Formation of Mn-derived impurity band in III-Mn-V alloys by valence band anticrossing

While the support for the existence of a Mn-derived impurity band in the diluted magnetic semiconductor ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ has recently increased, a detailed quantitative analysis of its formation and properties is still incomplete. Here, we show that such an impurity band arises as the result of an anticrossing interaction between the extended states of the GaAs valence band and the strongly localized Mn states according to the valence band anticrossing model. The anticrossing interpretation is substantiated by optical measurements that reveal a shift in the band gap of GaAs upon the addition of Mn and it also explains the remarkably low hole mobility in this alloy. Furthermore, the presence of a Mn-derived impurity band correctly accounts for the metal-to-insulator transition experimentally observed in ${\text{Ga}}_{1-x}{\text{Mn}}_x{\text{As}}_{1-y}{\left(\text{N},\text{P}\right)}_y$ with $y\le 0.02$.

Figure 1

(a) (Color online) PR spectra of ${\text{Ga}}_{1-x-y}{\text{Mn}}_x{\text{Be}}_y\text{As}$ demonstrate that the valence to conduction-band transition increases in energy with increasing Mn concentration but shows no movement with Be concentration, suggesting an anticrossing interaction between the GaAs and Mn states. The dashed line marks the PR transition of the underlying GaAs substrate while the arrows indicate the transitions of the film. (b) Experimentally determined movement of the band-gap energy of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ as well as the theoretical trend predicted by the VBAC model ($E_{-}$ valence band edge to conduction band) (Ref. 20). (c) Movement of the valence and impurity band-edge energies of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ as a function of Mn concentration.

Figure 2

(Color online) Hole mobility in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ and ${\text{Ga}}_{1-x}{X}_x\text{As}$ $\left(X=\text{Be},\text{C},\text{Zn}\right)$ as a function of hole concentration (Refs. 23, 24, 25, 26). The experimental data of the GaAs samples doped with nonmagnetic acceptors was theoretically fit with an ionized impurity scattering model, using heavy-hole effective masses of $m^{\ast }=0.47m_e$. Likewise, the ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ hole mobility was fit with an effective mass determined by the VBAC model $\left(\sim m^{\ast }=30m_e\right)$.

Figure 3

Dispersions of the impurity band in ${\text{Ga}}_{0.99}{\text{Mn}}_{0.01}\text{As}$ and ${\text{Ga}}_{0.96}{\text{Mn}}_{0.04}\text{As}$, illustrating the increase in the width of the impurity band with increasing Mn concentration.

Figure 4

(Color online) ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ heavy-hole effective mass and mobility as a function of Mn concentration.

Figure 5

(Color online) Impurity bandwidth (solid lines) and heavy-hole lifetime broadening (dashed lines) for ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ and ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{P}$ as a function of Mn concentration.

Figure 6

(Color online) Impurity bandwidth (solid line) and heavy-hole lifetime broadening (dashed line) for ${\text{Ga}}_{1-x}{\text{Mn}}_x{\text{As}}_{1-y}{\text{P}}_y$ $\left({\text{Ga}}_{1-x}{\text{Mn}}_x{\text{As}}_{1-y}{\text{N}}_y\right)$ as a function of P (N) concentration, $y$ (Ref. 32).