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Porosity variation as a function anodization time measured in both Si substrates. The used conditions are [HF] = 16% and current density of 35 mA/cm2. Our study is made on silicon P (100) and N (100). 3. Experimental protocol. Edited by Lakshmi Narayana Deepak Kallepalli. The obtained spectra are represented by Figure 10. For the N-type substrate (111), the thickness (the etch rate) of the porous layers increases linearly from 1.4 μm (0.7 μm/min) for j varying from 18 mA/cm 2 up to 106 mA/cm 2 . For N- (100) and P- (100) type substrates, we note that the variation in thickness (etch rate) versus current density is linear. Synoptic diagram of the cleaning protocol. 3.1. Design of the anodizing platform. Variation of PS layer thickness as a function of anodization time in N-type Si (100) and P-type Si (100) substrates. The used conditions are [HF] = 16% and current density of 35 mA/cm2. Keywords. Variation of reflection coefficient as a function of the incident light wavelength measured in naked Si sample used as reference and N-type and P-type Si with PS layer. For the N-type substrate (100), we obtained a variable porosity between 40 and 65% for a current density between 50 and 106 mA/cm 2 . The samples studied are obtained using an electrolytic solution of a concentration. 5.1. Porosification zone (I I PS ) Figure 1. From the Edited Volume. PS layers thickness variation and etch rate variation versus current density in (a) N-type Si (100) and (b) P-type Si (100) wafers. The variations in porosity as a function of the current density of the samples prepared are shown in Figure 8. 6.1. Influence of anodizing time on thickness. Table 3. Figure 2. If the anode potentials are at an intermediate level, there is a so-called transition zone. Since the morphology of the resulting surface is porous in nature, pore size increases rapidly with increasing potentials, leading to electropolishing of the surface. The latter are attracted by the electric field located on the surface defects; the engraving in these places will be predominant tending to smooth the surface. For the study of the I (V) characteristic the electrolytic solution which we used is formed of the following volume ratio fractions: 2 HF:3 ethanol. 7. Determination of porosity. The value of the applied potential and the reaction taking place at the interface influences on the formation of porous silicon. To know the influence of the current density on the thickness of the porous layer and on the etch rate, we set the attack time at 2 min for the three types of silicon that are available to us. For silicon types N (111) and P (100), we used an electrolytic solution concentrated at 16% HF. For the substrate type N (100), we have the same solution concentrated at 17.1%. The results obtained are presented by the graphs of Figure 7. Submitted: October 25th 2017 Reviewed: January 26th 2018 Published: November 5th 2018. chapter and author info. Anodization conditions and physical parameters of Si samples used for reflectance measurement. 4. Properties of substrates. Type and doping rate: A nano- and macroporous PS distribution was carried out on P- and N-type Si substrates. The spongy structure obtained is composed of nanocrystallites with sizes varied between 1 and 5 nm, separated by nanopores of the same type dimensions, for P-type substrates [11, 17, 18, 19], and macropores for N-type substrates [20, 21]. The increasing need of energy induces a strong greenhouse gas emission since energy production is mainly achieved by fossil fuel combustion. This gas excess has a harmful effect on the life on earth. To satisfy the increasing demand in energy, without altering our environment, it is indispensable to recourse to clean and renewable energies. Solar energy is one of the most promising renewable energy sources. Photovoltaic electricity is obtained by direct transformation of sunlight to electricity by means of solar cell. During the last few decades, photovoltaic market has an increasable progress. This leads to a growing research activity based on new materials and devices for obtaining more efficient solar cells with low cost. The reduction of optical energy losses is one of the most important factors in manufacturing high-efficiency silicon solar cells [1]. After its discovery in 1956 by Uhlir [2], porous silicon has attracted more intentions due to their interesting properties like antireflective coating, improving photovoltaic conversion efficiency [3, 4, 5, 6, 7]. Furthermore, its important specific surface has attracted earlier a technological interest in photoluminescence at room temperature and electroluminescence [8]. porous silicon antireflective coating electrochemical anodization solar cell HF. 3.3. Cleaning protocol. 3.4. Anodizing. This zone is characterized by a peak current corresponding to the formation of an oxide layer necessary for the surface electropolishing reaction [27]. 6.2. Influence of the current density on the thickness. 3.4.2. Anodizing parameters. According to the literature, this zone appears when the anode potentials are high [25]. For N-type substrates, when I > I SP the limiting factor becomes the diffusion of the ionic species in the electrolyte, the holes then in excess at the bottom of the pores penetrate the porous structure which gradually generates the total dissolution of the latter [26]. 7.2. Influence of anodization time on porosity. From Figure 6 the thickness of the porous layer increases linearly with the anodizing time, for a current density and a given RF concentration. The number of dissolved silicon atoms is therefore directly proportional to the amount of charge exchanged (Q = j × the dissolution time) showing that the dissolution valence is invariant in time. We measured the reflection factor of two samples obtained after electrochemical anodization of N (100) and P (100) silicon substrates. The formation conditions as well as the thicknesses and porosities for the two samples are summarized in Table 3. Salah Rahmouni * Figure 2 shows the schematic diagram of the anodizing device consisting of the anodizing nacelle, along with a stabilized power supply that provides a constant current. This anodizing cell uses a metal electrical contact on the back side of the silicon wafer, isolated from the HF/ethanol solution by an HF inert O-ring. Thus, only the front face is exposed to the electrolyte attack. Obviously, the diameter of the O-ring controls the diameter of the obtained porous silicon stain, which remains valid when the edge effects are neglected. According to Ozanam and Chazalviel, electropolishing exists with an oxide layer that forms on the silicon surface for I > I SP currents [25]. Authors. I (V) characteristic of silicon substrate electrochemical anodization types (a) N (100), (b) N (111), and (c) P (100). Figure 8. Experimental Study of Porous Silicon Films. 5. The I (V) characteristic. The porous silicon layers (PS) are obtained after electrochemical etching in solution of hydrofluoric acid (HF) and ethanol (C 2 H 5 OH). We note that the role of ethanol is to standardize the porous layer and to minimize the formation of hydrogen bubbles at the surface, which homogenizes the porous layer [11, 12]. The electrochemical dissolution is carried out in an impermeable material known as Teflon cell, by using the electrolyte of hydrofluoric acid solution having a high corrosive property. The cathode used in our electrochemical reactions was a circular gold or platinum grid. The Si substrate playing the role of anode is placed vertically against a circular orifice having a surface of 0.64 cm 2 in contact with the electrolyte. The shape of the cathode makes it possible to ensure a uniform distribution of the electric field lines, and subsequently the electrochemical etching of the substrate becomes homogeneous (see Figure 2). To ensure the reproducibility of the morphology of the layers and to control the porosity and the thickness, the constant-current dissolution which circulates between the two electrodes has been performed. In the case of P-type substrate, the density of holes on the silicon surface is important. Etching is limited by the diffusion of F-fluorine ions. PS layers are generally used as antireflective layer in front of solar cells to reduce the light losses. The total reflectance was measured within the 400–1100 nm wavelength range with an integrating sphere, as described in Figure 10, where we have reported the reflection coefficient of the three studied samples: the reference Si naked (N-type) that does not undergo any chemical etching and N-type and P-type Si with porous layer. The conditions used here, such as thickness and relative porosities to the two Si samples, are summarized in Table 1. From Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, one can deduce that the formation of PS layer reduces drastically the sample reflection coefficient due to the light entrapment in the formed pores. The reduction of losses by reflection caused by porous silicon layers indicates the antireflective character of this film type. This result agrees with what is returned in the literature [6, 8]. For type N (100), the variation increases from 1.4 μm (0.7 μm/min) for j = 54 mA/cm 2 to 3.19 μm (1.68 μm/min) for j = 106 mA/cm 2 . In the case of the substrate type P (100), the variation increases from 1.7 μm (0.12 μm/min) for j = 18 mA/cm 2 up to 2.9 μm (1 μm/min) for j = 70 mA/cm 2 . The present work deals with the production of porous silicon by electrochemical way, to use it as antireflective coating for solar cell. We have studied the influence of the experimental parameters such as anodization time, current, and substrate type N or P on the final porous layer thickness, porosity, and antireflective activity. PS layers’ porosity variation as a function of current density in (a) N-type Si (100) and (b) P-type Si (100) wafers. The used conditions are [HF] = 16% and current density of 35 mA/cm2. PS layer was fabricated on P-type and N-type single crystal silicon wafers with a (100) crystallographic orientation and a resistivity of 3–5 Ωcm. After a standard cleaning process, a good ohmic aluminum contact has been evaporated onto the back of samples. Anodization was then performed in a [2, 3] volume ratio of a solution composed of 40% HF and 98% ethanol. The silicon (Si) substrates used are monocrystalline, oriented (100), and (111) P and N type. Before anodization process, and in order to ensure a good electrical contact, an aluminum plate is placed on the back face of the substrate. 