# Electron Patterns Under Bistable Electro-Optical Absorption in Quantum Well Structures

## Abstract

Heterostructures with electrically biased quantum wells show bistable absorption in both, hybrid electro-optical devices (SEED’s) [1] and all-optical devices (wireless SEED’s [2], and multiple quantum well structures [3],[4]). We report a new phenomenon of formation of transversal electron patterns under bistable electro-optical absorption in wireless single and multiple quantum well heterostructures. The patterns consist of regions with different densities of two-dimensional photogenerated electron-hole plasma. This phenomenon results in patterning of optical absorption and light transmission.

We have formulated and analyzed a model addressing these self-sustained patterns which includes: self-consistent calculations of the wave functions and subband energies of photoexcited electrons and holes in a strongly biased quantum well, nonlinear interband light absorption, configuration of the electrostatic potential, its screening and the lateral motion of the bidimensional electron-hole plasma. The transversal characteristic length scale of the patterns is of the order of the ambipolar diffusion length of the two-dimensional plasma, *L* _{D.} For large transversal dimensions of the QW layer most of the patterns consist of wide plateaus with high (low) absorption and plasma density and relatively narrow domains with low (high) absorption and plasma density. There is a strong coupling between the vertical and transversal degrees of freedom of photoexcited carriers due to the electrostatic interaction. Transversal redistributions of the plasma induce complex configurations (two-, or three-dimensional) of the electrostatic potential. For a finite transversal dimensions of the QW layer the patterns are strongly affected by the boundary conditions at the edges of the layer. Depending on the heterostructure design there are either electrically charged, or quasineutral patterns (for the latter case the electron concentration, *n*, is almost equal to the hole concentration, *p*). If the distance, *d* _{c}, between the QW and the electrodes (heavy doped regions of the structure to which the bias is applied) is considerably greater than *L* _{D}, the patterns are quasineutral. In the opposite case, the patterns are charged. For all cases patterning of transmitted light is calculated.

## References

- 1.D. A. B. Miller
*et al*., Appl. Phys. Lett.**45**, 13 (1984). A. L. Levin, IEEE J. of Quant. Electron.**29**, 655 (1993).CrossRefGoogle Scholar - 2.
- 3.
- 4.V. A. Kochelap, L. L. Bonilla, V. N. Sokolov and C. A. Velasco, Phys. Stat. Solidi (b)
**204**, 559 (1997). L. L. Bonilla, V. A. Kochelap and C. A. Velasco, J. Phys. C**31**, L539 (1998). C. A. Velasco, L. L. Bonilla, V. A. Kochelap and V. N. Sokolov, Microelectronic Eng.**43-44**, 153 (1998). V. A. Kochelap, L. L. Bonilla and C. A. Velasco, Semiconductor Physics, Quantum Electronics and Optoelectronics**1(1)**, 50 (1998). V. A. Kochelap, L. L. Bonilla and C. A. Velasco, J. Opt. B: Quantum Semiclass. Opt.**1**, 84 (1999).CrossRefGoogle Scholar