A temperature correction calculation method for Si-based IMPATT diode radio frequency output power

Abstract

This invention discloses a temperature-corrected calculation method for the RF output power of a Si-based IMPATT diode. First, temperature-dependent corrections are applied to carrier mobility and collisional ionization rate. Based on this, the relationship between the breakdown voltage and the collisional ionization rate of the IMPAT diode is determined, and the critical electric field E of the Si-based IMPAT diode is established. m Breakdown voltage V B The relationship between the junction temperature T and the device equation is determined; secondly, the device equations are solved, and the negative conductance G is established by combining carrier mobility and collisional ionization rate. D The temperature characteristic model was used; finally, based on the RF output power calculation formula, combined with the breakdown voltage V, the temperature characteristic model was used. B and the negative conductance G of the diode D A temperature-corrected model for the RF output power of Si-based IMPATT diodes is constructed. Based on the traditional numerical calculation model for the RF output power of Si-based IMPATT diodes, this method establishes the temperature dependence of relevant characteristic parameters through various methods such as material parameter testing, empirical parameter fitting, and neural network training, thereby improving the calculation accuracy of the Si-based IMPATT diode RF output power simulation model under high and low temperature conditions.

Description

Technical Field

[0001] This invention belongs to the field of diode simulation technology, and in particular relates to a temperature correction calculation method for the RF output power of a Si-based IMPATT diode. Background Technology

[0002] Millimeter waves generally refer to electromagnetic waves with wavelengths ranging from 1 to 10 mm or corresponding frequency ranges from 30 to 300 GHz. They offer advantages such as large operating bandwidth, low latency, and high data rates. Millimeter wave devices are characterized by small size, light weight, narrow beamwidth, high resolution, and strong anti-interference capabilities. Compared to infrared and laser sensors, they exhibit good weather adaptability and can detect through smoke and dust. With the continuous increase in information volume, 5G millimeter waves, due to their technical characteristics, will become the main development frequency band for wireless communication.

[0003] Among known solid-state devices, impact-ionization avalanche transit time (IMPATT) diodes can generate the highest continuous power output in the millimeter-wave band, making them a relatively ideal millimeter-wave solid-state source widely used in defense and civilian communications. Current research on IMPATT diodes focuses primarily on improving their output power and efficiency. Because the DC-to-RF conversion efficiency of IMPATT diodes is generally very low, only a small portion of the energy is converted into microwave energy, while a larger portion is converted into heat, causing the diode junction temperature to rise. The performance and reliability of IMPAT devices largely depend on the junction temperature. Research results show that the critical electric field strength, carrier ionization rate, and drift current in the avalanche region of IMPATT diodes all increase with increasing temperature.

[0004] While research on the temperature dependence of IMPATT diodes based on wide bandgap semiconductor materials such as SiC and GaN is relatively mature, the temperature effect on Si-based IMPATT diodes remains inconclusive. Because the electron ionization rate (αn) of wide bandgap semiconductor materials like SiC and GaN is much smaller than the hole ionization rate (αp), i.e., αn << αp, hole ionization is significantly dominant during avalanche, with the ionization ratio kA = αn / αp << 1. This characteristic differs significantly from the relationship between electron and hole ionization rates in Si materials. Therefore, theoretical explanations of the temperature effect of wide bandgap semiconductor IMPATT diodes are insufficient for the study of the temperature effect on Si-based IMPATT diodes. Furthermore, since the influence of temperature on various performance parameters of Si-based IMPATT diodes is complex, existing research often only considers the impact of temperature on individual parameters such as carrier mobility, collisional ionization rate, differential resistance, and depletion layer width, without considering the comprehensive impact of temperature on the output power of the IMPATT diode.

