Spectroscopy for Materials Characterization. Группа авторов

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with Eq. (2.61), we obtain the expression of the luminescence time decay:

(2.65)

Equation (2.65) defines the time‐resolved luminescence, which can be experimentally tested by detecting PL spectra at fixed time delays from the excitation pulse.

      The measure of the lifetime at low temperature, at which non‐radiative rates can be neglected, is only dependent on the radiative rate (τ _r = 1/k _r ); it allows to determine the oscillator strength by using the following equation, derived from the relation between Einstein's coefficient for spontaneous and stimulated emission:

(2.66)

      2.2.2 Site‐Selective Luminescence

      The use of tunable lasers in the time‐resolved luminescence setup is very advantageous to improve the sensitivity in the acquisition of emission spectra. On the other hand, it allows a selective excitation of defects, on which the site‐selective luminescence is based. To provide a theoretical background on this technique, we consider the absorption and luminescence lineshapes discussed in Section 2.1.5 accounting for the homogeneous and inhomogeneous parts. In fact, each defect contributes to the absorption through a homogeneous lineshape governed by the coupling between the electronic transition and both the band vibration and the localized modes. Under the hypothesis of linear coupling with a single localized phonon ℏΩ, the homogeneous lineshape is expressed by:

      (2.67)

where E ₀₀ is the energy of the ZPL and is the Huang–Rhys factor associated with the localized mode. The inhomogeneity arises from the site‐to‐site nonequivalence of defects embedded in the amorphous network. It is well‐founded to assume that only the ZPL features a statistical distribution w _inh(E ₀₀); the total absorption lineshape, I ^abs(E _exc), is therefore given by the convolution:

      (2.68)

that makes explicit the dependence on the microscopic parameters (E ₀₀, , ℏΩ) in Eq. (2.57). Similarly, the luminescence lineshape is the convolution between a homogeneous function, which is mirror‐symmetric of against E ₀₀, and the inhomogeneous distribution w _inh(E ₀₀), while its amplitude is proportional to the absorbed intensity, scaled by the quantum yield factor η ≤ 1:

(2.69)

      that reproduces the lineshape function appearing in Eq. (2.63).

The attempt to single out homogeneous and inhomogeneous lineshapes by site‐selective luminescence is successful only for a peculiar subclass of defects having a very low electron–phonon coupling (). In this case, Eq. (2.69) becomes:

      (2.70)

      Under this condition, absorption and luminescence spectra overlap and the ZPL lies in this region. It is, therefore, possible to site‐selectively excite a specific defect subset within w _inh(E ₀₀); the site‐selective luminescence intensity is given by:

(2.71)

At low temperature, L _vib(E _exc − E ₀₀) as well as L _vib(E ₀₀ − E _em) vanish for negative arguments, so that the site‐selective luminescence is detected with the emission resonant to excitation, E E _ex = E _em, namely the ZPL, and Eq. (2.71) reduces to:

      (2.72)

      thus allowing the measure of the inhomogeneous distribution w _inh(E ₀₀).

      2.2.3 Basic Design of Experimental Setup: Pulsed Laser Sources; Monochromators; Detectors

      In this section, we describe a typical setup that can be conveniently used to perform time‐resolved photoluminescence measurements. The main components of the experimental station are: an integrated Tunable Laser System, a Spectrograph, an Intensified CCD Camera.

      2.2.3.1 Tunable Laser

      The tunable laser is an integrated system that provides the excitation radiation with a wavelength that can be conveniently adjusted within a wide spectral range covering UV‐Visible‐IR. A very common example exploits the third harmonic of a Q‐switched Nd:YAG laser (355 nm) to pump an optical parametric oscillator (OPO) that converts it into a tunable output.

      The laser active medium is a crystal of yttrium‐aluminum‐garnet (YAG) doped with Nd³⁺ ions, which is pumped by a flashed Xenon lamp via the ∼800 nm Nd³⁺ absorption transition. The Q‐switching is triggered by an electro‐optic crystal (Pockel cell, PC) placed within the laser cavity. When the PC is not polarized, the cavity Q‐factor is low and the population inversion is high without any laser oscillations. When the PC is polarized, the Q‐factor suddenly increases and the laser action starts with a strong initial inversion, thus resulting in the buildup of an intense pulse (~10² mJ, ~5 ns long).

      The laser beam at λ ₀ = 1064 nm (fundamental harmonic) produced by the Nd:YAG laser is directed on a second harmonic generator (SHG), where the wavelength is converted to λ ₀/2 = 532 nm, and then on a third harmonic generator (THG), where it is converted to λ ₀/3 = 355 nm. The SHG and THG are nonlinear KD*P (KH₂PO₄) birefringent crystals, cut at the proper angle for the required wavelength. The nonlinear conversion process critically depends on the relative orientation of the polarization axis of the incident beam and the axes of the nonlinear crystals.

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