5.3. Transition zone. 1. Introduction. Composition of the electrolyte: The electrolyte is composed of 40% HF and ethanol. Vial and Derrien [22] showed that porosity decreases with increasing concentration at a constant current density. In our case, we used several volume ratios for the different elaborations. Characteristic of the used substrates. Figure 7. Lilia Zighed. 8. Reflectivity measurement. Figure 4 shows the I (V) characteristic of the electrochemical anodization of a sample of monocrystalline silicon types (a) N (100), (b) N (111), and (c) P (100). Figure 8 shows that porosity increases as a function of current density [28]. It increases from 33% for a current density equal to 18 mA/cm 2 in the case of silicon type P (100), up to 63% for j = 70 mA/cm 2 . Figure 10. The electrochemical anodization of silicon is achieved by a homemade system; the experimental setup is presented in Figure 1. At the silicon/electrolyte interface, the electronic charge carriers in the silicon of ionic form pass into the solution. This conversion is carried out by means of a redox reaction. To know the influence of the anodization time on the porosity, we fixed the current density at j = 35 mA/cm 2 . The concentration of [HF] = 16% in the electrolyte, and we varied the anodizing time. We obtained the curves of Figure 9. Figure 4. Electrolyte concentration, current density, type and doping rate of silicon, electrolyte temperature, and illumination [12, 13, 14, 15, 16] are essential parameters for production of porous silicon. Table 1. Figure 7 shows the variation of the thickness of the porous layer and the etch rate versus anodization current density for silicon substrates: (a) type N (111), (b) type P (100), and (c) type N (100). We note that the thicknesses of the obtained layers and the etch rates are increasing in a function of the current density [28]. Table 1 shows detailed data of the training conditions relating to the various samples of porous silicon produced. The antireflective activity is more significant in the N-type Si > as example for the 600 nm wavelength, the measured reflection coefficients are, respectively, 13, 20, and 37% for N-type, P-type, and naked Si substrates. In our experimental work, we used absolute ethanol and a hydrofluoric acid concentration of 40%. The previous proportions, i.e., 2 HF:3 ethanol, reduce the concentration [HF] in the resulting electrolyte to 16%. Normal High School of Technological Education (ENSET), Algeria Department of Electrical Engineering, University of 20 August 1955, Algeria. The porous silicon samples were made by using the electrochemical anodizing method. This method is widely used, providing homogeneous porous layers, the porosity and the thickness of the elaborate layer are so controllable. Figure 6. In the present work, we have investigated the influence of anodization time and current density upon the PS layer formation on N-type and P-type Si substrate. The formed pores in N-type Si are uniformly distributed over the sample surface with a small size, indicating an isotropic and homogenous attack of HF. However, in the case of P type, the HF etching is anisotropic; it causes the formation of large tranches composed with pores at the bottom. We have noticed that the PS layer thickness and its porosity vary linearly with the anodization time and current density. Finally, due to the pore size and distribution, we found that PS layer formed on N-type Si exhibits better antireflective activity than P-type Si, making the obtained layers important tools in the solar cell. Figure 9. *Address all correspondence to: rahmouni.eln@gmail.com. In our study, the porous silicon layers are prepared at room temperature and without illumination. The electrolytic solution used is prepared from 40% concentrated hydrofluoric acid diluted in absolute ethanol. To know the variation of the porosity as a function of the current density, we fixed the anodization time at 2 min. Table 2. [HF] = 16%, in which the current density j is 35 mA/cm 2 , for the silicon P (100). For silicon N (100), we used a current density of 54 mA/cm 2 . In order to produce porous silicon layers with a diameter of ≈10 mm, we proceeded the design of an anodizing nacelle with a circular opening. 6. Measurement of the thickness. In the limit of the porous silicon formation regime, similar behaviors are observed, whatever the anodization current and the HF concentration [25, 26, 27, 28]. Mounting used for sample preparation. In our work, we have used substrates of monocrystalline silicon types N and P, whose characteristics are presented in Table 2 below. Photograph of used experimental device for Si substrate anodization. Figure 5. Before preparation, the samples must be well cleaned accordingly to the following protocol presented (Figure 3) in the synoptic diagram of the cleaning protocol. Diagram of the porous silicon manufacturing system. One of the important features of porous silicon is the degree of porosity, i.e., the percentage of void in the porous silicon volume [29]. In our work, the determination of the porosity of the studied samples was carried out by the gravimetric method. In regard to the thickness measurement by profilometry, we studied the influence of the various anodizing parameters. 3.4.1. Mounting of elaboration. 3.2. Preparation of the substrate. Figure 3. The (I-V) characteristic of the electrolyte semiconductor junction depends on the nature of the semiconductor substrate as well as the ionic and molecular species present in the electrolyte. The application of an electrical potential to the silicon bathed in a solution of HF (see Figure 1) induces a measurable current circulating through the system. Silicon quality Samples Anodizing current density (mA/cm 2 ) Anodizing time (s) Solution volume ratio (HF:C 2 H 5 OH) Solar A1(P100) A2(P100) A3(P100) A4(P100) 15 15 15 15 60 120 180 240 1:1 1:1 1:1 1:1 Solar B1(P100) B2(P100) B3(P100) B4(P100) 5 10 15 20 180 180 180 180 1:1 1:1 1:1 1:1 Electronic C1(P100) C2(P100) C3(N100) C4(N111) 30 10, 15, 18, 20, 30, 35, 54, 70 10, 18, 30, 35, 54, 70, 214 10, 20, 35, 106, 140 120 60, 120, 180, 240, 300, 360 60, 120, 180, 240, 300, 360 60, 120, 180, 240 300, 360 3:2 2:3 2:3, 1:3 2:3. This is due to the fact that in the N type, pores have a smaller size and are uniformly distributed on the sample surface in contrary to P-type Si, where the pores are larger and spatially localized in tranches. In the present study, porous silicon films were prepared on N- and P-type silicon wafer (100) crystallographic orientations. We have investigated the influence of the different anodization parameters and silicon wafers on the properties of the obtained porous silicon layer such as thickness and porosity. The reflectance measurement of the prepared samples has presented reduction of reflection due to the porous layers and suggests the antireflective character of the realized porous layer. There are three areas that characterize the anodizing process, the I (V) curves, showing the existence of an I PS current delineating the formation and electropolishing zones. The conditions of anodization of the used substrates. Anodizing current: Note that the anodizing current and the concentration of the electrolyte have opposite effects in the formation of pores [23]. For a given concentration of the electrolyte, the porosity increases as a function of the current density. In our case, the anodizing conditions are detailed in Table 1. In 6.1, we concluded that the thickness of the porous layer varies linearly with anodization time; from Figure 9, we note that the porosity also varies almost linearly over time in a function of the anodizing time. It ranges from 38 to 64% for a sample type N silicon (100), for anodizing time from 60 to 360 s, respectively. This porosity increases from 45% up to 71% for an anodizing time from 60 to 360 s for the P-type silicon sample (100). Substrates Dopant Resistivity Ωcm Orientation N Phosphore (5–7) 100 N Phosphore (3–5) 111 P Bore (3–5) 100 P Bore (0.01–2) 100. 7.1. Influence of current density on porosity. Laboratory of Chemical Engineering and Environment, University of 20 August 1955, Algeria. 9. Conclusion. Abstract. 2. Experimental details. By Salah Rahmouni and Lilia Zighed. Sample [HF] % j (mA/cm 2 ) t (s) d (nm) P % N (100) 16 54 360 3700 68.75 P (100) 16 70 120 2660 55. Electrochemical etching is considered as the most appropriate method to produce homogenous porous silicon [9, 10]. The aim of this study is the comparison between two types of porous silicon (P and N) generated with the above electrochemical method in order to see the effect of several experimental parameters (current density, anodization time, and hydrofluoric acid “HF” concentration) on the porosity, thickness, and antireflective activity, respectively.