[0005] In summary, the inventors have found that existing technologies have significant limitations, failing to consider the comprehensive impact of temperature effects on the output power of IMPATT diodes. Therefore, it is necessary to systematically construct a temperature model for the output power of Si-based IMPATT diodes, comprehensively considering the influence of temperature effects on different performance parameters of Si-based IMPATT diodes. Summary of the Invention

[0006] The purpose of this invention is to solve the problems mentioned in the background art and to provide a temperature correction calculation method for the RF output power of Si-based IMPATT diodes. This method considers the influence of temperature thermal effects on different performance parameters of Si-based IMPATT diodes and can propose the temperature dependence of the RF output power of Si-based IMPATT diodes.

[0007] To achieve the objective of this invention, a method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode is disclosed, characterized by the following steps:

[0008] S1. Determine the device parameters of the Si-based IMPATT diode. Obtain key characteristic parameters of the diode, such as junction area, transit region length, and doping concentration, through device measurement and process parameter analysis methods, and input them into the calculation model.

[0009] S2. Based on the carrier drift-diffusion equation, and by substituting the temperature effect factors of Si-based IMPAT diodes, a temperature effect correlation correction model for carrier mobility μ and carrier collisional ionization rate α is established.

[0010] S3. Based on the structural parameters of the Si-based IMPATT diode, and according to the relationship between the breakdown voltage and the collisional ionization rate of the IMPAT diode, combined with the linear relationship between the breakdown voltage model and the avalanche critical electric field model, the relationship between the critical electric field and the junction temperature of the Si-based IMPATT diode is established. Furthermore, the relationship between the breakdown voltage and the junction temperature is established, and the relationship between the critical electric field Em and the breakdown voltage V is established. B Temperature correction model;

[0011] S4. The total resistance and reactance are obtained by solving the device equations under static parameter input. Based on the calculation formula of diode negative conductance, a relationship model between negative conductance GD and carrier mobility and collisional ionization rate is established. On the basis of the temperature effect correlation correction model of carrier mobility μ and carrier collisional ionization rate α described in S2, a temperature correction model of diode negative conductance GD is further constructed.

[0012] S5. Based on the relationship formula between the RF output power of Si-based IMPATT diodes and the breakdown voltage VB and negative conductance GD, and on the basis of the temperature correction model of critical electric field Em and breakdown voltage VB described in S3 and the temperature correction model of negative conductance GD described in S4, a temperature correction calculation method for the RF output power of Si-based IMPATT diodes is finally established.

[0013] Furthermore, step S2 specifically includes:

[0014] The carrier drift-diffusion equation describes the movement of carriers in a semiconductor, including:

[0015]

[0016]

[0017] Among them, J n and J p D represents electron current and hole current. n D p Let μ be the electron and hole diffusion coefficient. n μ p Let m be the electron and hole mobility, q be the electron charge, and m be the... * Where n is the effective mass of charge carriers, and p is the electron and hole concentrations, respectively. Let E be the electron and hole concentration gradient, and E be the electric field strength.

[0018] The relationship between the diffusion coefficient D and the mobility μ can be expressed using the Einstein relation:

[0019] D n =μ n k B T / q

[0020] D p =μ p k B T / q

[0021] Where k B Boltzmann's constant is given by T, where T is the absolute temperature.

[0022] The carrier mobility μ, the carrier collisional ionization rate α, and the junction temperature T of a Si-based IMPAT diode satisfy the following relationships:

[0023]

[0024] In the formula, For the effective mass of an electron, A μ and B μ Here are the material parameters, and T is the temperature.

[0025]

[0026] In the formula, E is the electric field strength, T is the actual temperature, T0 is taken as the standard temperature of 300K, and A α b α c α d α γ α m α This is the ionization rate coefficient.

