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\newcommand{\commentC}[1]{ {\color{green} #1}} % AB - Alexey Bolshakov
\newcommand{\commentD}[1]{ {\color{magenta} #1}} % DP - Dmitry Permyakov
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\title{Influence of Au film surface morphology on optical phonons emission in a localized tunnel contact\\
Влияние свойств поверхности пленок золота на эмиссию оптических фотонов из локализованного туннельного контакта}

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\rtitle{Влияние свойств поверхности золота\dots} % TODO

% article title - for table of contents (usualy identical with \title)
\sodtitle{Влияние свойств поверхности золота на эмиссию оптических фотонов из локализованного туннельного контакта}


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% author(s) ( + e-mail)
\author{%
  В.\,А.\,Школдин$^{a, b}$ \thanks{e-mail: shkoldin@spbau.ru},
  Д.\,В.\,Пермяков$^{a}$ \thanks{e-mail: d.permyakov@metalab.ifmo.ru},
  К.\,С.\, Ладутенко$^{a}$,
  М.\,В.\,Жуков$^{a,c}$,
  А.\,А.\,Васильев$^{b}$,
  А.\,О.\,Голубок$^{a,c}$,
  А.\,В.\,Усков$^{a,d}$,
  А.\,Д.\,Большаков$^{b}$,
  А.\,А.\, Богданов$^{a}$,
  A.\, Bouhelier$^{e}$
  А.\,К.\,Самусев$^{a}$,
  и И.\,С.\,Мухин$^{a,b}$
}

% author(s) - for colontitle (at the top of the page)
%\rauthor{Д.\,В.\,Пермяков, И.\,С.\,Синев, С.\,К.\,Сычев, А.\,А.\,Богданов, А.\,В.\,Лавриненко and А.\,К.\,Самусев}
\rauthor{В.\,А.\, Школдин, Д.\,В.\,Пермяков, и др.}

% author(s) - for table of contents
\sodauthor{Школдин, Пермяков, Жуков, Васильев, Мамаева, Голубок, Усков, Самусев, Большаков, Мухин}

%%% author's address(es)
\address{%
$^a$ Университет ИТМО, 199034, Санкт-Петербург, Россия\\
$^b$ Санкт-Петербургский Академический университет РАН, 194021, Санкт-Петербург, Россия\\
$^c$ Институт аналитического приборостроения РАН, 198095, Санкт-Петербург, Россия\\
$^d$ Физический институт им.~П.Н. Лебедева РАН, 119991, Москва, Россия\\
$^e$ Université Bourgogne Franche-Comté
}

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\abstract{ In this paper, we study light emission in a tunnel contact between the tip of the scanning tunneling microscope tungsten probe covered with Au and Au film on glass substrate at ambient conditions. Dependence of the emission efficiency on the Au film surface morphology is investigated. Analysis of the experimental data demonstrates strong influence of the Au surface grains aspect ratio on the optical emission intensity in the tunnel contact. Maximum photon emission efficiency is obtained with the use of singular nearly atomically flat monocrystalline Au surface.
The observed phenomenon relates to dependence of the tunnel contact effective area on inverse square of the Au grain aspect ratio. The obtained results demonstrate critical contribution of the surface roughness in the tunnel contact in photonic emission efficiency.

}

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\begin{document}
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\maketitle

%\section{Introduction}

The ever-growing rate of transfer and processing of the digital data necessitates permanent improvement of the computational devices aimed at enhancement of their performance and decrease of the energy consumption. Modern established technologies allows fabrication of the processors based on traditional integrated circuit with data transfer via electronic signal processing. Performance of these devices is close to the theoretical limit nowadays. One of the perspective ways to overcome the existing limitation is transition to the optical logic. With this approach to transfer the data photons and surface plasmon-polaritons are used. The advantages of the technology involves faster data transfer due to higher speed of the photons in optical waveguides compare to speed of the electrical signal in the metal wires leading to higher operational frequencies. This approach allows to reduce quantity of the metal wires and consequently to decrease Joule heating in the devices leading to fall of the energy consumption.

