Barrier Height Measurement of Metal Contacts to Si Nanowires Using

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Barrier Height Measurement of Metal Contacts to Si Nanowires Using Internal Photoemission of Hot Carriers KunHo Yoon, Jerome K. Hyun, Justin G. Connell, Iddo Amit, Yossi Rosenwaks, and Lincoln J. Lauhon Nano Lett., Just Accepted Manuscript • Publication Date (Web): 13 Nov 2013 Downloaded from http://pubs.acs.org on November 17, 2013

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Barrier Height Measurement of Metal Contacts to Si Nanowires Using Internal Photoemission of Hot Carriers KunHo Yoon , Jerome K. Hyun , †, Justin G. Connell, Iddo Amit§, Yossi Rosenwaks§, Lincoln J. Lauhon*. AUTHOR ADDRESS Northwestern University, Materials Science and Engineering, 2220 Campus Dr. Evanston, IL 60208, United States §

†

Department of Physical Electronics, School of Electrical Engineering, Tel-Aviv University, Ramat-Aviv 69978, Israel

Present address: Department of Materials Science and Engineering, KAIST Institute for The Nanocentury, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 305-701, Republic of Korea.

KEYWORDS. Nanowire, Schottky barrier, internal photoemission, metal semiconductor interface, hot electrons, SPCM

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Table of Contents Graphic

ABSTRACT Barrier heights between metal contacts and silicon nanowires were measured using spectrally resolved scanning photocurrent microscopy (SPCM). Illumination of the metal-semiconductor junction with sub-bandgap photons generates a photocurrent dominated by internal photoemission of hot electrons. Analysis of the dependence of photocurrent yield on photon energy enables quantitative extraction of the barrier height. Enhanced doping near the nanowire surface, mapped quantitatively with atom probe tomography, results in a lowering of the effective barrier height. Occupied interface states produce an additional lowering that depends strongly on diameter. The doping and diameter dependencies are explained quantitatively with finite element modeling. The combined tomography, electrical characterization, and numerical modeling approach represents a significant advance in the quantitative analysis of transport mechanisms at nanoscale interfaces that can be extended to other nanoscale devices and heterostructures.

TEXT The Schottky barrier that forms between a metal and semiconductor controls charge injection and extraction; the engineering of band alignment, barrier height, and contact transparency is essential to control the performance of many electronic and optoelectronic devices.1-4 Even most


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ohmic junctions are associated with Schottky barriers whose widths have been narrowed by doping to the point that tunneling current dominates. The Schottky barrier height is often extracted by analyzing current-voltage (I-V) or capacitance-voltage (C-V) characteristics based on the thermionic emission model,5 which due to its simplicity has been widely adopted for measuring the barrier height in nanostructured devices incorporating semiconductor nanowires.69

However, electrical biasing changes the population of surface states, which complicates the

interpretation of the measurement. Furthermore, the geometry of nanowire contacts differs from that used in strictly one-dimensional models of transport in Schottky diodes, impacting the extracted barrier height and ideality factor.9, 10 In general, determining a reliable barrier height in small, highly doped nanowires is non-trivial,8 but critical to the optimization of highly scaled electronic, optoelectronic, spintronic, and chemical-biological sensor devices.1

Recently, there has been increasing interest in exploiting hot carrier transport across interfacial barriers for applications including photovoltaics,11 photo-detectors,4 and light emitting devices.12 Hot carriers generated by photoexcitation can be injected directly across the Schottky barrier in a process known as internal photoemission, and internal photoemission spectroscopy (IPS) provides a means to directly and accurately extract the barrier height.2-4 Here we apply IPS to nanowire contacts using spectrally resolved scanning photocurrent microscopy (SPCM). Subbandgap SPCM induces internal photoemission at the metal-semiconductor junction, enabling the isolation and analysis of the contact photoresponse, which is an important requirement for the IPS measurement.13 The scaling of the photocurrent magnitude with photoexcitation energy is consistent with the Fowler model for internal photoemission,14 from which we extract the barrier height. We find that the effective barrier height is substantially reduced by doping, and it