[0027] Furthermore, step S3 specifically includes:

[0028] The breakdown voltage is the integral of the electric field in the depletion layer, and is calculated as follows: Since the avalanche zone is a highly localized region, the breakdown voltage V is further optimized based on this. B The formula is V B =E m x a x a E represents the width of the avalanche zone. m The critical electric field;

[0029] Based on the device parameters of the Si-based IMPATT diode described in step S1, establish the avalanche critical electric field E of the Si-based IMPATT diode. m The temperature model is as follows:

[0030]

[0031] Where N is the carrier doping concentration, A e B e C e Temperature coefficient;

[0032] Given a given operating frequency, V B Temperature correlation model and E m The temperature model exhibits a linear relationship, thus establishing V B The temperature characteristic model is as follows:

[0033]

[0034] Furthermore, step S4 specifically includes:

[0035] By solving the following device equations with static parameters as input

[0036]

[0037]

[0038] In the formula, ρ is the negative resistivity of the diode, X is the depletion layer reactivity of the diode, and α nα p The ionization rate of electron-hole collisions. v is the average drift velocity of the charge carriers. sn v sp Let ρ be the saturation drift velocity of electrons and holes, and ε be the dielectric constant. The spatial variation formulas of the diode's negative resistivity ρ and depletion layer reactivity X are obtained, which are related to the carrier collisional ionization rate and carrier mobility.

[0039] The real part of the total impedance Z ρ And the imaginary part Z X The expressions are respectively

[0040] Combined with negative conductance G D Calculation formula Establish negative conductance G D The temperature model is as follows:

[0041]

[0042] Further analysis of negative conductance G D The temperature model is approximated and simplified to obtain:

[0043]

[0044] Where A, C, E, F, G, H, and I are temperature coefficients.

[0045] Furthermore, step S5 specifically includes:

[0046] Let the applied voltage across the IMPATT diode be V(t) = Vd + vRF, where the DC bias voltage Vd is approximately equal to the diode's breakdown voltage VB, and vRF is the radio frequency voltage. The expression is:

[0047]

[0048] In the formula, mx is the voltage modulation coefficient, f is the operating frequency, and φi is the initial phase; in this invention, mx is taken as 0.9, and the initial phase is 0; the formula for calculating the radio frequency output power (PRF) is as follows:

[0049]

[0050] In the formula, G D The peak negative conductance of the IMPATT diode device is obtained through step S4; A j The diode junction area is input via step S1; V RF The radio frequency voltage amplitude is calculated from the breakdown voltage obtained in step S3, i.e., m x V BThe final temperature-corrected calculation model for diode output power is as follows:

[0051]

[0052] Furthermore, as the operating temperature increases, the avalanche critical electric field Em of the IMPATT diode increases, which in turn leads to an increase in the transit current, thereby dominating the increase in RF output power.

[0053] Compared with the prior art, the significant progress of this invention is as follows: a theoretical model of the influence of junction temperature on output power of Si-based IMPATT diodes is established, the influence of temperature effect on multiple performance parameters of Si-based IMPATT diodes is considered, temperature effect correction is performed by calculating the carrier mobility and collisional ionization rate of IMPATT diodes, and temperature effect models of critical electric field, breakdown voltage and negative conductance of diodes are constructed by combining the junction temperature change of IMPATT diodes. The theoretical models of multiple performance parameters jointly determine the trend of output power change when temperature changes, and the corresponding temperature dependence relationship of RF output power is established.

[0054] To more clearly illustrate the functional characteristics and structural parameters of the present invention, further explanation is provided below in conjunction with the accompanying drawings and specific embodiments. Attached Figure Description

[0055] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0056] Figure 1 This is a flowchart illustrating a method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode, as provided in an embodiment of the present invention.

[0057] Figure 2(a) is a schematic diagram of the dual drift region structure of the IMPATT diode;

[0058] Figures 2(b), 2(c), and 2(d) are schematic diagrams of the doping distribution, electric field distribution, and ionization integral under breakdown conditions of the dual-drift region IMPATT diode, respectively.

[0059] Figure 3 This is a simulation diagram of the RF power output of a Si-based IMPATT diode at low temperature using a 120GHz signal source, based on the diode performance calculation model in the temperature correction calculation method for the RF output power of the diode provided in Embodiment 1 of the present invention.

