorbing layer deposited on glass:

J (0, t )  S L n (0, t ) and

J ( d , t )  S R n( d , t ) where J is the carrier flux and S is the surface/interface recombination velocity. Note that, in absence of HTM layer (Fig. 2a), S R characterizes the surface recombination at the free surface of the absorber. However, in presence of HTM layer (Fig. 2b), S R integrates both the carrier extraction from the absorber to the HTM layer as well as a possible SRH recombination due to defects at the interface. S L highlights the recombination velocity at the excited side of the substrate/sample film. It should be noted the analysis presented herein can be extended for a p-type absorber with extraction from ETM. In such case, the rate equation can be solved for electrons as excess minority carriers with acceptor concentration, N A . The initial distribution of carriers is given by

n ( z , t 0 )  N 0 e   z  where



(13)

is the linear coefficient of absorption of the absorbing material and N 0 is the initial photocarrier

concentration at the glass/absorber interface. The rate equation, Eq. (11), can be solved numerically to determine the carrier distribution

n( z, t ) . Considering the stiff nature of the problem, an implicit solver must be used.Main

observations about the approach can be pointed out: 1) The effect of carrier extraction is expected to becomes measurable only when the carrier diffusion length

L  D is comparable or larger than the thickness ( d ) of the absorbing layer. 2) The extraction of the carriers at the interface may lead to a charge build up at the interface which, in return, would affect the carrier extraction thus the parameter, S . Such possible effect would induce more complexity in the problem and is neglected in the current analysis. 6


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3) For high injection level, the rate equation in Eq. (11) can be rewritten in the same form using an ambipolar diffusion constant Dambipolar 

2 De Dh . As De (electrons) and Dh (holes) are comparable, D  Dambipolar .  De  Dh 

4) Although, the dynamics of hole trapping and detrapping can affect the time dependence of the PL, this behavior is not included in the approach. This is usually assessed by using an additional sub gap excitation that leads to an enhancement of the PL signal. 5) A more rigourous treatment of high-injection condition would require a set of two equations; one for electrons and one for holes, with different boundary conditions. A detailed treatment should also consider the induced electric field which would require a very expensive self-consistent solution.

7



a)

b) J ( z )  S  n( z )

Perovskite Absorber SL

0

SR

z

c)

Perovskite Absorber SR

SL

0

d

HTM

J ( z )  S  n( z )

Glass

Glass

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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z

d

Extracting Physical Parameters from TRPL

Modeling

Experiment

Charge dynamics Model

Raw TRPL measurements

Boundary Conditions Smooth data and reduce noise ,

Initial vector and physical limits for optimizing parameters

μ

Numerically solve TRPL intensity

Not Converged

E= Criteria: E

Analysis of Photocarrier Dynamics at Interfaces in Perovskite Solar

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