rus
Issue #6/2017
I.Obukhov, G.Gorokh, A.Lozovenko, E.Smirnova
Matrices of indium antimonide nanowires and their applications in microwave generators
Matrices of indium antimonide nanowires and their applications in microwave generators
The methods of manufacturing the matrices of the indium antimonide nanowires into regular pores of anodic alumina with various metal contacts on the different substrates have been described. It is shown that generators of terahertz electromagnetic radiation can be created on the basis of these matrices.
Теги: anodic aluminum oxide microwave generator relaxation instability terahertz анодный оксид алюминия релаксационная неустойчивость свч-генератор терагерц
The unique properties of indium antimonide (InSb) make this material one of the most optimal for the microwave electronics, focused on low power consumption [1, 2]. Owing to the small effective mass of conduction electrons, dimensional quantization affects the electrical characteristics of InSb structures with size of 60 nm and less at room temperature [1, 3].
Modern technologies allow the formation of InSb nanowires with a diameter of 30 nm or more in regular pores of anodic aluminum oxide (AAO) matrices [4–8]. Thus, it is possible to use in practice the dimensional quantization of the electron energy in these objects.
Fig.1 shows a schematic representation of a nanowire, and Fig.2 shows the characteristic potential reliefs of electrons in such a structure for different transverse size of the conducting channel. The boundaries of the contacts with the conducting channel are heterojunctions. The conducting channel with a cross section L⊥<Ldq is a potential barrier for electrons whose height is regulated by the quantity of L⊥. The smaller the cross-section, the higher the barrier and, correspondingly, the smaller the electron concentration in the channel [3].
These dependencies can be used to design functional electronic devices based on nanowires. It should be borne in mind that the flow of current through heterojunctions leads to the appearance of nonequilibrium electrons [3], whose properties are the basis for the functioning of the devices considered below.
FORMATION OF NANOWIRES
IN MATRIX OF ANODIC
ALUMINUM OXIDE
InSb nanowires in AAO matrices can be formed on glass, dielectric or semiconductor substrates, as well as on free membranes and substrates made of porous aluminium oxide [4–8]. The pore diameters in the AAO matrices and the thickness of the oxide itself are set in advance, based on the technical requirements for the device being created.
The method of preparation of AAO matrices intended for the formation of nanowires in them, the pore size, as well as the technology of synthesis of the conducting channels of nanowires and the material of contacts determine the properties and characteristics of matrix structures. Fig.3 schematically shows the sequence of processes for the formation of InSb nanowires in the pores of thin AAO matrices on silicon substrates (Fig.3a) and in nanoporous AAO substrates (Fig.3b). In the latter case, the ratio of the length of the conducting channels of nanowires to their diameter can reach thousands or more.
The electrochemical deposition of indium antimonide into the pores of the AAO matrices directly to the silicon surface or to the metal surface is carried out in a chloride electrolyte of the following composition: an aqueous solution of SbCl3 (0.1M), InCl3 (0.15M), citric acid (0.36M) and potassium citrate (0.17M) adjusted to pH = 2.0 with a 20% solution of HCl [9]. InSb deposition is carried out in a combined mode with alternating current (50 Hz) with a density of 8 mA/cm2 within 3 minutes and with constant current with a density of 4 mA/cm2 within 20–50 minutes with constant stirring of the solution by a magnetic stirrer. The cathode potential with respect to the reference electrode (Ag/AgCl) when deposited on the n-Si substrate is 1.2–1.7 V, and when deposited on the metal – 0.7–0.9 V. The electrolyte temperature is maintained in the range of 25 ± 1 °С.
This technology allows the formation of regular arrays of nanowires with diameters from 30 nm to 70 nm and distances between pores of 40–100 nm. The height of the matrices can vary from 200 nm to 50 μm. The "packing density" of nanowires is 1010–1011 wires/cm2, and the characteristic cross-sectional area of conducting channels is 10-11 cm2.
Electron microscopic images of AAO matrices on a silicon substrate for the deposition of nanowires, as well as an array of nanowires on a substrate after selective dissolution of the AAO matrix are shown in Fig.4. Fig.5 shows electron images of AAO substrate with InSb nanowires and nanowires themselves after selective dissolution of the substrate.
