This document discusses using a two-defect kinetic model and time-resolved photoluminescence spectroscopy (TRPL) to analyze carrier kinetics in a CdS/CIGSe junction. The model considers trapping and transport effects and is used to understand how the space charge region (SCR) affects bulk carrier dynamics. Key findings include: (1) the bulk shows a bi-exponential decay, with the SCR causing the initial decay time constant to change; (2) transport-limited recombination in the quasi-neutral region accounts for this changed time constant; (3) intensity- and wavelength-dependent TRPL measurements provide information about SCR and bulk carrier dynamics that can assess absorber quality.

1. Carrier kinetics analysis with two-defect level
model in a CdS/CIGSe junction using TRPL
spectroscopy
Ashwin Hariharan, Sascha Schäfer, Stephan Heise
Ultrafast Nanoscale Dynamics
Institute of Physics

2. Introduction and Motivation
Time resolved
photoluminescence
Minority
carrier
lifetime
Absorber quality, QFLS, device
parameter & performance
Trapping and
transport effects
Multi-exponential model: Which time
constant reflects the relevant lifetime ?
GOAL:
Understanding the effects
of:
1) Trapping
2) Transport
in TRPL
METHODOLOGY:
Modelling
- Two-defect kinetic model
- Two-defect drift-diffusion model
Experiments
- Intensity and wavelength based
MAIN OUTCOME:
Understanding the
effect of SCR on the
bulk (QNR) dynamics
Complex
interpretation
2

3. Decay kinetics of two non-interacting defects in bulk
[1]. J. A. Hornbeck and J. R. Haynes, Phys. Rev. 97, 311 (1955)
[2]. Maiberg et. al., J. Appl. Phys. 118, 105701 (2015)
[3]. Ferguson et. al., J. Appl. Phys. 127, 215702 (2020)
[4]. Hariharan et. al. Decay of Excess Carriers in a Two-Defect Model Semiconductor, Manuscript under preparation
 General two-defect level system
o Complex decay form
o 𝑓 𝑁𝐴
𝐸𝑓𝑓
, 𝑁𝑇,𝑅, 𝐸𝑇,𝑅, 𝛾𝑇,𝑅, Δ𝑛/𝑝
• 𝛾 = 𝑐𝑝/𝑐𝑛
 Two defect model analytically solvable
o Hornbeck-Haynes model for TPC experiment in Si[1]
o TRPL experiment in CIGS[2,3]
 Recently concluded an extensive study comparing the
both system[4]
o Main outcome: Under what conditions the
analytical model is valid?
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4. Key learnings from bulk analysis with kinetic model
[2]. Maiberg et. al., J. Appl. Phys. 118, 105701 (2015)
 𝑓 𝝉𝒏
𝑹𝟎
= 𝟓𝒏𝒔, 𝝉𝒏
𝑻𝟎
= 𝟐. 𝟓𝒏𝒔, 𝝉𝒏
𝒆𝑻
≡ 𝝉𝟏
𝑨𝒏𝒂𝒍𝒚𝒕𝒊𝒄
and 𝝉𝟐
𝑨𝒏𝒂𝒍𝒚𝒕𝒊𝒄[2]
 Absolute value of slope of 𝝉𝟏,𝟐
𝑨𝒏𝒂𝒍𝒚𝒕𝒊𝒄
can be simplified as
o 𝝉𝒆𝒇𝒇
𝟏,𝑨𝒏𝒂𝒍𝒚𝒕𝒊𝒄
(𝒕 → 𝟎) =
𝟏
𝝉𝒏
𝑹𝟎
+
𝟏
𝝉𝒏
𝑻𝟎
−𝟏
: Parallel capture process
o 𝝉𝒆𝒇𝒇
𝟐,𝑨𝒏𝒂𝒍𝒚𝒕𝒊𝒄
(𝒕 → ∞) = 𝝉𝒏
𝒆𝑻
𝟏 +
𝝉𝒏
𝑹𝟎
𝝉𝒏
𝑻𝟎
: Multiple trapping process
 Fixed: 𝑁𝐴
𝐸𝑓𝑓
, 𝑁𝑇,𝑅, 𝐸𝑅, 𝛾𝑅
 Varied:
• Δ𝑛
• 𝛾𝑇 = 𝑐𝑝
𝑇
/𝑐𝑛
𝑇
• 𝐸𝑇
4
Agrees numerically ∀ 𝐸𝑇
Agrees numerically for a range of 𝐸𝑇

