Pavesi photonics applications of nano silicon

Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học

Frontiers in Optical Technology, edited by P K Choudhury and O N Singh

Photonics applications of nano-silicon

In this chapter we will review the photonic applications of nanostructured silicon As we change the dimensionality

of silicon very fascinating and new optical properties of the material appear In particular, light emission starts to

be a very efficient process in nanostructured silicon and light emitting diodes with efficiency in excess of 1% have been fabricated Optical amplification has been also observed when silicon nanocrystals are embed into a dielectric matrix This makes the system a potential candidate for laser action In addition to electronic property variations, nanostructured silicon can be also used as a nanodielectric material, where controlled changes in the refractive index can lead to trapping or slow down of photons Some examples will be discussed where photonic Bloch oscillations, photonic Zener tunnelling and high quality microcavities are demonstrated All these various phenomena paves the way to a new field of applications for the "old dog" of microelectronics

1 INTRODUCTION

Low dimensional silicon is a fascinating material which still has many unfold properties The main motivation to study silicon comes from its success and dominance in modern technology, especially in microelectronics Indeed nanometre sized transistors are now switching in computers at working frequency exceedingly few GHz Convergence between microelectronics and telecommunications is looked for in order to couple the computing power of microprocessor with the transmission power of optical fibers In this effort, merging of various semiconductor technologies is attempted in order to improve on one side the optical properties of microelectronic materials and, on the other side, to reduce the cost of photonic devices With this respect silicon photonics is playing a key role We have already reviewed in the past several aspects of this emerging technology [1] In this chapter we aim to give an overview of our recent work towards the exploitation of low dimensional silicon to tune on one side its electronic properties and on the other side its dielectric properties

Figure 1 The De Broglie wavelength of an electron at 300 K

Let us define which dimensional scale we are concerned with If one computes the De Broglie wavelength of

electrons in silicon one notices that it is about 5 nm (Fig 1) So in this paper we are concerned with very tiny

amount of silicon whose size is only a few nanometre If the structure conserves a crystalline character we will call

it silicon nanocrystals, if not we will call it silicon nanoclusters In many instances this distinction is purely academic,

so we will refer simply to Si-nc, meaning that we are not concerned by the crystalline or amorphous character of

the particle

This chapter is organized in three sections: the first is about the way to produce Si-nc and the modification of its

electronic structure caused by the low-dimension, the second is about the improved optical properties of silicon

which are observed when it is reduced to small particles, and the third is about the optical properties caused by the

variation in its dielectric structures

2 LOW DIMENSIONAL SILICON

The best way to understand the effects of the reduced dimensionality on the energy spectrum of an electron is to

resort to the particle-in-a-box problem so familiar in quantum mechanics Within the effective mass approximation

in the envelope wave function description, the transition energy of an electron-hole pair of effective reduced mass

µ confined in a quantum dot of sizes Lx, Ly, Lz is

where we have assumed that the confining energy barrier is of infinite strength and that EG is the energy band gap

of the bulk semiconductor, nx,ny,nz are quantum numbers to describe a given quantized energy level Equation 1

shows that the effective energy band-gap of the quantum dot increases as the quantum dot dimension decreases

(Fig 2) When the dot is spherical with a diameter d, the transition energy scales with a 1/d2 law More accurate

calculations show that the scaling law does not follow an exact power 2 law but instead the exponent is lower [2] A

value of 1.7-1.8 seems to be more appropriate

Figure 2 Optical gap in Si quantum wells, wires, and dots versus system diameter The transition energy is

calculated for the lowest electron and heavy hole energies for infinite confining potentials From [3]

The assumption of having an infinite potential barrier is very crude since Si-nc are usually formed in a dielectric

matrix The matrix is usually a silica glass SiO2 but more recently the use of Al2O3, Si3N4 or of oxynitride (SiON) is

emerging as an alternative Also the effective mass approximation has strong limitation since the reconstruction of

the lattice in the dots caused by the strain and the different elastic properties of the host should be considered

