Physical Origins of the Transient Absorption Spectra and Dynamics in

Subscriber access provided by UNIV OF ALABAMA BIRMINGHAM

C: Energy Conversion and Storage; Energy and Charge Transport

Physical Origins of the Transient Absorption Spectra and Dynamics in Thin Film Semiconductors: The Case of BiVO

4

Jason K. Cooper, Sebastian E. Reyes-Lillo, Lucas Hess, Chang-Ming Jiang, Jeffrey B. Neaton, and Ian D. Sharp J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06645 • Publication Date (Web): 20 Aug 2018 Downloaded from http://pubs.acs.org on August 20, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 12 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

The Journal of Physical Chemistry

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

Page 2 of 12

log⁡(𝐼𝑝𝑢𝑚𝑝𝑒𝑑 ⁄𝐼𝑢𝑛𝑝𝑢𝑚𝑝𝑒𝑑 )

𝛼350⁡𝑛𝑚 )

𝛼350⁡𝑛𝑚

Ψ Δ

𝑑𝐴 = −log⁡(𝐼𝑝𝑢𝑚𝑝𝑒𝑑 ⁄𝐼𝑢𝑛𝑝𝑢𝑚𝑝𝑒𝑑 )

𝑑𝑇, 𝑑𝑅 =


Page 3 of 12 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


𝜅 𝑑𝑛/𝑑𝐸 𝑑3 𝑛/𝑑𝐸 3

𝜅 𝑑𝜅/𝑑𝐸

𝑑3 𝜅/𝑑𝐸 3

𝑑3 𝑛/𝑑𝐸 3

𝑑𝜅/𝑑𝐸

Δ𝐸𝑔

Δ𝐸𝑔 𝜅 d𝜅Δ𝐸𝑔 (𝐸, 𝑡) 𝛿(𝑡)

d𝜅Δ𝐸𝑔 (𝐸, 𝑡) = 𝜅(𝐸 − 𝛿(𝑡)) − 𝜅(𝐸) 𝜅

𝛿(𝑡)

𝜅𝐷𝑟𝑢𝑑𝑒 𝜅𝐷𝑟𝑢𝑑𝑒 (𝐸) = ℑ (√1 −


ℑ ℏ2

)

𝜀0 𝜌(𝜏𝐸 2 +𝑖ℏ𝐸)


Page 4 of 12

𝜅

𝑑/𝑑𝐸

𝑑3 /𝑑𝐸 3 𝜏

𝜌 𝜌(𝑡) =

𝑚∗ 𝑁(𝑡)𝑞 2 𝜏

=

1 𝑞𝜇𝑁(𝑡)

𝑚∗

𝑁 𝜇

𝑚∗

𝜏

𝑚∗ ⁡ 𝑚ℎ∗

𝑚𝑒∗

Γ

𝑚∗ = 0.8 ± 0.05𝑚𝑒

𝜇 = 0.85 ± 0.05 𝜏 = 0.39

0.8𝑚𝑒 𝑚ℎ∗ = 0.734

𝑚ℎ∗ = 0.795

Γ

𝑒 −1

𝑚𝑒∗ = 3.441

𝑚𝑒∗ = 0.3

𝜏 = 35 ± 10


Δ𝐸𝑔

Page 5 of 12 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


𝑑𝑇, 𝑑𝑅 = log[𝐼𝑇,𝑅 (𝑇)/𝐼𝑇,𝑅 (298⁡K)],

ΔΓ 𝜅 Δ𝐸𝑔

ΔΓ



Page 6 of 12

𝑑𝛼(𝐸, 𝑡) 𝑑𝛼(λ) =

4π 𝜆

𝑑𝜅Δ𝐸𝑔

(𝑑𝜅Δ𝐸𝑔 + 𝑑𝜅Γ + 𝜅𝐷𝑟𝑢𝑑𝑒 ) 𝑑𝜅Γ

𝜅𝐷𝑟𝑢𝑑𝑒

𝑑𝑂𝐷(𝜆) = −log⁡(𝑒 −𝐿𝑑𝛼(𝜆) )

𝑄(𝑡) 𝑑𝑂𝐷(𝜆, 𝑡) = 𝑑𝑂𝐷(𝑡) + 𝑄(𝑡)𝑑𝑂𝐷𝑡ℎ𝑒𝑟𝑚𝑎𝑙

Δ𝐸𝑔 ΔΓ 𝑑𝜅Δ𝐸𝑔

𝑑𝜅Γ 𝜅𝐷𝑟𝑢𝑑𝑒

Δ𝐸𝑔

Δ𝐸𝑔 ΔΓ

Δ𝐸𝑔

Δ𝐸𝑔

Δ𝐸𝑔

𝛥𝛤


Page 7 of 12 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


±

𝜔(𝑇) = 78 ± 2 − 5.5 × 10−4 ⁡𝑇 1.77

±



Page 8 of 12

Figure 8.

Δ𝐸𝑔 Δ𝐸𝑔 Δ𝐸𝑔

ΔΓ

ΔΓ Δ𝐸𝑔

𝑛𝑝𝑛

𝑝𝑛𝑝

𝑅𝑒𝑣 𝑡𝑟 −𝑑𝑝⁄𝑑𝑡 = 𝑘𝐴 𝑛(𝑝𝑛 − 𝑛𝑖2 ) + 𝑘𝑡𝑟 𝑝 − 𝑘𝑡𝑟 𝑁𝑝 −𝑑𝑛⁄𝑑𝑡 = 𝑘𝐴 𝑛(𝑝𝑛 − 𝑛𝑖2 ) + 𝑘𝐸𝑆𝑃 𝑛

𝑛𝑖 𝑁𝑝𝑡𝑟 𝑘𝐴 𝑘𝑡𝑟

𝑟𝑒𝑣 𝑘𝑡𝑟

𝑘𝐸𝑆𝑃

𝑛𝑖 𝑘𝑟𝑒𝑐 𝑅𝑒𝑣 𝑡𝑟 −𝑑𝑁𝑝𝑡𝑟 ⁄𝑑𝑡 = 𝑘𝑟𝑒𝑐 𝑁𝐸𝑆𝑃 𝑁𝑝𝑡𝑟 − 𝑘𝑡𝑟 𝑝 + 𝑘𝑡𝑟 𝑁𝑝

𝑘𝐴 = 3.2 × 𝑟𝑒𝑣 10−41 (cm−3 )−2 ⁡ps −1 𝑘𝑡𝑟 = 1.9 × 10−2 ⁡ps −1 𝑘𝑡𝑟 = 1.6 × 10−2 ⁡ps −1 𝑘𝐸𝑆𝑃 = 0.20⁡ps −1 𝑘𝑟𝑒𝑐 = 3.4 × 10−23 ⁡(cm−3 )−1 ps −1


Page 9 of 12 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

The Journal of Physical Chemistry 𝑘𝑡𝑟

𝑟𝑒𝑣 𝑘𝑡𝑟

Δ𝐸𝑔

ΔΓ

Δ𝐸𝑔

ΔΓ Δ𝐸𝑔

ΔΓ Δ𝐸𝑔

ΔΓ

▪

Δ𝐸𝑔

± ±

±

± ± 𝑚∗

Δ𝐸𝑔

ΔΓ

Δ𝐸𝑔 ΔΓ Δ𝐸𝑔

Δ𝐸𝑔

▪


ΔΓ


▪

▪


Page 10 of 12

Page 11 of 12 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




Page 12 of 12

TOC Graphic

12 ACS Paragon Plus Environment

Physical Origins of the Transient Absorption Spectra and Dynamics in

Recommend Documents