Exciton and electron-hole plasma formation dynamics in ZnO

We employ optical pump-THz probe measurements to study the formation of excitons and electron-hole plasmas following photogeneration of a hot electron-hole gas in the direct gap semiconductor zinc oxide. Below the Mott density, we directly observe the evolution of the hot electron-hole plasma into an insulating exciton gas in the $10\text{to}100\mathrm{ps}$ following photoexcitation. The temperature dependence of this process reveals that the rate determining step for exciton formation involves acoustic phonon emission. Above the Mott density, the density of the hot electron-hole plasma initially decreases very rapidly $(\sim 1.5\mathrm{ps})$ through Auger annihilation until a stable plasma is formed close to the Mott density. In contrast to exciton formation, Auger annihilation is found to be independent of lattice temperature, occurring while the plasma is still hot.

Figure 1

(a) Wannier exciton with Bohr radius $a_{\text{Bohr}}$. (b) An exciton gas below the Mott density, with the average distance between excitations much larger than the Bohr radius of an exciton in ZnO. (c) An exciton system excited above the Mott density.

Figure 2

(Color online) Conductivity dynamics for low density photoexcitation in ZnO at $30\mathrm{K}$. (a) The change in the complex conductivity for $0.6\mathrm{THz}$ as a function of time after excitation (real and imaginary parts: full and dotted lines, respectively). (b) Frequency dependent complex photoconductivity measured $15\mathrm{ps}$ after excitation. The response is well described by the Drude model for free charges (lines). (c) $200\mathrm{ps}$ after excitation most of the excited electrons and holes have paired to form excitons. The increased correlation of electrons and holes is shown by the sign flip of the imaginary conductivity: the lines represent the response expected from the polarizability of the $1\mathrm{s}$ exciton state (Ref. 21).

Figure 3

Conductivity of a gas of free charges (Drude) compared to that for a gas of bound electrons and holes (exciton). The restoring force introduced by the Coulomb interaction between electrons and holes results in a shift of the response resonance from effectively zero in the Drude model to a frequency ${\nu }_n$.

Figure 4

(a) Temperature dependence of the exciton formation rate in sample A investigated through the decay of the real conductivity ($N_0\sim 2\times {10}^{22}{\mathrm{m}}^{-3}$ and normalized to peak conductivity). Traces are offset vertically for clarity. The gray dotted line is an exponential fit with time constant of $20\mathrm{ps}$. (b) The exciton formation rate increases weakly with temperature. The dotted and full lines represent the dependence expected for formation determined by optical and acoustic phonon emission, respectively. (c) The residual dissociated exciton fraction increases with temperature. The full line indicates the dissociated fraction expected for a binding energy of $60\mathrm{meV}$, while the dotted and dashed lines represent the dissociated fraction expected for binding energies of $30\mathrm{meV}$ and $120\mathrm{meV}$, respectively, calculated according to Ref. 28.

Figure 5

(a) Exciton formation illustrated in terms of the “hot exciton cascade”: after excitation, hot exciton cooling occurs by optical (large curved arrows) and, as the exciton falls to the bottom of the well, acoustic (small curved arrows) phonon emission. (b) THz measurements suggest that the motion of electrons and holes remains uncorrelated for much of the cooling process. In this case, a more realistic description involves cooling through the electron-hole continuum, where the uncorrelated electron and holes have, on average, no net center of mass momentum $\left(\mathbf{K}\right)$.

Figure 6

(Color online) Conductivity dynamics for high excitation densities in sample A. At such high densities $(r⪡a_{\text{Bohr}})$, the system can no longer be described as a gas of excitons. (a) The open (real) and closed (imaginary) squares show the nonexponential dynamics for $266\mathrm{nm}$ photon excitation resulting in $N_0\sim 2\times {10}^{25}{\mathrm{m}}^{-3}$. (b) Decay of the real component for two different excitation densities: while both measurements show similar fast decays, the magnitude of the signal on long times does not vary strongly with excitation density. The dynamics are temperature independent: the gray line represents a measurement at $300\mathrm{K}$, coinciding perfectly with the $20\mathrm{K}$ data.