To realize the transition to the integrated optoelectronic circuits apart from development of the logic elements, amplifiers, receivers and waveguides the development of localized photonic and plasmonic electrically driven emitters have to be carried out. Semiconductor laser with Fabry-Perot resonator and micro disc laser are examples of such emitters. However, efficiency of these resonators is sufficiently reduced with their dimensions below the operating wavelength
~\cite{somelink}\commentD{нужна
  ссылка}\commentB{
Считается как-бы очевидным. Тут можно только на
  учебник какой-нибудь. Сошлемся на учебник Жукова (есть ли он на английском есть}. \commentA{
Moreover, these systems are not applicable for development of the single-photon emitters used in quantum telecom solutions.
} 
Thereby, traditional laser emitters do not satisfy the requirements of the optoelectronic IT cicuits.


One of the promising directions for development of the sub-micron-sized photonic emitter is the use of tunnel electrical contact. In a pioneer work~\cite{lambe1976light} the effect of light emission during the inelastic electron tunneling in a planar metal-dielectric-metal (M-D-M) structure with a thin potential barrier was demonstrated for the first time. As was demonstrated in several theoretical and experimental works ~\cite{schneider2010optical} [правильные ссыли] the light emission in this system is related to quantum oscillations of the tunnel current. The emission has broad spectral range and in a single-electron approximation, the photon energy is limited with a potential energy determined with the bias applied to the tunnel gap.

In~\cite{gimzewski1989enhanced} it was demonstrated that when a tunnel contact is realized between a metal tip of a scanning probe and a metal layer an enhanced photon emission is related with increase of the local density of optical states (LDOS) in the region under the probe tip. In this system tunnel contact has a size of few nanometers and can be considered as far-subwavelength-sized photonic source (including single photon emission potential) driven electrically.

Quantum yield of the photon emission in the discussed process is sufficiently low with an efficiency at the level of ($10^{-6}-10^{-4}$). To enhance probability of the photon or plasmon emission an optical nanoantenna having sub-wavelength size can be localized in a gap under the probe tip \cite{parzefall2017antenna}. In~\cite{Greffet2016nanoantenna} it was demonstrated theoretically that placement of a metal nanoantenna under the STM probe tip leads to narrowing of the optical emission spectrum in a tunnel junction and enhances quantum yield of the photon and plasmon emission for more than 2 orders of magnitude. In addition, an amplification of a planar metal structure electroluminescence with a placement of spherical Au nanoantenna in a tunnel gap was demonstrated experimentally in \cite{kern2015electrically}.

	In this work, we study influence of Au film surface properties on the photon emission efficiency in a tunnel gap under STM probe tip. Investigation of the surface morphology effects on emission is an extremely important problem on the way to development of efficient local light sources.
    
% Универсальным прибором для изучения туннельного контакта, является
% сканирующий туннельный микроскоп (СТМ). При работе с СТМ, для
% создания М-Д-М контакта используются металлический зонд и
% металлическая пленка на поверхности образца. При исследовании
% обсуждаемого эффекта важное значение имеет тот факт, что СТМ
% позволяет варьировать различные параметры туннельного
% контакта. Например, напряжение смещения влияет на спектр
% излучения\cite{gimzewski1989enhanced}. В данной работе показано, что
% кроме характеристик туннельного контакта, на квантовую эффективность
% излучающего контакта влияет морфология поверхности металлической
% пленки.

\section{Experimental setup and studied samples}

In this work, a tunnel gap was realized in a simple system of STM probe and a thin Au film deposited on a glass substrate. The probe was fabricated of a 150~mkm tungsten wire with electrochemical etching in KOH solution followed with thermal evaporation of a $\sim$30~nm thick Au layer with Cr adhesive underlayer on the probe tip. The tip characteristic radius of about 100~nm was controlled with scanning electron microscopy (SEM).

