Bulk Photorefractive Semiconductors
- PDF / 1,212,471 Bytes
- 5 Pages / 576 x 792 pts Page_size
- 44 Downloads / 202 Views
The PR Effect in Bulk Semiconductors The PR effect in a particular material depends on both its extrinsic (defect related) and intrinsic properties—photoconductivity and carrier diffusion properties on one side and electrooptic coefficients, dielectric constants, and refractive index on the other. Photoconductivity is responsible for the creation of a space-charge field by spatial redistribution of the trapped charges in deep levels due to non-uniform illumination by photons of below bandgap energy. The free carriers, created by photoionization of deep levels in the bright
MRS BULLETIN/MARCH 1994
region of the illumination pattern, take part in the redistribution of the charges through diffusion (no external applied field) or drift (under external applied field) toward the dark region, where they recombine. The electrooptic effect transforms the space-charge field in a spatially modulated index variation. These basic mechanisms give hints of the key properties of the PR effect: 1. The strength of the space-charge field depends on the quantity of redistributed charges and is then linked to the concentration of deep levels and to the defect occupancy. 2. The number of redistributed charges directly depends on the number of photons absorbed in the material, governing the PR effect strength by the optical beam energy (note that its speed is beam power dependent). Thus, noticeable refractive index modulations are obtained with lowpower CW lasers. 3. The strength of the space-charge field can be increased by applying an electric field. This leads to a charge redistribution effect controlled by the drift of free carri-
ers, which is more efficient than free carrier diffusion. The expression of the photoinduced space-charge field is derived following the band transport model,8'9 with a single defect in a concentration NT, an ionized part in concentration No and neutral part in concentration NT — N o (Figure 1). We consider both thermal (/3) and optical (S) emission of electrons and holes from the defect. The illumination is given by a spatially modulated interference pattern along coordinate axis 2,7 = I0(l + Re(me'kz)) with a wave number k (k = 2ir/A, with grating spacing A = A/2n0 sin 8, with d the half angle between the two interfering beams inside the crystal, n0 is the linear refractive index of the material, and A the wavelength), a modulation m and a total incident illumination Jo. In a first approximation, the space-charge field is spatially modulated with the same grating spacing as the illumination pattern and, when the stationary regime is reached, its amplitude is (for grating spacing smaller than the diffusion length of the carriers and no applied electric field):
e \ + {k2/klf°
(1)
with the electron-hole competition coefficient, Sn(NT - N()) - SpN 0 - No) with + SJp
SJo and SPIO
ND
Pn
Yn
Sn \
N T -N 0 /N 0
1
sP
Y
NA 1
Figure 1. Energy diagram of semiconductors as a function of a space coordinate. Symbols are defined in the text.
kBT
0.025 eV
The part of the absorption that generates electr
Data Loading...
