Role of Individual Bands in the Unusual Temperature-Dependent Band Gap of Methylammonium Lead Iodide

Abstract

The optical band gap of methylammonium lead iodide (CH3NH3PbI3) is known to increase with temperature; such a dependence is referred to as an unusual behavior when compared to conventional semiconductors. In addition, the band gap exhibits a sharp decrease in a narrow temperature range during the orthorhombic-to-tetragonal phase-transition of the material. In this work, we investigate the conduction and valence band energies to deliberate on the role of individual bands in yielding the unusual temperature dependence of the transport gap and also its sharp decrease at the transition temperature. Scanning tunneling spectroscopy (STS) of CH3NH3PbI3 films performed at different temperatures allowed us to derive the band energies across the two structural phases and at the transition temperature as well. The temperature dependence of band energies has been substantiated by the changes in the lattice parameters (from synchrotron radiation X-ray diffraction studies at different temperatures) vis-à-vis the orbital overlaps responsible in forming the conduction and valence bands. The STS studies have provided useful information in gaining deeper insights into the unusual temperature dependence of hybrid halide perovskite solar cells.

Spectroscopic Signature of Spin–Charge–Lattice Coupling in CuB2O4

“…Above the magnetic phase transition temperature, the band gap changes at a positive rate of . This value is in the same order with organic semiconductors. − Further theoretical calculations of the electronic band structure of CuB 2 O 4 are needed to understand the detailed nature of the unusual redshift of band gap energy with a decrease in temperature. Notably, the band gap displayed a sudden increase below 21 K. This anomaly and discontinuity correlated with the canted antiferromagnetic ordering, suggesting spin–charge interactions.…”

“…This behavior is opposite to those observed for typical semiconductors with dominating electron–phonon interaction, which shows the blueshift of the band gap energy with a decrease in temperature . Unusual temperature-dependent band gap has been detected in PbTe, CuBr, CuCl, PbS, CsSnI 3, , and most recently in halide perovskites of MAPbI 3 and MAPbBr 3 . − This has been explained by the dominant thermal lattice effects over the electron–phonon interaction. In a normal semiconductor, the band gap is expected to increase with a decrease in the lattice constants as temperature decreased.…”

Nanoscale properties of lead halide perovskites by scanning tunneling microscopy

“…For example, in MAPbI 3 , phase transitions occur from a cubic (>330 K) to tetragonal (160‐330 K) and orthorhombic (<160 K) crystal structure 62 . These transitions are accompanied with a change in the (unusual) temperature‐dependence transport gap 63 where the onsets of the VB and CB depend on the temperature 64 The nature of the STM tip‐sample junction is very sensitive and is strongly dependent on small variations in the ambient temperature or tip geometry.…”

Antibonding-Induced Anomalous Temperature Dependence of the Band Gap in Crystalline Ge2Sb2Te5

“…In most first-principles calculations, the electronic structure is usually considered to be fixed with temperature; this is called the rigid band approximation (RBA). Recently, temperature-dependent changes in the electronic structure have gained tremendous attention due to their effect on electrical, optical, and thermal properties of materials. − In contrast to the case of the conventional RBA, a temperature-dependent electronic structure is significantly affected by electron–phonon (e-ph) coupling and lattice thermal expansion. − As the temperature increases, the electron energy should be corrected by e-ph interactions and lattice thermal-expansion effects. The electron energy correction arising from e-ph interactions usually includes the Debye–Waller (DW) and Fan terms that represent two-phonon and one-phonon processes, respectively.…”

“…This phenomenon of a monotonic decrease of the gap with temperature is called the “Varshni” effect . Nevertheless, there are a few exceptional systems that exhibit a band gap increase with temperature, e.g., PbTe, lead halide perovskites, copper halides, and black phosphorus. ,− A number of theories have been proposed to explain the origin of the increasing gap with temperature based on the effects, such as lattice thermal expansion, energy band inversion, d-states in the valence band, and high-frequency optical phonons. − …”