WO2013026861A1

WO2013026861A1 - Method for the characterisation of at least one layer of material comprising semiconductor nanocrystals

Info

Publication number: WO2013026861A1
Application number: PCT/EP2012/066303
Authority: WO
Inventors: Mathieu Baudrit; Pierre Mur; Kavita Surana; Philippe Thony
Original assignee: Commissariat à l'énergie atomique et aux énergies alternatives
Priority date: 2011-08-24
Filing date: 2012-08-22
Publication date: 2013-02-28
Also published as: FR2979431A1; FR2979431B1

Abstract

The invention relates to a method for the characterisation of a layer (110) of material comprising semiconductor nanocrystals (108), including the following steps consisting in: forming an alternating stack of m first layers (110) having a complex refractive index n₁ and m second layers (106) having a complex refractive index n₂ that is different from n₁, in which the first layers (110) comprise semiconductor nanostructures (108), said stack being disposed on a substrate (102), wherein m ≥ 2; measuring the reflectivity of the stack in a wavelength range; calculating n₁ on the basis of m, the thicknesses of the first and second layers and the stack reflectivity measurement, using an optical transfer-matrix calculation; and calculating the capacitance C₁ of one of the first layers on the basis of the measurement of the capacitance of the stack and the substrate.

Description

PROCESS FOR CHARACTERIZING AT LEAST ONE LAYER OF SEMICONDUCTOR NANOCRYSTAL MATERIAL

DESCRIPTION

TECHNICAL AREA

The invention relates to a method for characterizing a layer of material comprising semiconductor nanocrystals. Such a method makes it possible to optically characterize the layer of material comprising the semiconductor nanocrystals, that is to say to determine the value of the complex refractive index of the layer, but also to characterize it electrically, by determining the electrical capacity of it, precisely.

STATE OF THE PRIOR ART

To optically and electrically characterize a layer of material comprising semiconductor nanocrystals, such a layer is generally produced on a semiconductor substrate, for example composed of silicon. The material, for example a dielectric material, of the layer comprising the nanocrystals forms a matrix in which these semiconductor nanocrystals are arranged. This material intrinsically possesses its own optical indices, that is to say a complex refractive index comprising a real part and an imaginary part called extinction coefficient. However, the optical indices of the layer considered as a whole, that is to say with nanocrystals semiconductor, vary according to the density and dimensions of the semiconductor nanocrystals. In addition, the electrical properties, and in particular the value of the electrical capacitance, of the layer depend in particular on the nature of the materials (material of the nanocrystals and the material in which the nanocrystals are located) as well as the thickness of the layer and the density of the nanocrystals in the layer.

The optical characterization of the layer comprising the semiconductor nanocrystals is performed by measuring the optical indices thereof in a desired wavelength range by spectroscopic ellipsometry. The electrical characterization of the layer comprising the semiconductor nanocrystals is achieved by measuring the electrical capacitance thereof.

However, the presence of the substrate makes the optical characterization of the layer imprecise. Indeed, from an optical point of view, the substrate creates optical interference that disturbs the measurement of the optical indices of the layer comprising the semiconductor nanocrystals, and distort it. Further, from an electrical point of view, measurement of the electrical capacitance of the layer is also imprecise because it is highly dependent on the spatial distribution of the semiconductor nanocrystals ^¬ conductor within the layer, the distribution may vary between different layers which theoretically have the same number of semi ^¬ conductor nanocrystals. STATEMENT OF THE INVENTION

An object of the present invention is to propose a method for characterizing a layer of material comprising semiconductor nanocrystals making it possible to characterize the layer at least optically, that is to say to determine the complex refractive index. of the layer, in a precise manner without the substrate on which the layer is arranged disturbing this characterization.

For this purpose, the present invention proposes a method for characterizing a layer of material comprising semiconductor nanocrystals, comprising at least the steps of:

performing at least one alternating stack of m first layers of complex refractive index ni and m second layers of complex refractive index n ₂ different from the complex refractive index ni, in which the first layers comprise the semiconductor nanocrystals, the stack being disposed on a substrate, m being an integer greater than or equal to 2,

measurement of the reflectivity, in a range of wavelengths, of the stack previously produced,

calculating the value of the complex refractive index or of one of the first layers of the stack from the value of m, the thicknesses of the first and second layers of the stack, and the measurement of reflectivity of the stacking, by implementing a method for calculating optical transfer matrices. The stack produced in this process forms a distributed Bragg reflector, also called Bragg grating or Bragg mirror, to minimize the amount of light arriving at the substrate and thus maximize the light absorption in the first m layers comprising the nanocrystals . This eliminates the optical contribution of the substrate, which makes it possible to achieve a better optical characterization of the layers comprising the semiconductor nanocrystals.

