Carrier transport properties of the Group-IV ferromagnetic semiconductor Ge1-xFex with and without boron doping

We have investigated the transport and magnetic properties of group-IV ferromagnetic semiconductor Ge1-xFex films (x = 1.0 and 2.3 %) with and without boron doping grown by molecular beam epitaxy (MBE). In order to accurately measure the transport properties of 100-nm-thick Ge1-xFex films, (001)-oriented silicon-on-insulator (SOI) wafers with an ultra-thin Si body layer (~5 nm) were used as substrates. Owing to the low Fe content, the hole concentration and mobility in the Ge1-xFex films were exactly estimated by Hall measurements because the anomalous Hall effect in these films was found to be negligibly small. By boron doping, we increased the hole concentration in Ge1-xFex from ~1018 cm-3 to ~1020 cm-3 (x = 1.0%) and to ~1019 cm-3 (x = 2.3%), but no correlation was observed between the hole concentration and magnetic properties. This result presents a contrast to the hole-induced ferromagnetism in III-V ferromagnetic semiconductors.

Ferromagnetic semiconductors (FMSs) have generated much interest from the viewpoint of physics, materials science, and possible applications to semiconductor-based spintronic devices. The origin of the ferromagnetism in FMSs was investigated by characterizing the magnetic properties and their correlation to other material properties, such as crystalline structure, carrier concentration, electrical properties, and electronic band structure. In III-V-based FMSs, 1,2 such as GaMnAs, it is well recognized that the ferromagnetism is induced by itinerant holes, 3 however, the origin of the ferromagnetism is still under debate 4 despite the tremendous research efforts for the past two decades. Also, there have been a number of studies on group-IV FMSs, especially on Ge 1-x Mn x . [5][6][7][8][9][10][11][12][13][14] So far, the ferromagnetism in most of the Ge 1-x Mn x films is considered to come from intermetallic or Mn-rich metallic phases contained in the Ge 1-x Mn x films, such as nanocolumnar precipitations. 6,8 Recently, we have grown epitaxial Ge 1-x Fe x films (x = 2.0 − 17.5 %) and have shown that the Ge 1-x Fe x films have a diamond-type crystal structure without any other crystallographic phase of precipitates, and their ferromagnetic band structures characterized by magnetic circular dichroism (MCD) spectra were of diamond-type, identical with those of Ge bulk materials 15,16 . These results indicate that the Ge 1-x Fe x films are single-crystalline films with a single-ferromagnetic phase. 15,16 However, so far there is little information which helps to understand the origin of the ferromagnetism in group-IV FMSs. In particular, the transport properties of Ge 1-x Fe x films, including the carrier concentration and mobility, have not been investigated, although these are important characteristics to clarify the origin of ferromagnetism. Indeed, it was difficult to estimate the carrier concentrations in the Ge 1-x Fe x films by Hall effect measurements, because the anomalous Hall effect is dominant and the Hall resistances showed hysteresis due to the anomalous Hall effect when the Fe content x was high ~ 10 %. 18 Studying the hole concentration dependence of the magnetic properties in Ge 1-x Fe x films is expected to be helpful to understand the ferromagnetism; if the ferromagnetism originates from itinerant holes in Ge 1-x Fe x (namely, carrier-induced ferromagnetism), ferromagnetic behavior is significantly enhanced with increasing the hole concentration.
In this paper, we study the transport and magnetic properties of Ge 1-x Fe x films with low Fe content (x = 1.0 % and 2.3 %) where we can exactly estimate the hole concentration and mobility by Hall measurements. Owing to the low Fe content, the anomalous Hall effect was found to be negligibly small which enables us to estimate these parameters in the Ge 1-x Fe x films. The hole concentration in the Ge 1-x Fe x films was varied by doping boron (B) atoms as acceptors.
We used (001)-oriented silicon-on-insulator (SOI) wafers as substrates, where the thickness of the Si layer was ~5 nm, in order to accurately measure the transport properties of Ge 1-x Fe x films by excluding the parallel conduction in the substrate. After chemical etching of a thermally-oxidized SiO 2 top layer with HF, a substrate was installed into our molecular beam epitaxy (MBE) chamber equipped with a reflection high-energy electron diffraction (RHEED) system. After thermal cleaning at a substrate temperature T S = 760°C for 30 sec, a 100-nm-thick Ge 1-x Fe x film was epitaxially grown at T S = 200°C with a rate of 120 nm/hour, where the Fe content x was varied; 1.0, 2.3, 6.5, 10.5, and 14.0 %. In some samples, a boron flux was also supplied to change the hole concentration during the MBE growth. The RHEED pattern of Ge 1-x Fe x showed bright 2×2 streaks indicating diamond crystal structure with an atomically flat surface. Finally, a 2-nm-thick Ge capping layer was grown on the Ge 1-x Fe x film. Figure 1(a) shows the schematic structure and Table I lists the parameters of the samples. Magnetization versus magnetic field (M-H) characteristics were measured using a Quantum Design MPMS superconducting quantum interference device (SQUID) magnetometer at 5 K. The Curie temperature T C was estimated by the Arrott plots of MCD spectra measured at various temperatures (5 − 120 K). 19 Using photolithography and wet etching with H 2 O 2 , the Ge 1-x Fe x films were fabricated into Hall bar-shaped devices with channel length of 200 µm and width of 50 µm. The boron concentration y was estimated by secondary ion mass spectroscopy (SIMS), and the hole concentration p was estimated by the Hall effect measured at 300 K. As a reference, a Ge film with a boron concentration of 4.4×10 19 cm -3 was also grown on a SOI (001) substrate with the same structure, and a part of it was fabricated into a Hall bar-shaped device in the same manner. Hereafter, this Ge film is referred to as boron-doped Ge film. Figure 1(b) shows X-ray diffraction (XRD) θ-2θ spectra of the samples, in which the assigned planes are indicated. The spectra clearly indicate that all the samples have the Ge 1-x Fe x films with diamond crystal structure, and that other crystalline phases of Ge-Fe compounds were not observed. This result is consistent with the characterizations using transmission electron microscopy and electron dispersive X-ray (EDX) spectroscopy in our previous studies. 16 The lattice constant a estimated from the Ge 1-x Fe x (004) peak in Fig. 1(b) decreased with increasing x, which is also consistent with the previous study. 18 It was found that a and the full width at half maximum (FWHM) of the Ge 1-x Fe x (004) peak were not changed by the boron doping when y = 4.4×10 19 cm -3 . On the other hand, a and the FWHM of the Ge 1-x Fe x (004) peak were changed by the boron doping when y = 4.8×10 20 cm -3 ; a becomes smaller and FWHM is significantly larger by the boron doping, as shown in Table I. In other words, the boron doping of y = 4.4×10 19 cm -3 does not affect the lattice parameters of Ge 1-x Fe x , but when y = 4.8×10 20 cm -3 , a variation in the lattice parameters (from y = 0) is not negligible.