[0060] Figure 4This is a temperature characteristic fitting curve of the breakdown voltage VB of a Si-based IMPATT diode at 10GHz, provided in the temperature correction calculation method for the RF output power of a Si-based IMPATT diode according to Embodiment 2 of the present invention.

[0061] Figure 5 This is a schematic diagram of the simulation results of the negative conductance GD temperature model of a Si-based IMPAT diode at 10GHz in a temperature correction calculation method for the RF output power of a Si-based IMPAT diode provided in Embodiment 2 of the present invention.

[0062] Figure 6 This is a simulation diagram of the RF power output of a Si-based IMPATT diode under high temperature at a 10GHz signal source, based on the diode performance calculation model in the temperature correction calculation method for the RF output power of the diode provided in Embodiment 2 of the present invention. Detailed Implementation

[0063] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] like Figure 1 As shown in the figure, in an embodiment of the present invention, a method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode is provided, including the following steps:

[0065] S1. Determine the structure of the Si-based IMPATT diode, and based on the analysis of the carrier drift-diffusion mechanism, combined with the temperature effect influencing factors of the Si-based IMPATT diode, perform temperature effect correlation correction on the carrier mobility μ and carrier collisional ionization rate α of the Si-based IMPATT diode.

[0066] S2. Based on the structure of the Si-based IMPATT diode, and according to the relationship between the breakdown voltage and the collisional ionization rate of the IMPAT diode, combined with the linear relationship between the breakdown voltage model and the avalanche critical electric field model, the critical electric field E of the Si-based IMPATT diode is constructed. m The relationship between doping concentration and junction temperature T is expressed; based on this, the breakdown voltage V is further constructed. B The relationship between the junction temperature T and the junction temperature T.

[0067] S3. By solving the device equations under static parameter input, the total resistance and reactance are obtained. Based on this, the negative conductance G is established according to the formula for calculating the negative conductance of a diode. DA model relating carrier mobility μ and collisional ionization rate is constructed. Combining the temperature model of carrier mobility μ and collisional ionization rate α described in S1, a model for the diode negative conductance G is further developed. D Temperature characteristic model.

[0068] S4. Assume the voltage applied across the IMPATT diode is V(t) = V d +v RF In the formula, the DC bias voltage V d The value is approximately equal to the diode's breakdown voltage V. B v RF This is the radio frequency voltage. Combined with the breakdown voltage V described in S2 and S3... B and the negative conductance G of the diode D The temperature model was used to construct the temperature model of the diode output power.

[0069] Taking the Si-based double-drift region IMPATT diode as an example, the entire process will be explained in detail below:

[0070] In step S1, the Si-based IMPATT diode is determined to have a dual-drift-region structure as shown in Figure 2. This is based on the relationship between the optimal operating frequency and the depletion region length. Determine the length W of the depletion region of the IMPATT diode with operating frequency f. D Based on this, where v s The carrier saturation velocity is used to modify the relationship between the carrier mobility μ, the carrier collisional ionization rate α, and the junction temperature T of the IMPATT diode.

[0071] The carrier mobility model (1) and carrier collisional ionization model (2) of the IMPATT diode are modified to take into account the effect of junction temperature T, respectively:

[0072]

[0073]

[0074] In the formula, Let E be the effective mass of the electron, E be the electric field strength, T be the junction temperature, and T0 be the standard temperature of 300K. A μ and B μ For material parameters, A α b α c α d α γ α m α The ionization rate coefficient is a material parameter that can be obtained through various methods such as material property testing, experimental data fitting, and neural network training.

[0075] When IMPATT operates in the microwave and millimeter-wave bands, the junction temperature T is relatively high. The effect of ionized impurity scattering on mobility is negligible, lattice vibration scattering plays a major role in mobility, and phonon scattering plays a major role in collisional ionization. Increased temperature leads to a decrease in carrier mobility and a decrease in collisional ionization.

