**5. Silicon and III-V solar cells with fianite antireflecting layer**

#### **5.1 Anti-reflection properties of fianite film on Ge and Si**

In theory, it is possible to eliminate the reflection completely (at the corresponding thickness of a film *d*) at *nd* = √ *n*f, where *n*f – optical refraction constant of a semiconductor. Since for Si and Ge the constants equal to 3.7 and 4, respectively, the reflection is completely eliminated at *nd* = √ *n*<sup>п</sup> 2. Therefore, a dielectric having its optical refraction constant *nd* = √ *n*~2 (at *n* = 3.7÷4) can be considered as an optimal material for the antireflecting film for solar cells and the other photosensitive devices. Theoretically, it is the case at the film thickness, which is equal to a quarter of optical wavelength *W* = *λ*/4*nd* , such dielectric allows a complete elimination of the reflection loss (R=0).

The refraction constant of SiO2 (*n* = 1.47) is considerably lower than that value. At this *n* value it is impossible to maintain the reflection loss lower than 10%. Refraction constants of fianite and ZrO2 are within (2.15÷2.18) and (2,13÷2.2), respectively, - that is close to the above optimum value. Thus providing an evidence that fianite and ZrO2 are very promising as antireflecting coatings for solar cells and the other photosensitive devices based on Ge, Si and AIIIBV compounds.

Experimental dependencies of antireflection (as dependencies of the reflection on wavelength) of fianite films on Si and Ge have been plotted (Fig. 24).

The plots apparently demonstrate that the reflection drops to 0 – 1.5 % in the minima.

Experimental study of antireflective properties of fianite oxide applied to Ge was performed. By the reason that, germanium photodetectors are designed for detecting radiation generated by lasers with wavelengths λ= 1.06; 1.3; 1.54 µm, the thickness of the antireflective fianite film was chosen as W=1300 Å; such thickness provides for minimal reflection losses in the said wavelength range λ= 1.06-1.54 µm. Fig. 23 a shows the comparison of experimental (thin line) and theoretical (bold line) R(λ) curves. The theoretical R(λ) curve was calculating using the following formula:

$$R = 1 - \frac{4n\_{II}n\_{\alpha\kappa}^{2}}{n\_{\alpha\kappa}^{2}(n\_{II}+1)^{2} - (n\_{II}^{2}-n\_{\alpha\kappa}^{2})(n\_{\alpha\kappa}^{2}-1)\sin^{2}\left(2\pi n\_{\alpha\kappa}W/\lambda\right)}.$$

According to the above formula, reflection may fall practically to zero at the optimal value of nok (note, that in case of SiO2 anti-reflective film, for which nok=1.47, it is impossible to obtain reflection lower than 10%). The minimal reflection is achieved at the following wavelength λmin:

$$\mathcal{A}\_{\text{min}} = 4Wn\_{\text{oc}}\dots$$

Fianite in Photonics 167

Experimental dependencies of antireflection of fianite films deposited on commercial solar cells were recorded. The reflection spectra of fianite obtained on two such samples are shown in Fig. 25a. The plots (Fig. 24) demonstrate excellent antireflecting properties of the fianite films. The plots also apparently demonstrate that the reflection drops to 0 – 1.5 % in the minima. A position of the minimum depends on the film thickness. At the film thinning the minimum occurs in the solar spectrum. Therefore, energy gain due to the application of

a b <sup>с</sup>

The majority of modern technologies of semiconductor devices are based on generation of different conductivity areas in the semiconductor and in particular of *p-n* junctions. For this purpose the crystals are doped, by means of three basic processes: diffusion, ion implantation, and irradiation. The donor and acceptor impurities coexist in real silicon crystals. Therefore there is an alternative possibility: to redistribute available impurities to fabricate the areas of different conductivity type. Traditional doping-based techniques (diffusion, ion implantation, a radiating doping) have the common drawbacks such as : (1) high temperatures of the processing. The diffusion doping is usually carried out at the temperature higher than 1100°C. After ion or radiating doping the subsequent high temperature annealing of the radiation defects should be carried out; (2) undesirable contamination of the crystal by new impurities could occur; (3) nearly all dopants are poisonous, leading to contamination of the environment. In the present work we consider a new technique of formation of p-n junctions in silicon, which provides facilitation and cost