Finally, chemical bonds among the surface Si atoms of the Si-nc and the atoms of the host, strongly modify the

energy spectrum of Si-nc An example of a theoretical calculation is shown in Fig 3

Fig 3 (a) Electronic energy gap as a function of the number of Si atoms for different bond configurations (b)

Electronic energy gap as a function of the number of Si=O double bonds at the cluster surface Circles: Si10Hn=Om,

squares: Si14Hn=Om, and triangles:Si35Hn=Om After [4]

In addition to the variation of the energy spectrum, also the wavefunctions of the electron and of the hole are

influenced by the quantum confinement in the dot Overlap of the wavefunctions in real space and spreading of

them in the k-space causes an increase in the optical transition probability (Fig 4)

Figure 4 Spread of the electron and hole wavefunction in a quantum dot (left) and calculated radiative lifetime

versus size for silicon quantum dots (right) The line corresponds to phonon-assisted recombination and the points

to phonon-less recombination After [5]

A quite indirect effect of the reduced dimensionality of Si-nc is the reduction of the effective refractive index n of the

composite matrix where the Si-nc are formed Indeed in a simple scheme one can consider that the refractive index

is an average of the refractive index of Si-nc and of the host matrix Thus, a composite layer formed by Si-nc with a

large refractive index of 3.5 dispersed in a matrix such as SiO2 with a refractive index of 1.45 has a smaller

refractive index than bulk silicon The exact value depends on the Si-content in the film and on the composition of

the host dielectrics A simple approximation is usually used, the Bruggeman approximation [6], where it is assumed

that small particles of silicon are dispersed in an host of dielectric function εM:

f is the volumetric fraction of Si and ε is its dielectric function With this formula n= εeff can be calculated The reduction in the refractive index has a positive influence when the Si-nc are used to enhance the emission efficiency of silicon In fact, the extraction efficiency of light from a material depends on its refractive index: the

smaller n is the larger is the light gathered

Figure 5 Silicon nanocrystal fabrication techniques The three lower techniques produce Si-nc in a SiO2matrix After [7] Various ways have been used in the past to form low dimensional silicon (Fig 5) We can divide them into three main approaches: 1 direct synthesis of silicon cluster, 2 formation of a silicon rich layer and subsequent thermal induced phase separation and 3 electrochemical erosion of bulk silicon

2.1 DIRECT SYNTHESIS OF SILICON CLUSTERS

Silicon nanoclusters can be directly synthesized by chemical reactions of suitable reactants Methods of synthesis

of Si colloids include pyrolysis of Si2H6 [8], formation by laser induced plasma in SiH4 [9], combustion of SiH4 [10], gas evaporation of Si [11] and controlled nucleation inside inverse micelles [12].The end product is a colloidal suspension of Si-nc in a solvent which usually is ethanol

Another way is to deposit Si-nc on a substrate after their formation in a molecular beam [13] Within this approach one can also mass filter the cluster in the cluster beam by time of flight methods which ends-up with a size selection of the clusters However during the deposition it is not clear whether the cluster remains isolated or collapses with the formation of large amass of Si-nc

2.2 SILICON CLUSTERS PRODUCED BY PHASE SEPARATION

The formation of Si-nc by phase separation of a silicon rich dielectrics is the most widely used approach Various techniques have been employed to form the sub-stoichiometric dielectric: ion implantation, plasma or low-pressure chemical vapour deposition(PE-CVD or LP-CVD), sputtering, and silicon evaporation The differences among them are related to the degree of purity of the film (better for ion implanted samples), to the degree of defects incorporated, to the porosity of the deposited films (which is known is greater for the sputtered samples), to the control of the Si-nc content profile (better for the CVD films) After deposition the films are thermally treated at high temperature to induce the phase separation between silicon and the dielectrics At the used temperatures, silicon diffusivity is large enough to cause clustering but it is small enough to avoid significant bulk reconstruction This balance is clearly dependent on the annealing temperature For example if SiO2 is used as the dielectric, typical temperatures for the formation of Si-nc are between 900 – 1200oC At the lower temperatures the Si-nc do not crystallize Temperatures larger than 1000oC are necessary to form small crystallites [14]