Using the electron-probe X-ray spectral microanalysis, the composition of InSb nanowires was studied. It was determined that in terms of weight, indium's share is 36.89%, and the share of antimony is 63.11%. Atomic ratio of these elements in the composition of nanostructures is somewhat different – 38.26% In and 61.74% Sb. The data obtained indicate that InSb is in the polycrystalline state in nanowires [10, 11].
Important role in the functioning of devices based on nanowire arrays is played by transitions between contact areas and a conducting channel. Contacts were formed from various materials (nickel, copper, aluminum), and measurements of the current-voltage characteristics of InSb nanowire matrices in AAO were performed. The measurement procedure is described in [11].
Fig.6 shows the current-voltage characteristics of InSb nanowire matrices with nickel and copper contacts. The current-voltage characteristic of structures with nickel contacts, presented in Fig.6a, had a nonlinear appearance, three sections can be distinguished in them by the degree of nonlinearity. The first is characterized by a weak nonlinear current dependence on the voltage: the current rises from 0 mA to 5 mA with an increase in voltage from 0 V to a threshold value of 3–3.5 V. In the second section, with a further increase in voltage to 4–4.5 V, the nonlinearity coefficient becomes maximum, and the current rise to 15–20 mA. In the third section, with an insignificant increase in the voltage, the current rises to its maximum value, while the current density through the contact connecting about 1,025 · 108 nanowires was 27.18 A/cm2. Despite the fact that the CVC measured at different contacts had the same form, the boundaries of the designated sections varied within ± 0.5 V.
On the CVC of matrices with copper contacts, after the first connection, the preaging of contact transitions of InSb/Cu occurred. The CVCs were stable with the exponential dependence of the current on the varying voltages for forward and reverse connection (Fig.6b). The currents through the nanowires reached 320 mA and were stable in time, which corresponded to a current density of 129.8 A/cm2. On some samples, an CVC with a hysteresis was observed, which disappeared after several series of measurements. This phenomenon is apparently connected with the presence of oxide and cuprous oxide and migration of oxygen in the contact layer of the matrix [11].
The CVC of the structure with aluminum contacts looked similar to the current-voltage characteristic of the copper contact structure shown in Fig.6b. The current density in such structures was about 100 A/cm2. There were kinks on the characteristic, which can be explained by heating the sample.
Experiments on samples with gold contacts continue to this day. They give hope for obtaining current densities close to 104–105 A/cm2, which were calculated in [1] and measured for a single InSb nanowire by the authors of [12]. Obtaining high current densities will indicate sufficient perfection of the investigated structures and the possibility of implementing on their basis the proposed device designs.
RELAXATION INSTABILITY
AND GENERATION OF MICROWAVE OSCILLATIONS
Under certain conditions, relaxation instabilities and damped oscillations of the electron concentration can arise in the contact regions of the nanowire [3]. Both of these phenomena have a threshold character and are possible only if the electron mobilities in the contacts and the conducting channel of the nanowire are different.
For definiteness, we will assume that the mobility of electrons in the conducting channel of the nanowire is greater than their mobilities in the emitter and collector contacts. This assumption is justified for InSb nanowires with contacts made of other semiconductor materials or metals. Then, with a positive displacement between the collector and the emitter, the relaxation instability can be observed in the collector contact, and the oscillations of the electron concentration – in the emitter contact.
Relaxation instability develops if the current density in the nanowire j exceeds the threshold value jins. The cause of the instability is the velocity (too high for j> jins) of nonequilibrium electrons that come from the conductive channel of the nanowire to the collector contact. They do not have time to relax to the state of thermodynamic equilibrium during the time of flight of the relaxation length, and accumulate in the contact area.
According to the calculations of [3], the electron concentration in the emitter junction increases exponentially with an increment of the order of 40 THz at room temperature. When a certain limiting concentration [13, 14] is reached, its growth is replaced by an exponentially fast decay with a decrement of the same order, or a thermal breakdown occurs. For nanowires with a short channel [3] and a low intrinsic electron concentration in the collector contact, the relaxation instability should lead to appreciable changes in the conductivity of the structure.