The semiconductor nanocrystals may be composed of amorphous or crystalline silicon. The first and / or second layers may comprise silicon dioxide and / or silicon oxide and / or silicon nitride and / or silicon oxynitride and / or silicon carbide. The substrate may be composed of silicon.

In a variant, the second layers may comprise semiconductor nanocrystals.

The realization of the stack may comprise:

- implementation of deposits of first and second layers of the stack on the substrate, the first layers of the stack can be deposited such that they contain excess semi ^¬ conductor for forming nanocrystals and

- the implementation of an anneal forming, in the first layers, the semi ^¬ conductor nanocrystals by precipitation with solid state semiconductor present in excess in the first layers deposited prior to annealing. The method for calculating optical transfer matrices may include the steps of:

a) choosing an arbitrary value of the complex refractive index,

b) calculating, for each layer of the stack and for each wavelength of said wavelength range, an optical transfer matrix,

c) calculating a matrix product of the optical transfer matrices previously calculated for each of the layers in step b), corresponding to the optical transfer matrix of the stack of layers,

d) calculating the reflectivity of the stack for each wavelength of said range of wavelengths,

e) comparing the reflectivity calculated in step d) and the measured reflectivity,

steps b) to e) being repeated for values different from the complex refractive index and when the reflectivity calculated in step d) does not correspond to the measured reflectivity.

The method may further comprise, after calculating the value of the complex refractive index or of one of the first layers of the stack, the steps of:

- Realizing a first electrode covering the stack and a second electrode disposed against the substrate such that the substrate is disposed between the second electrode and the stack, measuring a capacitance C between the first and the second electrode,

calculation of an electrical capacitance Ci of one of the first layers of the stack, such as:

with:

Cgu: electrical capacitance of the substrate, C2: electrical capacitance of one of the second layers of the stack.

Thus, it is possible to characterize electrically (determination of the electrical capacitance) precisely the layers of material comprising the semiconductor nanocrystals.

The measurement of the capacitance C of the characterization device can be carried out by applying a voltage between the first and the second electrode.

In this case, the electrical capacitance corresponding to the sum of the electrical capacitance of the stack and that of the substrate is measured. By knowing the number of first and second layers, it is possible to find the electrical capacitance value of one of the first layers comprising the semiconductor nanocrystals. This configuration increases the signal C (V) (measurement signal of the electrical capacitance obtained by applying a voltage V across the electrodes) of the layers comprising the nanocrystals and facilitates its measurement while avoiding any uncertainties of regularity. positioning of the nanocrystals since the signal C (V) is averaged over m layers.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood on reading the description of exemplary embodiments given purely by way of indication and in no way limiting, with reference to the appended drawings in which:

FIGS. 1A, 1B and 2 represent steps of a method of characterization, object of the present invention, according to a particular embodiment,

FIG. 3 represents the steps of a method for calculating the optical transfer matrices implemented during a characterization method that is the subject of the present invention.

Identical, similar or equivalent parts of the different figures described below bear the same numerical references so as to facilitate the passage from one figure to another.

The different parts shown in the figures are not necessarily in a uniform scale, to make the figures more readable.

The different possibilities (variants and embodiments) must be understood as not being exclusive of each other and can be combined with one another. DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS

Referring firstly to Figures 1A and 1B which show steps of producing a stack of layers especially comprising a material layer comprising semi ^¬ conductor nanocrystals that it is desired to characterize optically and electrically, it is that is to say, the values of the complex refractive index and the electrical capacitance are to be determined.

On a substrate 102 made of silicon, for example, is an alternating stack of first layers 104 composed of silicon-rich silicon dioxide (substoichiometric Si0 ₂ ) and second layers 106 composed of stoichiometric Si0 ₂ . In the example of FIG. 1A, the lower layer (that in contact with the substrate 102 and on which the other layers of the stack rest) is one of the first layers 104 and the upper layer (that disposed at the top of the stack) is one of the second layers 106. The layers 104 and 106 of this stack are for example deposited by PECVD (plasma enhanced chemical vapor deposition) with different thicknesses.

The thickness of each layer is a function of the refractive index of the material or materials of the layer as well as the wavelengths to be reflected. In general, each layer 104, 106 may have a thickness of between about 10 nm and 500 nm, or between about 1 nm and several micrometers. In a particular example, the thickness of each of the layers 104, 106 may be equal to about -, with λ corresponding to the wavelength An

central of the reflectance spectral window of the reflector formed by the stack, and n corresponding to the refractive index (real part) of the material of the layer.

