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

LaBellaa College of Nanoscale Science and Engineering, SUNY, Albany, New York 12203, USA Received 7 May 2013; accepted 4 November 2013; published online 11 November 2013 The Schottky bar

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

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The physics and chemistry of the Schottky barrier height

AIP Advances 1, 011304011304 (2014); 10.1063/1.4858400

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 7 May 2013; accepted 4 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 andballistic hole emission microscopy (BHEM), respectively Measurements using bothforward and reverse ballistic electron emission microscopy (BEEM) and (BHEM)injection conditions were performed The Schottky barrier heights were found byfitting 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 heightsare found to be below the region of best fit for the power law form of the BKmodel, 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

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, andrecovery time1and are a promising candidate for next generation solar cells.2The 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 ofthe metal and the electron affinity of the semiconductor.3Other effects must be added to get a moreaccurate prediction such as image forces, metal induced gap states, and interface defects, which can

be sensitive to the fabrication process.4Models based upon interface dipoles have been developedthat give a better prediction of the barrier height.5,6 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 croscopy (BEEM) and (BHEM) They are three terminal scanning tunneling microscopy (STM)techniques introduced by Bell and Kaiser in late 1980’s.7 9BEEM (BHEM) is performed by inject-ing 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 aremeasured as (BEEM) (BHEM) current The SBHs for many metal/semiconductor systems havebeen extensively studied using BEEM and BHEM.10–27With BEEM the tip can be positioned with

mi-a Electronic address: vlabella@albany.edu

2158-3226/2013/3(11)/112110/20 3, 112110-1 Author(s) 2013

nanoscale resolution giving spatially resolved spectra and barrier heights, which has been performedfor 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 standardmethod for extracting the Schottky barrier height from the BEEM spectra This form of the modelassumes zero temperature and shows deviations from the data near the threshold.26 One way tofurther quantify this effect is to linearize the data and utilize the band gap of the substrate as a metricfor 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.29They 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 BEEMand 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 (10−10mbar) deposition chamber.17,22The metal films were deposited onto the silicon surface using standardKnudsen cells through a 2 mm by 1 mm shadow mask The thickness of the metal films was 40 nmfor 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 sampleholder 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 thesilicon substrate

A modified low temperature UHV STM (Omicron) was utilized for all BEEM and BHEMmeasurements with a pressure in the 10−11mbar range.30The samples were inserted into the UHVchamber and loaded onto the STM stage that was cooled to 80 K for all measurements Two-

point 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 utilizedfor all BEEM and BHEM measurements The experiment is shown schematically in Fig.1 BEEMand BHEM spectra were acquired for both negative (hot-electron injection) and positive (hot-holeinjection) tip biasing conditions using a constant tunneling current set-point of 10.0 nA Both forwardand reverse spectra were taken at the same tip position every 50 nm throughout a 2.5μm by 2.5 μm

area of the metal surface This resulted in 2,500 spectra for each biasing condition that were thenaveraged 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 3 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

semiconductor metal

STM tip

z x y

VTIP

ITIP

IBEEMFIG 1 BEEM and BHEM wiring schematic.

tip vac metal n-typesemiconductor

FIG 2 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 whensemiconductor minority carriers are injected into the metal but majority carriers are measured at thesemiconductor 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

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 ∝ (φ b − V t)n , where n is an exponent given by the BK (n = 2) and Prietsch Ludeke (PL) (n = 5/2) models for forward biasing

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 the1

n 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 positivetip 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 = 2 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 itdecreases as the energy of the injected holes nears the SBH Here, negative transmission representspositive current and collection of holes at the BHEM collector and negative tip bias in units of eVindicates holes are being injected Figs.7 9(b)&(c) are the data linearized as described above for

n = 2 and n = 5/2 with a linear fit line (solid) and its extrapolation (dashed line) indicating the SBHs The barrier heights with the R2values of the fits for forward BEEM and BHEM and their sums aregiven in TableI