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decreases strongly with diameter. By combining atom probe tomography studies of the dopant distribution with 3-D device simulations, the doping and diameter dependence of the barrier height is quantitatively explained as arising from image potential lowering in the presence of non-uniform near surface doping15 and negatively charged interface states.

n-type Si nanowires were grown via the Vapor-Liquid-Solid (VLS) method in an H2-rich environment as described in reference 16. SiH4:PH3 ratios of 1500:1 and 500:1 were used to obtain nanowires with distinct doping levels, and Au colloids of 50, 100, and 150 nm diameters were used to grow nanowires of different diameters. Nanowires were mechanically transferred from the growth substrate to the device substrate (Si3N4) for fabrication of back-gated single nanowire field effect transistors (FETs). Electrical contacts of 2 µm width were defined by electron-beam lithography, metal deposition of Ni and Au, and lift-off. Because the devices were not annealed, the metal contact geometry should remain “wrapped” as opposed to “end-on”, as might be produced by silicidation.6,

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The devices have ohmic current versus voltage

characteristics (Figure 1b), and the nanowire diameters in devices were measured by atomic force microscopy (Figure 1c: left, Bruker Dimension ICON AFM). To spatially and spectrally resolve the local photo-response near the metal contacts, we employed SPCM in a scanning confocal microscope setup (Figure 1a; WITec) with excitation by a tunable super-continuum laser source (λ = 450 - 1700 nm; NKT Photonics). For visible and infrared wavelengths, the collimated light was focused to a diffraction-limited spot using 100X objective lenses with 0.90NA and 0.95NA, respectively. Finally, a lock-in amplifier was used to record the photocurrent at the laser modulation frequency of 1837 Hz. Reflection images were acquired concurrently during SPCM and later used to determine the precise location of the contacts


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(Figure 1c: right). While SPCM has been used to study the photocurrent response from the semiconducting channels of nanowire FETs,17-19 spectrally resolved SPCM measurements provide new mechanistic insights into photocurrent arising from the metal-semiconductor junction.

When a nanowire FET under moderate bias is illuminated by above bandgap photons, a photocurrent is observed in the channel due to the drift of excess carriers in the electric field established by the external bias (Figure 1d-ii).20 Even when the contacts are at the same potential (Figure 1d-i), photocurrents are still observed because band bending near the contacts results in strong minority carrier drift and diffusion currents.17 Two additional mechanisms of photocurrent generation should be considered in general. First, the temperature increase at the metal semiconductor junction due to photoexcitation produces a photothermoelectric (PTE) current or voltage, though the relative magnitude is expected to be small for the doped silicon nanowires considered here.20 Second, intra-band transitions can lead to internal photoemission (IPE) of nonequilibrium carriers over potential barriers at the junction. This contribution has not been previously considered in nanowire devices. By illuminating the device with photons of energy less than the silicon bandgap, interband transitions in the semiconductor are eliminated, as confirmed by the absence of channel photocurrent in Figure 1d-iv. Photocurrents at the grounded (biased) contacts arise from IPE of electrons (holes) from the metal into the semiconductor (Figure 1d-iii & iv); the PTE effect should produce a negative photocurrent at the biased contact, which is not observed. We note that photocurrents in silicon nanowire devices could be generated by sub-gap illumination due to a combination of defect-mediated absorption and the Franz-Keldysh effect near metal contacts under bias.21 We therefore analyze the sub-gap


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photocurrent with no applied bias in the remainder of this paper, and we show that the energy dependence of the photocurrent is well described by IPE.