 

 

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Figure 7 shows the variation of the thickness of the porous layer and the etch rate versus anodization current density for silicon substrates: (a) type N (111), (b) type P (100), and (c) type N (100). We note that the thicknesses of the obtained layers and the etch rates are increasing in a function of the current density [28]. PS layers are generally used as antireflective layer in front of solar cells to reduce the light losses. The total reflectance was measured within the 400–1100 nm wavelength range with an integrating sphere, as described in Figure 10, where we have reported the reflection coefficient of the three studied samples: the reference Si naked (N-type) that does not undergo any chemical etching and N-type and P-type Si with porous layer. The conditions used here, such as thickness and relative porosities to the two Si samples, are summarized in Table 1. From Figures 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, one can deduce that the formation of PS layer reduces drastically the sample reflection coefficient due to the light entrapment in the formed pores. The reduction of losses by reflection caused by porous silicon layers indicates the antireflective character of this film type. This result agrees with what is returned in the literature [6, 8]. Substrates Dopant Resistivity Ωcm Orientation N Phosphore (5–7) 100 N Phosphore (3–5) 111 P Bore (3–5) 100 P Bore (0.01–2) 100. Figure 3. From Figure 6 the thickness of the porous layer increases linearly with the anodizing time, for a current density and a given RF concentration. The number of dissolved silicon atoms is therefore directly proportional to the amount of charge exchanged (Q = j × the dissolution time) showing that the dissolution valence is invariant in time. Abstract. Before preparation, the samples must be well cleaned accordingly to the following protocol presented (Figure 3) in the synoptic diagram of the cleaning protocol. Normal High School of Technological Education (ENSET), Algeria Department of Electrical Engineering, University of 20 August 1955, Algeria. The conditions of anodization of the used substrates. 3.1. Design of the anodizing platform. Figure 6. We measured the reflection factor of two samples obtained after electrochemical anodization of N (100) and P (100) silicon substrates. The formation conditions as well as the thicknesses and porosities for the two samples are summarized in Table 3. To know the influence of the current density on the thickness of the porous layer and on the etch rate, we set the attack time at 2 min for the three types of silicon that are available to us. For silicon types N (111) and P (100), we used an electrolytic solution concentrated at 16% HF. For the substrate type N (100), we have the same solution concentrated at 17.1%. The results obtained are presented by the graphs of Figure 7. The porous silicon samples were made by using the electrochemical anodizing method. This method is widely used, providing homogeneous porous layers, the porosity and the thickness of the elaborate layer are so controllable. If the anode potentials are at an intermediate level, there is a so-called transition zone. Since the morphology of the resulting surface is porous in nature, pore size increases rapidly with increasing potentials, leading to electropolishing of the surface. Table 1 shows detailed data of the training conditions relating to the various samples of porous silicon produced. The samples studied are obtained using an electrolytic solution of a concentration. *Address all correspondence to: rahmouni.eln@gmail.com. Figure 1. The latter are attracted by the electric field located on the surface defects; the engraving in these places will be predominant tending to smooth the surface. Porosity variation as a function anodization time measured in both Si substrates. The used conditions are [HF] = 16% and current density of 35 mA/cm2. [HF] = 16%, in which the current density j is 35 mA/cm 2 , for the silicon P (100). For silicon N (100), we used a current density of 54 mA/cm 2 . The silicon (Si) substrates used are monocrystalline, oriented (100), and (111) P and N type. Before anodization process, and in order to ensure a good electrical contact, an aluminum plate is placed on the back face of the substrate. 2. Experimental details. In the limit of the porous silicon formation regime, similar behaviors are observed, whatever the anodization current and the HF concentration [25, 26, 27, 28]. Anodization conditions and physical parameters of Si samples used for reflectance measurement. Synoptic diagram of the cleaning protocol. The (I-V) characteristic of the electrolyte semiconductor junction depends on the nature of the semiconductor substrate as well as the ionic and molecular species present in the electrolyte. The application of an electrical potential to the silicon bathed in a solution of HF (see Figure 1) induces a measurable current circulating through the system. Figure 4 shows the I (V) characteristic of the electrochemical anodization of a sample of monocrystalline silicon types (a) N (100), (b) N (111), and (c) P (100). This is due to the fact that in the N type, pores have a smaller size and are uniformly distributed on the sample surface in contrary to P-type Si, where the pores are larger and spatially localized in tranches. Figure 9. Figure 10. 3.3. Cleaning protocol. In our study, the porous silicon layers are prepared at room temperature and without illumination. The electrolytic solution used is prepared from 40% concentrated hydrofluoric acid diluted in absolute ethanol. To know the variation of the porosity as a function of the current density, we fixed the anodization time at 2 min. By Salah Rahmouni and Lilia Zighed. 6. Measurement of the thickness. For type N (100), the variation increases from 1.4 μm (0.7 μm/min) for j = 54 mA/cm 2 to 3.19 μm (1.68 μm/min) for j = 106 mA/cm 2 . In the case of the substrate type P (100), the variation increases from 1.7 μm (0.12 μm/min) for j = 18 mA/cm 2 up to 2.9 μm (1 μm/min) for j = 70 mA/cm 2 . Variation of PS layer thickness as a function of anodization time in N-type Si (100) and P-type Si (100) substrates. The used conditions are [HF] = 16% and current density of 35 mA/cm2. Photograph of used experimental device for Si substrate anodization. 6.2. Influence of the current density on the thickness. 3.4.2. Anodizing parameters. 9. Conclusion. Variation of reflection coefficient as a function of the incident light wavelength measured in naked Si sample used as reference and N-type and P-type Si with PS layer. For the N-type substrate (111), the thickness (the etch rate) of the porous layers increases linearly from 1.4 μm (0.7 μm/min) for j varying from 18 mA/cm 2 up to 106 mA/cm 2 . For N- (100) and P- (100) type substrates, we note that the variation in thickness (etch rate) versus current density is linear. The variations in porosity as a function of the current density of the samples prepared are shown in Figure 8. Table 1. In the present work, we have investigated the influence of anodization time and current density upon the PS layer formation on N-type and P-type Si substrate. The formed pores in N-type Si are uniformly distributed over the sample surface with a small size, indicating an isotropic and homogenous attack of HF. However, in the case of P type, the HF etching is anisotropic; it causes the formation of large tranches composed with pores at the bottom. We have noticed that the PS layer thickness and its porosity vary linearly with the anodization time and current density. Finally, due to the pore size and distribution, we found that PS layer formed on N-type Si exhibits better antireflective activity than P-type Si, making the obtained layers important tools in the solar cell. Experimental Study of Porous Silicon Films. In our work, we have used substrates of monocrystalline silicon types N and P, whose characteristics are presented in Table 2 below. 5.1. Porosification zone (I I PS ) Diagram of the porous silicon manufacturing system. I (V) characteristic of silicon substrate electrochemical anodization types (a) N (100), (b) N (111), and (c) P (100). At the silicon/electrolyte interface, the electronic charge carriers in the silicon of ionic form pass into the solution. This conversion is carried out by means of a redox reaction. 1. Introduction. Figure 8. Characteristic of the used substrates. In our experimental work, we used absolute ethanol and a hydrofluoric acid concentration of 40%. The previous proportions, i.e., 2 HF:3 ethanol, reduce the concentration [HF] in the resulting electrolyte to 16%. To know the influence of the anodization time on the porosity, we fixed the current density at j = 35 mA/cm 2 . The concentration of [HF] = 16% in the electrolyte, and we varied the anodizing time. We obtained the curves of Figure 9. For the N-type substrate (100), we obtained a variable porosity between 40 and 65% for a current density between 50 and 106 mA/cm 2 . The electrochemical dissolution is carried out in an impermeable material known as Teflon cell, by using the electrolyte of hydrofluoric acid solution having a high corrosive property. The cathode used in our electrochemical reactions was a circular gold or platinum grid. The Si substrate playing the role of anode is placed vertically against a circular orifice having a surface of 0.64 cm 2 in contact with the electrolyte. The shape of the cathode makes it possible to ensure a uniform distribution of the electric field lines, and subsequently the electrochemical etching of the substrate becomes homogeneous (see Figure 2). To ensure the reproducibility of the morphology of the layers and to control the porosity and the thickness, the constant-current dissolution which circulates between the two electrodes has been performed. Silicon quality Samples Anodizing current density (mA/cm 2 ) Anodizing time (s) Solution volume ratio (HF:C 2 H 5 OH) Solar A1(P100) A2(P100) A3(P100) A4(P100) 15 15 15 15 60 120 180 240 1:1 1:1 1:1 1:1 Solar B1(P100) B2(P100) B3(P100) B4(P100) 5 10 15 20 180 180 180 180 1:1 1:1 1:1 1:1 Electronic C1(P100) C2(P100) C3(N100) C4(N111) 30 10, 15, 18, 20, 30, 35, 54, 70 10, 18, 30, 35, 54, 70, 214 10, 20, 35, 106, 140 120 60, 120, 180, 240, 300, 360 60, 120, 180, 240, 300, 360 60, 120, 180, 240 300, 360 3:2 2:3 2:3, 1:3 2:3. Salah Rahmouni * This zone is characterized by a peak current corresponding to the formation of an oxide layer necessary for the surface electropolishing reaction [27]. 