[0076] In step S2, firstly, according to the dual-drift region structure of the IMPATT diode shown in Figure 2, the shaded areas in Figure 2(b) and (c) are the active regions, with a length range of -W. D / 2 to W D Between / 2. The shaded area in Figure 2(d) represents the avalanche zone, with a length ranging from -x. a / 2 to x a / 2, located at the center of the depletion region and approximately symmetrical on both sides. The avalanche region is flanked by a p-type and an n-type transition region, respectively. The avalanche breakdown condition for the IMPATT diode with a dual-drift region is:

[0077]

[0078] In the formula, W D Let be the width of the depletion zone. Since the narrow region of the avalanche zone contributes approximately 95% to the overall avalanche ionization integral, equation (3) can be transformed into equation (4):

[0079]

[0080] In the formula, x a Let x be the width of the avalanche zone. At this point, the drift zone width is x. d Represented as W D -x a In this invention, the avalanche zone width x a A reasonable approximation is the width of the depletion region, W. D One-tenth, that is, x a =0.1W D .

[0081] Then, based on the structure of the Si-based IMPATT diode determined in step S1, the avalanche critical electric field E of the Si-based IMPATT diode is established. m The temperature model is:

[0082]

[0083] Where N is the carrier doping concentration, A e B e C e The temperature coefficient can be obtained through various methods such as material property testing, experimental data fitting, and neural network training.

[0084] Breakdown voltage V BIt is the integral of the electric field in the depletion layer, and the formula is:

[0085]

[0086] Because the avalanche zone is a highly localized area and the width of the avalanche zone is x a Extremely small, breakdown voltage V B The formula can be simplified from equation (6) to equation (7):

[0087] V B =E m x a (7)

[0088] In the formula, E m For the critical electric field, x a The width of the avalanche zone.

[0089] According to equation (7), under a given operating frequency, the temperature dependence model of the breakdown voltage is linearly related to the critical electric field temperature model. Therefore, the breakdown voltage V is determined by combining equation (5). B The temperature characteristic model is:

[0090]

[0091] Where, x a Where A is the avalanche region width, N is the carrier doping concentration, and A is the avalanche region width. e B e C e The temperature coefficient can be obtained through various methods such as material property testing, experimental data fitting, and neural network training.

[0092] In step S3, the impedance of the IMPATT diode is first calculated. In the small-signal analysis model, based on the operating characteristics of the avalanche and drift regions, the impedances of the avalanche and drift regions are obtained respectively. Combined with the parasitic resistance of the passive region, the total diode impedance is then obtained as follows:

[0093]

[0094] In the formula, R s For passive resistance, ω r For the optimal resonant frequency, θ d The crossing angle is the drift region angle. In this invention, to obtain the maximum negative resistance when the IMPATT diode is operating, the crossing angle θ is chosen. d The value is π. The first term on the right side of equation (9) is the real part R of the total diode impedance. a .

[0095] Then, calculate the negative conductance of the IMPATT diode. Diode negative conductance G D The calculation formula is:

[0096]

[0097] The real part Zp and the imaginary part Z of the total diode impedance in the formula X They are represented as follows:

[0098]

[0099]

[0100] In the formula, ρ is the negative resistivity of the diode, and X is the depletion layer reactivity.

[0101] The device equations with static parameter input are established as follows:

[0102]

[0103]

[0104] By solving the device equations (13) and (14), the spatial variation formulas of the diode's negative resistivity ρ and depletion layer reactivity X are obtained, which are related to the carrier collisional ionization rate and carrier mobility. Based on this analysis, and combining equations (10), (11), and (12), a temperature model for the negative conductance of the IMPATT diode is constructed:

[0105]

[0106] Where A, B, C, D, E, F, G, H, and I are temperature coefficients, which can be obtained through various methods such as material property testing, experimental data fitting, and neural network training. Considering the operating characteristics of the IMPATT diode at high temperatures, equation (15) is approximately simplified to obtain:

[0107]

[0108] Among them, A, C, E, F, G, H, and I are temperature coefficients, which can be obtained through various methods such as material property testing, experimental data fitting, and neural network training.

