Letter pubs.acs.org/NanoLett
Tunable Transport Gap in Phosphorene Saptarshi Das,*,† Wei Zhang,‡ Marcel Demarteau,§ Axel Hoffmann,‡ Madan Dubey,∥ and Andreas Roelofs† †
Center for Nanoscale Material, ‡Materials Science Division, and §Division of High Energy Physics, Argonne National Laboratory, Argonne, Illinois 60439, United States ∥ U.S. Army Research Laboratory, Adelphi, Maryland 20783, United States S Supporting Information *
ABSTRACT: In this article, we experimentally demonstrate that the transport gap of phosphorene can be tuned monotonically from ∼0.3 to ∼1.0 eV when the flake thickness is scaled down from bulk to a single layer. As a consequence, the ON current, the OFF current, and the current ON/OFF ratios of phosphorene field effect transistors (FETs) were found to be significantly impacted by the layer thickness. The transport gap was determined from the transfer characteristics of phosphorene FETs using a robust technique that has not been reported before. The detailed mathematical model is also provided. By scaling the thickness of the gate oxide, we were also able to demonstrate enhanced ambipolar conduction in monolayer and few layer phosphorene FETs. The asymmetry of the electron and the hole current was found to be dependent on the layer thickness that can be explained by dynamic changes of the metal Fermi level with the energy band of phosphorene depending on the layer number. We also extracted the Schottky barrier heights for both the electron and the hole injection as a function of the layer thickness. Finally, we discuss the dependence of field effect hole mobility of phosphorene on temperature and carrier concentration. KEYWORDS: Phosphorene, transport gap, field effect transistor, mobility phosphoerene as a function of the flake thickness. In this article, we validate this claim experimentally. We have devised a unique way to determine the bandgap associated with the carrier transport that we refer to as the “transport gap” from the experimental transfer characteristics of phosphorene FETs. Using this technique we were also able to extract the Schottky barrier heights for the electron injection into the conduction band and hole injection into the valence band. We found that along with the bandgap, these Schottky barrier heights also change dynamically with the layer number impacting the ON current, the OFF current, and the ON/OFF current ratio as well as the asymmetry of the ambipolar conduction. Finally, we investigated the dependence of the field effect hole mobility on temperature and carrier concentration for various phosphorene layer thicknesses. Single and few layer phosphorene flakes were micromechanically exfoliated on 20 nm thick SiO2 layers on highly doped Si substrates used as the back gates. The use of 20 nm thick SiO2 compared to conventionally used 300 nm thick SiO2 was motivated by the fact that scaled oxide reduces the screening length and makes the Schottky barriers more transparent for efficient carrier injection.17 Electron-beam lithography was used
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tomistically thin 2D semiconductors are being extensively investigated for post silicon nanoelectronics owing to their excellent material properties and aggressive channel length scalability when used in a field effect transistor (FET) geometry. Graphene, a single layer of hexagonally arranged carbon atoms, has captured most of the attention for the last 10 years due to its extremely high carrier mobility and the potential for ballistic transport.1,2 However, the absence of a bandgap has limited the use of graphene in logic circuits. Although finite bandgaps can be engineered in graphene nanoribbons through size quantization and in bilayer graphene through electric fields, it is still insufficient for conventional logic operations.3,4 More recently transition metal dichalcogenides (TMDs) like MoS2, MoSe2, WSe2, and others have received a lot of attention due to their layered structure similar to graphene but with the added advantage of an intrinsic bandgap that ranges from ∼0.4 to ∼2.3 eV.5−14 Phosphorene, a single layer of black phosphorus arranged in a puckered honeycomb structure, is the most recent addition to the exotic class of two-dimensional (2D) materials.15,16 Phosphorene layers are held together by the weak van der Waals force of attraction in a black phosphorus crystal similar to other natural 2D materials. Unlike TMDs, the carrier mobility in phosphorene has been found to be significantly higher (∼1000cm2/V.s) and in addition DFT calculations predict a considerable and dynamic change in the bandgap of © XXXX American Chemical Society
Received: July 7, 2014 Revised: August 5, 2014
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Figure 1. (a) Optical image of a prototype back gated phosphorene FET. (b) Transfer characteristics of a monolayer phosphorene FET at room temperature.