5. The I (V) characteristic. Sample [HF] % j (mA/cm 2 ) t (s) d (nm) P % N (100) 16 54 360 3700 68.75 P (100) 16 70 120 2660 55. Lilia Zighed. In 6.1, we concluded that the thickness of the porous layer varies linearly with anodization time; from Figure 9, we note that the porosity also varies almost linearly over time in a function of the anodizing time. It ranges from 38 to 64% for a sample type N silicon (100), for anodizing time from 60 to 360 s, respectively. This porosity increases from 45% up to 71% for an anodizing time from 60 to 360 s for the P-type silicon sample (100). For the study of the I (V) characteristic the electrolytic solution which we used is formed of the following volume ratio fractions: 2 HF:3 ethanol. In the present study, porous silicon films were prepared on N- and P-type silicon wafer (100) crystallographic orientations. We have investigated the influence of the different anodization parameters and silicon wafers on the properties of the obtained porous silicon layer such as thickness and porosity. The reflectance measurement of the prepared samples has presented reduction of reflection due to the porous layers and suggests the antireflective character of the realized porous layer. Figure 2 shows the schematic diagram of the anodizing device consisting of the anodizing nacelle, along with a stabilized power supply that provides a constant current. This anodizing cell uses a metal electrical contact on the back side of the silicon wafer, isolated from the HF/ethanol solution by an HF inert O-ring. Thus, only the front face is exposed to the electrolyte attack. Obviously, the diameter of the O-ring controls the diameter of the obtained porous silicon stain, which remains valid when the edge effects are neglected. In the case of P-type substrate, the density of holes on the silicon surface is important. Etching is limited by the diffusion of F-fluorine ions. Composition of the electrolyte: The electrolyte is composed of 40% HF and ethanol. Vial and Derrien [22] showed that porosity decreases with increasing concentration at a constant current density. In our case, we used several volume ratios for the different elaborations. The present work deals with the production of porous silicon by electrochemical way, to use it as antireflective coating for solar cell. We have studied the influence of the experimental parameters such as anodization time, current, and substrate type N or P on the final porous layer thickness, porosity, and antireflective activity. Laboratory of Chemical Engineering and Environment, University of 20 August 1955, Algeria. According to Ozanam and Chazalviel, electropolishing exists with an oxide layer that forms on the silicon surface for I > I SP currents [25]. Electrochemical etching is considered as the most appropriate method to produce homogenous porous silicon [9, 10]. The aim of this study is the comparison between two types of porous silicon (P and N) generated with the above electrochemical method in order to see the effect of several experimental parameters (current density, anodization time, and hydrofluoric acid “HF” concentration) on the porosity, thickness, and antireflective activity, respectively. 7.1. Influence of current density on porosity. The value of the applied potential and the reaction taking place at the interface influences on the formation of porous silicon. The obtained spectra are represented by Figure 10. Electrolyte concentration, current density, type and doping rate of silicon, electrolyte temperature, and illumination [12, 13, 14, 15, 16] are essential parameters for production of porous silicon. chapter and author info. The antireflective activity is more significant in the N-type Si > as example for the 600 nm wavelength, the measured reflection coefficients are, respectively, 13, 20, and 37% for N-type, P-type, and naked Si substrates. Type and doping rate: A nano- and macroporous PS distribution was carried out on P- and N-type Si substrates. The spongy structure obtained is composed of nanocrystallites with sizes varied between 1 and 5 nm, separated by nanopores of the same type dimensions, for P-type substrates [11, 17, 18, 19], and macropores for N-type substrates [20, 21]. Submitted: October 25th 2017 Reviewed: January 26th 2018 Published: November 5th 2018. Figure 7. The increasing need of energy induces a strong greenhouse gas emission since energy production is mainly achieved by fossil fuel combustion. This gas excess has a harmful effect on the life on earth. To satisfy the increasing demand in energy, without altering our environment, it is indispensable to recourse to clean and renewable energies. Solar energy is one of the most promising renewable energy sources. Photovoltaic electricity is obtained by direct transformation of sunlight to electricity by means of solar cell. During the last few decades, photovoltaic market has an increasable progress. This leads to a growing research activity based on new materials and devices for obtaining more efficient solar cells with low cost. The reduction of optical energy losses is one of the most important factors in manufacturing high-efficiency silicon solar cells [1]. After its discovery in 1956 by Uhlir [2], porous silicon has attracted more intentions due to their interesting properties like antireflective coating, improving photovoltaic conversion efficiency [3, 4, 5, 6, 7]. Furthermore, its important specific surface has attracted earlier a technological interest in photoluminescence at room temperature and electroluminescence [8]. PS layers thickness variation and etch rate variation versus current density in (a) N-type Si (100) and (b) P-type Si (100) wafers. Figure 8 shows that porosity increases as a function of current density [28]. It increases from 33% for a current density equal to 18 mA/cm 2 in the case of silicon type P (100), up to 63% for j = 70 mA/cm 2 . One of the important features of porous silicon is the degree of porosity, i.e., the percentage of void in the porous silicon volume [29]. In our work, the determination of the porosity of the studied samples was carried out by the gravimetric method. There are three areas that characterize the anodizing process, the I (V) curves, showing the existence of an I PS current delineating the formation and electropolishing zones. PS layer was fabricated on P-type and N-type single crystal silicon wafers with a (100) crystallographic orientation and a resistivity of 3–5 Ωcm. After a standard cleaning process, a good ohmic aluminum contact has been evaporated onto the back of samples. Anodization was then performed in a [2, 3] volume ratio of a solution composed of 40% HF and 98% ethanol. 4. Properties of substrates. Figure 5. Table 2. The porous silicon layers (PS) are obtained after electrochemical etching in solution of hydrofluoric acid (HF) and ethanol (C 2 H 5 OH). We note that the role of ethanol is to standardize the porous layer and to minimize the formation of hydrogen bubbles at the surface, which homogenizes the porous layer [11, 12]. 7. Determination of porosity. Authors. Figure 2. Figure 4. Anodizing current: Note that the anodizing current and the concentration of the electrolyte have opposite effects in the formation of pores [23]. For a given concentration of the electrolyte, the porosity increases as a function of the current density. In our case, the anodizing conditions are detailed in Table 1. 3.4.1. Mounting of elaboration. 5.3. Transition zone. PS layers’ porosity variation as a function of current density in (a) N-type Si (100) and (b) P-type Si (100) wafers. The used conditions are [HF] = 16% and current density of 35 mA/cm2. 3.4. Anodizing. According to the literature, this zone appears when the anode potentials are high [25]. For N-type substrates, when I > I SP the limiting factor becomes the diffusion of the ionic species in the electrolyte, the holes then in excess at the bottom of the pores penetrate the porous structure which gradually generates the total dissolution of the latter [26]. 6.1. Influence of anodizing time on thickness. Edited by Lakshmi Narayana Deepak Kallepalli. porous silicon antireflective coating electrochemical anodization solar cell HF. Mounting used for sample preparation. From the Edited Volume. Keywords. Table 3. 7.2. Influence of anodization time on porosity. In order to produce porous silicon layers with a diameter of ≈10 mm, we proceeded the design of an anodizing nacelle with a circular opening. 3.2. Preparation of the substrate. 8. Reflectivity measurement. In regard to the thickness measurement by profilometry, we studied the influence of the various anodizing parameters. The electrochemical anodization of silicon is achieved by a homemade system; the experimental setup is presented in Figure 1. Our study is made on silicon P (100) and N (100). 3. Experimental protocol.