If the current density in the nanowire exceeds another threshold value josc, damped high-frequency oscillations of the electron concentration appear in the emitter contact [3]. The reason for the oscillations is the inadequate concentration of electrons necessary to ensure, in a stationary mode, the required level of their injection from the emitter into the conducting channel of the nanowire.
In general, the threshold densities of jins and josc are different. However, by varying the parameters of the nanowire, it can be achieved that both of the considered phenomena will begin to develop at the same current density value [14]. In this case, as seen in Fig.7, an inductance appears in the emitter, and in the collector, as shown in Fig.8, a region with a negative differential resistance is formed. That is, the conditions necessary for generating microwave power arise.
Analysis of the relationships obtained in [3, 13, 14] shows that the generation of microwave oscillations in a quantum wire is possible only for certain relations between its geometric and electrophysical parameters. The results presented in Fig.7–9 were calculated for a nanowire with InSb conductor channel of 100 nm in length and silicon contacts of n-type. The length of the emitter contact was also 100 nm, and the electron concentration – 1014 cm3. The length of the collector contact was 500 nm, and the electron concentration – 5 ∙ 1014 cm3.
Calculation of the maximum power generating by such a nanowire to the external circuit is shown in Fig.9. At frequencies below 1.4 THz, it can generate about 10 nW of microwave power. At the same time, its estimated efficiency is about 13%. At frequencies exceeding 7.2 THz, the generation ceases and the quantum wire absorbs external energy [13, 14].
EQUIVALENT CIRCUIT
The electrical equivalent circuit for the matrix of nanowires is shown in Fig.10. It consists of the following elements: emitter (resistance Re, capacity Ce, inductance Le), region of conducting channels (resistance Rch), collector (resistances Rc1 and Rc2, capacitance Cs).
All parameters are current functions and are calculated on the basis of simulation results of charge transfer in the nanowire, taking into account the existence of instability and relaxation modes. The resistances of Re and Rc1 are the usual ohmic resistances of the emitter and collector, positive for all current values. The resistance Rc2 is positive for currents less than the relaxation instability threshold, and becomes negative when the current exceeds the threshold value. The value of Rc2 is determined by the damping decrement or the growth increment of electron concentration fluctuations in the collector. The Le inductance equals zero at currents less than the threshold of relaxation oscillations and is determined by their frequency when the current exceeds the threshold value.
To take into account the effect of the microwave electric field of the resonator on the processes in the semiconductor structure, the oscillator circuit must be supplemented by an oscillatory circuit. Therefore, numerical calculations were carried out with an oscillatory circuit (Fig.11), taking into account the basic design features of the electrodynamic system of the generator.
In this circuit, the diodes connected toward each other play the role of a frequency limiter, and the oscillatory circuit replaces the combined oscillatory system formed by the coaxial circuit of the structure and by the adjustable waveguide resonator connected to its resonator chamber.
MODELING
During the simulation, the numerical values of the elements of the equivalent circuit were optimized. The operating point was chosen so that the growth increment of the electron concentration fluctuations in the collector corresponded to the terahertz frequency range. As a result, a current of 4.10 A is selected. The circuit parameters at this current turn out to be: Re = 0.0574 Ohm, Ce = 0.184 pF, Le = 0.00 H, Rc1 = 0.0154 Ohm, Rc2 = 3.83 Ohm, Cc = 0.224 pF, Rch = 0.0313 Ohm.
Calculations of the characteristics of the generator in the housing showed that the inductance of the emitter makes it difficult for the device to go into the generation mode. For this reason, the emitter of the active element is made of gold, and not of silicon. In this case, relaxation oscillations in the emitter contact can occur only at very high currents, several orders of magnitude higher than the threshold current of the relaxation instability in the collector.
The trigger pulse was selected with an amplitude of 0.1 V at a frequency of 0.97 GHz. The inductance and capacitance of the external oscillatory circuit varied within 2.63–0.56 pH, 0.105–0.022 fF. As a result, excitation of oscillations at frequencies from 303 GHz to 994.7 GHz was provided. Fig.12 and Fig.13 show the calculated dependences of the voltage of the generated signal on time and the spectra of the signals at these frequencies. Numerical simulation showed that, when turned on, the generator starts "hard", the amplitude of the oscillations reaches a stationary value Uw = 0.8 V for the first half of the oscillation period, the available output power is 12.8 mW.
