Time-resolved electronic capture in $n$-type germanium doped with antimony

The low temperature ($T$ = 5–40 K) capture of free electrons into hydrogenlike antimony centers in germanium has been studied by a time-resolving experiment using the free electron laser FELBE. The analysis of the pump-probe signal reveals a typical capture time of about 1.7 ns that decreases with pump energy to less than 1 ns while the number of ionized donors increases. The dependence on the pump-pulse energy is well described by an acoustic phonon-assisted capture process. In the cases when (i) a significant number of the electrons is in the conduction band (flux densities larger than 5 × 10${}^{25}$ photons/(cm${}^2$ s), (ii) the lattice temperature is above ∼20 K, or (iii) a static electric field above ∼2 V/cm is applied to the crystal, the pump-probe technique reveals an additional intraband relaxation process with a characteristic time of ∼100 ps, which is much shorter than that of the capture of free electrons into the antimony ground state.

Figure 1

Discrete energy levels of Sb impurity in germanium bound to the minimum of the conduction band (CB) [4]. Only the $1s\left(A_1\right)$ and $1s\left(T_2\right)$ states are significantly populated at 4.5 K. The arrows indicate the photoionization by the FEL at a wavelength of 105 μm.

Figure 2

Absorbance (σNd) of the investigated Ge:Sb sample as a function of the temperature, showing spectral features corresponding to intracenter (discrete lines) and impurity-band transitions (continuum at energies larger than ∼10 meV). The discrete lines correspond to transitions originating from the $1s\left(A_1\right)$ and $1s\left(T_2\right)$ antimony states, which is thermally populated. Inset: Absorbance in the sample at the FEL pump photon energy of 11.8 meV (105 μm) as a function of the sample temperature.

Figure 3

Pump-probe signals of the Ge:Sb sample for different pump-pulse energies. Inset: Dependence of the maximum of the relative transmission on the pump pulse energy at 105 μm excitation wavelength. The temperature of the Ge:Sb sample was ∼5 K.

Figure 4

Pump-probe signal of the Ge:Sb sample at a pump-pulse energy of 0.3 nJ and a temperature of ∼5 K. The straight red line is a fit using Eq. (6). The decay time is 1.7 ns. The residual is the difference between fit and measurement.

Figure 5

Pump-probe signal of the Ge:Sb sample at a pump-pulse energy of 5.5 nJ. In this case the fit parameter $b$ is about 20% of $a$, which indicates that intraband processes are significant. The straight blue line is the calculated contribution to the total signal caused by phonon-mediated capture using the fit parameters $a$ and ${\tau }_{+}$. The straight green line is the same but for intraband processes using the fit parameters $b$ and ${\tau }_i$. The residual is the difference between fit and measurement.

Figure 6

Time constant ${\tau }_{+}$ as a function of the pump-pulse energy. The dashed curve is a fit according to the APY theory [37].

Figure 7

(a) Time constants ${\tau }_{+}$ and ${\tau }_i$ for a biexponential fit as a function of the heat sink temperature. For temperatures lower than 20 K, a single exponential was used. At 20 K and above, a second exponential [Eq. (6)] has to be included in order to obtain a good fit of the measured data. (b) Amplitude fit parameters $a$, $b$ of the biexponential fit [Eq. (6)].

Figure 8

(a) Time constants ${\tau }_{+}$ and ${\tau }_i$ for a biexponential fit as a function of the electric field. At electric fields higher than ∼2 V/cm, the second exponential decay [Eq. (6)] has to be included in order to fit the measured data. (b) Amplitude fit parameters $a$, $b$ of the biexponential fit [cf. Eq. (6)].