	In our experimental series 150~mkm thick glass wafers covered with (15-50)~nm thick Au layers with Cr underlayer were studied. Each of the sample differed from the others in technological parameters of Au deposition process affecting the morphology of the synthesized film surface. To verify the experimental data we fabricated test sample of 300nm thick crystalline gold film deposited on mica??? substrate. 

\begin{figure}[t]\centering
	\includegraphics[width=0.95\linewidth]{ExpSetup.eps}
	\caption{
		\label{rissetup}
		\textbf{Рис.~\ref{rissetup}.}  Experimental setup schematics. STM with integrated inverted optical microscope. Tunnel current flows between the tip of STM probe and Au film, deposited on glass substrate.  
                \commentA {Нужна сюда же картинка от Кости с двумя характерными геометриями островков с существенно разным аспектным отношением и площадью контакта. Типа artistic view. См. письмо от 19.07.2018 17:58.}
                }
\end{figure}

AIST-NT CombiScope – STM with integrated inverted optical microscope was used to study light emission in a tunnel junction. Typically, the emission collection from the gap was realized under the glass substrate covered with Au. To capture the light high aperture Olympus 100х, NA=0.95 lens was used. Single photon detector IDQ ID120 based on avalanche photodiode was used in our experiments. The setup schematics is presented in Fig.~\ref{rissetup}.

\section{Experimental results}
Emission of photons in a tunnel junction takes place if a non-zero ($V_b$) bias is applied to the contacts. During the electron tunneling an elastic and inelastic processes take place. In the first case, an electron saves its energy after the tunneling through the potential barrier, and in the latter case, part of the energy is lost during the tunneling. Probability of the photon emission is much higher with the inelastic tunneling. Schematic of the tunnel junction band diagram and spectral density $C(\omega)$ of the tunnel current fluctuations with time (!!!временных флуктуаций туннельного тока!!!) defining the photon emission spectrum \cite{kern2015electrically}, that can be expressed as $C(\omega) = (eV_b - h\omega)$, are presented in Fig.~\ref{risEnergyDiagrammTunCont}. The emission spectrum in a tunnel junction depends on several parameters, e.g. material of the contacts and value of the applied bias~\cite{berndt1991inelastic}. In the single-particle process having the highest probability during the tunneling process the photon energy is limited \KL{в наиболее вероятном одночастичном процессе фотон не рождается, доля неупругого туннелирования $10^-5$} \commentA {(Не совсем понятно к чему относится это замечание?)} with the bias value according to the: $\hbar\nu_o = |eV|$, - where $\nu_o$ is a threshold frequency~\cite{lambe1976light}. Hence, to obtain emission in the visible range we need to apply (1.5-3)~V bias.

\begin{figure}[t]\centering
	\includegraphics[width=0.95\linewidth]{EnergyDiagramm.eps}
	\caption{
		\label{risEnergyDiagrammTunCont}
		\textbf{Рис.~\ref{risEnergyDiagrammTunCont}.}  Band diagram of a tunnel junction between two metals: $I$ --- probe with Au-coated tip, $II$ --- potential barrier region, $III$ --- Au film, $E^1_F, E^2_F$ --- Fermi level in the regions I and III, correspondingly, $L$ --- gap between the probe tip and the sample, $E_1, E_2$ --- electron energy before and after the tunneling, $V_b$ --- applied bias. Process (a) corresponds to elastic tunneling and (b) --- inelastic tunneling with partial electron energy loss.
              }
\end{figure}

Our study was intentionally carried out in ambient conditions to provide peculiarities in the STM operation. Normally, the sample surface is covered with a thin water layer (less than 1nm thick)~\cite{somelink}\, ~\cite{gomez2003field} and when the tip approaches the surface a meniscus appears in between~\cite{gomez2003field}. When the applied bias value exceeds 1.23~V water molecules decompose with the following formation of ions~\cite{senftle2010low}. Consequently, current between Au film and STM probe tip has two contributions: tunnel current and ionic current of electrochemical nature. The photon emission relates to the tunnel current fluctuations, while, occurrence of the ionic current is a parasitic effect that negatively affects the tunnel contact stability~\cite{rogez2016mechanism}.

