Temperature-Dependence of Multiphonon Relaxation of Rare-Earth Ions in Solid-State Hosts

Abstract

Rare-earth ions are used in a wide range of emissive devices – ranging from lasers to displays – where high optical efficiency and narrow-linewidth are important. While their radiative properties are important, nonradiative properties are also critical since they can reduce optical efficiency and generate heat. In this paper, theories for multiphonon relaxation rate are reviewed for rare-earth excited states in solid-state dielectric hosts. A range of various approaches are used to simplify the mathematical form of the rate equations. The 2H9/2 excited state of Er3+, responsible for a technologically significant green emission, is modeled to show how the various theories manifest an order-of-magnitude variation in the thermal dependence of the multiphonon relaxation rate, as well as anomalous local minima in phonon scattering for temperatures above 0 K. This work proposes a corrective term of two quanta (Δν= + 2) of the mediating phonon energy to energy gap, so the calculated and the experimentally determined relaxation rates are equal. Radiative quantum efficiencies of both the 1G4→3H5 ~1.3 μm and 3F3→3F2 ~7 μm of Pr3+ are calculated to show the importance of both proper measurement of phonon energy and application of the multiphonon relaxation rate theory.

Electrochromic Switch Devices Mixing Small‐ and Large‐Sized Upconverting Nanocrystals

“…A detailed analysis of the total intensity of Tm 3+ , Er 3+ , and Ho 3+ transitions shows that all of them suffer thermal quenching upon temperature increase, although in distinct extents. In the visible spectral range, the total intensity of the 1 D 2 , 1 G 4 , 3 H 4 → 5 I 8 (Tm 3+ ), 5 S 2 , 5 F 3‐5 , 3 H 4 → 5 I 8 , 5 S 2 , 5 F 4 → 5 I 7 (Ho 3+ ), and 2 H 9/2,11/2 , 4 S 3/2 , 4 F 9/2 → 4 I 15/2 (Er 3+ ) transitions decreases by a factor I ( T )/ I ( T 0 ) ranging from 0.9 to 0.1 ( Table 2 ), for an applied electrical power of 1.3 W. The thermal quenching on microsized particles and bulk upconversion materials has been frequently attributed to multiphonon nonradiative relaxation mechanisms, resulting in higher decay probabilities; so, the observed trends are expected . However, and intriguingly, an emission enhancement occurs for small‐sized UCNPs when increasing the temperature (Figure d,f and Figure S10c,d in the Supporting Information for 1S/2S and 3S UCNPs, respectively).…”

Single-band near-infrared quantum cutting of Ho3+-Yb3+ codoped KLu2F7 phosphors by energy clustering

“…Besides, the energy in populated Yb 3+ : 2 F 5/2 state will be sequentially transferred to the 5 I 6 state of neighboring Ho 3+ by means of a called BET process [16,17], which is especially efficient in the energy clustering of KYb 2 F 7 host lattice with minimum Ho 3+ -to-Yb 3+ distance ~ 3.41-3.55 Å. Here the energy mismatch of about 1300 cm -1 between Yb 3+ : 2 F 5/2 and Ho 3+ : 5 I 6 states can be easily compensated by emitting three phonons [36]. As a result, even Yb 3+ concentration exceeds quenching threshold of x ~ 0.30, PL intensity of Yb 3+ ~ 1000 nm does not obviously improve at all [ Fig.…”

Synthesis of Eu3+‐doped BaBi2Ta2O9 based glass‐ceramic nanocomposites: Optical and dielectric properties

“…The excited rare earth ion can also have a nonradiative decay process through coupling of its electronic orbitals with local phonons in the host matrix via the rendering of lattice vibrations. Such nonradiative decay process shares an inverse exponential relationship with the energy gap (Δ E ) between levels involved in the process as:where T NR is the nonradiative decay rate, parameters A and β depend on the host matrix, p relates to the number of phonons required to bridge the energy gap and is the Bose–Einstein phonon occupation number.…”