Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part II: finite-difference algorithm and double-layer antireflection coatings

Faiz Ahmad; Benjamin J. Civiletti; Peter B. Monk; Akhlesh Lakhtakia

doi:10.1364/AO.474920

Applied Optics
Vol. 61,
Issue 33,
pp. 10049-10061
(2022)
•https://doi.org/10.1364/AO.474920

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part II: finite-difference algorithm and double-layer antireflection coatings

Faiz Ahmad, Benjamin J. Civiletti, Peter B. Monk, and Akhlesh Lakhtakia

Get PDF
Email
Share
Get Citation
Copy Citation Text
Faiz Ahmad, Benjamin J. Civiletti, Peter B. Monk, and Akhlesh Lakhtakia, "Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part II: finite-difference algorithm and double-layer antireflection coatings," Appl. Opt. 61, 10049-10061 (2022)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Check for updates

Related Topics
Table of Contents Category
- Optical Devices, Sensors, and Detectors
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: September 5, 2022
- Revised Manuscript: October 13, 2022
- Manuscript Accepted: October 16, 2022
- Published: November 18, 2022

Accepted Manuscript
Download Accepted Manuscript
Access to this article is made available via and is subject to Optica Publishing Group Terms of Use.

Abstract

In Part I [Appl. Opt. 58, 6067 (2019) [CrossRef] ], we used a coupled optoelectronic model to optimize a thin-film ${{\rm CuIn}_{1 - \xi}}{{\rm Ga}_\xi}{{\rm Se}_2}$ (CIGS) solar cell with a graded-bandgap photon-absorbing layer and a periodically corrugated backreflector. The increase in efficiency due to the periodic corrugation was found to be tiny and that, too, only for very thin CIGS layers. Also, it was predicted that linear bandgap-grading enhances the efficiency of the CIGS solar cells. However, a significant improvement in solar cell efficiency was found using a nonlinearly (sinusoidally) graded-bandgap CIGS photon-absorbing layer. The optoelectronic model comprised two submodels: optical and electrical. The electrical submodel applied the hybridizable discontinuous Galerkin (HDG) scheme directly to equations for the drift and diffusion of charge carriers. As our HDG scheme sometimes fails due to negative carrier densities arising during the solution process, we devised a new, to the best of our knowledge, computational scheme using the finite-difference method, which also reduces the overall computational cost of optimization. An unfortunate normalization error in the electrical submodel in Part I came to light. This normalization error did not change the overall conclusions reported in Part I; however, some specifics did change. The new algorithm for the electrical submodel is reported here along with updated numerical results. We re-optimized the solar cells containing a CIGS photon-absorbing layer with either (i) a homogeneous bandgap, (ii) a linearly graded bandgap, or (iii) a nonlinearly graded bandgap. Considering the meager increase in efficiency with the periodic corrugation and additional complexity in the fabrication process, we opted for a flat backreflector. The new algorithm is significantly faster than the previous algorithm. Our new results confirm efficiency enhancement of 84% (resp. 63%) when the thickness of the CIGS layer is 600 nm (resp. 2200 nm), similarly to Part I. A hundredfold concentration of sunlight can increase the efficiency by an additional 27%. Finally, the currently used 110-nm-thick layer of ${{\rm MgF}_2}$ performs almost as well as optimal single- and double-layer antireflection coatings.

Full Article | PDF Article

More Like This

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading. Part III: piecewise-homogeneous grading

Faiz Ahmad, Peter B. Monk, and Akhlesh Lakhtakia
Appl. Opt. 63(11) 2831-2836 (2024)

Efficiency enhancement of ultrathin CIGS solar cells by optimal bandgap grading

Faiz Ahmad, Tom H. Anderson, Peter B. Monk, and Akhlesh Lakhtakia
Appl. Opt. 58(22) 6067-6078 (2019)

Optoelectronic optimization of graded-bandgap thin-film AlGaAs solar cells. Part II: optimal antireflection front-surface texturing

Faiz Ahmad, Peter B. Monk, and Akhlesh Lakhtakia
Appl. Opt. 62(28) 7487-7495 (2023)

Previous Article Next Article

Supplementary Material (1)

Name	Description
Supplement 1	Supplementary Information

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the corresponding author upon reasonable request.

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (7)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (43)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Set No.	Unknown	Choice
1	$w = {\bar{E}}_{F_{n}} (\bar{z})$	$u = {\bar{μ}}_{n} (\bar{z}) \bar{n} (\bar{z})$
1	$g = {\bar{J}}_{n} (\bar{z})$	$f = - \bar{G} (\bar{z}) + \bar{R} (\bar{n}, \bar{p}; \bar{z})$
2	$w = {\bar{E}}_{F_{p}} (\bar{z})$	$u = {\bar{μ}}_{p} (\bar{z}) \bar{p} (\bar{z})$
2	$g = {\bar{J}}_{p} (\bar{z})$	$f = \bar{G} (\bar{z}) - \bar{R} (\bar{n}, \bar{p}; \bar{z})$
3	$w = \bar{ϕ} (\bar{z})$	$u = - λ^{2} (\bar{z})$
3	$g = {\bar{E}}_{d c} (\bar{z})$	$f = \bar{n} (\bar{z}) - \bar{p} (\bar{z}) - {\bar{N}}_{f} (\bar{z}) - {\bar{N}}_{D} (\bar{z})$