The stack thus produced then undergoes annealing at a temperature of, for example, less than or equal to approximately 1300 ° C. for a duration of between approximately a few seconds and several hours (for example 3 hours). This annealing results in a densification of the layers 104 and 106 and, in the first layers 104, a separation of the stoichiometric S 10 ₂ and the excess of silicon initially present in the first layers 104. This excess silicon rushes to the state solid forming nanocrystals 108 arranged in a dielectric matrix corresponding to S 1O ₂ from the layers 104. This produces first layers 110 composed of S 1O ₂ and having silicon nanocrystals 108. The realization of nanocrystals 108 in the first layers 110 thus ensures that the layers 106 and 110, both composed of the material S 10 ₂ , will have different complex refractive indices.

In each of the first layers 110, the nanocrystals 108 may have different dimensions or not with respect to each other. Thus, when a layer 104 has a thickness less than about 8 nm, the silicon nanocrystals 108 obtained from this layer 104 have dimensions substantially similar to each other. On the other hand, when a layer 104 has a thickness greater than or equal to approximately 8 nm, the silicon nanocrystals 108 obtained may have different dimensions with respect to each other. The nanocrystals 108, for example, each have a diameter of between approximately 1 nm and 20 nm. In the optical reflector formed by the stack of layers 106 and 110, the complex refractive indices and the first layers 110 are in particular a function of the density and the distribution of the nanocrystals 108 in the first layers 110, and therefore also of the quantity excess of silicon in the layers 104, annealing conditions and the thickness of the layers 104 from which the first layers 110 are obtained.

An alternating stack of m first layers 110 of complex refractive index n i and m second layers 106 of complex refractive index n ₂ different from the complex refractive index n i is thus obtained, in which the first layers 110 comprise the semiconductor nanocrystals 108, with m = 6 in the example described herein, the stack being disposed on the silicon substrate 102. the values of the real parts of the complex refractive indices ni and n ₂ may be for example between about 1.4 and 4.5 (at a wavelength of 632.8 nm).

The stack forms here a distributed Bragg network. The second layers 106 form dielectric layers electrically insulating the first layers 110 which comprise the semiconductor nanocrystals 108. The reflectivity of the stack produced, for example between about 300 nm and 1200 nm, is then measured. This reflectivity can be measured for example by a spectrophotometer. Such a device sends an incident light beam, of known intensity and at different wavelengths of a desired spectrum, on the stack, and measures the intensity of the light reflected at each of the different wavelengths. which makes it possible to determine the reflectivity of the stack in the desired spectrum.

Since the stack of first layers 110 and second layers 106 form a distributed Bragg grating, little or no light entering through the top of the stack reaches the substrate 102, thereby eliminating or making negligible optical interference due to substrate 102. within the stack, optical interference occurs, the interference being dependent on the difference between the complex refractive indices ni and n _2, the number m and of the stack layer thicknesses as well as optical characteristics of the materials around the stack.

The measured reflectivity corresponds to the response of a distributed Bragg grating, and therefore comprises a spectral reflectivity window, or photonic cutoff band, that is to say a range of wavelengths for which the Bragg grating distributed, formed by the stack of the first layers 110 and second layers 106, has a maximum reflectivity. From the previously measured reflectivity, the value of m, and the thicknesses of the layers of the stack, the value of the complex refractive index or of one of the first layers 110 of the stack is then calculated by the implementing a method for calculating optical transfer matrices.

An exemplary implementation of the method of calculating the optical transfer matrices is detailed below in connection with the diagram shown in FIG. 3.

The arbitrary values of the optical indices (complex refractive index) which one wishes to determine are firstly chosen.

Then, for each layer and for each wavelength λ of the spectrum considered, step 10 is calculated an optical transfer matrix M such that:

with E and H corresponding to the tangential components of the electric and magnetic fields in the considered layer, d corresponding to the optical coordinates across the thickness of the layer.

The matrix M corresponds to:

cos j sin ç / Y

M

jY sin φ cos φ

Ίπ

with φ = - nd cos ®,

AT

φ representing the phase shift of the light propagating through the layer, n corresponding to the complex refractive index of the layer, and Θ the expected angle of incidence of the light with respect to the layer (for example equal to 90 °).

Y is the optical admittance of the layer which is equal to, for the parallel polarizations (p or TE) and perpendicular M):

where εο and μο are the permittivity and the permeability of the vacuum.

The matrix of the complete system, that is to say the stack of layers, is then calculated (step 12) for each wavelength λ corresponding to the matrix product of the matrices M of each layer.

From this optical transfer matrix of the complete system, it is then possible to calculate (step 14), for each wavelength λ, the reflectivity r of the system such that:

r_Y ₀ M _n + Y ₀ Y _s M _l2 _2l + M -Y M _s

M _ab corresponding to the coefficient of line a and column b of the matrix.