The *p*-Si wafers were cut from boron-doped CZ crystals of various resistivities (with the boron concentration about 1015 cm-3). The wafers were irradiated by 1–5 keV Ar ions in a gas discharge plasma. Then the wafers were cleaved, and the depth profile of the conductivity type was inspected by SEM–EBIC (scanning electron microscopy-electron beam induced current) technique. For this purpose, a high quality Schottky barrier was made by metal coating. This process resulted in formation of an *n–p* junction at some depth, which is clearly

Fig. 24. Antireflecting properties of fianite films of 580 Å (a) and 1050 Å (b) thickness

**5.3 New ecologic technique of formation of** *p-n* **junctions in Si for solar sells** 

reduction of production process of semiconductor devices such as solar cells.

**5.4.1 Experimental** 

revealed as a sharp peak of EBIC signal (Fig. 25).

obtained on the industrial items (c) of Si solar cells of 4" x 4" size.

**5.2 Silicon solar cells with fianite antireflecting layer** 

the antireflecting fianite films approaches to 20-30%.

As it is shown on Fig. 24a, in the range of fundamental absorption (for λ<1.65 µm) the experimental curve 1 coincides with the theoretical curve 2. Some discrepancy at higher wavelengths (λ>1.65 µm) appears due to deep penetration of such radiation and its reflection from the back surface. It is important that at the optimal wavelength (λ=1.12 µm), fianite film provides for ideal antireflective properties – the reflection is actually absent. In rather large range 0.88 - 1.55 µm, into which radiation wavelengths of most wide spread lasers fall, the losses for reflection do not exceed 10%.

Fig. 23. Experimental (1) and theoretical (2) dependencies of the reflection on wavelength in Ge-fianite antireflecting film system (1300 Ǻ) (a); experimental dependencies of reflection of fianite film on Si and Ge (b).

The experimental dependences of enlightenment (the dependence of reflectance on the wavelength) of cubic zirconia films on Si and Ge, (Ge on their optical properties similar to GaAs) exhibit excellent antireflective properties of cubic zirconia (Fig. 23 b). As is evident from the graphs, the minimum reflection can drop to 0-1, 5%. Position of the minimum depends on the thickness of the film. When it gets thinned twice the minimum would be in the solar spectrum. Plateau in the curve shows the reflection from the back side of the substrate in the transmission range for Si. So the gain due to the use of antireflecting fianite film reaches 20-30%.

So, it was experimentally proved that in case of use of 1300 Å thick fianite film, reflection may actually fall to zero in the wavelength range λ= 1.06 – 1.54 µm.

A new, non-standard, fianite use as a reflecting film (in contrast to anti-reflective film!) was proposed. Such unexpected application may appear useful for screening of peripheral (nonphotosensitive) photodetector areas. For standard screening of such areas, forming of proper photosensitive areas, metallic masks sputtered to SiO2 have been used. But such solution causes notable spurious capacitance of the metal-oxide-semiconductor structure; provided that such capacities are inadmissible in a number of photodetectors, in particular – in high frequency photodetectors. In case of screening by the reflecting oxide (for this purpose the thickness should be chosen as W=1/2 λnok), no surface capacity is being formed, of cause; spurious capacitance is absent. In such case, fianite film may reflect about 60% of radiance from the surface.

As it is shown on Fig. 24a, in the range of fundamental absorption (for λ<1.65 µm) the experimental curve 1 coincides with the theoretical curve 2. Some discrepancy at higher wavelengths (λ>1.65 µm) appears due to deep penetration of such radiation and its reflection from the back surface. It is important that at the optimal wavelength (λ=1.12 µm), fianite film provides for ideal antireflective properties – the reflection is actually absent. In rather large range 0.88 - 1.55 µm, into which radiation wavelengths of most wide spread

a b

Fig. 23. Experimental (1) and theoretical (2) dependencies of the reflection on wavelength in Ge-fianite antireflecting film system (1300 Ǻ) (a); experimental dependencies of reflection of

