Modeling of electronic excitation and dynamics in swift heavy ion irradiated semiconductors

1. Modeling of electronic excitation and dynamics in swift heavy ion irradiated semiconductors TzvetaApostolova Institute for Nuclear Research and Nuclear Energy ELI-NP: THE WAY AHEAD March 11, 2011, Bucharest-Magurele

2. We consider a bulk GaAs semiconductor doped with electron concentration to form a 3D electron gas. • We separate the dynamics of a many-electron system into a center-of- • mass motion plus a relative motion under both dc and infrared fields. • The relative motion of electrons is studied by using the Boltzmann scattering equation including anisotropic scattering of electrons with phonons and impurities beyond the relaxation-time approximation. • The coupling of the center-of-mass and relative motionscan be seen from the impurity and phonon parts of the relative Hamiltonian

3. When the motion of electrons is separated into center-of mass and relative motions, the incident electromagnetic field is found to be coupled only to the center-of-mass motion but not to the relative motion of electrons • This will generate an oscillating drift velocity in the center-of mass motion, but the time-average value of this drift velocity remains zero • The oscillating drift velocity will, however, affect the electron-phonon and electron-impurity interactions. • The thermodynamics of electrons is determined by the relative motion of electrons This includes the scattering of electrons with impurities, phonons, and other electrons.

4. The effect of an incident optical field is reflected in the impurity- and phonon-assisted photon absorption through modifying the scattering of electrons with impurities and phonons. • This drives the distribution of electrons away from the thermal equilibrium distribution to a non-equilibrium one. At the same time, the electron temperature increases with the strength of the incident electromagnetic field, creating hot electrons.

5. Previously- Boltzmann scattering equation – impurity and phonon- assisted photon absorption and Coulomb electron scattering for a doped GaAs semiconductor

7. D. Huang, P. Alsing, T. Apostolova et. al.Phys. Rev. B 71, 195205 (2005)

8. Electron dynamics in ion-semiconductor interaction v/c<0.1 • The projectile has reached its equilibrium charge state - there will be only minor fluctuations of its internal state • It will move with constant velocity along a straight-line trajectory until deep inside the solid. • Thus, the projectile ion acts as a well defined and virtually instantaneous • source of strongly localized electronic excitation. G. Schiwietz et al. / Nucl. Instr. and Meth. in Phys. Res. B 225 (2004) 4–26

9. Electron dynamics in ion-semiconductor interaction • After investigating the electron dynamics in semiconductors on a femtosecond time scale in such a physical processes as irradiation by an intense ultrashort laser pulse we modify the technique to describe the passage of a highly charged ion through the solid. Same time scales of interaction • We consider only constant-velocity v/c < 0.1 , straight-line trajectories for the projectile. • In terms of three-dimensional Cartesian coordinates, we define the reaction to occur in the x-y plane with the beam directed along and the impact parameter b along defining the straight-line trajectory to be

11. We will establish a Boltzmann scattering equation for an accurate description of the relative scattering motion of electrons interacting with a swift heavy ion by including both the impurity- and phonon-assisted photon absorption processes as well as the Coulomb scattering between two electrons. • We study the thermodynamics of hot electrons by calculating the effective electron temperature as a function of impact parameter and charge of the ion.

12. We use the Hamiltonian

13. solve the Schrodinger equation L.Plagne et. al.Phys. Rev. B 61, (2000), J.C.Wells, et. al.Phys. Rev. B 54, (1996), with velocity of projectile

14. Looking closely at the problem parameters for justification of the approx.

15. The electron annihilation operator in the ion potential is given by: Boltzmann scattering equation

17. Numerical results K. Schwartz, C. Trautmann, T. Steckenreiter, O. Geiß, and M. Krämer, Phys. Rev. B 58, 11232–11240 (1998)

18. Calculated electron distribution function for bulk GaAs as a function of electron kinetic energy T=300K

19. Calculated electron distribution function for bulk GaAs as a function of electron kinetic energy T=300K

20. Calculated electron distribution function for bulk GaAs as a function of electron kinetic energy T=77K

21. Average electron kinetic energy as a function of impact parameter T=300K

22. Average electron kinetic energy as a function of ion charge Z T=300K

23. Conclusions • The effect of the potential of the incident ion is reflected in the phonon and impurity assisted electron transitions through modifying (“renormalizing”) the scattering of electrons with phonons and impurities • This method can offer unique ability to study the change in the collision dynamics when a single projectile characteristic is modified. • The same numerical code as with the excitation with a laser field is used.

24. Thank you for your attention!

25. For a general transient or steady-state distribution of electrons, there is no simple quantum statistical definition for the electron temperature in all ranges. However, at high electron temperatures we can still define an effective electron temperature through the Fermi-Dirac function according with the conservation of the total number of electrons. • In the nondegenerate case, the average kinetic energy of electrons is proportional to the electron temperature. The numerically calculated distribution of electrons in this paper is not the Fermi-Dirac function. We only use the Fermi-Dirac function to define an effective electron temperature in the high temperature range by equating the numerically calculated average kinetic energy of electrons with that of • the Fermi-Dirac function for the same number of electrons.