The microwave generator as an equivalent four-terminal network can be described by S-parameters measured in lines with matched loads, which is realized most simply at the ultrahigh frequencies. Using S-parameters of the generator measured at several frequencies, it is possible to determine (or refine) the elements of its equivalent circuit, and conversely, the known equivalent circuit allows calculating S-parameters at any frequency of the range in which this circuit is correct.
To calculate the S-parameters of the microwave generator with matrix of nanowires as the active element, the EMPro software was used. The results are shown in Figs.14 and 15. The reflection coefficient (S11) reaches the minimum value at a frequency of 650 GHz. At the same frequency, the transmission factor (S12) has a quite acceptable value of about 10 dB. Also there are local minima of S11 parameter at frequencies 300 GHz, 370 GHz, 910 GHz, etc.
Based on the analysis of the dependence of the S-parameters of the generator on frequency, it can be concluded that the frequencies of 300 GHz, 370 GHz, 650 GHz and 910 GHz are optimal for its operation. At these frequencies, the reflection coefficient has minima, the transmission coefficient – local maxima, and the VSWR takes values in the range from 4 to 15.
Fig.16 shows the distribution of the electric field E in the waveguide at selected frequencies. At a frequency of 300 GHz, the largest part of the power goes out in the direction of the payload, the amplitude change occurs uniformly along the wide wall of the waveguide. At 370 GHz, part of the power is spent in the direction of the regulating piston. At 650 GHz, the amplitude of the E-field reaches higher values than at 300 GHz, but its distribution along the waveguide is not uniform. At a frequency of 910 GHz, the formation of E-waves is not observed, that is, it is impossible to create a stable power source.
CONCLUSION
Modern technology allows the creation of matrix of InSb nanowires in regular pores of anodic aluminum oxide. The geometric characteristics of the conducting channels vary from 30 nm to 70 nm with lengths from 200 nm to 50 μm. The planar dimensions of the matrices, in principle, are unlimited. Contacts of nanowires can be created using various metals, semimetals and semiconductors.
In the conducting channels of InSb with dimensions less than 60 nm, already at room temperature, the quantization of the electron energy is realized. The nanowire contacts can be formed in such a way that heterojunctions are formed between them and the conducting channel. When current flows through heterojunctions, various non-equilibrium quantum phenomena are realized that determine the spectrum of possible applications of nanowire matrices.
In particular, generators of electromagnetic oscillations can be created in the frequency range from 300 GHz to 3 THz. Theoretical estimates indicate the uniqueness of the characteristics of these promising devices. The first experimental results confirm theoretical predictions. ■
Modern technologies allow the formation of InSb nanowires with a diameter of 30 nm or more in regular pores of anodic aluminum oxide (AAO) matrices [4–8]. Thus, it is possible to use in practice the dimensional quantization of the electron energy in these objects.
Fig.1 shows a schematic representation of a nanowire, and Fig.2 shows the characteristic potential reliefs of electrons in such a structure for different transverse size of the conducting channel. The boundaries of the contacts with the conducting channel are heterojunctions. The conducting channel with a cross section L⊥<Ldq is a potential barrier for electrons whose height is regulated by the quantity of L⊥. The smaller the cross-section, the higher the barrier and, correspondingly, the smaller the electron concentration in the channel [3].
These dependencies can be used to design functional electronic devices based on nanowires. It should be borne in mind that the flow of current through heterojunctions leads to the appearance of nonequilibrium electrons [3], whose properties are the basis for the functioning of the devices considered below.
FORMATION OF NANOWIRES
IN MATRIX OF ANODIC
ALUMINUM OXIDE
InSb nanowires in AAO matrices can be formed on glass, dielectric or semiconductor substrates, as well as on free membranes and substrates made of porous aluminium oxide [4–8]. The pore diameters in the AAO matrices and the thickness of the oxide itself are set in advance, based on the technical requirements for the device being created.
The method of preparation of AAO matrices intended for the formation of nanowires in them, the pore size, as well as the technology of synthesis of the conducting channels of nanowires and the material of contacts determine the properties and characteristics of matrix structures. Fig.3 schematically shows the sequence of processes for the formation of InSb nanowires in the pores of thin AAO matrices on silicon substrates (Fig.3a) and in nanoporous AAO substrates (Fig.3b). In the latter case, the ratio of the length of the conducting channels of nanowires to their diameter can reach thousands or more.
