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Black phosphorus has emerged as a promising two-dimensional semiconductor, which has a unique structure that is anisotropic in-plane. This structural anisotropy translates to some very interesting orientation dependent properties. In this paper we present directional characterization and analysis of the phonon and electrical properties in black phosphorus. Using polarization dependent Raman we show a simple method for estimating orientation. A complementary radially contacted field effect transistor (FET) was fabricated in order to measure orientation dependent electrical properties. Mobility and transconductance followed a sinusoidal like dependence on orientation with a 30% anisotropy. Correlating these results with Raman, we show how Raman methods might be used as a nondestructive technique to orient black phosphorus devices.
© 2016 Optical Society of America
1. Introduction
Black phosphorus (bP) has recently generated a great deal of interest as a two-dimensional (2D) material due to its exciting and unique physical properties. For electronic devices, it has attracted attention due to its high hole mobility of 1,000 cm2/Vs [1] and thickness tunable band gap (0.3 eV in bulk to 2 eV in mono-layer) [2]; and as such, a number of exciting nanoelectronic devices have already been demonstrated [3–6]. Structurally, bP is an elemental layered material, which can be isolated down to the thickness of one mono-layer, known as phosphorene. Individual layers of bP form a puckered ridge and valley type structure, which is anisotropic in the a and c directions, giving rise to an anisotropic band structure.
The structural anisotropy in bP in turn gives rise to some very interesting orientation dependent properties. Studies of orientation dependent electrical properties have demonstrated clear electrical anisotropy with a nearly 3x difference in the in-plane hole mobility between zigzag ([a]) and armchair ([c]) direction [3,7,8]. This anisotropy leads to some interesting polarization dependent optical properties like absorption [9] and linearly polarized emission [10]. The phonon properties are also strongly affected resulting in orientation dependent thermal transport [11] and a strong polarization dependent Raman response [12–15].
These anisotropic properties may lead to the development of new devices and applications for bP but can also make reliable fabrication of devices a challenge. Consistent device performance and characteristics across an array is critical for any integrated circuit technology, so a reliable non-destructive method for orienting bP materials and devices is desired. In this paper we use Raman as a way to orient thin bP flakes for electrical devices by combining polarization dependent Raman spectroscopy with orientation dependent device measurements.
2. Experimental
For characterization and device fabrication, thin bP flakes were mechanically exfoliated from bulk bP (purchased from 2D Semiconductors) followed by transfer to 285 nm SiO2 on p + Si substrate. Material and samples were stored and exfoliated in a nitrogen glove box to prevent oxidation. Flakes were identified by optical microscopy, and atomic force microscopy (AFM) was used to measure flake thickness. Raman measurements were carried out under a nitrogen atmosphere in a Linkam stage using a Renishaw inVia system. An accumulation of 20 scans, each of 30-second duration, was collected using a 250 µW 514nm excitation source, 20-µm slits and 3000 line/mm grating for each measurement. For polarization dependent measurements the incident beam and scattered polarizers were set parallel and scanned between 0 and 180° in 20° increments. A back-gated FET device was fabricated from a 25 nm thick bP flake. Radially oriented contacts were patterned every 45° using a JEOL JBX-6300FS direct-write e-beam lithography system. 20 nm/60 nm Ti/Au contacts with a 1.1 µm contact width and 5.2 µm gap distance between opposite contacts were used. FET characterization was performed using an Agilent 4156C precision semiconductor parametric analyzer.
3. Results and discussion
Raman has been shown to be a powerful tool to study 2D materials. In bP Raman has been used to characterize layer thickness [15–18] and orientation [12, 15]. In orthorhombic bP 12 phonon modes are allowed at the Г point of which 6 (A1g, A2g, B1g, B2g, B13g and B23g) are Raman active. Of these Raman active modes, the three high frequency modes (A1g, B2g and A2g) are typically observed in thin and bulk bP. These modes correspond to the out-of-plane vibration (A1g at 360 cm−1), in-plane along the zigzag direction (B2g at 436 cm−1) and in-plane along the armchair direction (A2g at 463 cm−1). As the thickness of bP is reduced below a few layers, a small shift (~2 cm−1) in the A1g and A2g modes has been observed, which can be used to estimate layer thickness. However, above ~4 layers no appreciable shift is observed in the high frequency modes. Since films with thickness greater than a few-layers are also quite important (FET mobility is a maximum around 5 nm [3]), other methods for determining bP thickness are desired. The low frequency modes have been used for layers > 5 monolayers thick [15] but require special filtering to detect scattered light near the excitation laser line. Another more accessible method may be to use intensity ratios, analogous to using IG/IG’ in graphene [19]. Lu et al. [17] showed strong thickness dependence on the A2g to A1g and Si to A2g intensity ratios for few-layer material, demonstrating the feasibility of using these ratios for estimating thickness. For thicker films, up to 12 nm, Castellanos-Gomez et al. [16] showed a linear increase in the A1g to Si intensity ratio with thickness. Figure 1(a) shows Raman spectra taken from 5, 10 and 25 nm thick bP with no shift in the A1g, B2g or A2g peaks, as expected. However, an obvious change in peak intensities is observed. Comparing the IA2g to IA1g ratio as a function of thickness, Fig. 1(b), shows a clear thickness dependence, which decreases linearly with increasing thickness. Comparing ISi to IA2g we did not observe any obvious trends with thickness within our sample set, which may be due to sample to sample variations in substrate to bP orientation. Therefore, for layers greater than a few-layers the IA2g to IA1g ratio appears to be a good method for estimating the thickness.