Figure 2. (a) Room-temperature transfer characteristics of phosphorene FETs with different layer thicknesses. (b) The device OFF current, (c) the device ON current (measured at VBG − VTH = 6 V) as a function of the layer thickness extracted for VDS = −0.2 V and (d) the device current ON/ OFF ratio as a function of the number of layers. Inset of panel c shows the resistive network model comprising of Thomas−Fermi charge screening and interlayer coupling that describes the nonmonotonic trend of the device ON current. The error bars represent device to device variation.
to pattern the source/drain contacts and electron beam evaporation was used to deposit 60 nm thick Ni as the contact metal. Figure 1a shows the optical image of a prototype phosphorene transistor gated from the back. Figure 1b shows
the transfer characteristics of a monolayer phosphorene FET for different source to drain biases (VDS). The ON/OFF current ratio was found to be ∼105 for the hole conduction and ∼103 for electron conduction that clearly suggests that the B
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Figure 3. (a) Room-temperature transfer characteristics of a bilayer phosphorene FET. (b) Band diagrams associated with the device characteristics at different gate bias conditions. (c) Simulated thermionic emission current corresponding to the band bending situation depicted in the brown semitransparent box and the left semitransparent green box in (b). (d) Simulated Schottky barrier current corresponding to the band bending situation depicted in the right semitransparent green box in (b). (e) Different electron current components through the Schottky barrier at the drain end.
the thickness of the gate oxide, dOX = 20 nm and for SiO2, εOX = 3.5 × 10−11 F/m, which gives COX ∼ 1.7 × 10−3 F/m2, and finally L ∼ 2 μm). The peak value of gm was used for the extraction of the mobility. The electron mobility value was not extracted because the electron conduction is limited by large Schottky barriers at the contacts. Figure 2a shows the transfer characteristics of phosphorene FETs with different layer thicknesses ranging from bilayer to ∼25 layers. It is interesting to note that the OFF state current
Fermi level of Ni is aligned closer to the valence band of phosphorene. The field effect mobility value was found to be 116 cm2/(V s) for holes in monolayer phosphorene by using the conventional equation for gm = μCOX(W/L)VDS (where gm is the trans-conductance, μ is the field effect mobility, and W and L are the channel width and the channel length, respectively. The channel width, W, was calculated as the average width of the flake at the source and the drain contacts. COX = εOX/dOX, where εOX is the dielectric constant and dOX is C
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increases monotonically as the layer thickness increases while the ON state current shows a nonmonotonic trend as depicted in Figure 2b,c, respectively. Figure 2d shows the current ON/ OFF ratio as a function of the layer thickness. The nonmonotonic trend of the ON current can be easily explained using a resistive network model (see inset of Figure 2c) comprised of Thomas-Fermi charge screening and interlayer resistive coupling that we successfully employed before to describe transport in multilayer MoS2 systems.18,19 In general, the use of a finite number of phosphorene layers is beneficial for the ON state performance since the impact of the substrate on the device performance can be eliminated. The highest field effect hole mobility was extracted to be ∼315 cm2/(V s) for a 6 nm (∼10 layers) thick flake. The monotonic increase of the OFF state current and decrease in the current ON/OFF ratio, however, indicates that the transport gaps of the phosphorene flakes are changing as a function of the layer thickness. In order to extract the transport gap from the transfer characteristics of phosphorene FETs we have devised a novel technique that we will describe next. Figure 3a shows the room-temperature back-gated transfer characteristics of a bilayer phosphorene FET for large VDS = −1.0 V. For large negative back gate biases (VBG) the band positions in the phosphorene channel allow easier injection of holes from the source Fermi level into the valence band and hence the device operates in the ON state as a p-type FET as shown in the purple semitransparent box in Figure 3b. Note that this ON-state current (IDS) has two components, thermionic emission current over the top of the Schottky barrier and the thermally assisted tunneling current through the Schottky barrier. As the back gate bias is made less negative, the tunneling component of the current starts to decrease and ultimately disappears at the flat band condition (VBG = VF) as shown in the brown semitransparent box in Figure 3b. For |VBG| < |VF|, the device current is pure thermionic emission current and hence the slope of the log(IDS) versus VGS curve is a constant, being equal to 60β mV/decade where β is the band movement factor: β = [1 + (CT + CQ)/COX], where CT, CQ, and COX are the interface trap capacitance, quantum capacitance, and oxide