[0109] In step S4, it is assumed that the voltage applied across the IMPATT diode is:

[0110] V(t)=V d +v RF (17)

[0111] In the formula, DC bias voltage V d The value is approximately equal to the diode's breakdown voltage V. B v RF For radio frequency voltage, the expression is:

[0112]

[0113] In the formula, f is the operating frequency, and ψ i For the initial phase, m x Let m be the voltage modulation coefficient. In this invention, m is taken as... x The initial phase is 0.9, and the RF output power P is calculated. RF The calculation formula is:

[0114]

[0115] In the formula, G D For the peak negative conductance of the IMPATT diode device, A j V is the effective cross-sectional area of ​​the diode. RF The amplitude of the radio frequency voltage, i.e., m x V B Based on the above analysis, the temperature model for diode output power is finally constructed as follows:

[0116]

[0117] By combining equation (19) with equations (8) and (16), the device output performance can be simulated and the RF output power can be obtained.

[0118] Furthermore, for a uniform avalanche region, the maximum breakdown voltage is V. B =E m W D According to Gauss's law, the maximum avalanche charge is E. m ε s The maximum current is equal to:

[0119]

[0120] Therefore, the upper limit of power density can be determined by V. B and J m The product yields:

[0121]

[0122] In the formula E m For the critical electric field, ε s v is the dielectric constant of the material. s This represents the carrier saturation drift velocity.

[0123] The embodiments of this invention select a Si-based dual-drift-region IMPATT diode. Embodiment 1 is a low-temperature data fitting of the Si-based dual-drift-region IMPATT diode under a 120GHz signal source, and Embodiment 2 is a high-temperature data fitting of the Si-based dual-drift-region IMPATT diode under a 10GHz signal source.

[0124] The electron concentration of the IMPATT diode designed in this embodiment of the invention is 3.5 × 10⁻⁶. 17 cm -3 Carrier saturation velocity v s 10 7 cm / s, and the remaining material parameters are the classic material parameters of Si.

[0125] As shown in Figure 2, Figure 3 As shown, the application scenario of the RF output power temperature effect model of a Si-based impact ionization avalanche transit time (IMPATT) diode provided in Embodiment 1 of the present invention is further explained. Specifically, as follows:

[0126] In Figure 2, Figure 2(a) is a schematic diagram of the dual drift region structure of the IMPATT diode, and Figures 2(b), 2(c) and 2(d) show the doping distribution, electric field distribution and ionization integral under breakdown conditions of the IMPATT diode, respectively.

[0127] Figure 3 The output power performance of Si-based IMPATT diodes in the low temperature range of 200K to 300K was simulated. It was observed that the optimal output power of Si-based double drift region IMPATT diodes in this temperature range still increases with the temperature. Moreover, the power model curve of IMPATT diodes obtained according to formula (22) is in good agreement with the test data.

[0128] like Figures 4 to 6 As shown, the application scenario of the RF output power temperature effect model of a Si-based impact ionization avalanche transit time (IMPATT) diode provided in Embodiment 2 of the present invention is further explained. Specifically, as follows:

[0129] The breakdown voltage (V) of the Si-based IMPATT diode is obtained using formula (8). B Temperature relationship as follows Figure 4 As shown. From Figure 4 It can be observed that the temperature coefficient A, obtained through various methods such as material property testing, experimental data fitting, and neural network training, can be... e B e C e Substituting into formula (8), the breakdown voltage V is established. B The temperature characteristic model satisfies the trend that the breakdown voltage increases with increasing temperature, and is very close to the breakdown voltage of a Si-based IMPATT diode with an operating frequency of 10 GHz at 100 ℃ to 200 ℃.