The experimental dependences of enlightenment (the dependence of reflectance on the wavelength) of cubic zirconia films on Si and Ge, (Ge on their optical properties similar to GaAs) exhibit excellent antireflective properties of cubic zirconia (Fig. 23 b). As is evident from the graphs, the minimum reflection can drop to 0-1, 5%. Position of the minimum depends on the thickness of the film. When it gets thinned twice the minimum would be in the solar spectrum. Plateau in the curve shows the reflection from the back side of the substrate in the transmission range for Si. So the gain due to the use of antireflecting fianite

So, it was experimentally proved that in case of use of 1300 Å thick fianite film, reflection

A new, non-standard, fianite use as a reflecting film (in contrast to anti-reflective film!) was proposed. Such unexpected application may appear useful for screening of peripheral (nonphotosensitive) photodetector areas. For standard screening of such areas, forming of proper photosensitive areas, metallic masks sputtered to SiO2 have been used. But such solution causes notable spurious capacitance of the metal-oxide-semiconductor structure; provided that such capacities are inadmissible in a number of photodetectors, in particular – in high frequency photodetectors. In case of screening by the reflecting oxide (for this purpose the thickness should be chosen as W=1/2 λnok), no surface capacity is being formed, of cause; spurious capacitance is absent. In such case, fianite film may reflect about 60% of radiance

may actually fall to zero in the wavelength range λ= 1.06 – 1.54 µm.

lasers fall, the losses for reflection do not exceed 10%.

1

2

fianite film on Si and Ge (b).

film reaches 20-30%.

from the surface.

#### **5.2 Silicon solar cells with fianite antireflecting layer**

Experimental dependencies of antireflection of fianite films deposited on commercial solar cells were recorded. The reflection spectra of fianite obtained on two such samples are shown in Fig. 25a. The plots (Fig. 24) demonstrate excellent antireflecting properties of the fianite films. The plots also apparently demonstrate that the reflection drops to 0 – 1.5 % in the minima. A position of the minimum depends on the film thickness. At the film thinning the minimum occurs in the solar spectrum. Therefore, energy gain due to the application of the antireflecting fianite films approaches to 20-30%.

Fig. 24. Antireflecting properties of fianite films of 580 Å (a) and 1050 Å (b) thickness obtained on the industrial items (c) of Si solar cells of 4" x 4" size.

#### **5.3 New ecologic technique of formation of** *p-n* **junctions in Si for solar sells**

The majority of modern technologies of semiconductor devices are based on generation of different conductivity areas in the semiconductor and in particular of *p-n* junctions. For this purpose the crystals are doped, by means of three basic processes: diffusion, ion implantation, and irradiation. The donor and acceptor impurities coexist in real silicon crystals. Therefore there is an alternative possibility: to redistribute available impurities to fabricate the areas of different conductivity type. Traditional doping-based techniques (diffusion, ion implantation, a radiating doping) have the common drawbacks such as : (1) high temperatures of the processing. The diffusion doping is usually carried out at the temperature higher than 1100°C. After ion or radiating doping the subsequent high temperature annealing of the radiation defects should be carried out; (2) undesirable contamination of the crystal by new impurities could occur; (3) nearly all dopants are poisonous, leading to contamination of the environment. In the present work we consider a new technique of formation of p-n junctions in silicon, which provides facilitation and cost reduction of production process of semiconductor devices such as solar cells.

#### **5.4.1 Experimental**

The *p*-Si wafers were cut from boron-doped CZ crystals of various resistivities (with the boron concentration about 1015 cm-3). The wafers were irradiated by 1–5 keV Ar ions in a gas discharge plasma. Then the wafers were cleaved, and the depth profile of the conductivity type was inspected by SEM–EBIC (scanning electron microscopy-electron beam induced current) technique. For this purpose, a high quality Schottky barrier was made by metal coating. This process resulted in formation of an *n–p* junction at some depth, which is clearly revealed as a sharp peak of EBIC signal (Fig. 25).