capacitance, respectively. β does not contain any depletion capacitance (Cd) contribution as frequently relevant in bulk type MOSFET devices since for ultrathin body devices Cd ≈ 0. In the subthreshold regime of the device operation, CQ is negligible and therefore the band movement factor becomes approximately constant. Therefore, VF can be determined by finding the point on the subthreshold regime of the device characteristics where the slope of the log(IDS) versus VBG curve deviates from the linear trend as marked by the black dotted line. Note that this is not the threshold voltage VTH of the device and that the above definition of flat band voltage only applies to Schottky barrier devices. In fact, VTH lies at higher positive gate voltages than VF as discussed by us before.6 The device current IF at the flat band voltage (VF) is the thermionic emission current over a barrier height ΦP that also happens to be the height of the Schottky barrier at the corresponding metal-to-semiconductor interface. Figure 3c shows the thermionic emission current (ITHERMIONIC) calculated using eq 1 as a function of the barrier height. ITHERMIONIC = q
ΦP
∫∞
M(E − ΦP)f (E)dE
M (E ) =
2 2mpE , h2
f (E ) =
1
( )
1 + exp
E kBT
(1b)
We have used Landauer formalism assuming ballistic transport20,21 to calculate ITHERMIONIC. In eq 1, q is the electronic charge, h is the Plank constant, kB is Boltzmann constant and T is the temperature. M(E) (in units of (eV-ms)−1) is the number of conducting modes calculated as the product of the density of states and the average velocity corresponding to 2D parabolic band structure, mp is the electron effective mass and f(E) is the Fermi distribution. The reader should note that scattering in the channel is not included in our ballistic injection model because most of our analysis is performed in the OFF state of the device characteristics. In the OFF state, the injection of carriers across the Schottky barrier into the channel is limiting current flow rather than scattering in the channel. Using the experimental data for the flat band current (IF) the height of the Schottky barrier was determined to be 0.21 eV for hole injection into the valence band of phosphorene from Ni contacts. In order to verify the accuracy of our technique, we also performed temperature-dependent measurements and extracted the Schottky barrier height using the conventional Arrhenius approach as described in great details in our earlier article.6 The extracted Schottky barrier height for the Arrhenius case was found to be 0.22 eV, which is similar to the one extracted using the simple technique described here. The reader might question the accuracy of determining the flat band current. However, note that even for an order of magnitude variation in IF, the barrier height extraction changes by only ∼50 meV, which is comparable to typical device-to-device variations as well as the error bar when employing the Arrhenius technique. Note that the Schottky barrier height was extracted at large VDS = −1.0 V in order to eliminate the impact of the barrier at the drain end. It is also worth mentioning that the Schottky barrier extracted by swapping the contact electrodes was found to be 0.23 eV for the same device that suggests that the Schottky barrier is symmetric at the source and the drain end. Next, we focus on the minimum current point (VM, IM) of the device characteristics. Because the minimum current is a result of the transition from an electron to a hole current it is the superposition of two equal components: 1. The thermionic hole emission current (IP = 0.5IM) injected from the source over the top of the effective thermal barrier ΦP +ΔΦ, where, ΔΦ is the band movement due to an applied gate voltage of VF − VM shown on the left semitransparent green box in Figure 3b. 2. The Schottky barrier electron current (IN = 0.5IM) injected from the drain that is comprised of both the thermionic emission current and thermally assisted tunneling current as shown in the right semitransparent green box in Figure 3b. The effective barrier height (ΦP +ΔΦ) for hole injection was found to be 0.36 eV from Figure 3c using the same technique as described above in the context of the ΦP-extraction, which corresponds to a ΔΦ of 0.15 eV. In essence, we are comparing the minimum current level measured with the predicted thermal emission current over a barrier with height ΦP +ΔΦ. An alternative way to determine ΔΦ is from the band movement factor β using the relation ΔΦ′ = (VF − VM)/β. We extracted ΔΦ′ ≈ 0.16 eV, which is in good agreement with the above quoted 0.15 eV.
(1a) D
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Figure 4. (a) Extracted transport gap, (b) Schottky barrier heights for electron and hole injection, (c) relative position of the conduction band minima (red) and valence band maxima (green) with respect to the Ni Fermi level, and (d) the ratio of hole conduction current to electron conduction current for similar gate overdrive voltage as a function of the layer number. The error bars represent the device to device variation and error due to finite temperature.