Fig. 1 (a) Raman spectra from bP flakes with different thickness exfoliated on to SiO2/Si (normalized and offset). (b) Comparison of the thickness dependence on IA2g/IA1g and ISi/IA2g ratios.
The anisotropic phonon properties of bP have been shown to have strong polarization dependence using Raman. As mentioned above the B2g, and A2g modes correspond to vibrations along perpendicular directions (zigzag and armchair), whose Raman intensities are strongly polarization dependent. From ref [12], the intensities under a parallel polarization are given as:
and,where θ is the polarization angle, and a and c are Raman tensors corresponding to the zigzag and armchair directions, respectively. The polarization dependent Raman spectra from a single flake with 5 and 17 nm thick regions was used to characterize anisotropic phonon properties in bP, Fig. 2(a). Raman spectra taken from the 5 nm thick region at different polarization angles are shown in Fig. 2(b). The intensity of the A1g, B2g and A2g modes show a clear dependence on the polarization angle, which can be further elucidated by plotting intensity vs. angle as shown in Figs. 2(c) and 2(d) from the 5 and 17 nm spots respectively. Comparison of Figs. 2(c) and 2(d) show excellent agreement at these two thickness. Fitting to Eqs. (1) and (2), A2g and A1g have minima every 180° at 85° and B2g every 90° at 5° and 95°. According to refs [9, 12, 15]. the Ag modes should be at a minimum (c > a) when the polarization is aligned along the zigzag and the B2g mode at a minimum when aligned with the armchair and zigzag directions. More recently Ling et al. [20] and Kim et al. [21] showed that the polarization dependent intensity of the A1g and A2g are impacted by thickness and excitation wavelength. This dependence is ascribed to anisotropic interference effects due to electron-photon and electron-phonon interactions, which can change the main polarization axis between armchair and zigzag [20]. Both Refs [20,21]. account for these variations using an interference enhancement factor to unambiguously determine direction regardless of thickness or excitation wavelength. In the dozen samples in the thickness range of 5 to 25 nm we investigated in this work, we consistently observe A1g and A2g in phase and c > a.Fig. 2 (a) Optical micrograph of exfoliated bP flake with 5 and 17 nm thick regions, measured by AFM. (b) Polarization dependent Raman spectra from a 5 nm thick bP flake offset for clarity. Plots of IB2g, IA1g and IA2g vs. polarization angle taken from the 5(normalized and offset) (c) and 17 nm (d) thick regions. Symbols are experimental data and dashed lines correspond to fits to Eq. (1) and Eq. (2).
In order to study the electrical properties of bP, a radial back-gated FET was fabricated with contacts positioned every 45°, Fig. 3(a). An AFM image from the flake used to fabricate the device is shown in Fig. 3(b). Line scans across the edges were used to measure the flakethickness. A step height of 25 nm was consistently measured across all four edges. The transistor behavior of this device was measured across all four sets of contacts in the dark under ambient conditions. The characteristic output curves measured from contacts 3 to 7 for Vg from −20 to 20 V are shown in Fig. 3(c), exhibiting typical p-type behavior. In the range of Vds = −0.5 to 0.5 V, the FET exhibits a linear response indicating good Ohmic contacts. Similar linear I-V responses were observed across 2-6 and 4-8. Only measurements across contacts 1 and 5 had a nonlinear Ids response for negative Vds. This suggests that Ti/Au can be used as an Ohmic contact for bP as discussed in [21]. Transfer curves across 3-7 show an increase in Ids with increasing negative Vg, Fig. 3(d). A slight shift in the curve with increasing Vds to higher p-type conductivity is observed. This shift could be caused by a nonlinear I-V or most likely by gate stress as observed previously in similar bP FETs [4]. The on/off ratio of this device is quite low ~6 for bP, based on the expected carrier density (n) from back-gating, which should be ~1.6 x 1018 cm−3, assuming n = Vbg*Cg/t, where Cg is gate capacitance (Cg = 7.88 x 1010 cm−2/V) and t is thickness. Other papers have reported on/off of 104 for much thinner bP layers. We expect this low on/off is due to screening effects caused by thickness similar to what has been observed in other back-gated van der Waals FETs [22, 23]. Even though the on/off is low, it is consistently 6 across all contacts demonstrating transistor operation and indicating good device uniformity.
