Holographic Time of Flight

Abstract

The Holographic Time of Flight (HTOF) method for the all-optical, contact-less investigation of charge transport in non-centrosymmetric insulators and semiconductors is based on the instantaneous photoexcitation of a spatially modulated distribution of charge carriers and on the linear electro-optic (Pockels) effect to visualize a charge-displacement by its associated refractive index change. It can be used with a free-carrier density so low that it does not otherwise have any detectable influence on the optical properties of a material, and with short free carrier lifetimes of the order of nanoseconds or less. HTOF is an especially striking example of how several independent linear and nonlinear light-matter interaction mechanisms can join to deliver a peculiar wave-mixing effect that is directly determined by a seemingly unrelated microscopic parameter: the free-carrier mobility. This chapter reviews the HTOF method and provides a detailed theoretical treatment that will be invaluable to experimentalists interested in applying this method to new materials. The author discusses the experimental parameters that influence the HTOF results and presents the basic assumptions and experimental conditions that allow the characterization of charge transport in the bulk of a material, with a sub-nanosecond time resolution only limited by the duration of the laser pulses, and for transport lengths down to a fraction of a micrometer. IntroductionBy illuminating a dielectric material with a pulsed laser it is possible to optically excite free electrons or holes, either from donor centers in the energy band gap between valence and conduction band, or directly by interband transitions. This leads to a transient increase in the number of free charge carriers, and therefore of the conductivity. Transient studies of current initiated by optical excitation of charge carriers lead to several ways to study charge transport processes in insulators and semiconductors.Homogenous charge-carrier photoexcitation in the bulk of a sample can be achieved by photoionization of impurity centers with energy levels inside the energy band gap. The analysis of such a homogenous photoconductivity transient gives some information on the charge transport properties, but generally delivers only indirect information on the charge-carrier mobility.On the other hand, the optical excitation of a packet of charges localized at the surface of a sample, either by interband excitation or by charge-carrier injection, is at the basis of conceptually simple methods to measure drift mobilities [1]. These methods rely on the observation of the drift of a charge-carrier packet in an applied electric field by its controlled photoexcitation and the detection of its time-of-arrival after a well-defined transport length. A well-established tool to CHAPTER 4

Photorefractive Organic Materials and Applications

“…The mobility can be deduced from the observation of the dynamic response of the diffraction efficiency under pulsed illumination [145]. Of course this technique only works with material exhibiting the entire photorefractive response.…”

“…The models herein presented are limited to low electric fields (less than 50 V/μm) because effects such as grating bending [144], grating fanning [145], grating competition [146], and effects of chromophore reorientation in the formation of the photorefractive gratings [147] are not described within this formalism, but are nonetheless commonly encountered. Despite limitations, current models offer already important insight into factors affecting the space-charge field strength and build-up speed.…”