The electrochemical deposition of indium antimonide into the pores of the AAO matrices directly to the silicon surface or to the metal surface is carried out in a chloride electrolyte of the following composition: an aqueous solution of SbCl3 (0.1M), InCl3 (0.15M), citric acid (0.36M) and potassium citrate (0.17M) adjusted to pH = 2.0 with a 20% solution of HCl [9]. InSb deposition is carried out in a combined mode with alternating current (50 Hz) with a density of 8 mA/cm2 within 3 minutes and with constant current with a density of 4 mA/cm2 within 20–50 minutes with constant stirring of the solution by a magnetic stirrer. The cathode potential with respect to the reference electrode (Ag/AgCl) when deposited on the n-Si substrate is 1.2–1.7 V, and when deposited on the metal – 0.7–0.9 V. The electrolyte temperature is maintained in the range of 25 ± 1 °С.
This technology allows the formation of regular arrays of nanowires with diameters from 30 nm to 70 nm and distances between pores of 40–100 nm. The height of the matrices can vary from 200 nm to 50 μm. The "packing density" of nanowires is 1010–1011 wires/cm2, and the characteristic cross-sectional area of conducting channels is 10-11 cm2.
Electron microscopic images of AAO matrices on a silicon substrate for the deposition of nanowires, as well as an array of nanowires on a substrate after selective dissolution of the AAO matrix are shown in Fig.4. Fig.5 shows electron images of AAO substrate with InSb nanowires and nanowires themselves after selective dissolution of the substrate.
Using the electron-probe X-ray spectral microanalysis, the composition of InSb nanowires was studied. It was determined that in terms of weight, indium's share is 36.89%, and the share of antimony is 63.11%. Atomic ratio of these elements in the composition of nanostructures is somewhat different – 38.26% In and 61.74% Sb. The data obtained indicate that InSb is in the polycrystalline state in nanowires [10, 11].
Important role in the functioning of devices based on nanowire arrays is played by transitions between contact areas and a conducting channel. Contacts were formed from various materials (nickel, copper, aluminum), and measurements of the current-voltage characteristics of InSb nanowire matrices in AAO were performed. The measurement procedure is described in [11].
Fig.6 shows the current-voltage characteristics of InSb nanowire matrices with nickel and copper contacts. The current-voltage characteristic of structures with nickel contacts, presented in Fig.6a, had a nonlinear appearance, three sections can be distinguished in them by the degree of nonlinearity. The first is characterized by a weak nonlinear current dependence on the voltage: the current rises from 0 mA to 5 mA with an increase in voltage from 0 V to a threshold value of 3–3.5 V. In the second section, with a further increase in voltage to 4–4.5 V, the nonlinearity coefficient becomes maximum, and the current rise to 15–20 mA. In the third section, with an insignificant increase in the voltage, the current rises to its maximum value, while the current density through the contact connecting about 1,025 · 108 nanowires was 27.18 A/cm2. Despite the fact that the CVC measured at different contacts had the same form, the boundaries of the designated sections varied within ± 0.5 V.
On the CVC of matrices with copper contacts, after the first connection, the preaging of contact transitions of InSb/Cu occurred. The CVCs were stable with the exponential dependence of the current on the varying voltages for forward and reverse connection (Fig.6b). The currents through the nanowires reached 320 mA and were stable in time, which corresponded to a current density of 129.8 A/cm2. On some samples, an CVC with a hysteresis was observed, which disappeared after several series of measurements. This phenomenon is apparently connected with the presence of oxide and cuprous oxide and migration of oxygen in the contact layer of the matrix [11].
The CVC of the structure with aluminum contacts looked similar to the current-voltage characteristic of the copper contact structure shown in Fig.6b. The current density in such structures was about 100 A/cm2. There were kinks on the characteristic, which can be explained by heating the sample.
Experiments on samples with gold contacts continue to this day. They give hope for obtaining current densities close to 104–105 A/cm2, which were calculated in [1] and measured for a single InSb nanowire by the authors of [12]. Obtaining high current densities will indicate sufficient perfection of the investigated structures and the possibility of implementing on their basis the proposed device designs.