Next, we analyze the electron conduction current (IN) to extract the Schottky barrier height for the electron injection at the drain terminal. The band bending situation at the drain end is depicted in Figure 3e with ΨDRIVE as the bias across the tunneling barrier, λ as the band bending length and ΦN as the barrier height. Figure 3d shows the Schottky barrier current ITUNNEL (which is the sum of both the thermionic emission current IN1 and the thermally assisted tunneling currents IN2 and IN3) as a function of the Schottky barrier height calculated using eq 2.20,21 IN1 = q
ΦN
∫∞
M(E + ΨDRIVE − ΦN)f (E)dE ,
ΨDRIVE = qVDS + Δϕ
IN2 = q
−ΦP
∫Φ
M (E ) =
M(E + ΨDRIVE − ΦN)TWKB − 2(E)f (E)dE
ΦN −ΨDRIVE
M(E + ΨDRIVE − ΦN)TWKB − 3(E)f (E)
P
dE
1
( )
1 + exp
E kBT
(2d)
⎛ 8π λ ⎞ TWKB − 2(E) = exp⎜ − 2mp(ΦN − E)3 ⎟ ΨDRIVE ⎠ ⎝ 3h
(2e)
⎛ 8π λ ⎞ 2mp(ΦN + ΦP)3 TWKB − 3(E) = exp⎜ − ⎟ ΨDRIVE ⎠ ⎝ 3h
(2f)
λ=
tOXt BODY
εBODY εOX
=
tOXt BODY
εenvironment εOX
≈
tOXt BODY
(2g)
Note that the assumption ΨDRIVE = qVDS + ΔΦ is justified because the device operates in the off-state without substantial short channel effects as evident from the measurements. At the same time, our evaluation takes place for very low current levels where the injection of carriers into the channel is not expected to impact the band position in return. Hence most of the VDS
(2b)
∫−Φ
f (E ) =
ITUNNEL = IN1 + IN2 + IN3
(2a)
N
IN3 = q
2 2meE , h2
(2c) E
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Figure 5. Field effect hole mobility of bilayer and 10 layer thick phosphorene as a function of (a) temperature and (b) carrier concentration.
such system but the changes in the bandgap as a result of that is expected to be much smaller than what we have observed in phosphorene. In fact, for other 2D crystals like MoS2 the change in the bandgap as a function of the thickness is insignificant (from bilayer to bulk the bandgap changes from 1.3 to 1.1 eV). The abrupt change from direct bandgap of 1.8 eV in monolayer MoS2 to indirect bandgap of 1.3 eV in bilayer MoS2 is an entirely different physical phenomenon of stacking and has nothing to do with the quantum confinement effects. This is true for other semiconducting layered transition metal dichalcogenides as well.24 So in principal the extreme tunability of bandgap of phosphorene by a factor of 3× over a relatively large flake thickness range is unique and unexpected and requires further theoretical investigation into the electronic structure of phosphorene. Figure 4b shows the extracted Schottky barrier heights for electron injection into the conduction band and hole injection into the valence band and Figure 4c shows the relative position of the conduction band minima (red) and valence band maxima (green) with respect to the Ni Fermi level as a function of the flake thickness. Figure 4d shows the ratio of the hole current (IP) and the electron current (IN) as a function of the flake thickness. For thinner phosphorene flakes the height of the Schottky barrier for electron injection is significantly higher which results in reduced electron current and hence higher IHole/IElectron ratio. For thicker flakes, the barrier heights for electron and hole injection are more symmetric, which results in smaller IHole/ IElectron ratio. Next we evaluated the temperature dependence of the field effect hole mobility of phosphorene as shown in Figure 5a for two different flake thicknesses. The mobility values are found to increase as the temperature is reduced from 300 to 100 K indicating reduced phonon scattering. The temperature dependence of mobility in this range can be approximated using a power law μαT−γ. The exponent γ depends on the flake thickness and ranges from 0.54 for bilayer phosphorene to 0.26 for 10 layer phosphorene. Finally, we extracted the field effect mobility as a function of the charge carrier concentration for different flake thicknesses as shown in Figure 5b. The mobility follows a power law dependence μαQ−η that indicates that the surface roughness scattering dominates the transport. The exponent η also depends on the flake thickness and ranges from 0.16 for bilayer phosphorene to 0.43 for 10 layer phosphorene. In conclusion, we have successfully demonstrated how the transport gap of phosphorene can be tuned dynamically by
