schottky barrier height measurements of cu si 001 ag si 001 and au si 001 interfaces utilizing ballistic electron emission microscopy and ballistic hole emission microscopy

Schottky barrier height measurements of Cu/Si(001), Ag/Si(001), and Au/Si(001) interfaces utilizing ballistic electron emission microscopy and ballistic hole emission microscopy Robert Balsano, Akitomo Matsubayashi, and Vincent P LaBella Citation: AIP Advances 3, 112110 (2013); doi: 10.1063/1.4831756 View online: http://dx.doi.org/10.1063/1.4831756 View Table of Contents: http://aip.scitation.org/toc/adv/3/11 Published by the American Institute of Physics Articles you may be interested in The physics and chemistry of the Schottky barrier height AIP Advances 1, 011304011304 (2014); 10.1063/1.4858400 AIP ADVANCES 3, 112110 (2013) Schottky barrier height measurements of Cu/Si(001), Ag/Si(001), and Au/Si(001) interfaces utilizing ballistic electron emission microscopy and ballistic hole emission microscopy Robert Balsano, Akitomo Matsubayashi, and Vincent P LaBellaa College of Nanoscale Science and Engineering, SUNY, Albany, New York 12203, USA (Received May 2013; accepted November 2013; published online 11 November 2013) The Schottky barrier heights of both n and p doped Cu/Si(001), Ag/Si(001), and Au/Si(001) diodes were measured using ballistic electron emission microscopy and ballistic hole emission microscopy (BHEM), respectively Measurements using both forward and reverse ballistic electron emission microscopy (BEEM) and (BHEM) injection conditions were performed The Schottky barrier heights were found by fitting to a linearization of the power law form of the Bell-Kaiser BEEM model The sum of the n-type and p-type barrier heights are in good agreement with the band gap of silicon and independent of the metal utilized The Schottky barrier heights are found to be below the region of best fit for the power law form of the BK model, demonstrating its region of validity C 2013 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License [http://dx.doi.org/10.1063/1.4831756] I INTRODUCTION Metal/semiconductor Schottky barrier diodes are of high scientific and technological importance as they are widely utilized in power applications due to their low turn on voltage, capacitance, and recovery time1 and are a promising candidate for next generation solar cells.2 The Schottky barrier height (SBH) in a n-type semiconductor is the energy offset of the conduction band minimum with respect to the metal’s Fermi level at the interface For a p-type semiconductor, it is the energy offset of the valance band maximum with respect to the metal’s Fermi level at the interface The sum of the n and p Schottky barrier heights is then equal to the band gap of the semiconductor The standard Schottky-Mott model of the barrier height equates it to the difference between the work function of the metal and the electron affinity of the semiconductor.3 Other effects must be added to get a more accurate prediction such as image forces, metal induced gap states, and interface defects, which can be sensitive to the fabrication process.4 Models based upon interface dipoles have been developed that give a better prediction of the barrier height.5, Experimentally, the Schottky barrier height should increase with the work function of the metal and the sum of the barrier heights of n-type and p-type diodes fabricated under similar conditions with the same metal should be equivalent to the band gap of the semiconductor Powerful techniques to measure Schottky barrier heights are ballistic electron emission microscopy (BEEM) and (BHEM) They are three terminal scanning tunneling microscopy (STM) techniques introduced by Bell and Kaiser in late 1980’s.7–9 BEEM (BHEM) is performed by injecting hot electrons (holes) into a grounded metal film deposited onto the surface of a semiconductor Electrons (holes) with energy greater than the SBH are collected at the semiconductor and are measured as (BEEM) (BHEM) current The SBHs for many metal/semiconductor systems have been extensively studied using BEEM and BHEM.10–27 With BEEM the tip can be