Stability \comment{Может все таки "Значение" , а не "стабильность"?} of the total current is maintained with the microscope feedback system. The system drives the scanner movement along Z axis to promote constant value of the current. Three operating modes of the STM operating at ambient conditions and high applied bias can be distinguished~\cite{rogez2016mechanism}: <<stable current>> mode, <<unstable current>> mode providing fluctuations of the tunnel current and <<threshold>> mode with excited feedback \comment{ ОС возбуждена }. In the latter mode scanner promotes fast approach of the probe tip to the sample and when large current passing through the probe occurs the feedback system immediately brakes the contact moving the probe from the sample. As a result, oscillations of the gap size occur consequently leading to the \comment{tunnel} current oscillations while the total integral current value remains constant. It was demonstrated that the <<threshold>> regime provides maximum photon emission efficiency~\cite{rogez2016mechanism}. In our experimental series the maintained total current value was 165~nA with applied bias value of 2.2~V and the probe oscillation frequency was 52~Hz.

Prior to the photon emission study the samples surface morphology was investigated with atomic-force microscope (AFM). The obtained images (not presented in the paper) \KL{Почему? Очень интересно было бы увидеть картинки для образцов 3 и 5, которые почти не отличаются по толщинам, но
  радикально по эффективности эмиссии.}) \KL{Без картинок оно не} demonstrate 3D structure of the film surface with specific grain geometry for each of the sample. \commentA{По мне, так нормальная фраза. Я бы не приводил АСМ картинки. Иначе нужно приводить все 6 штук, и на них реально хрен чего разглядишь. Таблица намного информативнее} Parameters of the samples morphology: grains mean diameter ($D_{grain}$), height ($Z_{grain}$), their aspect ratio ($A$), mean surface roughness ($R_a$) and the deposited metal films thickness ($h_{Cr}$,$h_{Au}$), - are presented in Table~\ref{tabExpData}. 

According to the experimental setup (see Fig. ~\ref{rissetup}) the emission is collected after it passes through the substrate. In this geometry, part of the emission is absorbed and reflected. To obtain optical and geometrical parameters of the studied samples the transmission spectra were measured (see Fig.~\ref{risTransmission}a). \KL{Светло-серые линии соответствуют экспериментальным данным, поверх них наложены более гладкие черные линии, полученные в расчёте методом матриц переноса в коммерческом пакете ... (a правда им?).} \commentB{пакет TFCalc. Пираченый, но можно уточнить, и договориться с Тидексом} \KL{Экспериментальные кривые аппроксимировались с использованием двух подгоночных параметров для каждого образца: толщины слоев хрома и золота. Частотные дисперсии хрома и золота были взяты из литературы \cite{olmon2012optical}. В результате с высокой точностью удалось восстановить значения толщин слоев металлов для каждого из образцов, см. таблицу~\ref{tabExpData}. Например, для образцов №3 и №5 общая толщина нанесённого покрытия отличается менее чем на 2~нм, однако этого достаточно для видимых различий в спектрах пропускания.} Resonant enhancement of the transmission in the spectral region close to 530nm relates with the features of Au dielectric function dispersion \KL{\sout{[нужна ссыль]} есть выше}. According to the experimental data (see Table~\ref{tabExpData}) the integral transmission coefficient manly depends on the total thickness of the deposited metal layers, rather than on their surface morphology features.

During the investigation of the emission efficiency in our experimental series we used the same STM probe with the same tunnel contact parameters \commentC{а что такое параметры тун контакта?} and feedback system setup for each of the samples. To verify reproducibility of the experimental data we first measured the emission of the sample 5 (providing the maximum intensity). We then carried out the study of the samples 1 to 4 and after that investigated the sample 5 again. The repeated measurement of the latter sample emission demonstrated good proximity to the initial measurement results. Thus, we conclude that the probe was not modified sufficiently during the experimental series. The normalized value of the measured mean photon emission efficiency $I_n$ in the tunnel junction is presented in Table~\ref{tabExpData}. The measured emission intensity was normalized over the transmission coefficient at 740~nm wavelength (see Fig. .~\ref{risTransmission}a). This value was chosen, according to the analysis of the reference data on Au-Au STM tunnel contact photon emission spectra obtained with similar experimental setup~\cite{parzefall2017antenna}.