The reflectivity r obtained is compared with that previously measured (step 16). If the calculated reflectivity r does not correspond to that measured, then the initially arbitrarily chosen parameters (optical indices) are modified, and the calculations are repeated until a system whose calculated reflectivity corresponds to the measured reflectivity, meaning that the optical indices, that is to say the complex refractive index, chosen are correct.

After having optically characterized one of the first layers 110 comprising semiconductor nanocrystals 108, this first layer 110 is electrically characterized.

A first electrode 112 is firstly made covering the stack of layers 106 and 110, and a second electrode 114 under the substrate 102 (FIG. 2). These electrodes 112 and 114 are for example composed of an electrically conductive transparent oxide such as ITO.

An electric potential is then applied, for example between about -15 V and + 15 V, on the electrodes 112, 114, and the capacitance C between the electrodes 112 and 114 is measured, that is to say the capacitance cumulative of the substrate 102 and the stack of layers 106 and 110. This capacitance C can be measured for the different values of λ of the spectrum considered during the optical characterization previously performed, since the conduction and the capacitive effect are variables according to the illumination (monochromatic) of the layers of the stack.

From this or these measurements of the electrical capacitance C, the value of the capacitance Ci of one of the first layers 110 comprising the semiconductor nanocrystals 108 is determined. The relation is used for this:

with:

C _sub : electrical capacitance of the substrate 102, C2: electrical capacitance of one of the second layers 106.

Knowing the values of C _sub and C ₂ (the materials of these elements being known), it is therefore possible to calculate the value of the capacitance Ci of one of the first layers 110 of the stack such that:

Knowing that the value of a capacitance C of a layer of material is such that:

C = € _r € ₀ .- e

With

s _r : effective electrical permittivity of the layer,

So: electrical permittivity of the vacuum (8,854.10 ^-12 Fm- ¹ ),

S: surface of the layer,

e: thickness of the layer.

Knowing the thickness and the area occupied by the first layers 110, it is therefore possible to calculate the electrical permittivity of one of the first layers 110 which comprises semiconductor nanocrystals 108.

Claims

A method of characterizing a layer (110) of material having semiconductor nanocrystals (108), comprising at least the steps of:

- Making at least one alternating stack of m first layers (110) of complex refractive index n and m second layers (106) of complex refractive index n ₂ different from the complex refractive index n, in wherein the first layers (110) comprise the semiconductor nanocrystals (108), the stack being disposed on a substrate (102), m being an integer greater than or equal to 2,

calculating the value of the complex refractive index or of one of the first layers of the stack from the value of m, the thicknesses of the first (110) and second layers (106) of the stacking, and the measurement of reflectivity of the stack, by implementing a method for calculating optical transfer matrices,

- Realization of a first electrode

(112) covering the stack and a second electrode (114) disposed against the substrate (102) such that the substrate (102) is disposed between the second electrode (114) and the stack,

measuring a capacitance C between the first (112) and second (114) electrodes, calculating an electrical capacitance Ci of one of the first layers (110) of the stack such that:

with:

C _SUb : electrical capacity of the substrate (102), C2: electrical capacitance of one of the second (106) of the stack.

2. A method of characterization according to Claim 1, wherein the semiconductor nanocrystals ^¬ conductor (108) are composed of amorphous or crystalline silicon, and / or wherein the first (110) and / or second layers (106) comprise dioxide silicon and / or silicon oxide and / or silicon nitride and / or silicon oxynitride and / or silicon carbide, and / or wherein the substrate (102) is composed of silicon.

3. Method according to one of the preceding claims, wherein the realization of the stack comprises:

the implementation of deposits of the first (104) and second layers (106) of the stack on the substrate (102), the first layers (104) of the stack being deposited such that they comprise in excess the semi -conductor for forming the nanocrystals (108), and

- The implementation of annealing forming, in the first layers (110), the semiconductor nanocrystals (108) by solid state precipitation semiconductor present in excess in the first layers (104) deposited prior to annealing.

4. Method according to one of the preceding claims, wherein the method of calculating optical transfer matrices comprises the steps of:

a) choosing an arbitrary value of the complex refractive index,

b) calculating, for each layer (106, 110) of the stack and for each wavelength of said wavelength range, an optical transfer matrix,

c) calculating a matrix product of the optical transfer matrices previously calculated for each of the layers in step b), corresponding to the optical transfer matrix of the stack of layers (106, 110),

5. Method according to one of the preceding claims, wherein the measurement of the capacitance C is performed by applying a voltage between the first (112) and the second electrode (114).