positioned with a Electronic address: vlabella@albany.edu 2158-3226/2013/3(11)/112110/20 3, 112110-1 C Author(s) 2013 112110-2 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) nanoscale resolution giving spatially resolved spectra and barrier heights, which has been performed for Au/GaAs(001) diodes where a Gaussian distribution of barrier heights was observed in support of interface dipole models.27 The power law form of the Bell and Kaiser model is the standard method for extracting the Schottky barrier height from the BEEM spectra This form of the model assumes zero temperature and shows deviations from the data near the threshold.26 One way to further quantify this effect is to linearize the data and utilize the band gap of the substrate as a metric for quality of fit since the Schottky barrier height can vary depending upon processing conditions A few studies have measured both n and p SBHs using the same fabrication conditions Bell and coworkers measured both n and p Au/Si(001) barriers heights and found the sum to be in good agreement with the band gap of silicon.9, 28 Che et al introduced a novel four-terminal ambipolar BEEM/BHEM technique where the carrier type and density was controlled via electrostatic doping of the silicon using a back gate.29 They report that the sum of the n and p, Au/Si(001) and Cu/Si(001) Schottky barrier heights were in good agreement with each other and independent of the metal.29 In this article, measurements of both the n and p type SBHs for Cu/Si(001), Ag/Si(001), and Au/Si(001) diodes are performed using both minority and majority carrier injection modes of BEEM and BHEM A linear fitting method, not sensitive to an initial guess, was utilized to extract the SBH The sums of the n and p barrier heights are found to be in good agreement with the band gap of silicon and independent of the metal It was also found that forward biasing fits using the BK model (n = 2) gave the best fit to the spectra and the best agreement with the band gap of silicon II EXPERIMENTAL Copper, silver, and gold Schottky diodes were fabricated under ultra high vacuum (UHV) using n-type and p-type Si(001) single crystal wafers with a resistivity of 100 -cm (phosphorus doped) and 10 -cm (boron doped), respectively The native oxide layer was removed utilizing a standard chemical hydrofluoric acid treatment immediately prior to loading into a UHV (10−10 mbar) deposition chamber.17, 22 The metal films were deposited onto the silicon surface using standard Knudsen cells through a mm by mm shadow mask The thickness of the metal films was 40 nm for all samples The copper and silver layers were capped with an additional 10 nm thick gold layer to inhibit oxide formation Deposition rates were calibrated using ex situ Rutherford backscattering spectrometry (RBS) After deposition, the sample was mounted onto a custom designed sample holder for BEEM and BHEM measurements The plate allowed for simultaneous grounding of the metal film using a BeCu contact and connection of the silicon to the ex situ pico- ammeter to measure the BEEM and BHEM current Ohmic contacts were established by cold pressing indium into the silicon substrate A modified low temperature UHV STM (Omicron) was utilized for all BEEM and BHEM measurements with a pressure in the 10−11 mbar range.30 The samples were inserted into the UHV chamber and loaded onto the STM stage that was cooled to 80 K for all measurements Twopoint current-voltage measurements were taken in situ for each sample at low temperatures using a Keithley 2400 source measurement unit to verify rectifying behavior All measurements were taken in the absence of ambient light Pt/Ir STM tips, mechanically cut at a steep angle, were utilized for all BEEM and BHEM measurements The experiment is shown schematically in Fig BEEM and BHEM spectra were acquired for both negative (hot-electron injection) and positive (hot-hole injection) tip biasing conditions using a constant tunneling current set-point of 10.0 nA Both forward and reverse spectra were taken at the same tip position every 50 nm throughout a 2.5 μm by 2.5 μm area of the metal