	The obtained data presented in Table~\ref{tabExpData} demonstrates that correlation between the Au film surface morphology features and tunnel gap emission intensity exists. Increase of the Au grains lateral dimension leads to rise of the emission intensity. Similar dependence is obtained with decrease of the grains mean height $Z_{avg}$. The most pronounced relation is the dependence of the emission intensity on the aspect ratio $A$ calculated as $Z_{avg}$ divided by the grain diameter $D_{grain}$. Decrease of the grains aspect ratio dramatically increases the emission intensity.

In our study we investigated the emission in the tunnel gap obtained with 300~nm thick monocrystalline Au film representing the utmost case of the film as parameter $A$ approaches zero. In this case, generated photons cannot penetrate the substrate so collection of the emission was obtained directly from the gap with the use of long-focus lens installed aside the STM at an angle of 25$^\circ$ relative to the substrate surface. To provide correct comparison of the measurement results obtained with different geometries of the lens installation the intensity of the emission registered with monocrystalline gold was normalized over the intensity of the sample 5 emission measured with the same lens installation setup. The experimental data demonstrates that the photon emission efficiency can be increased by an order of magnitude with the use of monocrystalline Au (see Table~\ref{tabExpData}).


\begin{figure}[t]\centering
	\includegraphics[width=0.95\linewidth]{Transmission_of_Au_films.eps}
	\includegraphics[width=0.95\linewidth]{FDTD-spectra.eps}
	\caption{
		\label{risTransmission}
		\textbf{Рис.~\ref{risTransmission}.}  Light transmission spectra of the different thickness Au films. а) Experimental and theoretical curves obtained numerically with the use of the transfer-matrix method for collimated beam, b) FDTD modeling results for dipole source. The curves numbering corresponds to Table~\ref{tabExpData}. }
\end{figure}

% \begin{figure}[t]\centering
% 	\includegraphics[width=0.95\linewidth]{AFM.eps}
% 	\caption{
% 		\label{risAFM}
% 		\textbf{Рис.~\ref{risAFM}.}
% 		АСМ-изображение участка поверхности пленки золота на образце~№3.
% 	}
% \end{figure}



\begin{table}[ht]
\centering
\begin{tabular}{@{}lccccrr@{}} \toprule %{|c|c|c|c|c|c|c|}
\textbf{N}  & \textbf{$h_{Cr}$} & \textbf{$h_{Au}$} & \textbf{$D_{grain}$} & \textbf{$Z_{avg}$}& \textbf{A} &  \textbf{$I_n$ } \\
  & {nm} & {nm}     & {nm}         & {nm}   & {nm}        &  \\ \midrule
1 & 5,6  & 47       & 32           & 14     & 0,44        & 0,15\%          \\
2 & 6,1  & 43       & 40           & 14     & 0,35        & 0,44\%          \\
3 & 4,0  & 27       & 40           & 4      & 0,10        & 2,65\%         \\
4 & 4,6  & 16       & 60           & 4      & 0,068       & 3,76\%         \\
5 & 2,7  & 26       & 84           & 2,8    & 0,033       & 100\%      \\
\midrule
SC$^a$  & - & 300 &$\rightarrow\!\infty$ & $\rightarrow\! 0$& $\rightarrow \! \infty$ & 900\%$^b$ \\ \bottomrule
\end{tabular}
\caption{
   \label{tabExpData} 
   \textbf{Table \ref{tabExpData}.} Parameters of the samples and experimental data. a) monocrystalline Au, b) the measured value obtained with the lens installed at an angle of $25^\circ $ relative to the substrate surface and normalized over the intensity of the sample 5 emission measured with the same lens installation setup.  }
%        \textbf{Таблица 1.} Параметры образцов и экспериментальные данные}
\end{table}

\section{Numerical modeling results}

As was discussed in the previous section to compare the emission efficiencies of the samples we normalized the measured intensity values considering differences in transparency of the samples. The transmission coefficients were measured at normal incidence of the collimated beam. At the same time, emission in STM tunnel junction is equivalent to emission of a vertical dipole localized in the tunnel gap~\commentA{[ссылка Андрей? Grefet] }. Moreover, in this orientation dipole does not emit light strictly perpendicular to the substrate surface. So how the emission was captured with the lens in experiment?