Fianite in Photonics 169

Fig. 27. Influence of surface damage in Si wafer on the shape of inversion *p-n* junction

Fig. 28. Influence of non-uniformity of Si wafer on the form of inversion *p-n* junction

These results indicate to the role of the irradiation-induced self-interstitials: the local selfinterstitial concentration is sensitive to the sinking ability of the sample surface. Particularly, the scratches at the backside may getter the surface impurities from the adjacent regions of

One can argue that the *p–n* inversion is caused by some fast-diffusing donor impurity introduced during Ar irradiation. To check this possibility, we used the secondary-ion massspectrometry. An irradiated sample with a shallow *p–n* junction and a reference nonirradiated sample were inspected using layer-by-layer etching. No difference in the impurity content between the two samples was found which proves that the irradiation did not lead

It is therefore accepted that the *p–n* inversion is caused by in-diffusion of intrinsic point defects (self-interstitials) which leads to a loss of boron acceptors by kicking out the boron atoms Bs into the interstitial state Bi. The Bi atoms are known to be donors in *p*-Si [63]. Most likely, Bi will be paired to Bs, into neutral BiBs defects. The conductivity will then change to n-type, due to either isolated Bi or due to residual donors (phosphorus and grown-in thermal donors) that are present already in the initial state, before the

The thermal donors are well known to be produced by a heat treatment around 450OC, and to be annihilated by annealing at T > 600OC. It was found that after several hours at 450OC, the *n–p* junction persisted. However, after one hour at 750OC the p–n junction disappeared. This result can be treated as an indication of role of the thermal donors. On the other hand,

it can be attributed to conversion of Bi back into Bs by annealing at higher T.

the surface, thus improving the sinking ability of those regions.

to any contamination of the sample near the surface.

irradiation.

The formation of an *n*-type region below the irradiated surface was also confirmed by a conventional thermo-probe technique. Upon increasing the irradiation time, the depth of the *n–p* junction (denoted by Xd) increases (Fig. 26). Some *n*-type (phosphorus-doped) wafers were also irradiated and inspected; in this case no *p–n* junction was found [61, 62]. The junction depth Xd is a non-linear function of the irradiation time t. No junction was found in reference non-irradiated wafers. There is some "dead" time (1–15 min) in the junction propagation. After prolonged irradiation, the junction reaches some final position (Fig. 26 b) that can be quite close to the back (non-irradiated) surface of the wafer. In some range of duration (neither too short nor too long) the depth is roughly proportional to t1/2 – a typical dependence for a diffusion process.

Fig. 25. Scheme of experiment

*Peculiarities of n–p junction propagation.* The *n–p* junction propagation was found to be sensitive to the state of the wafer surface. If the irradiated surface is bright polished, the junction moves faster, in comparison to the abrasion-polished surface. The surface defects, like scratches, cause a local distortion of the junction shape. The scratches at the backside 'attract' the junction. On the contrary, near the wafer edges, the junction propagation is retarded (Fig. 27). Striation non-uniformity of Si affects the shape of inversion *p-n* junction too (Fig. 28).

Fig. 26. SEM microphotograph made both in secondary emission and EBIC modes of inversion *p-n* junctions on a cleaved Si wafer (a). The wafers were irradiated at the left side. The dark vertical strip is the image of *p-n* junction. The *p-n* junction depth Xd in dependence of the time of exposure to Ar ions (b).

The formation of an *n*-type region below the irradiated surface was also confirmed by a conventional thermo-probe technique. Upon increasing the irradiation time, the depth of the *n–p* junction (denoted by Xd) increases (Fig. 26). Some *n*-type (phosphorus-doped) wafers were also irradiated and inspected; in this case no *p–n* junction was found [61, 62]. The junction depth Xd is a non-linear function of the irradiation time t. No junction was found in reference non-irradiated wafers. There is some "dead" time (1–15 min) in the junction propagation. After prolonged irradiation, the junction reaches some final position (Fig. 26 b) that can be quite close to the back (non-irradiated) surface of the wafer. In some range of duration (neither too short nor too long) the depth is roughly proportional to t1/2 – a typical

*Peculiarities of n–p junction propagation.* The *n–p* junction propagation was found to be sensitive to the state of the wafer surface. If the irradiated surface is bright polished, the junction moves faster, in comparison to the abrasion-polished surface. The surface defects, like scratches, cause a local distortion of the junction shape. The scratches at the backside 'attract' the junction. On the contrary, near the wafer edges, the junction propagation is retarded (Fig. 27). Striation non-uniformity of Si affects the shape of inversion *p-n* junction

dependence for a diffusion process.

