Light-induced charge transport in lithium niobate is an essential part of the photorefractive effect and is also of particular relevance to work presented in this thesis. Buse has produced a comprehensive two part review on this subject, with
the first concentrating on models and experimental methods (Buse, 1997a) and the second discussing the effect in a range of materials (Buse, 1997b); the main points are discussed below.
The charge transport processes which can take place are dependent on the material, the light intensity, doping and thermal annealing. Consequently, exposure to continuous wave or pulsed light may result in different effects within the crystal. Free charge carriers can move under the influence of three effects;
Drift: Arises from the Coulomb interaction of an electric field (including internal fields) on the charge carriers.
Bulk Photovoltaic Effect: Charges generated in non-centrosymmetric crystals may have to move in a particular direction due to the neighbouring atoms.
Diffusion: Non-uniform illumination generates uneven concentrations of charges, which subsequently result in diffusion currents.
When exposed to continuous wave light, iron or copper doped lithium niobate experiences light induced charge transport that is described well by a one-centre model. This is the simplest model, where electrons are excited from filled traps into the crystal’s conduction band and free electrons can move from the conduction band to recombine with empty traps. In lithium niobate, the traps are Fe2+ /Fe3+ ions; this applies even to undoped material, as lithium niobate inevitably contains some iron impurities. The process is illustrated in Figure 2.6.
conduction band
valence band Fe2+
Fe3+ e-
Figure 2.6:Energy level diagram for the one-centre model of charge transport in LiNbO3.
Once the charges are generated, the dominant transport mechanism is the bulk photovoltaic effect (Glass et al., 1974), which causes the free electrons to drift along
thecaxis. According to Glass et al. the current density, J, is proportional to the intensity,I:
J =k1αI (2.11)
whereαis the absorption coefficient andk1is a constant, dependent on the type of
absorbing centre and wavelength. However, Jis independent of crystal geometry and impurity concentration. No photo-current was detected normal to the polar axis and no light induced absorption changes were observed.
The current density was later found to also depend on the light polarisation (Belinicher et al., 1977), so becomes
J =αi jkEjEk (2.12)
whereEj andEk are components of the electric field vector of the light, andαi jk is the photovoltaic tensor, which can be written as
αi jk = 0 0 0 0 α15 −2α22 −α22 α22 0 α15 0 0 α31 α31 α33 0 0 0 (2.13)
The photovoltaic current along a particular axis, in crystals of point group 3m, is given by the relevant expression in Table 2.1, taken from Festl et al. (1982). βis the angle formed between the light polarisation plane and the corresponding crystal axis andIis the intensity.
Table 2.1: Components of the photovoltaic current for different current directions and directions of incident light.
current direction direction of incident light
x y z
Jx 0 α15Isin 2β −α22Isin 2β
Jy α15Isin 2β+α22Icos2β −α22Icos2β α22Icos 2β
Jz α31I+(α33−α31)Icos2β α31I+(α33−α31)Icos2β α31I
Fradkin and Magomadov measured the photovoltaic current along all three crystal axes, for various orientations of light polarisation planes and currents were detected for the first time along the x and y axes. The results shown in Figure 2.7 were taken using linearly polarised light of wavelengthλ = 500µm and intensity I =
2.3 ×10−3
W cm−2 .
The results fit the theoretical expectations well. The currents along the x and y
Figure 2.7: Dependence of the photovoltaic current components Jz(a), Jy(b), Jx(c) on the plane of light polarisation in Fe:LiNbO3, taken from Fradkin and Magomadov (1979). The direction of light propagation is shown in the inserts.
polarisation is rotated by 360° the Jx and Jy currents reverse sign twice. Hence when light is polarised perpendicular to a yaxis, current still flows, but along the
−ydirection. The amplitude of these currents is an order of magnitude less than the
amplitude ofJz, and never becomes negative (i.e. charge always flows along the+z direction). If the light is propagating along thezaxis, then the currentJz=α31Iand so is independent of the direction of polarisation. The values of the coefficients are
α22=1.5×10−10A/W,α31=6×10−9A/W andα33 =6.8×10−9A/W.
Another prediction of the one centre model is a light-induced refractive index change with a saturation value that depends only on the concentration of empty traps. The light intensity only affects the rate of the refractive index change. The energy band gap of lithium niobate has been reported to be between 3.7 eV to 3.9 eV (Prokhorov and Kuuzminov, 1990), so when lithium niobate is exposed to UV light (e.g. photons with wavelength of 248 nm and energies of 5 eV), direct excitation of the valence band electrons into the conduction band becomes possible, leaving behind holes which can contribute to the conductivity. Electrons can also be excited from the valence band to the Fe+3 impurity levels and electrons from Fe2+ can recombine with valence band holes (Orlowski and Kratzig, 1978).
At high intensities (I ≥ 106 W/m2) the one centre model does not sufficiently
describe the charge transport which takes place in Fe:LiNbO3. The one centre
model predicts a linear photoconductivity increase with light intensity and no light- induced absorption changes. Both of these are true for low light intensities, but are not valid at high intensities. Jermann and Otten (1993) proposed a new model which can quantitatively explain these and other experimental results at both low and high intensities. The model assumes a second centre and allows direct charge transfer between the two centres (Fig. 2.8).
conduction band valence band Fe2+ Fe3+ e e - - X+ X 0
Figure 2.8:Energy level diagram for the two-centre model of charge transport in LiNbO3.
The second centre, which only becomes active at high light intensities, is denoted by ‘X’, and although has it has not been conclusively proven, there is evidence that these centres are small polarons, Nb3Li•(self-trapped electrons at Nb4+ions on Li+ sites). Calculations by Jermann and Otten show that the concentrations for X centres are required to be much greater than for the Fe centres, which suggests that the centres consist of intrinsic defects. This is supported by experimental observation that the refractive index changes at high intensities are lower for stoichiometric lithium niobate than for congruent (Malovichko et al., 1992).