RELAXATION INSTABILITY
AND GENERATION OF MICROWAVE OSCILLATIONS
Under certain conditions, relaxation instabilities and damped oscillations of the electron concentration can arise in the contact regions of the nanowire [3]. Both of these phenomena have a threshold character and are possible only if the electron mobilities in the contacts and the conducting channel of the nanowire are different.
For definiteness, we will assume that the mobility of electrons in the conducting channel of the nanowire is greater than their mobilities in the emitter and collector contacts. This assumption is justified for InSb nanowires with contacts made of other semiconductor materials or metals. Then, with a positive displacement between the collector and the emitter, the relaxation instability can be observed in the collector contact, and the oscillations of the electron concentration – in the emitter contact.
Relaxation instability develops if the current density in the nanowire j exceeds the threshold value jins. The cause of the instability is the velocity (too high for j> jins) of nonequilibrium electrons that come from the conductive channel of the nanowire to the collector contact. They do not have time to relax to the state of thermodynamic equilibrium during the time of flight of the relaxation length, and accumulate in the contact area.
According to the calculations of [3], the electron concentration in the emitter junction increases exponentially with an increment of the order of 40 THz at room temperature. When a certain limiting concentration [13, 14] is reached, its growth is replaced by an exponentially fast decay with a decrement of the same order, or a thermal breakdown occurs. For nanowires with a short channel [3] and a low intrinsic electron concentration in the collector contact, the relaxation instability should lead to appreciable changes in the conductivity of the structure.
If the current density in the nanowire exceeds another threshold value josc, damped high-frequency oscillations of the electron concentration appear in the emitter contact [3]. The reason for the oscillations is the inadequate concentration of electrons necessary to ensure, in a stationary mode, the required level of their injection from the emitter into the conducting channel of the nanowire.
In general, the threshold densities of jins and josc are different. However, by varying the parameters of the nanowire, it can be achieved that both of the considered phenomena will begin to develop at the same current density value [14]. In this case, as seen in Fig.7, an inductance appears in the emitter, and in the collector, as shown in Fig.8, a region with a negative differential resistance is formed. That is, the conditions necessary for generating microwave power arise.
Analysis of the relationships obtained in [3, 13, 14] shows that the generation of microwave oscillations in a quantum wire is possible only for certain relations between its geometric and electrophysical parameters. The results presented in Fig.7–9 were calculated for a nanowire with InSb conductor channel of 100 nm in length and silicon contacts of n-type. The length of the emitter contact was also 100 nm, and the electron concentration – 1014 cm3. The length of the collector contact was 500 nm, and the electron concentration – 5 ∙ 1014 cm3.
Calculation of the maximum power generating by such a nanowire to the external circuit is shown in Fig.9. At frequencies below 1.4 THz, it can generate about 10 nW of microwave power. At the same time, its estimated efficiency is about 13%. At frequencies exceeding 7.2 THz, the generation ceases and the quantum wire absorbs external energy [13, 14].
EQUIVALENT CIRCUIT
The electrical equivalent circuit for the matrix of nanowires is shown in Fig.10. It consists of the following elements: emitter (resistance Re, capacity Ce, inductance Le), region of conducting channels (resistance Rch), collector (resistances Rc1 and Rc2, capacitance Cs).
All parameters are current functions and are calculated on the basis of simulation results of charge transfer in the nanowire, taking into account the existence of instability and relaxation modes. The resistances of Re and Rc1 are the usual ohmic resistances of the emitter and collector, positive for all current values. The resistance Rc2 is positive for currents less than the relaxation instability threshold, and becomes negative when the current exceeds the threshold value. The value of Rc2 is determined by the damping decrement or the growth increment of electron concentration fluctuations in the collector. The Le inductance equals zero at currents less than the threshold of relaxation oscillations and is determined by their frequency when the current exceeds the threshold value.
To take into account the effect of the microwave electric field of the resonator on the processes in the semiconductor structure, the oscillator circuit must be supplemented by an oscillatory circuit. Therefore, numerical calculations were carried out with an oscillatory circuit (Fig.11), taking into account the basic design features of the electrodynamic system of the generator.