SPCM imaging at 1100 to 1700 nm yields photocurrents of opposite sign at opposite electrodes with magnitudes that increase with decreasing wavelength (Figure 2a). We note that these measurements were conducted at zero bias, so there is no “dark current”. The dependence of the photocurrent yield Y on photon energy is consistent with internal photoemission over a barrier at the metal semiconductor interface, as described by the Fowler model:14, 22

I ph (hν )2 Y= = CF (hν − qφ B )2 (qPopt )

(1)

where Iph is the photocurrent, Popt is the power of the laser source (held constant at 50 µW), hν is the photo-excitation energy, CF is the Fowler constant, and ϕB is the barrier height. The data in Figure 2b were taken on a 150 nm diameter nanowire device, and result in an extracted barrier height of 0.52 eV that is significantly lower than the reported Schottky barrier height for Ni on ntype Si of 0.74 eV.5 There are several possible contributions to this barrier lowering, including dopant-induced barrier lowering23,

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and geometric effects. We therefore applied the same

analysis to nanowires with a range of diameters for two different doping levels (high and low), specified by the gas phase ratio of silane to phosphine (500:1 and 1500:1). As shown in Figure 2c, we observe a strong decrease in effective barrier height with increasing doping and decreasing diameter. To quantitatively explain these trends, we used Sentaurus TCAD 3-D device simulator (Synopsys, Inc) combined with analytical models to identify the influence of dopants, interface states, and the associated image potentials on the measured effective barrier height.


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Shannon showed that heavy doping near the metal semiconductor junction can be used to control the barrier height; when the doping the interlayer enhances the surface field, the effective barrier height can be lowered by 0.1-0.2 eV in Si.23, 24 Significantly, we recently used atom probe tomography (APT) to show that P-doped Ge and B-doped Si nanowires grown by the VLS process exhibit strong surface enrichment of dopant atoms even in the absence of gas phase surface doping,15 indicating that quantitative dopant mapping is critical to understanding NW devices. Figure 3a presents APT results for a P-doped Si nanowire grown under the same conditions as the nanowires used for devices, suggesting that the barrier height in contacts to these n-type nanowires is strongly influenced by the enhancement in near-surface doping. While it is obvious that the non-uniform dopant distribution should be accounted for in device modeling, the presence of inactive species such as P2 also indicates that the electron concentration will not be equal to the total P concentration. We therefore developed a core-shell model (Figure 3b) in which 100% of the dopants are active in the interior of the nanowire, whereas only ~30% are active near the surface due to clustering (Figure 3a), inactive defect complexes,25 and increased ionization energies.26-28 Such a model was found to be necessary in prior Kelvin probe force microscopy studies of the active dopant concentrations in nanowires grown under the conditions used in this study.29 While the precise fraction of active dopant species is not known, the modeling based on this estimate describes the experimental data very well, as shown below.

Equilibrium potential and electric field profiles were first calculated in Sentaurus using the geometry and doping concentrations shown in Figure 3b without including interface states or image potentials. Accordingly, the barrier height is simply the difference between the


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semiconductor electron affinity and the metal work function (0.74 eV). In examining the equilibrium conduction band profile moving into the semiconductor and away from the interface (Figure 3c), we observe that the heavy doping near the surface constrains the depletion region to within ~5 nm of the metal semiconductor interface, and that the width of the depletion region shows little dependence on the nanowire diameter (Figure 3c). Clearly, the doping and diameterdependent effective barrier height observed in Figure 2c cannot be explained without including additional influences on the potential profile.

The measured effective barrier heights can be explained by the influence of image potential lowering and negatively charged interface states on the built-in potential. The total potential energy PE(x) through which the electron moves is given by:

PE(x) = PE Built−In (x) + PEImage−Force (x) + PE IS (x, R) ,

(2)

where x is the distance away from the metal/semiconductor interface in the direction indicated by the arrow in Figure 3b, and R is the radius of nanowire. We note that states at the metalsemiconductor interface are often referred to as metal induced gap states (MIGS). States at the semiconductor-dielectric interface just outside the contact region will also influence the 3-D potential profile. However, as both the MIGS and the semiconductor-dielectric interface states introduce a similar diameter dependence of the potential profile within the nanowire, here we focus on modeling the interface states beneath the contact (MIGS) while using the more general term “interface states”.