Fig. 3 (a) Optical micrograph of bP radial FET. (b) AFM image of the 25 nm bP flake before device processing, insets show line scans taken across two edges used to measure thickness. (c) I-V characteristics across contacts 3 and 7 from Vg −20 to 20 V. (d) Transfer curves between contact 3 and 7 at Vds = 10 and 50 mV.
To probe the orientation dependence of electrical properties we looked at the angular transconductance and field effect mobility. From the linear portion of the transfer curves measured across each set of contacts, we estimate the transconductance from Gm = dIds/dVg and field effect mobility using µFE = GmVdsL/(WCg), where L and W are the channel length and width. Figure 4(a) shows the transconductance and field effect mobility as a function of angle. The Fig. inset shows how the sample is oriented. A clear dependence on crystallographic orientation is observed following a sinusoidal type dependence, with the Gm ranging from 0.55 to 0.8 µS and µFE from 170 to 240 cm2/V-s. The minimum Gm and µFE occur at around 90° with a period of 180°. From early work on the electrical properties of bP [7], it was established that electrical transport across the perpendicular zigzag ([a]) and arm chair ([c]) directions is quite different. Interestingly enough, transport in the armchair direction or perpendicular to the ridges has the lowest effective mass. In bulk the mobility along this direction is reportedly 3x more than in the zigzag [7], while more recent works on thin bP have measured the mobility to be ~1.8x higher [9]. From our measurements we observe a 30% anisotropy in the mobility, even though our simple device structure likely under-estimates mobility due to current spreading and low angular resolution.
Fig. 4 (a) Orientation dependent transconductance (Gm) and field effect mobility (µFE) from a 25 nm thick bP FET. Gm and µFE were estimated from the linear portion of transfer curves take at Vds = 50mV. The inset shows the de-vice orientation. (b) Polarization dependent Raman intensity from the same 25 nm flake. The symbols represent experimental data and dashed line are fits to Eqs. (1) and (2). The plot shows the A2g and B2g intensities as a function of angle. The Raman data was shifted by + 12° in order to align with electrical measurements using the bottom edge as a reference, inset.
The corresponding polarization dependent Raman from this bP FET was measured. Figure 4(b) presents the peak intensity of the A2g and B2g modes as a function of polarization angle. Using the bottom edge of the bP flake, the zero polarization angle was adjusted to match the device orientation. Clear polarization dependence is again observed where the A2g mode has a minimum at 82° with a period of 180° and B2g has a minimum at 88° and period of 90°. Accordingly, this would orient the armchair and zigzag directions at ~0 and 90°. This determination is consistent with the orientation dependent electrical results. As such, this demonstrates the ability to use polarization dependent Raman using a 514 nm excitation as a way to align electrical devices up to 25 nm. This will be extremely useful as bP devices progress from fabrication of flakes on the laboratory scale to large area wafer scale processing.
4. Conclusions
The anisotropic structure of bP gives rise to orientation dependent electrical and phonon properties, which can present challenges to device fabrication. Using polarization dependent Raman in a parallel configuration, we take advantage of this anisotropy in order to estimate crystallographic orientation by comparing the intensity of the Ag and B2g modes as a function of angle. As a complement, a radial FET was fabricated with contacts placed every 45° to study the orientation dependent electrical properties. Mobility followed a sinusoidal type dependence ranging from 170 to 240 cm2/V-s with a 180° period. Correlating these measurements showed a clear agreement between the orientation determined by Raman and electrical characterization.
Acknowledgments
The authors would like to thank Timothy Prusnick for his help. This work is funded by Air Force Office of Scientific Research under task number 16RYCOR331, Program Manager Dr. Kenneth Goretta. This support is gratefully acknowledged.
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