Figure 6 reports the evolution of the crystalline fraction as a function of the annealing temperature While the Si-nc gets more crystalline, their size increases but their density stays almost constant Only at the highest temperatures collapse among Si-nc occurs and the density decreases The phase separation is not complete, which means that the density of Si-nc is lower than the number which results by taking into account all the excess silicon deposited in

the film This in turn means that the host is not formed by pure SiO2 but by either a SiOx or by a composite oxide with a larger Si content near the Si-nc [15]

Figure 6 (a) Crystalline fraction (obtained from the comparison of energy filtered TEM and standard TEM), (b) density of Si-nc (obtained from EFTEM images), (c) concentration of clustered Si atoms and (d) density of amorphous (na) and crystalline (nc) Si-nc, as a function of the annealing temperature The lines are drawn to guide the eye From [14]

Figure 7 (left) Fabrication of amorphous SiO/SiO2 superlattice and thermally induced phase separation and crystallization (right) Cross-sectional transmission electron microscope image of layer-arranged Si crystals (3 nm) closely separated by oxide After [17]

The main problem related to these techniques of fabrication is the lack of control on the size dispersion of the Si-nc: large dispersion of sizes, larger than 25%, is usually obtained Recently a method to avoid this dispersion has been proposed [16] By depositing controlled thicknesses of Si rich amorphous silica layers separeted by pure silica layers, and by subsequent annealing treatments, Si-nc are formed whose size is fixed by the initial thickness

of the Si-rich silica layers

2.3 ELECTROCHEMICAL ETCHING OF SILICON

In 1990 a paper boosted the research on low dimensional silicon [18] This paper reported on intense room-temperature visible luminescence from porous silicon (PS) due to quantum confinement effects Porous silicon is obtained by the electrochemical etching of silicon in an HF rich electrolyte [19] Following the partial wafer dissolution a porous structure is formed where the silicon skeleton is composed either by interconnected Si-nc or

by thin silicon wires What is astonishing in this processing is the fact that the etching process is self-regulated: once the porous layer is formed no further etching of the porous layer occurs The reason for this is the depletion of holes in the etched region of the samples In fact holes need to be exchanged with the electrolyte to achieve dissolution of Silicon For this reason the process is performed in the dark for p-type silicon while it needs illumination for n-type silicon (Fig 8) Care has to be taken to limit the anodic current to values lower than the electropolishing current, above which electropolishing of the silicon occurs and the final layer has a mirror-like aspect without any porous silicon on it

Figure 8 Typical I-V characteristics of an electrochemical cell for porous silicon fabrication The hashed region corresponds to the useful regime where porous silicon can be achieved, assuming the I-V characteristic marked with hollow circles In the anodic regime, the characteristics of a cell with n-type Si will lay in the region bounded by the characteristic in dark (dashed line) and in full light (hollow circles)

Figure 9 Examples of PS structures: microporous (left), mesoporous (center) and macroporous (right)

The current as well as the doping of the wafer control the size of the pores, and in turn the size of the low dimensional silicon in the silicon skeleton The higher is the wafer resistivity the smaller the Si-nc sizes A rough measure of the Si-nc size is given by the porosity of the layers: porosity is defined as the void density in the film

Porosity Etching rate Electropolishing threshold

In addition, by suitable techniques, it is possible to form colloidal suspension of Si-nc by crumbling it into small particles Si nanocrystal solutions have been obtained by sonication of p-Si in acetonitrile and toluene, in acetone

and other solvents For in vivo applications, however, it would be much more interesting to prepare Si-nc in water

since most of their biological applications occur in aqueous environment A simple sonication of naturally oxidized porous layer is shown to produce colloidal suspension in water [21]