Modeling of the dipole emission was carried out with the use of two methods: finite difference time-domain [Lumerical FDTD https://www.lumerical.com/] and T-matrix methods [Smuthi http://smuthi.readthedocs.io, Amos Egel, Siegfried W. Kettlitz, and Uli Lemmer, "Efficient evaluation of Sommerfeld integrals for the optical simulation of many scattering particles in planarly layered media," J. Opt. Soc. Am. A 33, 698-706 (2016)]. The FDTD modeling results are presented in Fig.~\ref{risTransmission}b. These results are in good agreement with the calculations carried out with T-matrix and transfer-matrix methods shown in Fig. ~\ref{risTransmission}a. \comment {А почему не представлены результаты для метода Т-матриц? Может просто написать, что полученные результаты были также подтверждены методом Т-Матриц}


To ensure correct comparison of the modeling results with experimental data we considered collection of the dipole emission with the lens having a given aperture. Worth noting that despite difference in integration region: with FDTD we calculated the energy flow in the near-field along part of the plane overlapping the aperture while with T-matrix method we carried out integration along angle in far field, - similar results were obtained. 

Good agreement between the transmission of the dipole emission and of the collimated beam through the same substrate is a fact of interest. The ratios of the different samples spectra were similar for two mentioned cases while their absolute values were different. The latter fact is due to consideration of only part of the emission collected with the lens aperture in case of the transmission calculation with the dipole source. With this approach, only the wave vectors having dominating component in the direction perpendicular to the sample surface are considered which is qualitatively similar to transmission of a planar wave. Because in our modeling we normalized the calculated transmitted emission value over the integral dipole emission spectrum in vacuum the absolute values obtained with dipole source are smaller than the corresponding values for collimated beam. Thus, we conclude that normalization of the intensity over the transmission spectra is proper for straightforward comparison of the emission efficiencies in tunnel gaps of different samples.


Special attention should be payed to the results of the sample 5 and monocrystalline gold spectra modeling obtained with the lens installed aside the tunnel gap. For these samples energy collected with the lens aperture in spectral range corresponding to the photon emission from the gap is almost the same with only 10 to 30\% difference. In other words, difference in efficiency of the radiation output from the gap for these two samples does not relate to 9-fold gain in the detected optical signal. 



\section{Discussion}

	Worth noting broad range of the photon emission efficiency obtained experimentally in our work: with the same tunnel current, the measured intensity can be varied for almost four orders of magnitude depending on the sample, while morphological parameters are insufficiently changed for only few times.

	Comparison of the results obtained with samples 3 and 5 demonstrates that despite similar thickness of the Au film and moderate (two times) difference in the grain dimensions the emission intensity is $\sim$37 times different.

The tunnel current plays the main role in the photon emission intensity. The obtained difference in the radiation of the samples can be related with variation of the current and with different emission output efficiency from the gap (Purcell factor)\cite{purcell1995spontaneous}.

Results of the numerical modeling allow to state the following claims:

\begin{itemize}
\item Material properties of Au film and Cr sublayer do not depend on the deposition technique parameters – the spectra obtained experimentally can be approximated with high accuracy in a broad range of wavelengths using the transfer-matrix method with only two fitting parameters – thickness of Au and Cr layers. 

\item 	Neglecting the films surface roughness the near-field effects do not influence the emission efficiency. Independent calculations carried out with the use of FDTD and T-matrix methods demonstrate that Purcell factor for the dipole source (equivalent of the tunnel gap – source) does not change sufficiently in our samples. With these calculations sample 1 having maximum thickness of Au film and sample with monocrystalline Au possess almost identical spectral dependencies of Purcell factor.