surface This resulted in 2,500 spectra for each biasing condition that were then averaged into a single representative spectrum for each sample and biasing condition III RESULTS Current-voltage (IV) spectroscopy results for all the diodes are displayed in Fig The IV plots indicate rectification and a negative turn-on voltage for the n-type diodes and positive turn on voltage for the p-type diodes Schottky barrier heights were extracted by fitting IV data to the diode equation and are in good agreement with previously published values for IV measurements.3 112110-3 Balsano, Matsubayashi, and LaBella y z AIP Advances 3, 112110 (2013) x STM tip VTIP ITIP metal semiconductor IBEEM FIG BEEM and BHEM wiring schematic Forward BEEM (a) e Forward BHEM (b) p-type semiconductor - VTIP EF tip EF VTIP n-type vac metal semiconductor + tip VTIP h vac metal VTIP ITIP (c) IBEEM Reverse BEEM e h VTIP ITIP (d) - p-type semiconductor - e - e VTIP + EF h + tip IBHEM Reverse BHEM h n-type vac metal semiconductor VTIP tip EF + vac metal VTIP ITIP IBEEM ITIP IBHEM FIG Band diagrams for (a) forward BEEM, (b) forward BHEM, (c) reverse BEEM, and (d) reverse BHEM The BEEM and BHEM data is described grouped by forward and reverse tip biasing conditions Forward tip biasing is when semiconductor majority carriers are injected into the metal and measured in the semiconductor collector region For example, electrons are injected into the metal and electrons are measured in the n-type semiconductor as depicted in Fig 2(a) If holes are injected into the metal, holes are measured in the p-type semiconductor as depicted in Fig 2(b) Reverse tip biasing is when semiconductor minority carriers are injected into the metal but majority carriers are measured at the semiconductor collector region due to an Auger-like conversion process at the interface.28 If holes are injected into the metal, electrons are collected at the n-type semiconductor as demonstrated by 112110-4 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) -3 10 -4 Current (A) 10 10 10 Cu/n-Si(001) (80 K) -5 -7 -8 10 -3 (a) -6 10 10 Current (A) 10 10 Cu/p-Si(001) (80 K) (d) -5 -7 10 -9 10 -9 -10 10 -11 10 -11 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 10 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Bias (V) Bias (V) -1 10 Ag/n-Si(001) (80 K) 10 -3 Ag/p-Si(001) (80 K) -3 (b) 10 10 Current (A) Current (A) 10 -5 -7 10 -7 -9 -11 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 10 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Bias (V) 10 Bias (V) -6 Au/n-Si(001) (80 K) -2 10 10 (c) -8 10 -9 (f) -4 10 10 -6 -8 10 -10 10 -11 10 Au/p-Si(001) (80 K) -7 Current (A) Current (A) 10 (e) -5 10 10 -9 -11 10 10 -10 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Bias (V) 10 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Bias (V) FIG Current-voltage (IV) data for Cu, Ag, and Au Schottky diodes for both n-type (a)–(c) and p-type (d)–(f) Si(001) taken at 80 K Fig 2(c) When electrons are injected into the metal, holes are collected at the p-type semiconductor as depicted in Fig 2(d) These are referred to as forward BEEM and BHEM and reverse BEEM and BHEM, respectively The barrier heights are extracted by fitting to I B ∝ (φb − Vt )n , where n is an exponent given by the BK (n = 2) and Prietsch Ludeke (PL) (n = 5/2) models for forward biasing 112110-5 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) conditions and BK (n = 4) and PL (n = 9/2) for reverse biasing conditions The transmission is linearized by taking its absolute value and raising it to the n1 power A Forward BEEM & BHEM results Forward BEEM spectra for copper, silver, and gold films grown on n-type silicon substrates are presented in Figs 4–6 (a), respectively At low tip bias, measurable transmission is not observed As the tip bias nears the SBH the transmission increases The positive transmission and positive tip bias in units of eV indicate that electrons are being injected and collected as BEEM current Figs 4–6 (b)&(c) are the data linearized with n = and n = 5/2 as previously described and the best fit line (solid) with its extrapolation (dashed