First, we note that an electron moving towards the metal/semiconductor interface generates an image potential5 (Figure 4b, blue):


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PEImage−Force (x) =

−q 2 16πε 0 ε s x

(3)

where ε0 and εs are dielectric constants for vacuum and semiconductor, respectively. Within the image-force approximation, one can describe the potential barrier profile near the interface by superposition of the built-in potential with the image-force potential.30 This contribution lowers the potential barrier by 0.12 eV in the absence of interface states (Figure 4c, blue). The magnitude of barrier height lowering is consistent with what one would expect from the highly doped near-surface layer, and the corrected barrier height of 0.62 eV agrees with the experimentally measured barrier height for the less-doped, larger diameter nanowires, which should exhibit more bulk-like behavior (Figure 2c). We note that while the Sentaurus package can incorporate the image potential when solving the 3-D Poisson equation, we calculated the image potential and surface state potential analytically prior to adding them to the line profiles extracted from the 3-D simulations of the built-in potentials. The barrier lowering we observe is consistent with inclusion of the image potential during 3-D calculations, and provides the additional benefit of capturing the rapid change in potential near the interface (~within 1 nm) without the computational demand associated with extremely fine meshing.

To explain the diameter dependence, we consider the influence of occupied acceptor-type interface states, which induce positive charge in the depletion region (Figure 4a). The configuration can be modeled as a cylindrical coaxial capacitor.31, 32 The influence of charges of distinct origins on the barrier shape is included by adding an additional electric field to equation (2).30 The magnitude of the electric field between the two oppositely charged layers is given by:


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 λ , if 0 < x < w  EIS (x, R) =  2πε 0ε s (R − x)  0, otherwise 

    

(4)

where λ is the total charge per unit length and w is the depletion width of nanowire. Inspection of equation (4) indicates that ESS will facilitate the injection of electrons into the semiconductor, i.e. lower the potential barrier, and that the magnitude of barrier lowering will increase as the nanowire diameter (2R) is decreased. The work done on a charge carrier moving between the two oppositely charged layers is given by:

PEIS (x, R) = ∫

final

initial

−qE(x ')dx ' = ∫

w x

−qλ dx ' . 2πε 0 ε s (R − x ')

(5)

Under the depletion approximation, the charge per length enclosed within the Gaussian surface

λ (x) = QDepletion × π (R − x)2 − (R − w)2  in the depletion region. Using the charge neutrality condition, we equate the total charge in the depletion region (QDepletion) to the charge in interface states:31-33 QDepletion = QSurface = qDitψ S

2π R , π R2

(6)

where the surface potential qψS = 0.62 eV and Dit is the density of interface states (Dit = 1 × 1013 states/cm2/eV).34

This additional potential energy term was used to recalculate the total potential energy as a function of distance and determine the diameter dependent barrier lowering (Figure 4c). In agreement with experiment, the barrier height decreases with decreasing diameter (Figure 4c: solid (220 nm) and dashed (40 nm) red lines). This approach was also used to calculate the barrier height for the range of measured nanowire diameters for both doping concentrations. The effect of doping concentration is reflected by the difference in the built-in potential profile and,


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therefore, the different amount of the barrier lowering. The modeling results are plotted as dashed lines in Figure 2c. The experimentally measured values and the calculated barrier heights are in good agreement across a range of nanowire diameters and doping concentrations.

In summary, using spectrally resolved scanning photocurrent microscopy, we have directly extracted the barrier height at metal contacts to semiconductor nanowires. We identified the observed photoresponse as internal photoemission from the metal to the semiconductor over a Schottky barrier, and used the Fowler model to extract the barrier heights. While others have investigated the effect of interface states on the barrier height at the metal/semiconductor interface in bulk samples,35 or on the surface barrier at the semiconductor/air interface in ZnO nanowires,36 our work indicates that the interface states in a nanowire will also play an important role in controlling the hot carrier injection and extraction across the metal/semiconductor interface by changing the barrier height. The combination of spatially and spectrally resolved photocurrent analysis demonstrated here could be usefully extended to other functional heterojunctions in, for example, photovoltaic37 and photo-electrochemical applications.38, 39


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FIGURES

Figure 1. (a) SPCM measurement scheme. (b) Current-voltage characteristic of 50 nm diameter Si (1500:1 doping) with ohmic contacts. (c) AFM topography of device (left) and reflection image taken during SPCM measurements (right). (d) Photocurrent images of the same NW device: i-ii: above gap excitation at 532 nm for grounded and biased contacts, respectively; iii-iv: sub gap excitation at 1200 nm for grounded and biased contacts, respectively; scale bar: 4 µm; photocurrent scale bar in nA. Dashed white lines indicate contact edges determined by reflection image taken concurrently. (e) Qualitative energy diagrams illustrate distinct photocurrent generation mechanisms involving above- (green) and below- (red) bandgap photons at 0 V (left) and 1 V (right) drain-source bias.