Fig. 25. Scheme of experiment

20 45 60 90 min

of the time of exposure to Ar ions (b).

a b

Fig. 26. SEM microphotograph made both in secondary emission and EBIC modes of inversion *p-n* junctions on a cleaved Si wafer (a). The wafers were irradiated at the left side. The dark vertical strip is the image of *p-n* junction. The *p-n* junction depth Xd in dependence

too (Fig. 28).

Fig. 27. Influence of surface damage in Si wafer on the shape of inversion *p-n* junction

Fig. 28. Influence of non-uniformity of Si wafer on the form of inversion *p-n* junction

These results indicate to the role of the irradiation-induced self-interstitials: the local selfinterstitial concentration is sensitive to the sinking ability of the sample surface. Particularly, the scratches at the backside may getter the surface impurities from the adjacent regions of the surface, thus improving the sinking ability of those regions.

One can argue that the *p–n* inversion is caused by some fast-diffusing donor impurity introduced during Ar irradiation. To check this possibility, we used the secondary-ion massspectrometry. An irradiated sample with a shallow *p–n* junction and a reference nonirradiated sample were inspected using layer-by-layer etching. No difference in the impurity content between the two samples was found which proves that the irradiation did not lead to any contamination of the sample near the surface.

It is therefore accepted that the *p–n* inversion is caused by in-diffusion of intrinsic point defects (self-interstitials) which leads to a loss of boron acceptors by kicking out the boron atoms Bs into the interstitial state Bi. The Bi atoms are known to be donors in *p*-Si [63]. Most likely, Bi will be paired to Bs, into neutral BiBs defects. The conductivity will then change to n-type, due to either isolated Bi or due to residual donors (phosphorus and grown-in thermal donors) that are present already in the initial state, before the irradiation.

The thermal donors are well known to be produced by a heat treatment around 450OC, and to be annihilated by annealing at T > 600OC. It was found that after several hours at 450OC, the *n–p* junction persisted. However, after one hour at 750OC the p–n junction disappeared. This result can be treated as an indication of role of the thermal donors. On the other hand, it can be attributed to conversion of Bi back into Bs by annealing at higher T.

Fianite in Photonics 171

In the subsequent discussion, we concentrate on the boron acceptor loss, assuming that the near-surface region contains some concentration of donors, Nd, which is less than the initial

A change in the substitutional boron concentration, due to the kick-out reaction (and due to the inverse reaction of kicking out the silicon lattice atoms by Bi), is described by a simple

 dNs/dt = -α (NsC - KNi) (1) where C is the local (depth-dependent) self-interstitial concentration, α is the kinetic constant of the direct kick-out reaction and K is the equilibrium constant in the mass-action law that relates the concentration for the case of equilibrium between the reacting species (NsC/Ni = K). The highest self-interstitial concentration, Cf, is reached near the front surface; it is defined by the balance of the production rate (proportional to the Ar flux) and the consumption rate by local Ar-produced vacancies and by sinking of self-interstitials at the front surface. With specified C, the concentration ratio of the interstitial and substitutional boron species, Ni/Ns, tends to C/K due to the reaction (1). A strong loss of acceptors occurs if C >> K. It is therefore assumed that this inequality holds at least at the front surface: Cf >> K. *Initial stage of boron acceptor loss.* At short irradiation time, the term KNi in Eq. (1) is

negligible, and the boron concentration near the front surface is lost exponentially,

 Ns(t) = No exp(-α Cf t) (2) The *n–p* junction appears when Ns becomes less than Nd. This moment (td) lies experimentally, between 1 and 10 min. The product α Cf is estimated, from Eq. (2), to be in