In this circuit, the diodes connected toward each other play the role of a frequency limiter, and the oscillatory circuit replaces the combined oscillatory system formed by the coaxial circuit of the structure and by the adjustable waveguide resonator connected to its resonator chamber.
MODELING
During the simulation, the numerical values of the elements of the equivalent circuit were optimized. The operating point was chosen so that the growth increment of the electron concentration fluctuations in the collector corresponded to the terahertz frequency range. As a result, a current of 4.10 A is selected. The circuit parameters at this current turn out to be: Re = 0.0574 Ohm, Ce = 0.184 pF, Le = 0.00 H, Rc1 = 0.0154 Ohm, Rc2 = 3.83 Ohm, Cc = 0.224 pF, Rch = 0.0313 Ohm.
Calculations of the characteristics of the generator in the housing showed that the inductance of the emitter makes it difficult for the device to go into the generation mode. For this reason, the emitter of the active element is made of gold, and not of silicon. In this case, relaxation oscillations in the emitter contact can occur only at very high currents, several orders of magnitude higher than the threshold current of the relaxation instability in the collector.
The trigger pulse was selected with an amplitude of 0.1 V at a frequency of 0.97 GHz. The inductance and capacitance of the external oscillatory circuit varied within 2.63–0.56 pH, 0.105–0.022 fF. As a result, excitation of oscillations at frequencies from 303 GHz to 994.7 GHz was provided. Fig.12 and Fig.13 show the calculated dependences of the voltage of the generated signal on time and the spectra of the signals at these frequencies. Numerical simulation showed that, when turned on, the generator starts "hard", the amplitude of the oscillations reaches a stationary value Uw = 0.8 V for the first half of the oscillation period, the available output power is 12.8 mW.
The microwave generator as an equivalent four-terminal network can be described by S-parameters measured in lines with matched loads, which is realized most simply at the ultrahigh frequencies. Using S-parameters of the generator measured at several frequencies, it is possible to determine (or refine) the elements of its equivalent circuit, and conversely, the known equivalent circuit allows calculating S-parameters at any frequency of the range in which this circuit is correct.
To calculate the S-parameters of the microwave generator with matrix of nanowires as the active element, the EMPro software was used. The results are shown in Figs.14 and 15. The reflection coefficient (S11) reaches the minimum value at a frequency of 650 GHz. At the same frequency, the transmission factor (S12) has a quite acceptable value of about 10 dB. Also there are local minima of S11 parameter at frequencies 300 GHz, 370 GHz, 910 GHz, etc.
Based on the analysis of the dependence of the S-parameters of the generator on frequency, it can be concluded that the frequencies of 300 GHz, 370 GHz, 650 GHz and 910 GHz are optimal for its operation. At these frequencies, the reflection coefficient has minima, the transmission coefficient – local maxima, and the VSWR takes values in the range from 4 to 15.
Fig.16 shows the distribution of the electric field E in the waveguide at selected frequencies. At a frequency of 300 GHz, the largest part of the power goes out in the direction of the payload, the amplitude change occurs uniformly along the wide wall of the waveguide. At 370 GHz, part of the power is spent in the direction of the regulating piston. At 650 GHz, the amplitude of the E-field reaches higher values than at 300 GHz, but its distribution along the waveguide is not uniform. At a frequency of 910 GHz, the formation of E-waves is not observed, that is, it is impossible to create a stable power source.
CONCLUSION
Modern technology allows the creation of matrix of InSb nanowires in regular pores of anodic aluminum oxide. The geometric characteristics of the conducting channels vary from 30 nm to 70 nm with lengths from 200 nm to 50 μm. The planar dimensions of the matrices, in principle, are unlimited. Contacts of nanowires can be created using various metals, semimetals and semiconductors.
In the conducting channels of InSb with dimensions less than 60 nm, already at room temperature, the quantization of the electron energy is realized. The nanowire contacts can be formed in such a way that heterojunctions are formed between them and the conducting channel. When current flows through heterojunctions, various non-equilibrium quantum phenomena are realized that determine the spectrum of possible applications of nanowire matrices.
In particular, generators of electromagnetic oscillations can be created in the frequency range from 300 GHz to 3 THz. Theoretical estimates indicate the uniqueness of the characteristics of these promising devices. The first experimental results confirm theoretical predictions. ■
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