[0130] Figure 5This is a temperature characteristic diagram of the negative conductance of a Si-based IMPATT diode operating at 10 GHz. It shows that the negative conductance of the IMPATT diode decreases continuously with increasing temperature in the range of 100°C to 200°C. According to drift-diffusion theory, the reverse saturation current increases exponentially with increasing junction temperature. This increased reverse saturation current accelerates the accumulation of avalanche current and reduces the negative resistance of the device. Figure 5 It can be seen that the negative conductance model of the Si-based IMPATT diode obtained by formula (15) decreases with increasing temperature.

[0131] Figure 6 The output performance simulation of the Si-based IMPATT diode power model obtained using formula (20) is described in the temperature range of 120℃ to 260℃. Observation Figure 6 It is evident that the optimal output power of the Si-based double-drift region IMPATT diode increases with increasing temperature. Theoretical analysis reveals that, in order to ensure its operation in avalanche mode, the input voltage and breakdown voltage of the IMPATT diode are related. When the same DC bias current density is applied, the breakdown voltage of the IMPATT diode increases with increasing temperature, requiring a larger input power to operate, thus resulting in a larger output power.

[0132] Implementing the embodiments of the present invention has the following beneficial effects: The present invention establishes a theoretical model of the influence of junction temperature on output power of Si-based IMPAT diodes, considers the influence of temperature effect on multiple performance parameters of Si-based IMPAT diodes, corrects for temperature effect by calculating carrier mobility and collisional ionization rate of IMPAT diodes, and constructs temperature effect models of critical electric field, breakdown voltage and negative conductance of diodes in combination with junction temperature changes of IMPAT diodes. Multiple performance parameter sub-models jointly determine the trend of output power change when temperature changes, and establish a corresponding output power model.

[0133] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, disk, optical disk, etc.

[0134] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0135] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode, characterized in that, Includes the following steps: S1. Determine the device parameters of the Si-based IMPATT diode. Obtain the key characteristic parameters of the diode, including junction area, transit region length, and doping concentration, through device measurement and process parameter analysis methods, and input them into the calculation model. S2. Based on the carrier drift-diffusion equation, and by substituting the temperature effect factors of Si-based IMPAT diodes, a temperature effect correlation correction model for carrier mobility µ and carrier collisional ionization rate α is established. S3. Based on the structural parameters of the Si-based IMPATT diode, and according to the relationship between the breakdown voltage and the collisional ionization rate of the IMPAT diode, combined with the linear relationship between the breakdown voltage model and the avalanche critical electric field model, the relationship between the critical electric field and the junction temperature of the Si-based IMPATT diode is established. Furthermore, the relationship between the breakdown voltage and the junction temperature is established, and the critical electric field E is determined. m With breakdown voltage V B Temperature correction model; S4. By solving the device equations under static parameter input, the total resistance and reactance are obtained. Based on the calculation formula of diode negative conductance, the negative conductance G is established. D Based on the temperature-effect-correlation model of carrier mobility µ and collisional ionization α described in S2, a model relating carrier mobility µ and collisional ionization α to the diode negative conductance G is further constructed. D Temperature correction model; S5, RF output power and breakdown voltage V based on Si-based IMPATT diodes B and negative conductance G D The relationship formula, and the critical electric field E described in S3 m With breakdown voltage V B Temperature correction model and negative conductance G as described in S4 D Based on the temperature correction model, a temperature correction calculation method for the RF output power of Si-based IMPATT diodes was finally established. Step S3 is as follows: The breakdown voltage is the integral of the electric field in the depletion layer, and is calculated as follows: W represents the width of the depletion layer, x represents the spatial coordinate, and E(x) represents the electric field intensity at location x in the depletion layer. Since the avalanche region is a highly localized area, the breakdown voltage V is further optimized based on this. B The formula is x a E represents the width of the avalanche zone. m The critical electric field; Based on the device parameters of the Si-based IMPATT diode described in step S1, establish the avalanche critical electric field E of the Si-based IMPATT diode. m The temperature model is as follows: Where N is the carrier doping concentration, A e B e C e Temperature coefficient; Given a given operating frequency, V B Temperature correlation model and E m The temperature model exhibits a linear relationship, thus establishing V B The temperature characteristic model is as follows: Where T is the absolute temperature; Step S5 is as follows: Let the applied voltage across the IMPATT diode be V(t) = Vd + v RF In the formula, the value of the DC bias voltage Vd is approximately equal to the diode's breakdown voltage V. B v RF For radio frequency voltage, the expression is: In the formula, m x Here, φ is the voltage modulation coefficient, f is the operating frequency, and φ is the voltage modulation coefficient. i Let m be the initial phase; x The initial phase is 0.9, and the RF output power P is 0.