line) indicating the SBHs The forward BHEM spectra for copper, silver, and gold on p-type silicon are displayed in Figs 7–9 (a), respectively No measurable transmission is observed at low tip biases and then it decreases as the energy of the injected holes nears the SBH Here, negative transmission represents positive current and collection of holes at the BHEM collector and negative tip bias in units of eV indicates holes are being injected Figs 7–9 (b)&(c) are the data linearized as described above for n = and n = 5/2 with a linear fit line (solid) and its extrapolation (dashed line) indicating the SBHs The barrier heights with the R2 values of the fits for forward BEEM and BHEM and their sums are given in Table I B Reverse BEEM & BHEM Results Reverse BEEM spectra for copper, silver, and gold on n-type substrates are shown in Figs 10–12 (a), respectively The negative tip bias in units of eV indicates the injection of holes and the positive transmission indicates electrons are collected as BEEM current The transmission increases very gradually as the tip bias nears the SBH Figs 10–12 (b)&(c) are the data linearized with n = and n = 9/2 as previously described with the best fit line (solid) and its extrapolation (dashed line) indicating the SBHs Reverse BHEM data for p type substrates with films of copper, silver, and gold are shown in Figs 13–15 (a), respectively The positive tip bias in units of eV indicates the injection of electrons Near the SBH, the transmission decreases very gradually Here the negative transmission indicates the collection of holes as BHEM current Figs 13–15 (b)&(c) are the data linearized with n = and n = 9/2 as previously described and the best fit line (solid) with its extrapolation (dashed line) indicating the SBHs The barrier heights with the R2 values of the fits for reverse BEEM and BHEM and their sums are given in Table II IV DISCUSSION The fitting is performed utilizing a linearization of the power law form of the Bell and Kaiser model I B E E M /IT i p = A(Vti p − φ B )n , where A is the proportionality constant that accounts for scattering, Vti p is the tip bias, φ B is the Schottky barrier height, and n is the exponent as previously 1 described This is linearized and rewritten into point slope form I B E E M /IT i p n = A n Vti p − A n φ B , where the absolute value has been added to account for negative collector currents as observed in BHEM This is fit using linear regression This model is applicable over ∼ 0.2 eV, and a starting tip bias must be found first where the BEEM current initially increases This is accomplished by starting at the maximum transmission and successively comparing several adjacent points in the spectra and stopping at the first point where the slope changes sign or becomes zero for lower tip biases The data above this point is then linearized and successively fit for all biases above this point over a 0.2 eV window The best fit has the maximum R2 value and a Schottky barrier height that is within the fit window of the starting bias of the fit This can result in barrier heights and BEEM currents below the starting point of the fit as displayed in the figures It was found that increasing the fit window size reduces the R2 value and alters the barrier height by a few thousandths of an eV overall the samples studied 112110-6 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) Cu/n-Si(001) (80 K) 100 (%) IBEEM/ITIP (a) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.9 Cu BEEM Cu Fit (n=2) (|IBEEM/ITIP| 100 (%)) 1/2 0.8 0.7 0.6 0.5 0.4 0.3 b = 0.62 eV (b) 0.2 0.1 0.0 0.5 0.6 0.7 0.8 0.9 1.0 0.8 Cu BEEM Cu Fit (n=5/2) 100 (%)) 2/5 0.7 0.6 0.5 (|IBEEM/ITIP| 0.4 0.3 b = 0.59 eV 0.2 (c) 0.1 0.0 0.4 0.5 0.6 0.7 0.8 0.9 Tip Bias (eV) FIG (a) Forward BEEM spectra of Cu on n-type Si (001) (b) Spectra linearized to BK (n = 2) model showing the SBH (c) Spectra linearized to PL (n = 5/2) model showing the SBH 112110-7 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) 2.0 100 (%) Ag/n-Si(001) (80 K) 1.5 IBEEM/ITIP 1.0 0.5 (a) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.6 Ag BEEM Ag Fit (n=2) 100 (%)) 1/2 0.5 0.4 (|IBEEM/ITIP| 0.3 0.2 b = 0.66 eV (b) 0.1 100 (%)) 2/5 0.0 0.4 0.6 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Ag BEEM Ag Fit (n=5/2) 0.5 0.4 (|IBEEM/ITIP| 0.3 0.2 b = 0.61 eV (c) 0.1 0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Tip Bias (eV) FIG (a) Forward BEEM spectra of Ag on n-type Si (001) (b) Spectra linearized to BK (n = 2) model showing the SBH (c) Spectra linearized to PL (n = 5/2) model showing the SBH 112110-8 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) Au/n-Si(001) (80 K) IBEEM/ITIP 100 (%) (a) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 1.4 Au BEEM Au Fit (n=2) 100 (%)) 1.0 (|IBEEM/ITIP| 1/2 1.2 0.6 0.8 b = 0.84 eV 0.4 (b) 0.2 0.0 0.7 0.8 0.9 1.0 1.1 1.2 1.4 Au BEEM Au Fit (n=5/2) (|IBEEM/ITIP| 100 (%)) 2/5 1.2 1.0 0.8 0.6 b = 0.83 eV 0.4 (c) 0.2 0.0 0.7 0.8 0.9 1.0 1.1 1.2 Tip Bias (eV) FIG (a) Forward BEEM spectra of Au on n-type Si (001) (b) Spectra linearized to BK (n = 2) model showing the SBH (c) Spectra linearized to PL (n = 5/2) model showing the SBH 112110-9 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 -6 (a) -8 1.2 1.0 0.8 0.6 = 0.51 eV (b) b 0.4 1/2 1.4 100 (%)) Cu BHEM Cu Fit (n=2) -10 (|IBHEM/ITIP| Cu/p-Si(001) (80 K) IBHEM/ITIP -4 100 (%) -2 0.2 0.0 -0.6 -0.5 -0.4 Cu BHEM Cu Fit (n=5/2) 1.4 1.2 1.0 0.8 b 0.6 = 0.48 eV 0.4 (c) 2/5 -0.7 100 (%)) -0.8 (|IBHEM/ITIP| -0.9 0.2 0.0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 Tip Bias (eV) FIG (a) Forward BHEM spectra of Cu on p-type Si (001) (b) Spectra linearized to BK (n = 2) model showing the SBH (c) Spectra linearized to PL (n = 5/2) model showing the SBH 112110-10 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 -6 -8 (a) -10 IBHEM/ITIP -4 100 (%) -2 -12 Ag/p-Si(001) (80 K) -14 1.0 0.4 = 0.50 eV (b) 0.2 -0.6 -0.5 0.0 -0.3 0.9 -0.4 Ag BHEM Ag Fit (n=5/2) 0.8 0.7 0.6 0.5 0.4 b = 0.45 eV 0.3 (c) 0.2 2/5 -0.7 100 (%)) -0.8 (|IBHEM/ITIP| b 100 (%)) 0.6 (|IBHEM/ITIP| 0.8 1/2 Ag BHEM Ag Fit (n=2) 0.1 0.0 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 Tip Bias (eV) FIG (a) Forward BHEM spectra of Ag on p-type Si (001) (b) Spectra linearized to BK (n = 2) model showing the SBH (c) Spectra linearized to PL (n = 5/2) model showing the SBH 112110-11 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 -15 (a) -20 IBHEM/ITIP -10 100 (%) -5 -25 Au/p-Si(001) (80 K) -30 1.5 b = 0.33 eV (b) 1.0 0.5 1/2 100 (%)) 2.0 (|IBHEM/ITIP| Au BHEM Au Fit (n=2) 2.5 0.0 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 2.5 b = 0.31 eV (c) 1.0 0.5 100 (%)) 1.5 (|IBHEM/ITIP| 2.0 2/5 Au BHEM Au Fit (n=5/2) 0.0 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Tip Bias (eV) FIG (a) Forward BHEM spectra of Au on p-type Si (001) (b) Spectra linearized to BK (n = 2) model showing the SBH (c) Spectra linearized to PL (n = 5/2) model showing the SBH 112110-12 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) TABLE I Barrier heights for both n-type and p-type substrates as measured by forward BEEM and BHEM and their sums The uncertainty is 0.02 eV, which was computed from the linear regression For reference the Eg of Si is 1.1669 eV p p Metal n φbn (eV) R2 φb (eV) R2 φbn + φb (eV) Cu Ag Au 2 5 0.62 0.66 0.84 1.000 1.000 0.999 0.51 0.50 0.33 1.000 1.000 0.999 1.13 1.16 1.18 0.59 1.000 0.48 0.999 1.07 0.61 1.000 0.45 1.000 1.07 0.83 0.997 0.31 0.998 1.14 Cu Ag Au The benefits of the linear fitting technique is that it does not require an initial estimation of the fitting parameters, as in non-linear fitting routines, which can impact the results It was found that generally the R2 values for forward BEEM and BHEM were greater than those for reverse BEEM and BHEM This is attributed to the smaller signal to noise ratio for reverse BEEM and BHEM as the signal is about ten times smaller than for forward BEEM and BHEM The linear regression also computed an uncertainty of 0.02 eV to the Schottky barrier height across all the samples and is quoted as the measured uncertainty of the barrier heights Schottky barrier heights from each individual spectra were also computed and showed a Gaussian distribution in their values centered on Schottky barrier height of