\item Circumstance that the measured transmission spectra are well described with the model of the structure with flat interfaces of the metal films, allows to claim that occurrence of surface features having the size smaller than wavelength do not result in resonant optical effects. Due to that, antenna effects providing additional local enhancement of electromagnetic field and Purcell effect \commentC{[ссылка на Парселл в туннельных токах]} do not contribute in emission efficiency in the studied system.

\item Normalization of the optical signal over the measured transmission spectra for comparison of the photon emission in a tunnel gap of different samples is straightforward. This claim is stipulated with good agreement of the ratios of the calculated transmission spectra in the model with the dipole source and experimental data.

\item 	Comparison and renormalization of the data obtained in two different geometries (transmission and reflection) are straightforward. In spectral region, corresponding to the emission in a gap, energy flow collected with aperture installed aside the gap does not differ sufficiently between the samples with thin Au film and monocrystalline Au in the model with the same dipole source parameters.

\end{itemize}

	The stated above claims approve that difference in the photon emission intensity is not related with the radiation output efficiency form the tunnel gap. Quantity of emitted photons in a tunnel gap is governed with the tunnel current value and can be varied in a broad range depending on the sample properties and mainly – on its surface roughness.
    
\begin{figure*}[t]\centering
	\includegraphics[width=0.95\linewidth]{islands.eps}
	\caption{
		\label{risIslands}
		\textbf{Рис.~\ref{risIslands}.}  
        Influence of the Au islands shape on the contact effective area.
        }
\end{figure*}


	It is well known, that the tunnel current density depends exponentially on the gap size. One of the parameters of this exponential dependence is electron wave function decay length in isolator:
$\kappa^{-1} = [2m(eV_b-\varepsilon_{F})]^{-1/2}$\cite{harrison1961tunneling}, where $m$ -- electron mass, $\varepsilon_{F}$ -- Fermi level of electron in metal. The maximum current value is obtained with a zero gap corresponding to short circuit. 

	In earlier work\cite{krylov1985electron} it was demonstrated that tunnel current (as well as short circuit current) between the two metal surfaces is proportional to the contact effective area $S$. If one of the surfaces is 3D structured with typical island (or grain) height $a$ and radius $b$ this area can be expressed as $S \propto (b / \kappa a)^2 = (\kappa A)^{-2}$, where $A=a / b$ - grain aspect ratio. 

In Fig. ~\ref{risIslands} it is demonstrated schematically how does the contact effective area increases with decrease of the grain height ($\kappa a$) and with increase of its diameter $b$. Worth mentioning that the model is correct while the grain size is much lower than the probe tip radius. In the case of a smooth sample surface corresponding to monocrystalline Au the major impact on the contact area has the probe tip shape. 

	The considerations above allow to explain the experimental results presented in Table~\ref{tabExpData}. Fast growth of the tunnel current together with increase of the emission intensity more than two orders of magnitude is obtained with decrease of the grains aspect ratio $A$ (see samples 1 to 5). When the probe approaches atomically flat surface of monocrystalline Au film the emission efficiency limited in this case only with the tip curvature increases another order of magnitude.  

\commentA{РЕБЯТА! ОЧЕНЬ НУЖЕН SEM ТОГО САМОГО ЗОНДА!!!}
\commentB{Есть SEMы 12 зондов, один из которых был использован в этом эксперименте. какой именно - к сожалению, не известно.}


\section{Conclusions}
In this paper, photon emission in a tunnel gap between the probe of STM and Au films surface having different morphology was studied. We demonstrate experimentally that increase of the Au grains mean diameter as well as decrease of their height leads to sufficient increase of the emission intensity in the gap that can be tailored in a broad range covering four orders of magnitude. The obtained phenomenon is explained via crucial influence of the surface geometry on effective area of a tunnel contact which is inversely proportional to square of the grain aspect ratio.