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 holesand the positive transmission indicates electrons are collected as BEEM current The transmissionincreases very gradually as the tip bias nears the SBH Figs.10–12(b)&(c) are the data linearized

with n = 4 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 indicatesthe collection of holes as BHEM current Figs.13–15(b)&(c) are the data linearized with n= 4

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 R2values of the fits for reverse BEEM and BHEMand their sums are given in TableII

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 /I T i p = A(V ti p − φ B)n , where A is the proportionality constant that accounts for scattering, V ti pis the tip bias,φ B is the Schottky barrier height, and n is the exponent as previously

described This is linearized and rewritten into point slope formI B E E M /I T i p1

at the maximum transmission and successively comparing several adjacent points in the spectra andstopping at the first point where the slope changes sign or becomes zero for lower tip biases Thedata above this point is then linearized and successively fit for all biases above this point over a0.2 eV window

The best fit has the maximum R2value 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 startingpoint of the fit as displayed in the figures It was found that increasing the fit window size reduces

the R2value and alters the barrier height by a few thousandths of an eV overall the samples studied

(b)

(c)

0 1 2 3 4 5 6

(|IBEEM/ITIP

(|IBEEM/ITIP

FIG 4 (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.

(b)

(c)

0.0 0.5 1.0 1.5 2.0

(|IBEEM/ITIP

(|IBEEM/ITIP

FIG 5 (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.

(b)

(c)

0 1 2 3 4 5 6

(|IBEEM/ITIP

(|IBEEM/ITIP

FIG 6 (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.

(b)

(c)

-10 -8 -6 -4 -2 0

(|IBHEM/ITIP

(|IBHEM/ITIP

FIG 7 (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.

(b)

(c)

-14 -12 -10 -8 -6 -4 -2 0

(|IBHEM/ITIP

(|IBHEM/ITIP

FIG 8 (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.

(b)

(c)

-30 -25 -20 -15 -10 -5 0

(|IBHEM/ITIP

(|IBHEM/ITIP

FIG 9 (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.

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 Egof Si is 1.1669 eV.

an uncertainty of 0.02 eV to the Schottky barrier height across all the samples and is quoted as themeasured uncertainty of the barrier heights Schottky barrier heights from each individual spectrawere also computed and showed a Gaussian distribution in their values centered on Schottky barrierheight of the average spectra with a standard deviation of about 0.2 eV This is similar to BEEMmeasurements of Au/GaAs(001) diodes and in support of interface dipole models of the barrierheight.5,27

The appearance of transmission below the barrier height and deviations from the linearizationnear the barrier are due to limitations of the power law form of the BK model This form assumeszero temperature and parabolic conduction band in the semiconductor Finite temperature effectscontribute to the appearance of the measured BEEM current below the predicted Schottky barrierheights.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 isattributed to differences in interface bonding and hot electron transport through the diode, since allthese 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 TableI&II, which isconsistent with theoretical models of the Schottky barrier height.5However, Schottky barrier heightvalues can vary depending upon processing and fabrication conditions of the diode and thereforeare not the best figure to judge the quality of the fitting or the model utilized The band gap of thesubstrate is more fundamental and a better number to compare to since it has been measured usingoptical methods to be 1.1669 eV at 77 K for Si.31The 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 = 2 give the best agreement to the gap and best R2values overall

Generally the sum of the barrier heights are a few hundredths of an eV lower than the bandgap, which can be a result of the effect of image force lowering of the Schottky barrier which woulddecrease the sum of the measured barrier heights The depletion fields, E for theses junctions is

estimated to be 8× 103V/cm for n-type diodes and 3× 103V/cm for p- type diodes The image force lowering of the barrier height for both p and n silicon was calculated using e ×  I F L = e√e E/4π s,where sis 11.60 The sum of the p and n lowering is≈0.02 eV.3

It appears that fits performed using the BK model (n = 2 and n = 4) give higher barrier height, better agreement with the band gap, and better R2 values overall The silicon utilized is highlyresistive, which would have a large depletion width and suppress the quantum mechanical tunneling