3 OPTICAL PROPERTIES OF LOW DIMENSIONAL SILICON

The first motivation to the study of silicon nanocrystals was the hope to get luminescent silicon In fact silicon has

an indirect band-gap which causes a very long radiative lifetime (ms) for excited electron-hole pairs Competing non-radiative recombinations prevail and cause most of the excited electron-hole pairs to recombine non radiatively In addition, when the number of excited electron-holes increases other non-radiative recombination processes start to play a role These are Auger recombinations and free carrier absorption In Auger an electro-hole pair recombines giving the excess energy to a third particle (electron or hole); free carrier absorption is

a process for which the photon is absorbed by free carriers via an intra-band optical transition Both are dependent

on the density of excess free carriers and dominate the recombinations for heavily excited or doped silicon [22]

Figure 10 Schematic diagram of silicon nanocrystals in an amorphous matrix Electron-hole pairs (dots) are locally excited: if the nanocrystal has a recombination centre (star), the electron and hole recombine non-radiatively If the nanocrystal is free of recombination centres, the electron and hole recombine radiatively The system shown in the figure has three electron-hole pairs excited of which one recombines non-radiatively and two radiatively, i e the internal quantum efficiency of this system is 2/3 ~ 67%

The hope in using nanocrystals was to increase the radiative recombination rate by exploiting quantum confinement However another effect improved the emission efficiency of Si-nc This is the spatial localization of excited electron-hole in a small region of the sample If this region has a killer centre, the nanocrystal is dark On the contrary if it is free of killer centres, the nanocrystal is bright and the excited electron-hole recombine radiatively, even though with a long lifetime In this case the system has locally an internal quantum efficiency of 100% This is shown in Fig 10

3.1 LUMINESCENCE

Room temperature emission in Si-nc is routinely observed independently on the preparation method The emission

is usually characterized by a first band centred at about 500 nm whose position is independent on the processing parameters used to form the Si-nc and a second band in the wavelength range 600-900 nm whose exact spectral position depends strongly on the process parameters (Fig 11) The first band is defect related and can be quenched by post-growth passivation with hydrogen It is absent in sample of high quality The second band is related to the presence of the Si-nc: when the Si-nc size decreases due to a low Si-content in the deposited film or

to a low annealing temperature treatments the emission band shifts to the blue On the contrary for high Si-content

in the film or high annealing temperature the emission band shows a red-shift

Figure 11 Schematic diagram of a Si-nc (left) and of the corresponding emission spectrum (right) The influence of the various processing parameters on the emission spectrum is shown by the arrows

Figure 12 The resonant luminescence spectrum of naturally (a) and heavily oxidized (b) porous silicon The arrows show the energy position of Si TA and TO momentum-conserving phonons with respect to the triplet exciton grounds state From [23]

The exact origin of the emission is not clear Certainly quantum confinement effects are playing a crucial role However the role of the surface cannot be discarded As we show in Fig 11, the structure of the Si-nc is formed by three regions: the central region made of amorphous or crystalline silicon, the interface region made of substoichiometric and stressed silica and the embedding amorphous dielectric [15] Resonant photoluminescence experiments have shown a structured emission spectrum which is interpreted in term of crystalline Silicon phonon assisted recombinations (Fig 12) These data are interpreted in the frame of a pure quantum confinement process Other experiments have shown that the emission is strongly dependent on the exposure to ambient oxygen which seems to support a key role played by silicon-oxygen bond in the emission processes (Fig 13) The most reasonable conclusion is that both mechanisms are co-present in Si-nc

Figure 13 Measured photoluminescence spectra in various porous silicon samples before (left) and after (middle) exposure to oxygen air The samples are labelled according to their emission wavelength The average Si-nc size decreases from 4 nm (red) to < 2 nm (blue) Calculated conduction band and valence band energy levels (right) for H-passivated Si-nc and calculated energy levels associated with a trapped electron and a trapped hole at a Si=O bond at the Si-nc surface As the size decreases the band-gap increases by quantum confinement and the Si=O levels appear in the band-gap Zone I, Zone II and Zone III mark the region where the Si-nc emission is predominantly band-to-band (Zone I), involves a trapped electron (Zone II) or involves a trapped electron and a trapped hole (Zone III) After [24]