The resistivity was measured for the Hall bar-shaped devices using a four-terminal method. All the samples exhibited linear current-voltage characteristics in the temperature range from 5 K to 300 K (not shown here). Figure 2  To estimate the hole concentration p in the temperature range of 5 − 300 K, the Hall voltage was measured for the devices with a constant current in the range of 10 µA to 1 mA while a perpendicular magnetic field was swept from -1 to 1 T. In general, the Hall coefficient R H of magnetic materials consists of the ordinary Hall effect and the anomalous Hall effect. The anomalous Hall effect which is proportional to the magnetization decreases with increasing temperature and becomes negligible well above the Curie temperature. In the boron-doped Ge 1-x Fe x films (x = 1.0 and 2.3 %; sample B, C, and E), Hall voltage versus magnetic field characteristics are linear without hysteresis and R H was almost constant in the whole temperature range (5 − 300 K). Thus, these temperature-insensitive R H data are caused by the ordinary Hall effect, since the contribution of the anomalous Hall effect, which is temperature-sensitive, is negligible. This is also supported by the result that the resistivity obtained for the boron-doped Ge 1-x Fe x films (sample B, C, and E) are temperature insensitive, as shown in Fig. 2 (a) and (b). Consequently, the hole concentration p of the Ge 1-x Fe x films (x = 1.0 and 2.3 %) can be estimated from R H = 1/qp, where q is the elementary charge. with increasing x when y is same, and these results are reasonable because the mobility usually decreases with increasing the impurity density in semiconductors. 17 On the other hand, µ of the Ge 1-x Fe x films without boron doping (y = 0; sample A and D) is greatly reduced at low temperatures as shown in Fig. 2 (e) and (f), which reflects the large increase in the resistivity of these films at low temperatures as shown in Fig. 2 (a) and (b). This result suggests that the conduction is dominated by hopping of holes in these undoped samples since the temperature dependence of µ cannot be fitted by neither phonon scattering (µ ∝ T -3/2 ) nor by ionized impurity scattering (µ ∝ T 3/2 ). A possible mechanism of the hole conduction is hopping of holes via neutral impurity Fe atoms. We think that most of the Fe atoms are neutral, as suggested by the relatively high mobility data in Fig. 2 (e) and (f) and by the very low activation rate of Fe (less than 0.5 %) estimated by the data in Fig.   2 (c) and (d).  Fig. 3 (partially due to the subtracting procedure described above), T C listed in Table I was estimated from the Arrott plots of MCD spectra measured in the temperature range from 5 to 20 K (see supplementary material). 19 The slight difference in T C between various p is not essential but due to the slight difference in sample quality, because T C of the Ge 1-x Fe x films significantly depends on the growth temperature as shown in the previous study. 20 In general, the ferromagnetism in FMSs is considered to be induced by itinerant carriers, and the mean field Zener model 3,21 or double-exchange model 22,23 have been frequently used to explain the observed magnetic properties. 4 In the boron-doped Ge 1-x Fe x films (sample B, C, and E), the resistivity ( Fig. 2 (a) and (b)) and mobility (Fig. 2 (e) and (f)) indicate that the Fermi level exists in the valence band. Moreover, the increase in p by two orders of magnitude with increasing y (Fig. 2 (c) and (d)) is attributable to a significant shift of the Fermi level in the valence band of the Ge 1-x Fe x films. However, it was found that there is no correlation between p and the magnetic properties, as shown in Table I and Fig. 3.
Even though the transport in the Ge 1-x Fe x (x = 1.0 %, 2.3 %) changed from insulating to metallic, T C was almost unchanged. This result presents a contrast to the hole-induced ferromagnetism in (III,Mn)V FMSs. 1,2 Namely, the mean field Zener model is not applicable, since this model derives a monotonic increase in T C with p. At present, the double exchange model is one of the possible candidate mechanisms, but we cannot conclude whether this or other models are applicable or not, and further study is needed to clarify the origin of the ferromagnetism in Ge 1-x Fe x films.
In summary, we have revealed the transport properties of Ge 1-    axis. The inset shows the close-up view near zero magnetic field.  Table I. These MCD signals were measured in the temperature range from 5 to 20 K while a perpendicular magnetic field was swept from -1 to 1 T.