5.  TCAD (1D) simulations with and without SCR with CdS
buffer
o 2 wavelength & 3 average power & 3 𝜏𝑛
𝑅0
 The bulk shows a bi-exponential decay with 𝜏1
𝐵𝑢𝑙𝑘
at
17 𝑛𝑠
 With a SCR , 𝜏1
𝐵𝑢𝑙𝑘
→ 𝜏2
𝑄𝑁𝑅
along a fast initial drop[5]
o 𝜏2
𝑄𝑁𝑅
=
1
𝜏𝑛
𝑅0
+
1
𝜏𝑛
𝑇0
+
1
𝜏𝑛
𝐶𝑇
−1
= 11 𝑛𝑠
 TCAD shows a spatially constant[6] E-field in QNR between
1 to 10 ns
o 𝜏𝑛
𝐶𝑇
=
𝜇𝑛𝐸𝑎𝑣𝑔
2
4𝐷𝑛
−1
= 41 𝑛𝑠
o 𝜇𝑛 = 10 𝑐𝑚2
/𝑉𝑠
o 𝐸𝑎𝑣𝑔 = 500 𝑉/𝑐𝑚
 Good quality absorber reveals better physics
Change in bulk (QNR) kinetics due to SCR
[5]. Jundt et. al. 47th IEEE PVSC, (2020)
[6]. Maiberg et. al. Thin Film Solids, 582 (2015) 5

6. Intensity and wavelength dependent measurements for CdS/CIGS
 Injection level estimated to vary around
o 5 × 1015
cm−3
to 7.8 × 1015
cm−3
for 867 nm
o 1.0 × 1016
cm−3
for 620 nm at 215 𝜇W
o 𝑁𝐴
𝐸𝑓𝑓
= 2.0 × 1016
cm−3
 From TCAD simulations we can summarize:
o 𝜏1
𝑆𝐶𝑅
: SCR dynamics (and trapping?)
 Electrostatics of junction
 Interface charge transfer
o 𝜏2
𝑄𝑁𝑅
: QNR bulk dynamics of free electrons
 𝜏2
𝑓𝑖𝑡
= 𝑓 𝑁𝐴/𝐷
𝐸𝑓𝑓
, 𝑁𝑇,𝑅, 𝐸𝑇,𝑅, 𝛾𝑇,𝑅, 𝜇𝑒/ℎ, Δ𝑛/𝑝
o 𝜏3
𝑄𝑁𝑅
: QNR bulk dynamics of trapped electrons
 Energetic position of trap level
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Sample provided by Nice Solar Energy GmbH

7. Conclusion
1) Learnings from two-level kinetic model for bulk
o 𝜏1
𝐵𝑢𝑙𝑘
independent of trap energy level for both models
o 𝜏2
𝐵𝑢𝑙𝑘
has an energy dependent range of agreement between both models
2) Addition of a SCR
o Modifies 𝜏1
𝐵𝑢𝑙𝑘
to 𝜏2
𝑄𝑁𝑅
o Transport dependent time constant (𝜏𝑛
𝐶𝑇
) could be responsible for this
3) Main take away and outlook
o 𝜏2
𝑄𝑁𝑅
could be helpful understanding absorber quality in a device operating condition
o A better understand on 𝜏1
𝑆𝐶𝑅
, 𝜏2
𝑄𝑁𝑅
, 𝜏3
𝑄𝑁𝑅
o Fitting experimental data to TCAD for both wavelengths
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8. Thank you for your kind
attention!
Comments or questions?
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