Modification to the central-cell correction of germanium acceptors

In this paper, we report a correction to the model potential of the Ga acceptor in germanium, evidenced by high-magnetic-field photoconductivity measurements. We found that under high magnetic fields the chemical shift of the binding energy of Ga acceptors vanishes, contrary to the results given by the generally accepted theory. To fit our data, we found that the central-cell correction should contain a repulsive part (i.e., it must be bipolar), in contrast to the purely attractive screened point-charge potential widely used in the literature.

Figure 1

Photocurrent as a function of magnetic field measured in the Ge crystal illuminated with FEL radiation at (a) 46 $\mu$m, (b) 60.5 $\mu$m, (c) 75 $\mu$m, and (d) 88 $\mu$m. The magnetic field is directed along the [001] direction. A 100-mV voltage bias was applied to the facets perpendicular to the magnetic field. The inset of (a) shows the photoconductivity data as a function of reciprocal magnetic field. Vertical arrows point to transitions from the two lowest acceptor states, bound to $2^1$ and $1^1$ Landau levels, into the resonant states bound to $3^1$ (arrows 3 and 4) and $2^2$ (arrows 1 and 2) Landau levels, respectively (see explanation of the notations in the text).

Figure 2

Energies of the valence-band Landau levels presented in units of the cyclotron energy for free electrons $\hslash \frac{eB}{m_{0}c}$. Each Landau level is labeled according to the notation explained in the text, while the notations according to Ref.20 are given in the brackets.

Figure 3

Energies of the ground state of the acceptor as a function of magnetic field, calculated using central-cell correction (1) and ${\kappa }_{\text{eff}}=1.07$, $l=3$ Å (solid lines), potential (1) and ${\kappa }_{\text{eff}}=10$, $l=10$ Å (dashed lines) and without taking the central-cell correction into account (dotted lines).

Figure 4

Summary of the experimentally obtained position of the resonances as a function of magnetic field (symbols). Solid lines show calculations of the transition energies from the two lowest acceptor states bound to the magnetic subbands $1^1$ and $2^1$ into resonant states bound to the subbands $2^2$ and $3^2$ calculated without taking into account the central-cell correction. Dashed lines correspond to the same transitions calculated using central-cell correction (1) and $k_{\text{eff}}=10$, $l=10$ Å. Numbers indicate corresponding maxima in the photoconductivity spectra (see Fig. 1).

Figure 5

Magnetic-field dependencies of the lowest acceptor-state energy calculated using no central-cell correction (dotted line), with central-cell correction (1) and ${\kappa }_{\text{eff}}=1.07$, $l=3$ Å (dashed line), with central-cell correction (6) with the following parameters: ${\kappa }_{{\text{eff}}_1}=3.84$, $l_1=25$ Å, ${\kappa }_{{\text{eff}}_2}=3.07$, $l_2=20$ Å (line 1), ${\kappa }_{{\text{eff}}_1}=2$, $l_1=20$ Å, ${\kappa }_{{\text{eff}}_2}=1.5$, $l_2=14$ Å (line 2), and ${\kappa }_{{\text{eff}}_1}=5.12$, $l_1=30$ Å, ${\kappa }_{{\text{eff}}_2}=3.84$, $l_2=25$ Å (line 3).