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Figure 2. (a) A reflection image (far left) and photocurrent maps at decreasing sub gap wavelengths (1700 – 1100 nm); scale bar: 2 µm. (b) Fowler plot for a 150 nm NW device; the slope of the linear fit line is ~2.1 and the extracted barrier height is 0.52 eV. (c) Effective barrier


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height dependence on diameters and dopant concentration; blue and red data points are for lightly (1500:1) and heavily (500:1) doped nanowires, respectively. Black dashed line: reference Ni/n-Si barrier height (0.74eV5); blue and red dashed lines are from the model described in Figure 4.


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Figure 3. (a) Radial P dopant (left) and P2 cluster (right) distribution in the cross section of a Si nanowire from APT reconstruction. (b) Three-dimensional view of the nanowire structure simulated to calculate the equilibrium energy bands by Sentaurus TCAD software package; the nanowire cross section shows the core-shell model of active dopants that we adapted for the


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simulation. (c) The conduction band edges extracted from the simulation results for 50 nm (red) and 150 nm (blue) nanowire devices.


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Figure 4. (a) A quadrant of a nanowire cross section of radius R with negatively charged surface states and the equal number of positive charges in the adjacent depletion region of width w. (b) Potential energy contributions versus distance (x) from the metal/semiconductor interface toward the nanowire center due to image-force (blue) and occupied interface states (red) as described by Equations 3 and 5, respectively. (c) The total potential energy near the metal/semiconductor interface: PEBuilt-In (Black), PEBuilt-In + PEImage-Force (Purple), and PEBuilt-in + PEImage-Force + PEIS for


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220 nm (solid green) and 40 nm (dashed green) diameter nanowires in solid and dashed line, respectively.


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AUTHOR INFORMATION Corresponding Author *To whom correspondence should be addressed. E-mail: [email protected] Author Contribution These authors contributed equally.

Notes The authors declare no competing financial interest. ACKNOWLEDGMENT L.J.L. acknowledges DOE-BES for the primary support of this work through DE-FG0207ER46401 (K.H.Y, J.K.H.), as well as the support of NSF under DMR-1006069 (J.G.C.) for nanowire growth and atom probe tomography. Y.R. would like to acknowledge the support of the Israel Binational Science Foundation (BSF) and the Israel Science foundation (ISF).