*Propagation of the n–p junction* The near-surface region – where a large fraction of boron is already displaced into interstitial state Bi (and then paired into BiBs) –expands as more selfinterstitials diffuse from the front surface into the bulk. The mass action law, NsC/Ni=K, is valid at duration longer than the kick-out reaction time (10 min or less). The boron-depleted region corresponds, approximately, to the condition С(x) > K. At not too long duration, the self-interstitials penetrate to some limited depth (Fig. 30 b), and the n–p junction resides at some intermediate position within the sample. Finally, the С(x) profile approaches a steadystate linear shape: the interstitials generated at the front surface are consumed at the back surface (Fig. 30 b). Therefore, the *n–p* junction does not reach the back surface but stops at

The self-interstitial flux into the sample bulk is, approximately, DCf/ xd, where xd is the size of the boron-depleted region (xd is almost identical to position Xd of the n–p junction). The total amount of the remaining boron is equal to Co(L-xd), where L is the wafer thickness. The boron loss rate, dQ/dt, is twice as large as the above self-interstitial flux (each consumed SiI leads to a loss of two Bs: one by kick-out, and the other by pairing of Bi to Bs). The following

 xd = (4DCft/No)1/2 (3) The DCf product is estimated to be 5x107 см2с-1 from Eq. (3). Above, we estimated the product α Cf (where α is the kick-out kinetic coefficient). By these numbers, the α / D ratio is of the order of 10-10 cm. If the kick-out reaction were limited just by self-interstitial diffusion (which means

concentration of the boron acceptors, No.

equation,

the range 0.01–0.001 s-1.

some final position, just like observed.

equation provides a solution for the junction depth xd(t),

Fig. 29. Schematic profiles of self-interstitials and substitutional boron after irradiated at the front side (a) and back side (b), the horizontal line shows the zero level; model of the depth profile of the SEM–EBIC signal for a sample with two (c) and three (d) irradiation-induced p–n junctions.

By varying the irradiation conditions (for instance, using a two-side irradiation), multiple junctions can be produced. An example of a double and a triple junction is shown in Fig. 29.

#### **5.4.2 Model**

A proposed mechanism of this process consists mainly in the following [64]. The irradiation of the sample by inert ions generates a flux of silicon interstitial atoms SiI directed from a surface in the bulk of the sample. Due to very high diffusivity of SiI [65] (even at low temperatures), the steady non-uniform distribution of SiI in a sample is formed (Fig. 30 a). Equilibrium concentration SiI at low temperatures is very low, therefore a huge supersaturation of SiI is created, which results in a sharp increase in the boron interstitial component, Bi. Reaction of kicking-out boron and the backward reaction (Bi -> Bs + SiI) establish dynamically equilibrium ratio between Bi and SiI. This ratio is proportional to the supersaturation of SiI. Therefore the loss of boron acceptors will be more pronounced in the wafer part with a higher concentration SiI. As a result the local inversion of conductivity occurs in this part. This model implies that the self-interstitials diffuse very fast at low T (below 100 OC), and penetrate to the depth of at least 300 µm within 100 min (Fig. 30b). Accordingly the self-interstitial diffusivity, at the irradiation temperature, is at least as high as 10 -7 cm2/s.

Fig. 30. Schematic profiles of self-interstitials and substitutional boron in the beginning of the process (a) and at successive time of intermediate stage of junction propagation (b).

a b c d

p–n junctions.

**5.4.2 Model** 

Fig. 29. Schematic profiles of self-interstitials and substitutional boron after irradiated at the front side (a) and back side (b), the horizontal line shows the zero level; model of the depth profile of the SEM–EBIC signal for a sample with two (c) and three (d) irradiation-induced

By varying the irradiation conditions (for instance, using a two-side irradiation), multiple junctions can be produced. An example of a double and a triple junction is shown in Fig. 29.