	We conclude that improvement of the sample surface quality can be used for enhancement of the photon emission intensity in a tunnel gap. Due to low quantum yield of the emission in the tunneling process the results of the paper have critical impact on development of effective single photon emitters – elemental base components for optoelectronic chips.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Acknowledgements
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Экспериментальные измерения были выполнены при финансовой поддержке Российского научного фонда (грант \# 15-12-20028). Численный расчет был выполнен при финансовой поддержке РФФИ (грант \#17-02-01234).
%Работы были выполнены при финансовой поддержке Российского научного фонда (грант \# 15-12-20028).
Авторы выражают благодарность Артуру Глейму и Семену Смирнову за
помощь в проведении экспериментальных измерений.


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%% References
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\bibliography{STM-Electroluminescence}
\bibliographystyle{jetpl}


% \begin{thebibliography}{10}
% 	\providecommand{\selectlanguage}[1]{\relax}

% 	\bibitem{tamir2013guided}
% 	T.~Tamir, G.~Griffel, and H.~L. Bertoni.
% 	\newblock {\em Guided-Wave Optoelectronics: Device Characterization, Analysis,
% 		and Design\/}.
% 	\newblock Springer Science \& Business Media, 2013.
	
% \end{thebibliography}

\end{document}


\commentA{НЕВЕРНО:
\sout{
1. Quenching and hot spots 
2. Red shift due to aspect ratio increase
3. Crystalline gold: siriously supressed quenching due to islands absence
Для понимания полученные экспериментальных данных вначале обсудим
влияние свойств поверхности для тонких не кристаллических пленок. Как
известно, зерна золота имеют свои локализованные плазмонные резонансы
[правильная ссыль], при которых наблюдается усиление электромагнитного
излучения на границах зерен (hot spots). Ввиду наличия слоя золота и
бианизотропии подложки hot spots в основном локализованы в области
золотой пленки, а не в воздухе, что приводит к существенному
поглощению энергии, связанному с оптическими потерями золота и
Джоулевым нагревом. Понятно, что чем меньше диаметр зерен, тем больше
плотность hot spots на поверхности золота. Таким образом, увеличение
диаметра зерна золота должно приводить к уменьшению оптических потерь,
и как следствие к увеличению интенсивности излучения туннельного
контакта.
	Как показано в работах [...] аспектное отношение для зерен серебра и
золота влияет на спектральное положение оптических резонансов
зерен. Увеличение аспектного отношения приводит к смещению данных
резонансов в длинноволновую область. При этом известно, что мощность
изучения туннельного контакта увеличивается при увеличении длины волны
и максимум излучения находится в диапазоне около 750 нм. Таким
образом, при изменении аспектного отношения зерен меняется перекрытие
спектра мощности излучения и спектра рассеяния зерен золота, связанных
с наноантенными эффектами. Таким образом, увеличение аспектного
отношения зерен золота может приводить к более эффективному перекрытию
двух явлений и усилению интенсивности излучения туннельного контакта.
	И в конце рассмотрим случай кристаллического золота. Можно
предположить, при переходе к экспериментальной схеме с боковым сбором
фотонов существенную роль будет играть толщина пленки золота, при
увеличении которой увеличивается отражение от образца, и как следствие
вероятность рожденных фотонов быть собранными объективом. Проведенное
нами численное моделирование (см. саплементари) показало, что для
пленок с характерными толщинами 26 нм и 150 нм (5-ый и SC образцы,
соответственно), усиление фактора Парселла для излучения точечного
оптического диполя, расположенного в непосредственной близости над
образцом, и усиление коэффициента отражения фотонов от поверхности
пленки практически не имеет место (менее 20 процентов). Таким образом
усиления интенсивности излучения туннельного контакта под острием СТМ
над кристаллическим золотом связано с отсутствием зерен и как
следствие hot spots в пленке золота. Другими словами, в
кристаллическом золоте меньше оптические потери по сравнению с
зернистыми тонкими пленками, полученными термическим осаждением.
}
}