The fundamental parameters of majority and minority charge carriers—including their type, density and mobility—govern the performance of semiconductor devices yet can be difficult to measure. Although the Hall measurement technique is currently the standard for extracting the properties of majority carriers, those of minority carriers have typically only been accessible through the application of separate techniques. Here we demonstrate an extension to the classic Hall measurement—a carrier-resolved photo-Hall technique—that enables us to simultaneously obtain the mobility and concentration of both majority and minority carriers, as well as the recombination lifetime, diffusion length and recombination coefficient. This is enabled by advances in a.c.-field Hall measurement using a rotating parallel dipole line system and an equation, ΔμH = d(σ2H)/dσ, which relates the hole–electron Hall mobility difference (ΔμH), the conductivity (σ) and the Hall coefficient (H). We apply this technique to various solar absorbers—including high-performance lead-iodide-based perovskites—and demonstrate simultaneous access to majority and minority carrier parameters and map the results against varying light intensities. This information, which is buried within the photo-Hall measurement1,2, had remained inaccessible since the original discovery of the Hall effect in 18793. The simultaneous measurement of majority and minority carriers should have broad applications, including in photovoltaics and other optoelectronic devices.
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The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.
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S.R.P. and B.S. acknowledge financial support from the Technology Development Program to Solve Climate Changes of the National Research Foundation (NRF) funded by the Ministry of Science, ICT & Future Planning (no. 2016M1A2A2936757), and from the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (no. 20173010012980). J.H.N. acknowledges financial support from NRF grants funded by the Korea government (MSIP) (2017R1A2B2009676, 2017R1A4A1015022). D.B.M. and O.G. thank the National Science Foundation for support under grant no. DMR-1709294. We thank S. Guha for managing the IBM photovoltaics program; H. Hamann for support; M. Pereira and K. F. Tai for PDL Hall system development; B. Hekmatshoartabari for the silicon sample; and J. Kim for Supplementary Table 4.
The PDL Hall system was developed at IBM Research and documented in the following patent families: (1) O. Gunawan & T. Gokmen, US 9,041,389 (ref. 21); (2) O. Gunawan & M. Pereira, US 9,772,385 (ref. 22), US 9,678,040, US 15/581183 and related patent applications (WO 2016162772A1, UK 1717263.6, Japan 2017-552496, Germany 112016000875.9); (3) O. Gunawan, US 15/281,968; (4) O. Gunawan & W. Zhou, US 16/382,937. Patent families (1) and (2) cover the basic a.c. field/PDL Hall system, and (3) and (4) cover the related photo-Hall setup and method.
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Peer review information Nature thanks Henry Snaith and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
a, Current density–voltage (J–V) curves measured by reverse (black) and forward (red) scans. The photovoltaic performance values are summarized in the table. b, The external quantum efficiency spectrum. c, Histogram of the power conversion efficiencies obtained from J–V curves measured by reverse scan (grey) and forward scan (blue), and the average for 80 cells (red).
This file contains Supplementary Text, sections A–H; Supplementary Figures S1–S8; Supplementary Tables 1–4, Supplementary Equations 4–38; and Supplementary References 31–83.
Supplementary Video 1 | Animation of the rotating parallel dipole line (PDL) Hall system and its field evolution The master magnet generates a counterclockwise field rotation (red) while the slave magnet follows synchronously but in the opposite direction, generating a clockwise field rotation (green). This results in a total field (blue) that is unidirectional (always pointing normal to the sample) and single harmonic at the centre where the sample resides.
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Gunawan, O., Pae, S.R., Bishop, D.M. et al. Carrier-resolved photo-Hall effect. Nature 575, 151–155 (2019) doi:10.1038/s41586-019-1632-2