Cantor Dielectric Heterostructures Made of Nanostructured Multilayers of Porous Silicon

Abstract

The wave propagation in the nanostructured porous silicon multilayers, where the geometrical length follows the Cantor code, is presented. The total thickness of the multilayered structure is maintained as 9000nm. The heterostrucutres were fabricated by the porous silicon layers having the refractive indices of 1.9 and 1.2 corresponding to the low and high porosity respectively. The thickness of the high and low porosity layer varied from 1000 to 12nm for making the Cantor heterostructures up to 7th order. In the re∞ectance spectra of the Cantor structure of 6th order (63 layers), two major photonic band gaps (PBG) are observed in the visible region with a narrow resonance at 652nm. In the Cantor structures, with order more than 6, instead of any PBG approximately equidistant fringes are observed. PS has been extensively studied for the last 15 years (1{6). High re∞ectivity multilayered struc- tures (2), e-cient visible photoluminescence (1), compatibility with standard silicon processes for integrated optoelectronics (3), photonic applications (2,4{6) and biosensors (7) have been major attractions of this fleld. The fabrication of porous silicon by electrochemical etching of crystalline silicon (c-Si), gives us the ability of having a wide refractive index contrast within the same ma- terial, avoiding the problem of inter-difiusion or lattice mismatch between the layers, through an easy and cheap process. Since we can control both, the layer thickness (through anodization time) and refractive index (through porosity), this method can be used to study experimentally the mul- tilayered structures. Recently, Luigi Moretti etal. (8) compared the sensitivities of resonant optical biochemical sensors, based on both periodic and aperiodic porous silicon structures, such as the Bragg and the Thue-Morse multilayer. The shifts of the re∞ectivity spectra of these devices on exposure to several chemical compounds have been measured and the aperiodic multilayer is re- ported to be more sensitive than the periodic one. The optical properties of several other kinds of quasiregular systems have been investigated in difierent systems (9{12). In (9) the authors presented theoretical calculation in a Cantor photonic crystal waveguides and the optical spectra of fractal multilayer dielectric structures has been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Following an example of the work demonstrated in (8), we show our prelimnary experimental results on the relationship between the geometry and the optical properties of the multilayers made of nanostructured porous silicon (taking two difierent refractive indices), where geometrical length of the layers follows the Cantor code and maintains the total thickness (for difierent orders) of the multilayered structure as 9000nm. 2. EXPERIMENTAL DETAILS We have used boron doped p ++ type crystalline silicon with resistivity 0.001{0.005ohm-cm, (100) oriented substrates for fabricating our samples. To have a better control over the interfaces and thickness of the porous layers, anodization was performed by alternating square pulses with a frequency of 100Hz (Ref. Escorcia etal. PSS), with a 50% of duty cycle. The electrochemical reaction took place at room temperature. The electrolyte with volume ratio of 3:7 of HF (48 wt%): ethanol (98 wt%) was taken for electrochemical anodization process. The current density was controlled by the computer. A high porosity H ( current density 50mA/cm 2 , with efiective refractive index of 1.35) and low porosity (35%, current density 5mA/cm 2 , with nb = 2:0), were repeated to form the cantor type structures. The refractive indices of the pSi layers have been estimated using