A proposed mechanism of this process consists mainly in the following [64]. The irradiation of the sample by inert ions generates a flux of silicon interstitial atoms SiI directed from a surface in the bulk of the sample. Due to very high diffusivity of SiI [65] (even at low temperatures), the steady non-uniform distribution of SiI in a sample is formed (Fig. 30 a). Equilibrium concentration SiI at low temperatures is very low, therefore a huge supersaturation of SiI is created, which results in a sharp increase in the boron interstitial component, Bi. Reaction of kicking-out boron and the backward reaction (Bi -> Bs + SiI) establish dynamically equilibrium ratio between Bi and SiI. This ratio is proportional to the supersaturation of SiI. Therefore the loss of boron acceptors will be more pronounced in the wafer part with a higher concentration SiI. As a result the local inversion of conductivity occurs in this part. This model implies that the self-interstitials diffuse very fast at low T (below 100 OC), and penetrate to the depth of at least 300 µm within 100 min (Fig. 30b). Accordingly the self-interstitial diffusivity, at the

irradiation temperature, is at least as high as 10 -7 cm2/s.

a b

Fig. 30. Schematic profiles of self-interstitials and substitutional boron in the beginning of the process (a) and at successive time of intermediate stage of junction propagation (b).

In the subsequent discussion, we concentrate on the boron acceptor loss, assuming that the near-surface region contains some concentration of donors, Nd, which is less than the initial concentration of the boron acceptors, No.

A change in the substitutional boron concentration, due to the kick-out reaction (and due to the inverse reaction of kicking out the silicon lattice atoms by Bi), is described by a simple equation,

$$\text{dN}\_{\text{v}}/\text{dt} = \text{-a (N}\_{\text{t}}\text{C} \text{ - KN}\_{\text{i}}) \tag{1}$$

where C is the local (depth-dependent) self-interstitial concentration, α is the kinetic constant of the direct kick-out reaction and K is the equilibrium constant in the mass-action law that relates the concentration for the case of equilibrium between the reacting species (NsC/Ni = K). The highest self-interstitial concentration, Cf, is reached near the front surface; it is defined by the balance of the production rate (proportional to the Ar flux) and the consumption rate by local Ar-produced vacancies and by sinking of self-interstitials at the front surface. With specified C, the concentration ratio of the interstitial and substitutional boron species, Ni/Ns, tends to C/K due to the reaction (1). A strong loss of acceptors occurs if C >> K. It is therefore assumed that this inequality holds at least at the front surface: Cf >> K.

*Initial stage of boron acceptor loss.* At short irradiation time, the term KNi in Eq. (1) is negligible, and the boron concentration near the front surface is lost exponentially,

$$\mathbf{N}\_s(\mathbf{t}) = \mathbf{N}\_o \exp(\cdot a \, \mathbf{C}\_\mathbf{t} \, \mathbf{t}) \tag{2}$$

The *n–p* junction appears when Ns becomes less than Nd. This moment (td) lies experimentally, between 1 and 10 min. The product α Cf is estimated, from Eq. (2), to be in the range 0.01–0.001 s-1.

*Propagation of the n–p junction* The near-surface region – where a large fraction of boron is already displaced into interstitial state Bi (and then paired into BiBs) –expands as more selfinterstitials diffuse from the front surface into the bulk. The mass action law, NsC/Ni=K, is valid at duration longer than the kick-out reaction time (10 min or less). The boron-depleted region corresponds, approximately, to the condition С(x) > K. At not too long duration, the self-interstitials penetrate to some limited depth (Fig. 30 b), and the n–p junction resides at some intermediate position within the sample. Finally, the С(x) profile approaches a steadystate linear shape: the interstitials generated at the front surface are consumed at the back surface (Fig. 30 b). Therefore, the *n–p* junction does not reach the back surface but stops at some final position, just like observed.

The self-interstitial flux into the sample bulk is, approximately, DCf/ xd, where xd is the size of the boron-depleted region (xd is almost identical to position Xd of the n–p junction). The total amount of the remaining boron is equal to Co(L-xd), where L is the wafer thickness. The boron loss rate, dQ/dt, is twice as large as the above self-interstitial flux (each consumed SiI leads to a loss of two Bs: one by kick-out, and the other by pairing of Bi to Bs). The following equation provides a solution for the junction depth xd(t),

$$\chi\_{\rm d} = (4 \text{DC}\_{\rm t} \text{t}/\text{N}\_{\rm o})^{1/2} \tag{3}$$

The DCf product is estimated to be 5x107 см2с-1 from Eq. (3). Above, we estimated the product α Cf (where α is the kick-out kinetic coefficient). By these numbers, the α / D ratio is of the order of 10-10 cm. If the kick-out reaction were limited just by self-interstitial diffusion (which means