 

 

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Electrocorticographic Frequency Alteration Mapping: A Clinical Technique for Mapping the Motor Cortex. The low frequency bands had a high sensitivity (88.9–100%) and a lower specificity (79.0–82.6%) for identifying electrodes with either hand or tongue ECS motor responses. The high frequency bands had a lower sensitivity (72.7–88.9%) and a higher specificity (92.4–94.9%) in correlation with the same respective ECS positive electrodes. Electrocortical stimulation (ECS) has been well established for delineating the eloquent cortex. However, ECS is still coarse and inefficient in delineating regions of the functional cortex and can be hampered by after-discharges. Given these constraints, an adjunct approach to defining the motor cortex is the use of electrocor-ticographic signal changes associated with active regions of the cortex. The broad range of frequency oscillations are categorized into two main groups with respect to the sensorimotor cortex: low and high frequency bands. The low frequency bands tend to show a power reduction with cortical activation, whereas the high frequency bands show power increases. These power changes associated with the activated cortex could potentially provide a powerful tool in delineating areas of the motor cortex. We explore electrocorticographic signal alterations as they occur with activated regions of the motor cortex, as well as its potential in clinical brain mapping applications. © 2019 Oxford University Press. Eric C. Leuthardt, Kai Miller, Nicholas R. Anderson, Gerwin Schalk, Joshua Dowling, John Miller, Daniel W. Moran, Jeff Ojemann, Electrocorticographic Frequency Alteration Mapping: A Clinical Technique for Mapping the Motor Cortex, Operative Neurosurgery , Volume 60, Issue suppl_4, April 2007, Pages ONS–260–ONS–271, https://doi.org/10.1227/01.NEU.0000255413.70807.6E. Abstract. Download citation file: The concordance between stimulation and spectral power changes demonstrate the possible utility of electrocorticographic frequency alteration mapping as an adjunct method to improve the efficiency and resolution of identifying the motor cortex. We evaluated seven patients who underwent invasive monitoring for seizure localization. Each patient had extraoperative ECS mapping to identify the motor cortex. All patients also performed overt hand and tongue motor tasks to identify associated frequency power changes in regard to location and degree of concordance with ECS results that localized either hand or tongue motor function.

 

 

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© 2019 Oxford University Press. Electrocortical stimulation (ECS) has been well established for delineating the eloquent cortex. However, ECS is still coarse and inefficient in delineating regions of the functional cortex and can be hampered by after-discharges. Given these constraints, an adjunct approach to defining the motor cortex is the use of electrocor-ticographic signal changes associated with active regions of the cortex. The broad range of frequency oscillations are categorized into two main groups with respect to the sensorimotor cortex: low and high frequency bands. The low frequency bands tend to show a power reduction with cortical activation, whereas the high frequency bands show power increases. These power changes associated with the activated cortex could potentially provide a powerful tool in delineating areas of the motor cortex. We explore electrocorticographic signal alterations as they occur with activated regions of the motor cortex, as well as its potential in clinical brain mapping applications. The concordance between stimulation and spectral power changes demonstrate the possible utility of electrocorticographic frequency alteration mapping as an adjunct method to improve the efficiency and resolution of identifying the motor cortex. Abstract. Download citation file: Electrocorticographic Frequency Alteration Mapping: A Clinical Technique for Mapping the Motor Cortex. The low frequency bands had a high sensitivity (88.9–100%) and a lower specificity (79.0–82.6%) for identifying electrodes with either hand or tongue ECS motor responses. The high frequency bands had a lower sensitivity (72.7–88.9%) and a higher specificity (92.4–94.9%) in correlation with the same respective ECS positive electrodes. We evaluated seven patients who underwent invasive monitoring for seizure localization. Each patient had extraoperative ECS mapping to identify the motor cortex. All patients also performed overt hand and tongue motor tasks to identify associated frequency power changes in regard to location and degree of concordance with ECS results that localized either hand or tongue motor function. Eric C. Leuthardt, Kai Miller, Nicholas R. Anderson, Gerwin Schalk, Joshua Dowling, John Miller, Daniel W. Moran, Jeff Ojemann, Electrocorticographic Frequency Alteration Mapping: A Clinical Technique for Mapping the Motor Cortex, Operative Neurosurgery , Volume 60, Issue suppl_4, April 2007, Pages ONS–260–ONS–271, https://doi.org/10.1227/01.NEU.0000255413.70807.6E.

 

 

