Theoretical modeling of a “giant” colloidal core–shell quantum dot with an alloyed interfacial layer for solar cell applications

Anupam Sahu; Dharmendra Kumar

doi:10.1364/JOSAB.414664

Journal of the Optical Society of America B
Vol. 38,
Issue 3,
pp. 842-849
(2021)
•https://doi.org/10.1364/JOSAB.414664

Theoretical modeling of a “giant” colloidal core–shell quantum dot with an alloyed interfacial layer for solar cell applications

Anupam Sahu and Dharmendra Kumar

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Anupam Sahu and Dharmendra Kumar, "Theoretical modeling of a “giant” colloidal core–shell quantum dot with an alloyed interfacial layer for solar cell applications," J. Opt. Soc. Am. B 38, 842-849 (2021)

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Abstract

We proposed a theoretical modeling of a “giant” colloidal core–shell quantum dot with a strain-adapting alloyed interfacial layer between the core and shell materials for solar cell applications. The recently modified detailed balance model [J. Appl. Phys. 125, 174302 (2019) [CrossRef] ] is further modified in this paper to obtain a more realistic conversion efficiency (CE) of the ${\rm CdSe}/{{\rm CdSe}_x}{{\rm S}_{1 - x}}/{\rm CdS}$ quantum dot solar cell. This proposed model computes the CE, considering the significant impact of the energy gap and oscillator strength simultaneously. The CE is investigated for different alloying factors “$x$” by considering the strain effect between the heterostructure. The results obtained in terms of CE and photoluminescence peak wavelength nearly approximate the experimental studies of similar dot structure and dimensions.

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Core $A (0 \leq r_{i} < r_{1})$	Interfacial Layer ${B (r}_{1} < r_{i} < r_{2})$	Outermost Shell ${C (r}_{2} \leq r_{i} < R)$
$f_{1}^{A} (r_{i}) = j_{l} (k_{A} r_{i})$	$f_{1}^{B} (r_{i}) = {\begin{cases} j_{l} (k_{B} r_{i}) E_{i} > V_{i}^{B} \\ h_{l} (k_{B} r_{i}) 0 < E_{i} < V_{i}^{B} \end{cases}$	$f_{1}^{C} (r_{i}) = {\begin{cases} j_{l} (k_{C} r_{i}) E_{i} > V_{i}^{C} \\ h_{l} (k_{C} r_{i}) 0 < E_{i} < V_{i}^{C} \end{cases}$
	$f_{1}^{B} (r_{i}) = {\begin{cases} n_{l} (k_{B} r_{i}) E_{i} > V_{i}^{B} \\ κ_{l} (k_{B} r_{i}) 0 < E_{i} < V_{i}^{B} \end{cases}$	$f_{2}^{C} (r_{i}) = {\begin{cases} n_{l} (k_{C} r_{i}) E_{i} > V_{i}^{C} \\ κ_{l} (k_{C} r_{i}) 0 < E_{i} < V_{i}^{C} \end{cases}$

Parameters	CdSe	CdS
$m_{e}^{*} / m_{o}$	0.13 [39]	0.20 [40]
$m_{h}^{*} / m_{o}$	0.45 [39]	0.70 [40]
$a (n m)$	0.605 [41]	0.582 [41]
$E_{g} (e V)$	1.751 [42]	2.50 [42]
$a_{c} (e V)$	−2.00 [41]	−2.54 [41]
$a_{v} (e V)$	0.9 [41]	0.4 [41]
$E_{Y} (10^{11} d y n / {c m}^{2})$	2.87 [43]	3.26 [43]
$p r$	0.408 [43]	0.410 [43]
$E_{p} (e V)$	21 [44]	—

	Theoretical CE (%)
	Modified Model Eq. (21)	Proposed Model Eq. (22)
Alloying “ $x$ ”	$M = 1$	$M = 1$	$M = 4$
0.3	27.59	7.97	8.29
0.5	28.25	7.77	8.14
0.7	29.01	6.92	7.27
1.0	30.54	5.65	5.98

Core $A (0 \leq r_{i} < r_{1})$	Interfacial Layer ${B (r}_{1} < r_{i} < r_{2})$	Outermost Shell ${C (r}_{2} \leq r_{i} < R)$
$f_{1}^{A} (r_{i}) = j_{l} (k_{A} r_{i})$	$f_{1}^{B} (r_{i}) = {\begin{cases} j_{l} (k_{B} r_{i}) E_{i} > V_{i}^{B} \\ h_{l} (k_{B} r_{i}) 0 < E_{i} < V_{i}^{B} \end{cases}$	$f_{1}^{C} (r_{i}) = {\begin{cases} j_{l} (k_{C} r_{i}) E_{i} > V_{i}^{C} \\ h_{l} (k_{C} r_{i}) 0 < E_{i} < V_{i}^{C} \end{cases}$
	$f_{1}^{B} (r_{i}) = {\begin{cases} n_{l} (k_{B} r_{i}) E_{i} > V_{i}^{B} \\ κ_{l} (k_{B} r_{i}) 0 < E_{i} < V_{i}^{B} \end{cases}$	$f_{2}^{C} (r_{i}) = {\begin{cases} n_{l} (k_{C} r_{i}) E_{i} > V_{i}^{C} \\ κ_{l} (k_{C} r_{i}) 0 < E_{i} < V_{i}^{C} \end{cases}$

Parameters	CdSe	CdS
$m_{e}^{*} / m_{o}$	0.13 [39]	0.20 [40]
$m_{h}^{*} / m_{o}$	0.45 [39]	0.70 [40]
$a (n m)$	0.605 [41]	0.582 [41]
$E_{g} (e V)$	1.751 [42]	2.50 [42]
$a_{c} (e V)$	−2.00 [41]	−2.54 [41]
$a_{v} (e V)$	0.9 [41]	0.4 [41]
$E_{Y} (10^{11} d y n / {c m}^{2})$	2.87 [43]	3.26 [43]
$p r$	0.408 [43]	0.410 [43]
$E_{p} (e V)$	21 [44]	—

Abstract

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Journal of the Optical Society of America B