drop will occur in the drain region. WKB approximation for a triangular potential barrier has been used to calculate the tunneling probabilities. The expression for the geometric screening length λ22,23 could be simplified for an ultrathin body channel material in FET geometry as the field-lines between the source and the drain contacts lie mostly in the “environment” rather than the inside of the channel. εbody, therefore, should be replaced by εenvironment, which in a backgated transistor geometry can be assumed to be the average of the dielectric constant of air, εbody and εox. For IN = 1.7 × 10−3 μA/μm, ΦN = 0.49 eV was extracted from Figure 3d. Note that the extraction of ΦN also has an error bar of around 50 meV due to finite temperature effects and device-to-device variations. Because the bandgap of the material is the sum of the Schottky barrier height for the holes and the Schottky barrier height for the electrons, we can calculate it to be about 0.72 eV for bilayer phosphorene. At this stage it is worth noting the limitations of the approach described above. If, for example, the source/drain metal Fermi level is aligned with the middle of the semiconducting band gap, the flat band point (VF, IF) and the minimum current point (VM, IM) become indiscriminable. In this case, our technique cannot be employed for obvious reasons. Moreover, in order to identify both the minimum current and the current at flat band with satisfactory accuracy ΔΦ > ∼kBT/q should be satisfied. Also increasing the magnitude of ΨDRIVE by applying increasing drain voltages increases the minimum current up to the point that it obscures the flat band point entirely. This effect will be more pronounced for semiconductors with smaller bandgaps. In essence, as long as the two pairs (VF, IF) and (VM, IM) are clearly resolved, our approach is believed to provide straightforward access to the Schottky barriers at the source/ drain metal interface and bandgap of the channel material. Figure 4a shows the transport gap of phosphorene as a function of the layer number extracted using the technique described above. The transport gap decreases monotonically as the layer thickness is increased and ultimately saturates at the bulk value of ∼0.3 eV. Note that scaling the thickness of any bulk material will change the bandgap due to quantum confinement effects. However, for natural 2D crystals the boundary conditions do not change when layer thickness is scaled. So the monotonic change in the bandgap of phosphorene cannot be explained within the conventional theory of quantum confinement. Overlap of the atomic orbitals in the neighboring layers will certainly cause perturbation in F
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(13) Larentis, S.; Fallahazad, B.; Tutuc, E. Field-effect transistors and intrinsic mobility in ultra-thin MoSe2 layers. Appl. Phys. Lett. 2012, 101, 223104. (14) Das, S.; Prakash, A.; Salazar, R.; Appenzeller, J. Towards Low Power Electronics: Tunneling Phenomena in TMDs. ACS Nano 2014, 8 (2), 1681−1689. (15) Li, L.; Yu, Y.; Ye, G. J.; Ge, Q.; Ou, X.; Wu, H.; Feng, D.; Chen, X. H.; Zhang, Y. Black Phosphorous Field Effect Transistor. Nat. Nanotechnol. 2014, 9, 372−377. (16) Liu, H.; Neal, A. T.; Zhu, Z.; Xu, X.; Tomanek, D.; Ye, P. D. Phosphorene: An Unexplored 2D Semiconductor with High Hole Mobility. ACS Nano 2014, 4, 4033−41. (17) Das, S.; Appenzeller, J. Evaluating the scalability of multilayer MoS2 FETs, Device Research Conference (DRC), Notre Dame, IN, June 23−26, 2013; IEEE: Bellingham, WA, 2013; pp 153−154. (18) Das, S.; Appenzeller, J. Where Does the Current Flow in TwoDimensional Layered Systems? Nano Lett. 2013, 13, 3396−402. (19) Das, S.; Appenzeller, J. Screening and interlayer coupling in multilayer MoS2. Phys. Status Solidi RRL 2013, 7, 268−273. (20) Lundstrom, M. Nanoscale Transistors: Device Physics. Modeling and Simulation; Springer: New York, 2006. (21) Datta, S. Quantum Transport: Atom to Transistor; Cambridge University Press: New York, 2005. (22) Note that the expression for λ was applied in the space between the source and the drain contacts and its expression was calculated based on the articles by Yan et al. [23] for a planar geometry. A more detailed evaluation should involve the transfer length and the interlayer coupling resistance of the semiconducting channel underneath the metal contacts. (23) Yan, R. H. Scaling of Si MOSFET: from bulk to SOI to bulk. IEEE Trans. Electron Devices 1992, 39, 2. (24) Kang, J.; Tongay, S.; Zhou, J.; Li, J.; Wu, J. Band offsets and heterostructures of two-dimensional semiconductors. Appl. Phys. Lett. 2013, 102, 012111.
scaling the layer thickness. We also report a new technique to extract the transport gap of an ultrathin body semiconductor from the transfer characteristics of a field effect transistor of the same material. We also discussed the impact of bandgap and band alignment on the device performance of phosphorene FETs.
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ASSOCIATED CONTENT
S Supporting Information *
Extraction of Schottky barrier height using Arrhenius technique. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work by W.Z. and A.H. was supported by the U.S. Department of Energy, Office of Science, Materials Science and Engineering Division. The work of Saptarshi Das is supported by the DOE Office of High Energy Physics under DoE contract number DE-AC02-06CH11357. Use of the Center for Nanoscale Materials was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02- 06CH11357.
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