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Swiss mice (P0–P4) were anesthetized and dissected in artificial cerebrospinal flu > Na 2 HPO 4 , 8.5 NaHCO 3 , 30 d -glucose, 1.26 CaCl 2 , and 1.15 MgCl 2 . Hindbrains were quickly removed and embedded within a 4% (wt/vol) agarose block and glued to the pedestal of a Leica microtome. Transverse slices were cut from the medulla (450 μm thick) where the rostral surface was 400–500 μm caudal to the caudal end of the facial nucleus in line with the calibrated atlas of ref. 53. Slices were then placed into a recording chamber and held down by a platinum gr > [ K + ] was exchanged with 3 mM [ K + ] ACSF to suppress spontaneous population activity once a recorded neuron was identified. For voltage-clamp recordings, we used a command potential of −60 mV, and recordings with unclamped spikes were discarded. Further details are given in SI Appendix , Materials and Methods . ↵ 1 To whom correspondence should be addressed. Email: david.holcman ens.fr . In the absence of any external input, we found that local spontaneous spiking can generate rhythmic activity among the population (Fig. 1 C and SI Appendix , Fig. S1 B ), and like in experimental studies (13), the model reproduced the cycle-to-cycle variability both in the > ± 140 ms and were followed by silent periods lasting on average 5.1 ± 1.2 s ( SI Appendix , Fig. S1 C and D ), which is in the range observed for inspiratory cycles in vitro (3) ( SI Appendix , Fig. S3). Pacemaker neurons can generate an intrinsic oscillation based on their biophysical properties such as persistent sodium current ( I N a P ). For I N a P , this current slowly inactivates to hyperpolarize and terminate bursts, whereas subsequent deinactivation causes the next depolarization and burst (8, 40, 41), which sustains rhythmic activity under certain parameter regimes. A calcium-activated nonspecific cation current ( I C A N ), ubiquitous in preBötC neurons (11, 42), can also give rise to intrinsic bursting activity (41, 43) and may contribute to SF in preBötC neurons by enhancing excitatory postsynaptic potentials (EPSPs) (42). However, electrophysiological recordings (4, 11, 44, 45) revealed that endogenous rhythmic activity was not driven by pacemaker neurons, as inhibiting them does not suppress population bursting or change the frequency. This result led to the conclusion that bursting oscillations could be generated by other mechanisms, such as the group-pacemaker hypothesis (5, 7, 11, 33), where respiratory rhythm is thought to emerge from the dynamics of synaptic input impinging on inspiratory neurons and those interactions with intrinsic cellular properties. The synaptic current for each neuron is ∑ j I s y n , j , which is the sum of the postsynaptic currents over all connected neurons ( SI Appendix ). These currents are computed for each synapse from the short-term facilitation and depression properties, modeled by two pools of vesicles ( SI Appendix ). These two pools generate two different time scales for the synaptic depression. The model we adopted for the facilitation dynamics is, however, classical, as developed in ref. 54. Synaptic depression results from the depletion of the RRP, where synaptic vesicles are gathered at the membrane before fusion. We also account for the other pool of recycling vesicles (RP) that are diffusing. for neuron i and j , where d ( i , j ) is the Euclidian distance between neurons i and j normalized by the minimal distance between two neurons. Modeled characteristics of burst induction comply with physiology. ( A ) Effect of deleting random neurons on the network rhythm. ( a ) 125 neurons (31% of the network) have been removed. ( b ) Corresponding mean membrane potential over the whole lesioned network. ( c ) Comparison between simulated (blue) and experimental lesions (red, extracted from ref. 20) of increasing numbers of preBötC neurons (see also SI Appendix , Fig. S7). ( B ) Consequences of gradually decreasing synaptic strength. Comparison between simulations (blue) and experimental results (red, extracted from ref. 26). The initial synaptic strength, controlled via K I in the model and via [NBQX] in the experimental protocol, is gradually decreased (see also SI Appendix , Fig. S8). ( C ) Hyperpolarizing and depolarizing the network from its resting state (green arrowhead) leads, respectively, to slower more variable and accelerated more regular rhythms in simulated (blue) and experimental conditions (red, extracted from ref. 28); see also SI Appendix , Fig. S9. ( D ) Response of the network to increasing stimulations. ( a ) Probability of stimulus evoked population bursts as a function of the number of randomly stimulated neurons ( n = 1–17) and the number of stimuli per train ( n = 1–6 pulses). ( b ) ( Left ) Mean V over the whole network for spontaneous and stimulated bursts ( n = 9 neurons, six pulses at 60 Hz, starting at t = 550 ms, red arrowhead). ( Right ) Magnification of the burst induction. The vertical calibration bar applies to all burst, each having a baseline potential of −65 mV. Depolarizing Neurons Increase the Rhythm Frequency. To further characterize bursting in this model, we illustrate the four principal state variables of a neuron with respect to time (Fig. 1 D and E ): its voltage V , its facilitation variable x , and the normalized depression-related variables Y free and Y dock . The fraction of vesicles in the RP ( Y free ) is quite stable, oscillating between 80% and 98% of its maximum value, whereas the fraction of docked vesicles in the RRP ( Y dock ) fluctuates between 20% and 100% of its filled state. Thus, the RRP alternates between an empty and full state, where the mean maximum number of vesicles is 4.5. When the percentage of vesicles in the RRP ( Y dock ) reaches its minimal value, the bursting period ends, leading to a decrease in the facilitation variable ( x ) that relaxes back to equilibrium (Fig. 1 E ). On the contrary, x increases exponentially when each population burst begins (Movie S2), which, associated with the decrease in Y dock , is reflected by a transient increase and subsequent decrease in the amplitude of synaptic currents during the bursts ( I syn ; Fig. 1 E ). Each neuron within the network that reaches its minimum y dock min enters a refractory state that shuts down its synaptic transmission ( SI Appendix , Fig. S1 E and F ). This minimum value leads to burst termination across the population because recurrent excitation ceases. As synapses recover, a subsequent burst can begin when several connected neurons spike in a short time interval to facilitate postsynaptic neuronal activation. This nonlinearly promotes spiking activity to spread through neighboring neurons and invade the entire network (Movies S2 and S3). These features were characteristic of additional networks with similar topologies and each network resulted in similar cycle periods (CPs), burst durations (BDs), and interburst intervals (IBIs) of 5.5 ± 1 s, 694 ± 138 ms, and 4.8 ± 1 s, respectively ( n = 10 networks), which is in the range observed in vitro. Additionally, the CP and BD can be altered by changing synaptic parameters ( SI Appendix , Figs. S4 and S5), and the spiking frequency during a burst (normally up to 60 Hz) can be modified by changing the HH-model parameters ( SI Appendix , Fig. S6). Altogether, this suggests that a large range of in vitro and in vivo data can be accounted for by this model. To support the possibility that SD, and also SF, may be occurring in vitro on timescales that could impact normal respiratory rhythms, we recorded synaptic responses in inspiratory preBötC neurons in slice preparations (Fig. 3 A ) evoked by electrical stimulation of preBötC commissural axons (35) (Fig. 3 B ). The experiments were performed in the presence of picrotoxin and strychnine (5 μM) suppressing GABAergic and glycinergic synaptic currents known to be dispensable for rhythm generation (10, 36, 37) to best reproduce the predominant glutamatergic synaptic transmission of the model. We concurrently reduced the extracellular [ K + ] from 8 to 3 mM to minimize spontaneous population activity after identifying recorded inspiratory neurons (Fig. 3 C ), and these recordings did not exhibit unclamped spikes ( SI Appendix , Fig. S12). For electrical stimulation we used trains (2- to 5-s duration) of repetitive (10–30 Hz) stimuli. The intensity of stimulation was set so that at low frequency (1/9 s) the stimulus resulted in about 50% EPSC failures. Central pattern generators (CPGs) are neuronal circuits that generate coordinated activity in the absence of sensory input (1). One such mammalian CPG, the preBötzinger complex (preBötC), gives rise to the eupneic respiratory rhythm (2, 3). Located in the medulla, the preBötC preserves a spontaneous respiratory-like rhythm when isolated in transverse slices, but the precise nature of the cellular and synaptic mechanisms underlying rhythmogenesis remains elusive (3 ⇓ ⇓ ⇓ –7). An early hypothesis was that the neuronal activity is driven by intrinsically bursting pacemaker neurons synchronized via excitatory synaptic connections (2, 6, 8, 9). However, electrophysiological and modeling studies (7, 10 ⇓ –12) now suggest the rhythm emerges through stochastic activation of intrinsic currents conveyed by recurrent synaptic connections, without the need for pacemaker neurons (3, 4, 11, 13, 14). In either case, excitatory synapses are required for rhythm generation; the possibility that synaptic properties also underlie periodic burst initiation and termination is yet to be demonstrated. Construction of the network connectivity. Few Active Neurons Are Sufficient to Trigger Population Bursts. The preBötzinger complex model and resulting network activity. ( A ) Schematic representation of the presynaptic bouton: vesicles are div > Y free = y free / y free max , Y dock = y dock / y dock max for a single neuron chosen randomly from the network (the mean bursting duration is 777 ± 98 ms, and the mean interburst interval is 5.2 ± 1.0 s). ( E ) Magnification of V , x , Y dock , and I syn for the neuron in D , during 1.5 s (same simulation as C and D ). At hyperpolarized potentials we also observed, during the IBI or immediately preceding bursts, patterns of activity