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18. Allen, J. E.; Perea, D. E.; Hemesath, E. R.; Lauhon, L. J. Nonuniform Nanowire Doping Profiles Revealed by Quantitative Scanning Photocurrent Microscopy. Adv. Mater. 2009, 21, 3067-3072. 19. Hyun, J. K.; Lauhon, L. J. Spatially resolved plasmonically enhanced photocurrent from Au nanoparticles on a Si nanowire. Nano Lett. 2011, 11, 2731-2734. 20. Ahn, Y.; Dunning, J.; Park, J. Scanning photocurrent imaging and electronic band studies in silicon nanowire field effect transistors. Nano Lett. 2005, 5, 1367-1370. 21. Zhou, Y.; Liu, Y. H.; Cheng, J.; Lo, Y. H. Bias dependence of sub-bandgap light detection for core-shell silicon nanowires. Nano Lett. 2012, 12, 5929-5935. 22. Crowell, C. R.; Sarace, J. C.; Sze, S. M. Tungsten-Semiconductor Schottky-Barrier Diodes. Trans. Met Soc. AIME 1965, 233, 478-481. 23. Shannon, J. M. Reducing the effective height of a Schottky barrier using low-energy ion implantation. Appl. Phys. Lett. 1974, 24, 369. 24. Shannon, J. M. Control of Schottky-Barrier Height Using Highly Doped Surface-Layers. Solid-State Electronics 1976, 19, 537-543. 25. Sato, K.; Castaldini, A.; Fukata, N.; Cavallini, A. Electronic Level Scheme in Boron- and Phosphorus-Doped Silicon Nanowires. Nano Lett. 2012, 12, 3012-3017. 26. Bjork, M. T.; Schmid, H.; Knoch, J.; Riel, H.; Riess, W. Donor deactivation in silicon nanostructures. Nat. Nanotechnol. 2009, 4, 103-107. 27. Fernández-Serra, M.; Adessi, C.; Blase, X. Surface Segregation and Backscattering in Doped Silicon Nanowires. Phys. Rev. Lett. 2006, 96, 166805. 28. Fukata, N.; Seoka, M.; Saito, N.; Sato, K.; Chen, J.; Sekiguchi, T.; Murakami, K. Doping and segregation of impurity atoms in silicon nanowires. Physica B 2009, 404, 5200-5202. 29. Amit, I.; Givan, U.; Connell, J. G.; Paul, D. F.; Hammond, J. S.; Lauhon, L. J.; Rosenwaks, Y. Spatially resolved correlation of active and total doping concentrations in VLS grown nanowires. Nano Lett. 2013, 13, 2598-2604. 30. Afanas'ev, V., Internal Photoemission Spectroscopy: Principles and Applications. Ch. 2, Elsevier: Oxford, UK, 2008. 31. Park, J. T.; Kim, J. Y.; Islam, M. S. Extraction of Doping Concentration and Interface State Density in Silicon Nanowires. IEEE Trans. Nanotechnol. 2011, 10, 1004-1009. 32. Kim, C. J.; Lee, H. S.; Cho, Y. J.; Kang, K.; Jo, M. H. Diameter-dependent internal gain in ohmic Ge nanowire photodetectors. Nano Lett. 2010, 10, 2043-2048. 33. Zhang, S.; Lopez, F. J.; Hyun, J. K.; Lauhon, L. J. Direct detection of hole gas in Ge-Si core-shell nanowires by enhanced Raman scattering. Nano Lett. 2010, 10, 4483-4487. 34. Koren, E.; Berkovitch, N.; Azriel, O.; Boag, A.; Rosenwaks, Y.; Hemesath, E. R.; Lauhon, L. J. Direct measurement of nanowire Schottky junction depletion region. Appl. Phys. Lett. 2011, 99, 223511. 35. Cowley, A. M.; Sze, S. M. Surface States and Barrier Height of Metal Semiconductor Systems. J. Appl. Phys. 1965, 36, 3212-3220. 36. Soudi, A.; Hsu, C.-H.; Gu, Y. Diameter-Dependent Surface Photovoltage and Surface State Density in Single Semiconductor Nanowires. Nano Lett. 2012, 12, 5111-5116. 37. Grancini, G.; Maiuri, M.; Fazzi, D.; Petrozza, A.; Egelhaaf, H. J.; Brida, D.; Cerullo, G.; Lanzani, G. Hot exciton dissociation in polymer solar cells. Nat. Mater. 2013, 12, 29-33. 38. Mayer, M. T.; Du, C.; Wang, D. Hematite/Si Nanowire Dual-Absorber System for Photoelectrochemical Water Splitting at Low Applied Potentials. J. Am. Chem. Soc. 2012, 134, 12406-12409.


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39. Esposito, D. V.; Levin, I.; Moffat, T. P.; Talin, A. A. H2 evolution at Si-based metalinsulator-semiconductor photoelectrodes enhanced by inversion channel charge collection and H spillover. Nat. Mater. 2013, 12, 562-568.


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BRIEFS (Word Style “BH_Briefs”). If you are submitting your paper to a journal that requires a brief, provide a one-sentence synopsis for inclusion in the Table of Contents. SYNOPSIS (Word Style “SN_Synopsis_TOC”). If you are submitting your paper to a journal that requires a synopsis, see the journal’s Instructions for Authors for details.


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Barrier Height Measurement of Metal Contacts to Si Nanowires Using

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