Fianite in Photonics 173

Prototypes of the solar cells have been manufactured using the obtained samples. Fianite films were used as antireflecting and protective coatings [68, 69]. The films were deposited

The study of characteristics of the prototypes of the heterostructure solar cell has shown 20-

<sup>а</sup><sup>b</sup>

Fig. 31. Prototype sample of the heterostructure solar cell of 40x40 mm size supplied with fianite antireflecting coating: functional side with Au contacting routs (a), reverse side with

The unique properties of fianite as monolithic substrute and buffer layer for Si, Ge and АIIIBV compounds epitaxy; protecting*,* stabilizing and antireflecting coatings, as well as a gate dielectric in photosensitive opto-electronic devices have been demonstrated. The results obtained in this work have actually demonstrated advantages of fianite as novel

[1] V.I. Aleksandrov, V.V. Osiko, A.M. Prokhorov, V.M. Tatarintsev. New technique of the

[2] V.I. Aleksandrov, V.V. Osiko, V.M. Tatarintsev, A.M. Prokhorov. Synthesis and crystal

[3] E.E. Lomonova, V.V. Osiko: Growth of Zirconia Crystals by Skull-Melting Technique. In:

[4] Yu.S. Kuz'minov, E.E. Lomonova, V.V. Osiko Cubic zirconia and skull melting Cambridge International Science Publishing Ltd., UK, 346 рр. 2009 [5] V.V.Osiko, M.A.Borik, E.E.Lomonova Synthesis of refractory materials by skull melting technique. Handbook of Crystal Growth, Springer, 2010, p.433-469. [6] I. Golecki, H.M. Manasevit, L.A. Moudy, J.J. Yang, and J.E Mee. Heteroepitaxial Si films

synthesis of refractory single crystals and molten ceramic materials. Vestnic AN

growth of refractory materials by RF melting in a cold container. Current Topics in

Crystal Growth Technology. Ed. by H.J. Scheel and T. Fukuda (John Wiley @ Sons,

on yttria–stabilized, cubic zirconia substrates. // Appl. Phys. Lett., 1983, v. 42, No.

multipurpose material for new optoelectronics technologies.

SSSR №12 (1973) 29-39. (in Russian)

Materials Science. 1 (1978) 421-480.

Chichester, England 2003) pp. 461-484

6, p. 501–503.

30 % efficiency gain due to the application of the fianite antireflecting films.

by means of magnetron sputtering (Fig. 31).

Au+Ti contacting layer (b)

**6. Conclusions**

**7. References** 

that any 'encounter' of a self-interstitial with the boron atoms immediately leads to the boron displacement into the interstitial state), the coefficient a/D ratio would be equal to 4r=4 x 10-7 cm, where r is of the order of the interatomic distance. The difference between the two numbers indicates some kinetic barrier (roughly, 0.25 eV) for the kick-out reaction.

*A possibility of long-range migration of interstitial boron.* It was assumed in the above discussion that the boron atoms displaced into interstitial state do not diffuse much from the initial location. The alternative possibility is that the Bi species are of high mobility (comparable to the self-interstitial mobility), and therefore they can migrate to the distance comparable to the sample thickness. In this case, a considerable spatial redistribution of boron impurity would occur. The final profile of Bi would be smoothed by diffusion to some constant (depth-independent) concentration Ni. The mass-action law would then imply that the substitutional boron concentration, Ns = NiK/C, is inversely proportional to C(x). Therefore, substitutional boron would accumulate near the back surface, where C(x) is at minimum. Such a profile of substitutional impurity (with a well-pronounced accumulation at the back surface) is typical during in-diffusion of Au and Pt impurities [65, 66].

A formation of triple junction (Fig. 29 b) can be accounted for by the long-distance migration of Bi. The boron profile after the first irradiation is of the type shown in Fig. 30 b (t=t2), with just one junction. The second (back-side) irradiation creates an *n*-region near the back surface, and also results in the boron acceptor accumulation near the front side (now nonirradiated). Then a region adjacent to the front side becomes again of *p*-type conductivity. The resulting structure is *p–n–p–n* (Fig. 29b, d).