reminiscent of burstlets, described in the preBötC as rhythmic bouts of low-rate spiking ( SI Appendix , Fig. S10) (29). These patterns d > ∼ 90% of preBötC neurons. Rather, these simulated patterns constitute low amplitude events that may seed burstlets and preinspiratory activity (29). All animal studies were done in accordance with the guidelines issued by the European Community and have been approved by the research ethics committee in charge (Comité d’éthique pour l’expérimentation animale) and the French Ministry of Research. Acknowledgments. Local Network Structure and Dynamics. Network connectivity within the preBötC could influence the dynamics of population activity (49). Other preBötC–related studies have used all-to-all coupling (9) or various degrees of sparse networks (13, 25) including small-world topology (7). In this study, we modeled a realistic-sized preBötC network using random connections between neurons with a distribution law that decays exponentially with the distance between neurons (Fig. 1 B and SI Appendix , Fig. S2 B ). This decay has been used in several models such as the visual cortex (figure 5 from ref. 50) or the auditory cortex (51). Connectivity between preBötC neurons could be as high as 13% when recorded in local proximity ( ∼ 60 μm) (10), whereas it could be as low as 1% as determined from multielectrode array experiments (13). Additionally, experiments with organotypic slices suggest that a preBötC–like network could be organized into loosely connected clusters, i.e., a small-world network (22). Results. Computing the synaptic current. At 20 and 30 Hz, stimulation frequently resulted in population recruitment even in our suppressed excitability. In three of seven preBötC neurons stimulated at 10 Hz, the amplitude of evoked EPSCs (eEPSCs) varied according to their timing during the stimulus trains. Typically in these cells, the amplitude of successive eEPSCs in the train showed a rap > ± 0.9 pA/s, n = 4 vs. −20.1 ± 8.3 pA/s, n = 3, t test: P = 0.043). These stationary cells may belong to the ∼ 50% fraction of nonrhythmogenic inhibitory neurons within the preBötC (38) and were not considered further. We thank C. A. Del Negro and C. S. Poon for critical reading of the manuscript. This work was supported by the CNRS, Agence Nationale de la Recherche Grant ANR-32-BSV5-0011-02, and Fondation pour la Recherche Médicale Grant DEQ20130326472 (to G.F.). D.H. thanks Labex MemoLife and the Fondation pour la Recherche Médicale Grant FDT20140931147 for support. Significance. Modeling approaches (12, 46) have shown that the cooperation of I C A N , activated by synaptic activity, coupled with activity-dependent outward currents, can generate periods of bursting separated by quiescent phases. These quiescent periods can also be achieved by transient inactivation of an I N a P similar to the one observed in pacemaker neurons, which is equivalent to activating an outward current. However, that model requires intrinsic regular spiking to activate I C A N and initiate the bursts even when the system is driven by synaptic noise, and I C A N -mediated SF and depolarization-block dependent SD alone are not sufficient for regular bursting. We show here that random networks connected with these synaptic properties, with random spiking, are sufficient for periodic bursting and examine a variety of experimental scenarios testing this model. The present model shows that an ensemble of excitatory neurons driven by synaptic dynamics can generate population-wide rhythmic activity and behaves in a manner similar to the preBötC under different conditions observed in vitro. Finally, we show experimentally that excitatory inputs to preBötC neurons often exhibit dynamically changing excitatory postsynaptic currents (EPSCs), supporting the modeled concept that SF/SD occurs on a timescale relevant to influence respiratory periods. Author contributions: G.F. and D.H. designed research; C.G. and J.A.H. performed research; C.G., J.A.H., G.F., and D.H. analyzed data; and C.G., J.A.H., G.F., and D.H. wrote the paper. Discussion. Mathematical Modeling. Materials and Methods. Can Bursting Oscillations Be Generated in Neuronal Networks Without Any Intrinsically Rhythmic Neurons? We found that a neuronal network based on Gaussian-distributed sparse synaptic connections can generate an endogenous rhythm initiated by neuronal noise. A key feature of the network is the SF and SD dynamics. Here, SD was based on a two-pool model where vesicles of one pool interact with the RRP and is a refinement of the classical SD model (39). The connectivity map for the network is implemented between every neuron. They are distributed on a square lattice (Fig. 1 B ) and connected randomly according to the probability distribution P ( i → j ) = exp [ − d ( i , j ) 2 / ( 2 s 2 ) ] , [2] The mechanism underlying mammalian respiratory rhythm generation in the preBötzinger complex is still under debate. Here, we developed a simulation model to show that a synaptic depression/facilitation mechanism sufficient for neurons to generate network rhythms, without the need for intrinsically rhythmic neurons. Simulations of the model under several normal or pathological conditions the living system experiences, together with critical electrophysiological experiments, converge to show that randomly connected neuronal networks with synaptic dynamics underlie rhythmic activity. This study provides a generally applicable mechanism for other central pattern generator systems that are less well understood. Synaptic depression is described classically as the depletion of vesicles following activation (52). Here we had to account for the depletion of both the RRP and the RP so that vesicles can arrive with the proper dynamics, which is not contained in the classical coarse-grained depression model where the rate of synaptic depression depends on the resource’s availability (39). In the classical depression model, presynaptic stimulation through a spike train produces a regime of stationary EPSPs postsynaptically after a few spikes, which does not result in burst termination due to full depletion of available vesicles. The two-pool model where vesicles can either be in the RRP or RP compartments resolves this difficulty: the arrival of a presynaptic AP triggers fusion of vesicles from the RRP, and the postsynaptic current is proportional to the amount of fused vesicles. Bursting termination in the preBötC is still unknown and might be due to several different processes such as synaptic depression, voltage-dependent/ion-activated outward currents (48), or, as postulated in previous models, due to the deactivation of inward currents (8), or a combination. In our model, burst termination is based on short-term SD, where the ready-to-fuse vesicles are lacking. Indeed, they are released in the high firing rate bursting that lasts several hundreds of milliseconds and take up to seconds to recover, consistent with respiratory refractory periods observed experimentally in vitro (34). Our approach shows that bursting oscillations can be generated in an ensemble of neurons connected by synapses, driven by depression/facilitation dynamics, without the need for any underlying endogenously rhythmic pacemaker neurons. In addition, the IBI is controlled by recurrent excitations arising from the network’s spontaneous activity. This phenomenon may be quite generic and could explain oscillations in other neuronal networks, where the mechanism remains unclear, such as the circuits for chewing, swallowing, whisking, locomotion, or, indeed, any coordinated ensembles of repetitively synchronous neuronal activities. To test the role of unitary synaptic strength, in contrast to the spread of excitatory transmission through the network, we simulated a decrease in the maximum synaptic transmission from 100% to 65% to mimic pharmacological blockade of AMPA receptors, until population burst cessation with the full 400 neuron network (Fig. 2 B and SI Appendix , Fig. S8). The results were similar to experimental conditions (26) and were notably similar to Fig. 2 Ac with respect to the exponential divergence of cycle period as well. The latter point further suggests that the net strength of connections between neurons is of principal importance for burst induction, and thereby, rhythm generation. Role of Synaptic Depression in Burst Termination. The preBötC is the target of many neuromodulators, the balance of which can affect the tonic excitability of the network (27). To investigate how tonic changes in V affect bursting, we modulated the neuronal excitability by adding an applied current ( I app ) to the current balance equation of the entire network. Positive I app is equivalent to increasing extracellular [ K + ] . After hyperpolarization ( I app = −0.5 pA), the IBI and variability in rhythm increases drastically (Fig. 2 C and SI Appendix , Fig. S9), whereas depolarizing the network ( I app = 0.75 pA) decreased the CP and variability in rhythm. At higher depolarization, the frequency of bursting reaches a plateau principally constrained by the refractoriness in the model ( CP plateau = 3.5 ± 0.1 s and BD plateau = 560 ± 227 ms compared with control values I app = 0 pA: CP = 5.1 ± 0.8 s and BD = 660 ± 161 ms). These values are comparable to the ones reported in physiological experiments (28) for CP = 5.7 ± 0.5 s and CP plateau = 3.5 ± 0.2 s, with no notable decreases in BD and spike frequency. In the case of hyperpolarization, we detected very few bursts after 1,500 s, corresponding to CP = 240.6 ± 185.7 s, which is comparable to the long CP (143.2 ± 3.9 s) reported in ref. 28. We conclude that changing the tonic excitability in our model has drastic consequences on CP owing to changes in IBI but not BD, in agreement with previous experimental data. Our choice of connectivity is broadly consistent with the three previous experimental results (10, 13, 22) when the pair-to-pair coupling decays fast at large distances. The decay of neuronal connectivity with the distance between neurons prevents the emergence of nonhomogeneous connectivity in the network. Indeed, in the > s ≤ 0.8, the IBI has large variability, and when s ≥ 1, waves of APs at low frequency can emerge in the network ( SI Appendix , Fig. S2 F and Movies