3.2 ELECTROLUMINESCENCE

From a device point of view, photoluminescence is interesting but much more appealing is electroluminescence where light is generated by current injection into the Si-nc [25] Here the problem is tough since carriers have to pass through a dielectric to excite the Si-nc Indeed in most of the reported device the electroluminescence is produced either by black-body radiation (the electrical power is converted into heat which raises the sample temperature which, in turn, radiates) or by impact excitation of electron-hole pairs in the Si-nc by energetic electrons which tunnel through the dielectric by a Fowler-Nordheim process (see Fig 14)

Electron-hole pairs excited in this way recombine radiatively with an emission spectrum which is very similar to that obtained by photo-luminescence Fowler-Nordheim tunnelling has very peculiar characteristics, such as a squared dependence of the current on the voltage The problem with this kind of excitation mechanism is its inefficiency and the damage it induces in the oxide due to the energetic electron flow LED based on such a unipolar injection mechanism were reported with low external efficiency of 0.1% and low turn on voltage of 5 V when the overall thickness of the active layer is lower than 25 nm [26]

However, to get high electroluminescence efficiency one should try to get bipolar injection What most impedes this is the fact that the effective barrier for tunnelling of electrons is much smaller that the one for holes That such separate tunnelling of electrons and holes is possible is well known in the literature (see e g [27] and reference therein) and has been proved also in the recent paper [28] Here by the use of a single layer of Si-nc formed in a very thin gate of a FET transistors, bipolar injection has been achieved by changing the sign of the gate voltage

(Fig 15) When the voltage is positive electrons are tunnelling into the Si-nc, when the gate is negative holes are tunnelling into the Si-nc By periodically changing the gate voltage the Si-nc are filled by electrons and holes and electroluminescence occurs After each switching of the gate voltage, electroluminescence goes to a maximum and then decays as the other sign charge carriers are consumed.

Figure 14 Schematic view of the process of generation of electron-hole pairs in silicon nanocrystals by impact excitation Here an energetic electron tunnel trough the oxide under a strong electric field When in the Si-nc, it losses energy by exciting an electron-hole pair Then it tunnels again in another Si-nc driven by the high field strength The impact-excited electron-hole pair in the Si-nc may then recombine radiatively

Figure 15 Schematic of the field-effect electroluminescence mechanism in a silicon nanocrystal floating-gate transistor structure Inset band diagrams depict the relevant tunnelling processes a–c, The array of silicon nanocrystals embedded in the gate oxide of the transistor can be sequentially charged with electrons (a) by Fowler-Nordheim tunnelling, and holes (b) via Coulomb field enhanced Fowler–Nordheim tunnelling to prepare excitons that radiatively recombine (c) From Ref [28]

Recently, a breaktrough of 1.6 % external quantum efficiency in Si-nc LED has been reported [29] The idea was to decrease the tunneling barrier by replacing SiO2 by Si3N4 and to block one charge carrier in the active region by using a suitable material on top of the diode, in this work amorphous SiC was used

3.3 ABSORPTION AND REFRACTIVE INDEX

In order to exploit the optical properties of Si-nc in photonics another parameter of paramount importance is the refractive index of the Si/nc rich oxide A simple picture of it would be to assume an effective medium where the refractive index is given by the Bruggemann formula (equation 2)

1.4 1.5 1.6 1.7 1.8

1.9 Thermal oxide

Fused silica Fit

a silicon-oxynitride layer or of a three component matrix with Si, SiO2 and Si3N4 The presence of nitrogen in the film increases the refractive index of the layer significantly (See Table 2)

1.46 1.48 1.50 1.52 1.54

1.56 Annealing at 900 °C