9. RF The calculation formula is: In the formula, G D The peak negative conductance of the IMPATT diode device is obtained through step S4; A j The diode junction area is input via step S1; V RF The radio frequency voltage amplitude is calculated from the breakdown voltage obtained in step S3, i.e., m x V B The final temperature-corrected calculation model for diode output power is as follows: 。 2. The method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode according to claim 1, characterized in that, Step S2 is as follows: The carrier drift-diffusion equation describes the movement of carriers in a semiconductor, including: Among them, J n and J p D represents electron current and hole current. n D p The electron and hole diffusion coefficients are, , Let q be the electron and hole mobility, and q be the electron charge. Where n is the effective mass of charge carriers, and p is the electron and hole concentrations, respectively. , Let E be the electron and hole concentration gradient, and E be the electric field strength. The momentum relaxation time; The relationship between the diffusion coefficient D and the mobility µ can be expressed using the Einstein relation: Where k B Boltzmann's constant is given by T, where T is the absolute temperature. The carrier mobility µ and carrier collisional ionization rate α of a Si-based IMPAT diode satisfy the following relationships with absolute temperature T: In the formula, For the effective mass of an electron, A µ and B µ Here are the material parameters, T is the absolute temperature, and N is the temperature. i This refers to the concentration of ionized impurities. In the formula, E is the electric field strength, T is the absolute temperature, T0 is taken as the standard temperature of 300K, and A α b α c α d α γ α m α The ionization rate coefficient, This is the power term in the collisional ionization rate that is related to the electric field strength.

3. The method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode according to claim 1, characterized in that, Step S4 is as follows: By solving the following device equations with static parameters as input ， ， In the formula, , , X represents the negative resistivity of the diode, and X represents the depletion layer reactivity of the diode. , The ionization rate of electron-hole collisions. v is the average drift velocity of the charge carriers. sn v sp For electron and hole saturation drift velocities, The dielectric constant is used to obtain the negative resistivity of the diode. The spatial variation of the depletion layer reactivity X is related to the carrier collisional ionization rate and carrier mobility; x is the spatial coordinate. is the coefficient of the electric field index. The operating angular frequency, The weighted average ionization coefficient. It is the differential of the weighted average ionization coefficient with respect to the electric field strength. DC current density, For electric field; The real part of the total impedance Z ρ And the imaginary part Z X The expressions are respectively , Combined with negative conductivity G D Calculation formula Establish negative conductance G D The temperature model is as follows: Further analysis of negative conductance G D The temperature model is approximated and simplified to obtain: Where W is the depletion layer width, T is the absolute temperature, and A, B, C, D, E, F, G, H, and I are temperature coefficients.

4. The method for calculating the temperature correction of the RF output power of a Si-based IMPATT diode according to claim 1, characterized in that, As the operating temperature increases, the avalanche critical electric field E of the IMPATT diode... m The increase in power leads to an increase in the transit current, which in turn dominates the increase in RF output power.

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