S6 and S7). We model a neuronal network consisting of 20 × 20 (i.e., 400) connected neurons organized on a square lattice and account for synaptic dynamic and voltage properties. To model the membrane potential of each neuron, we use a simplified Hodgkin–Huxley model, where we cons > Na + , K + , and leak channels. The associated currents are I N a , I K , and I L . The resting potential of each neuron is at a mean of −65.1 mV, distributed randomly according to a Gaussian distribution with a variance of 0.2. To account for spontaneous fluctuations of the membrane potential, we add a Gaussian noise source term W ˙ to the potential with a variance σ . The general equation for one neuron is C V ˙ = − I N a − I K − I L + ∑ j I s y n , j + σ W ˙ . [1] Experimental support for rap > Robust Rhythmic Activity Generated in the Model Network. Electrophysiology. To compute the synaptic current between two connected neurons, we use the synaptic model described above ( SI Appendix ). The postsynaptic current i ( t ) , due to an action potential generated in the presynaptic neuron, is proportional to the amount of released vesicles. Neuronal network modeling. Rhythmic Activity Depends on the Number and Strength of Connected Neurons. For the recordings that exhibited dynamic synapses (Fig. 3 E , black), normalizing their eEPSC amplitudes with respect to the maximal eEPSC of each neuron’s mean train revealed a more consistent trend among the data than the raw data may have initially suggested (Fig. 3 F , gray; n = 3, n = 5–16 trials), with exponential fits to their rising and falling components. The rising exponential suggests the presence of short-term SF, (as illustrated by x in Fig. 1 E ) and the falling exponential consistent with short-term SD (an amalgamation of x and Y dock ; Fig. 1 E ). These electrophysiological data match the predicted model dynamics of I syn in Fig. 1 E and would suggest that, together with the rest of the favorable modeling tests performed here recapitulating experimental results (20, 26, 28, 34), the modeling approach we exercised is applicable to the respiratory rhythm-generating network in vitro. To investigate whether rhythmic activity can emerge from randomly connected neurons with dynamic synapses, we simulated the membrane potential ( V ) in 400 neurons ( Materials and Methods ), comparable to the number of preBötC rhythm-generating neurons (20). For each neuron, the key active properties are the RP and RRP for synaptic vesicles (Fig. 1 A ), whereas neuronal spikes are governed by Hodgkin–Huxley equations and driven by random membrane noise. The network has a structure where the neurons were la > s = 0.9 ; Eq. 2 ), which represents a neuron-to-neuron connection probability of about 2%. The connection probability required to obtain rhythmicity, with these cellular parameters, is in the range 1.2–2.5% ( Discussion and SI Appendix , Fig. S2). To conclude, our modeling confirms the group pacemaker hypothesis (11), where eupneic respiratory rhythm is attributed to the cooperative interactions between inspiratory neurons. The present results show that periodic inspiratory bursts can emerge from recurrent neuronal connections and synaptic dynamics, without the need of any underlying neuronal rhythm driven by pacemaker neurons or a subpopulation of oscillatory firing neurons. Synaptic dynamics are thus a plausible mechanism of preBötC rhythmogenesis, even if other nonsynaptic mechanisms might be involved to fully reproduce the range of respiratory behaviors. Synaptic transmission relies on the release of vesicles, which can be modulated at the presynaptic terminal. Synaptic depression (SD), based on vesicular release, consists of decaying release probability after sustained activity, which subsequently decreases excitability within the underlying connected network. Conversely, synaptic facilitation (SF) enhances vesicular release probability and promotes neuronal synchronization. These synaptic dynamics are critical for short-term synaptic plasticity, and here they are explored in the context of preBötC rhythm generation. Another important feature of the preBötC network is its rapid responsiveness to phasic inputs from central or peripheral (reflex) origins (30 ⇓ –32). Therefore, we sought to evaluate the minimal number of concurrently active neurons necessary for initiating a preBötC network response. To do so, we depolarized a variable number of randomly chosen neurons with graded trains of stimulation (one to six stimulations per train, 50 μs, 60 Hz). We quantified the probability of evoked bursts for the respective conditions (Fig. 2 D and SI Appendix ). When 17 neurons (4.25% of the network) were stimulated with a single stimulus, or with a two-stimulus train, it was possible to induce a burst with a low probability ≤ 15%. However, using trains of five to six stimuli, the probability was higher than 80%, and in these cases, decreasing the number of stimulated neurons revealed that 5–10 neurons were sufficient to induce network bursts. The early phase of the evoked burst, manifesting the propagation of excitatory synaptic inputs in the network (Movie S3), was similar to that of spontaneously occurring bursts (Fig. 2 Db ), in agreement with the group-pacemaker hypothesis (11, 12, 33) and burstlet-dependent generation of bursts (29). Finally, these results are in keeping with the recent physiological demonstration in slice preparations that targeting four to nine preBötC neurons with glutamate uncaging was sufficient to induce ectopic endogenous-like bursts (34). We first consider a randomly connected network where each neuron is modeled using a generalized Hodgkin–Huxley system of equations and exhibits spontaneous spiking activity based on a random process, but the neurons do not have intrinsic bursting mechanisms. These neurons are sparsely connected within a realistically sized network by excitatory synapses. The distinction of this model, from previous preBötC models, is that synapses express SF and SD that is implemented using two separate pools of vesicles and creates dynamic synapses. The first pool is the readily releasable pool (RRP) and the other is the recycling pool (RP) (15), modeled with mass-action kinetics. Synaptic dynamics has been repeatedly used to describe changes in spike rates in neural network populations (16) and emergence of gamma oscillations (17). Furthermore network connectivity can also participate to define bursting or the oscillation frequency in neural networks (18, 19). How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrophysiological recordings, that SF/SD can occur at preBötC synapses on timescales that influence rhythmic population activity. We conclude that nondeterministic neuronal spiking and dynamic synaptic strengths in a randomly connected network are sufficient to give rise to regular respiratory-like rhythmic network activity and lability, which may play an important role in generating the rhythm for breathing and other coordinated motor activities in mammals. Abstract. Robust network oscillations during mammalian respiratory rhythm generation driven by synaptic dynamics. The authors declare no conflict of interest. Here, we modeled a neuronal network that contains sparse connections and is based on SF with a two-pool state for SD. Burst initiation relies on spontaneous spiking of a small number of neurons that recruit the entire network by recurrent excitation among neurons. The increase in SF in our model promotes the recurrent excitation, similar to the I C A N evoked by intrinsic activity in ref. 12, and observed in electrophysiological recordings in vitro (45, 47). To propagate to the entire network, nearly synchronous firing must first occur in several neurons. This synchronization may be caused by synaptic inputs coinc > τ f (see x in Fig. 1 E ), the effective degree of network connectivity (Fig. 2 A and SI Appendix , Fig. S2–S7), the maximal synaptic strength K I (Fig. 2 B and SI Appendix , Fig. S8), and the amount of spontaneous spiking (Fig. 2 C and D and SI Appendix , Fig. S9). Changing any one of these factors affects the bursting frequency and regularity. With some neurodegenerative diseases, brainstem neurons die and are not replenished (23). Similar conditions in rats cause sleep apneas that could lead to death without intervention (24). To investigate the role of network size in our model, we randomly removed neurons as shown in Fig. 2 A . When 12.5% of the network neurons were removed (50 neurons; SI Appendix , Fig. S7), the network activity was not perturbed. When 25% (100 neurons) of the network was removed, the rhythm started to be affected, whereas bursts became erratic when this fraction reached 31% (125 neurons; Fig. 2 Aa and Ab ), and disappeared when more than 44% of neurons were removed ( ≥ 175 neurons; SI Appendix , Fig. S7). Lesioning 175 neurons resulted in a CV of ∼1, indicating a very unstable rhythm, and lesions beyond that eliminated all spontaneous bursts. Normalizing the number of lesioned neurons to the total required for complete rhythm cessation resulted in exponential increases in the CPs and variability (Fig. 2 Ac ), comparable to those obtained in previous physiological in vitro experiments (20, 25). The proportion of lesioned neurons required to stop bursting is nevertheless higher than observed experimentally in vitro ( Discussion and SI Appendix , Fig. S7 E ). The BD (about 670 ms) was not statistically changed by reduction of the network size by 50, 100, and 125 neurons, whereas the CP increased from 5.5 ± 1.1 to 7.1 ± 2.2 to 10.2 ± 5.3, and to 15.5 ± 13.3 s, respectively. If CP depends on the number of neurons within the population, it could be because each lesioned cell creates holes in the network that put at risk the spread of activity within the population (Movies S4 and S5). In addition, these lesions also effectively decrease the number of inputs to each remaining neuron and thus the strength of inputs to each of them. Short-Term Synaptic Plasticity in the preBötC Inspiratory Rhythm Generator. Footnotes. Edited by Richard L. Huganir, The Johns Hopkins University School of Medicine, Baltimore, MD, and approved June 29, 2015 (received for review December 1, 2014)

 

 

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