the average spectra with a standard deviation of about 0.2 eV This is similar to BEEM measurements of Au/GaAs(001) diodes and in support of interface dipole models of the barrier height.5, 27 The appearance of transmission below the barrier height and deviations from the linearization near the barrier are due to limitations of the power law form of the BK model This form assumes zero temperature and parabolic conduction band in the semiconductor Finite temperature effects contribute to the appearance of the measured BEEM current below the predicted Schottky barrier heights.26 In addition, the inclusion of tunneling can also give rise to transmission below the barrier and is one reason why the PL model fits (n = 5/2) result in lower barrier heights overall Interestingly the sub threshold current is lowest for Au and is most significant for Cu This is attributed to differences in interface bonding and hot electron transport through the diode, since all these were measured at the same temperature and with the same tip material The value of the barrier heights measured here are in good agreement with what has been measured before with BEEM, with the exception of Ag/p-Si which, to the best of our knowledge, has not been published before In addition, The n- type barrier heights decrease and the p-type barriers increase with decreasing work function of the metal as reported in Table I & II, which is consistent with theoretical models of the Schottky barrier height.5 However, Schottky barrier height values can vary depending upon processing and fabrication conditions of the diode and therefore are not the best figure to judge the quality of the fitting or the model utilized The band gap of the substrate is more fundamental and a better number to compare to since it has been measured using optical methods to be 1.1669 eV at 77 K for Si.31 The sum of the p and n type barriers tabulated in the tables are in good agreement with the gap and independent of the metal overlayer It appears that fits using n = give the best agreement to the gap and best R2 values overall Generally the sum of the barrier heights are a few hundredths of an eV lower than the band gap, which can be a result of the effect of image force lowering of the Schottky barrier which would decrease the sum of the measured barrier heights The depletion fields, E for theses junctions is force estimated to be × 103 V/cm for n-type diodes and × 103 V/cm for p- type diodes The image √ lowering of the barrier height for both p and n silicon was calculated using e × I F L = e eE/4π s , where s is 11.6 The sum of the p and n lowering is ≈0.02 eV.3 It appears that fits performed using the BK model (n = and n = 4) give higher barrier height, better agreement with the band gap, and better R2 values overall The silicon utilized is highly resistive, which would have a large depletion width and suppress the quantum mechanical tunneling 112110-13 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) Cu/n-Si(001) (80 K) 1.4 0.8 0.6 (a) 0.4 IBEEM/ITIP 1.0 100 (%) 1.2 0.2 0.0 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.4 0.3 0.25 1/4 0.35 100 (%)) Cu BEEM Cu Fit (n=4) b 0.15 = 0.57 eV (b) 0.1 (|IBEEM/ITIP| 0.2 0.05 0.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 0.5 b 0.2 = 0.54 eV (c) 0.1 100 (%)) 0.3 (|IBEEM/ITIP| 0.4 2/9 Cu BEEM Cu Fit (n=9/2) 0.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 Tip Bias (eV) FIG 10 (a) Reverse BEEM spectra of Cu on n-type Si (001) (b) Spectra linearized to BK (n = 4) model showing the SBH (c) Spectra linearized to PL (n = 9/2) model showing the SBH 112110-14 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) 0.3 Ag/n-Si(001) (80 K) 0.2 100 (%) 0.25 0.1 (a) IBEEM/ITIP 0.15 0.05 0.0 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.3 0.25 0.2 100 (%)) 1/4 Ag BEEM Ag Fit (n=4) b = 0.62 eV 0.1 (b) (|IBEEM/ITIP| 0.15 0.05 0.0 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 0.2 100 (%)) 0.25 2/9 0.3 Ag BEEM Ag Fit (n=9/2) b = 0.59 eV 0.1 (c) 0.05 (|IBEEM/ITIP| 0.15 0.