$ξ$	$E_{g, m i n}$ (eV)		$J_{s c}$ $({m A c m}^{- 2})$	$V_{o c}$ (mV)	$F F$ (%)	$η$ (%)
0	0.95	Model	37.79	460	79.32	13.79
		Experiment (Ref. [50])	40.58	491	66	14.5
		Experiment (Ref. [50])	41.10	491	75	15.0
0.25	1.12	Model	33.95	630	82	17.64
		Experiment (Ref. [50])	35.22	692	79	19.50
		Experiment (Ref. [51])	37.8	741	81	22.60
1	1.626	Model	14.78	1030	70	10.66
		Experiment (Ref. [50])	14.88	823	71	9.53
		Experiment (Ref. [50])	18.61	905	75	10.20

$L_{C I G S}$ (nm)	$E_{g, m i n}$ (eV)	$J_{s c}$ $({m A c m}^{- 2}$ )	$V_{o c}$ (mV)	$F F$ (%)	$η$ (%)
100	1.33	14.55	680	78	7.78
200	1.31	19.53	710	76	10.57
300	1.28	22.99	710	76	12.53
400	1.28	24.16	720	77	13.55
500	1.27	24.92	720	79	14.18
600	1.26	26.09	720	79	14.94
900	1.26	27.35	730	81	16.20
1200	1.25	28.43	730	81	16.96
2200	1.19	31.86	700	82	18.39

$L_{C I G S}$ (nm)	$E_{g, m i n}$ (eV)	$E_{g, m a x}$ (eV)	A	$J_{s c}$ ( ${m A c m}^{- 2}$ )	$V_{o c}$ (mV)	$F F$ (%)	$η$ (%)
100	0.96	1.52	0.99	14.99	840	82	10.29
200	0.96	1.62	0.98	21.51	910	79	15.55
300	0.96	1.62	0.98	24.49	900	80	17.55
400	0.96	1.62	0.98	27.19	890	80	19.32
500	0.95	1.62	0.99	28.61	880	80	20.17
600	0.95	1.62	0.98	30.02	870	80	21.01
900	0.95	1.62	0.99	32.61	850	81	22.49
1200	0.95	1.62	0.98	34.01	840	81	23.18
2200	0.95	1.62	0.98	36.38	810	82	24.17

$L_{C I G S}$ (nm)	$E_{g, m i n}$ (eV)	A	$α$	$K$	$ψ$	$J_{s c}$ ( ${m A c m}^{- 2}$ )	$V_{o c}$ (mV)	$F F$ (%)	$η$ (%)
100	1.07	1.0	8	0.60	0.36	17.10	950	87	14.10
200	1.07	1.0	8	0.60	0.36	23.74	970	87	19.98
300	1.07	1.0	8	0.60	0.36	27.49	980	86	23.28
400	1.07	1.0	8	0.60	0.36	30.06	990	86	25.45
500	1.07	1.0	8	0.60	0.36	32.01	990	85	27.04
600	1.07	1.0	8	0.60	0.36	32.78	990	85	27.56
900	1.07	1.0	8	0.60	0.36	35.36	1000	83	29.32
1200	1.07	1.0	8	0.60	0.36	36.36	1000	82	29.74
2000	1.07	1.0	8	0.60	0.36	37.84	990	80	30.03
2200	1.07	1.0	8	0.60	0.36	38.02	980	80	29.98

Bandgap		$L_{A R C 1}$ or				$J_{s c}$				Relative Change
Grading	ARC Type	$L_{{M g F}_{2}}$ (nm)	$L_{A R C 2}$ (nm)	$n_{1}$ or $n_{{M g F}_{2}}$	$n_{2}$	(mA ${c m}^{- 2}$ )	$V_{o c}$ (mV)	$F F$ (%)	$η$ (%)	in $η$ (%)
Homogeneous	${M g F}_{2}$	110	–	$1.38 \pm 0.01$	–	31.86	700	82	18.39
	SLARC	106	–	1.40	–	31.50	700	83	18.39	0
	DLARC	120	76	1.28	1.74	32.05	700	83	18.71	$+ 1.74$
Linear	${M g F}_{2}$	110	–	$1.38 \pm 0.01$	–	36.38	810	82	24.17
	SLARC	106	–	1.40	–	36.59	810	81	24.11	$- 0.25$
	DLARC	120	76	1.28	1.74	37.20	810	81	24.54	$+ 1.78$
Nonlinear	${M g F}_{2}$	110	–	$1.38 \pm 0.01$	–	38.02	980	80	29.98
	SLARC	106	–	1.40	–	37.83	990	80	30.02	$+ 0.13$
	DLARC	120	76	1.28	1.74	38.47	990	80	30.57	$+ 1.83$

Bandgap Grading	Previous Algorithm (s)	New Algorithm (s)	Ratio
Homogeneous	1668	196	8.51
Linear	2813	276	10.19
Nonlinear	3398	287	11.83

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (7)

Tables (7)

Equations (43)

Applied Optics