Spatial structures of islands of electron-hole liquid in semiconductor quantum wells

The formation of the different structures of islands of electron-hole liquid in the quantum well is studied in a statistical model. The interaction between the islands of electron-hole liquid is considered by influencing of neighboring islands through exciton gas around the considered island. Two restricted regions were studied: an infinite strip and a disk. The theory gives the possibility to determine the probability of different states realization and to find the most probable state. The dependence of the radius, mutual positions of the electron-hole liquid islands, the number of the islands in the disk on the pumping, temperature and parameters of the system (the size and the shape) are calculated.