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 Tip Bias (eV) FIG 11 (a) Reverse BEEM spectra of Ag on n-type Si (001) (b) Spectra linearized to BK (n = 4) model showing the SBH (c) Spectra linearized to PL (n = 9/2) model showing the SBH 112110-15 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) 0.6 Au/n-Si(001) (80 K) 0.3 0.2 (a) IBEEM/ITIP 0.4 100 (%) 0.5 0.1 0.0 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.4 Au BEEM Au Fit (n=4) 0.25 100 (%)) 0.3 1/4 0.35 b 0.15 = 0.82 eV (b) 0.1 (|IBEEM/ITIP| 0.2 0.05 0.0 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 0.5 b = 0.79 eV (c) -1.1 -1.0 -0.9 -0.8 -0.7 0.2 0.1 100 (%)) 0.3 (|IBEEM/ITIP| 0.4 2/9 Au BEEM Au Fit (n=9/2) 0.0 -0.6 Tip Bias (eV) FIG 12 (a) Reverse BEEM spectra of Au on n-type Si (001) (b) Spectra linearized to BK (n = 4) model showing the SBH (c) Spectra linearized to PL (n = 9/2) model showing the SBH 112110-16 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 IBHEM/ITIP 100 (%) -0.2 -0.4 -0.6 (a) -0.8 -1.0 Cu/p-Si(001) (80 K) ( | IBHEM/ITIP | 100 (%)) 1/4 -1.2 0.3 Cu BHEM Cu Fit (n=4) 0.25 0.2 0.15 0.1 b = 0.40 eV (b) 0.05 0.0 0.3 0.4 0.5 0.6 0.7 0.8 ( | IBHEM/ITIP | 100 (%)) 2/9 0.4 Cu BHEM Cu Fit (n=9/2) 0.35 0.3 0.25 0.2 0.15 b = 0.37 eV 0.1 (c) 0.05 0.0 0.2 0.3 0.4 0.5 0.6 0.7 Tip Bias (eV) FIG 13 (a) Reverse BHEM spectra of Cu on p-type Si (001) (b) Spectra linearized to BK (n = 4) model showing the SBH (c) Spectra linearized to PL (n = 9/2) model showing the SBH 112110-17 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0 IBHEM/ITIP 100 (%) -0.2 -0.4 -0.6 (a) -0.8 -1.0 Ag/p-Si(001) (80 K) -1.2 0.35 Ag BHEM Ag Fit (n=4) 100 (%)) 0.25 (|IBHEM/ITIP| 1/4 0.3 0.15 0.2 b = 0.43 eV 0.1 (b) 0.05 0.0 0.3 0.4 0.5 0.6 0.7 0.8 0.4 Ag BHEM Ag Fit (n=9/2) 100 (%)) 2/9 0.35 0.3 0.25 (|IBHEM/ITIP| 0.2 0.15 b = 0.46 eV 0.1 (c) 0.05 0.0 0.3 0.4 0.5 0.6 0.7 0.8 Tip Bias (eV) FIG 14 (a) Reverse BHEM spectra of Ag on p-type Si (001) (b) Spectra linearized to BK (n = 4) model showing the SBH (c) Spectra linearized to PL (n = 9/2) model showing the SBH 112110-18 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 IBHEM/ITIP 100 (%) -1 -2 -3 -4 -5 -6 (a) -7 -8 -9 Au/p-Si(001) (80 K) 0.8 Au BHEM Au Fit (n=4) 100 (%)) 1/4 0.7 0.6 0.5 (|IBHEM/ITIP| 0.4 0.3 b = 0.32 eV (b) 0.2 0.1 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Au BHEM Au Fit (n=9/2) 100 (%)) 2/9 0.7 0.6 0.5 (|IBHEM/ITIP| 0.4 0.3 b = 0.30 eV 0.2 (c) 0.1 0.0 0.2 0.3 0.4 0.5 0.6 0.7 Tip Bias (eV) FIG 15 (a) Reverse BHEM spectra of Au on p-type Si (001) (b) Spectra linearized to BK (n = 4) model showing the SBH (c) Spectra linearized to PL (n = 9/2) model showing the SBH 112110-19 Balsano, Matsubayashi, and LaBella AIP Advances 3, 112110 (2013) TABLE II Barrier heights for both n-type and p-type substrates as measured by reverse BEEM and BHEM and their sums The uncertainty is 0.02 eV, which was computed from the linear regression For reference the Eg of Si is 1.1669 eV p p Metal n φbn (eV) R2 φb (eV) R2 φbn + φb (eV) Cu Ag Au 4 9 0.57 0.62 0.82 0.999 0.991 0.998 0.40 0.43 0.32 0.995 0.997 0.999 0.97 1.05 1.14 0.54 0.999 0.37 0.960 0.91 0.59 0.989 0.46 0.914 1.05 0.79 0.998 0.30 0.999 1.09 Cu Ag Au that is included in the PL model that gives rise to the extra 1/2 power in the exponent.32 The agreement with the gap suggests that the interface effects which alter the n and p Schottky barrier heights are similar and occur in a manner that preserves the gap Similar processing conditions are utilized to fabricate the diodes and the carrier type is a small structural perturbation that has dramatic effects on the conductivity of the bulk silicon It is not expected to have a significant impact on the bonding at the interface that gives rise to the defects and charge traps which can affect the barrier height V CONCLUSION A linearized algorithm was utilized to fit BEEM and BHEM data for Cu, Ag, and Au metal films on Si(001) The sum of the n and p Schottky barrier heights from this fitting was shown to be in good agreement with the band gap of the semiconductor and independent of the metal The linearized fitting does not require an initial estimation of the fitting parameters, and 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