CN108717471B - Modeling method for volt-ampere characteristic of voltage domain oscillation quantum device - Google Patents
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Abstract
The invention relates to a modeling method of volt-ampere characteristics of a voltage domain oscillation quantum device. According to the current distribution mechanism of the voltage domain oscillation quantum device, analog analysis is carried out on a simulation test curve of the volt-ampere characteristic of the similar device structure, and curve decomposition is carried out; and establishing a mathematical model for the decomposed curve components. Superposing the component mathematical models to obtain an initial complete volt-ampere characteristic curve model, and adopting simulation fitting model parameters; comparing and analyzing the model result curve and the numerical simulation test curve, and optimizing fitting parameters according to regularity with errors; and obtaining an accurate volt-ampere characteristic model result by adopting an error reduction method. The invention solves the problems that the volt-ampere characteristic of the voltage domain oscillation quantum device is difficult to directly analyze and solve and the simulation test curve is difficult to directly analyze and express. The obtained voltage-domain oscillation quantum device volt-ampere characteristic accurate model lays an analytic theoretical basis for the volt-ampere characteristic of the voltage-domain current oscillation quantum well device, the device structure and the manufacturing process design.
Description
Technical Field
The invention belongs to the technical field of volt-ampere characteristics of voltage domain oscillation quantum devices, and relates to a modeling method of the volt-ampere characteristics of the voltage domain oscillation quantum devices.
Background
The current distribution of the voltage domain oscillation quantum device follows the wave-particle diamorphism law, the volt-ampere characteristic of the voltage domain oscillation quantum device is generally described by a complex Schrodinger equation and Maxwell equation set and a complex boundary condition and initial condition equation set, and the initial condition equation set is more complex for the device with an initial polarization electric field and an initial magnetic field in the structure of the device. As is known, only a complex Maxwell equation set is difficult to solve directly, so that the volt-ampere characteristic of the voltage domain oscillation quantum device is more difficult to solve directly. For the solution of the volt-ampere characteristic of the voltage domain oscillation quantum device, a semiconductor quantum device simulation software platform is conventionally utilized, and a finite element numerical iteration simulation method is adopted to carry out numerical solution. The solving method requires that research personnel have a solid quantum device physical theory foundation, and simultaneously must be capable of skillfully using a semiconductor quantum device simulation software platform to edit and adjust the device structure, set and optimize grids, select a finite element numerical simulation model and method, define simulation input and output parameters, set a simulation process, output and analyze and process simulation results. The device structure needs to be estimated in the links of editing and adjusting the device structure, an estimation means of direct analysis and solution is lacked at present, most of the estimation means combines the theoretical basis of work and experience of research and development personnel with a semi-subjective and semi-objective idea, and a large accidental deviation exists between the estimation means and an optimized device structure target, so that the subsequent adjustment of structure parameters and the optimization process are long and time-consuming, and the volt-ampere characteristic simulation result curve is difficult to be directly analyzed and described, so that the method is not convenient to be directly used for circuit design and analysis. On the one hand, the license cost of the commercial semiconductor device simulation software platform is relatively expensive; on the other hand, free open source semiconductor device simulation software for scientific research is rare, and some open source software are not developed enough and not perfect in function. Therefore, it is urgent to provide a scientific means capable of reducing accidental deviation of the voltage domain oscillation quantum device design and directly analyzing and describing the volt-ampere characteristic simulation result curve.
Disclosure of Invention
The invention aims to provide a modeling method of volt-ampere characteristics of a voltage domain oscillation quantum device aiming at the problems in the research and development process of the voltage domain oscillation quantum device, so that the purposes of reducing accidental deviation between a preset structure and an optimized structure of the voltage domain oscillation quantum device and directly analyzing and describing a volt-ampere characteristic simulation result curve are achieved.
The invention comprises the following steps:
firstly, analog analysis is carried out on a simulation test curve of the volt-ampere characteristic of the similar device structure according to a current transport mechanism of a voltage domain oscillation quantum device, and curve decomposition is carried out by combining the current transport mechanism and the volt-ampere characteristic curve characteristic.
Step two, respectively establishing mathematical models for the decomposed curve components, and fitting model parameters by adopting Matlab; establishing a mathematical model for the balance current component according to the Voltan characteristic analysis in the step one; decomposing according to the Voltan characteristic curve in the first step, and establishing a mathematical model for the oscillation current component;
step three, superposing the mathematical model established for the balance current component and the mathematical model established for the oscillation current component in the step two to obtain an initial complete model of the volt-ampere characteristic of the voltage domain oscillation quantum device, and gradually adjusting the parameters of a fitting model by adopting Matlab simulation;
step four, comparing and analyzing the initial complete model obtained in the step three and the simulation test result of the volt-ampere characteristic curve obtained in the step one, and further optimizing fitting parameters according to regularity of errors;
and obtaining a comparison graph of the optimized total current model result curve, the peak value envelope curve model result, the valley value envelope curve model result and the simulation test result curve.
And step five, according to the total current model result curve in the step four, the initial complete model obtained in the step three and the volt-ampere characteristic curve simulation test result obtained in the step one, an error reduction method is adopted to correct model parameters, so that the model result is matched with the simulation test result, and an accurate volt-ampere characteristic model result of the voltage domain oscillation quantum device is obtained.
And step six, drawing a regular curve of each parameter of the volt-ampere characteristic model of the voltage domain oscillation quantum device along with the change of the bias voltage in the step five by adopting Matlab or other curve drawing software with a fitting analysis function. And establishing a mathematical model of the regularity according to the analysis of the regular curve of each parameter along with the change of the bias voltage, and performing parameter fitting to continuously improve the precision of the model.
And step seven, when one structural parameter of the voltage domain oscillation quantum device is changed, and other parameters are kept unchanged. And respectively establishing a model of the test curve under the condition of each group of parameters by adopting the same method as the first step to the sixth step, fitting a functional relation between the fitting parameters and the changed parameters of each model, and then substituting the functional relation into a high-precision integral model relational expression according to layers to obtain a high-precision complete mathematical model of the volt-ampere characteristic curve of the device, which contains the influence of the structural parameters.
The invention provides a physical mechanism analog decomposition and superposition modeling method for voltage domain oscillation quantum device volt-ampere characteristics, aiming at the problem that the volt-ampere characteristics of the voltage domain oscillation quantum device are difficult to directly analyze and solve. According to the current distribution mechanism of the device, analog analysis is carried out on a simulation test curve of the volt-ampere characteristic of the device, and curve decomposition is carried out by combining the current distribution mechanism and the characteristic of the volt-ampere characteristic; respectively establishing mathematical models for the decomposed curve components, and fitting model parameters by adopting Matlab; then, overlapping the respectively established curve component mathematical models to obtain an initial complete model of the volt-ampere characteristic of the device; comparing and analyzing the obtained initial complete model and a simulation test result of the volt-ampere characteristic curve to obtain regularity with errors; and then, performing necessary model parameter correction by adopting an error reduction method to ensure that the model result is matched with the simulation test result, thereby obtaining a voltage-domain oscillation quantum device volt-ampere characteristic model result with sufficient accuracy.
The finally obtained voltage domain oscillation quantum device volt-ampere characteristic accurate model can lay an analytic theoretical basis for the volt-ampere characteristic, the device structure and the manufacturing process design of the quantum well device, and provides a scientific means for solving the problems that a large accidental deviation exists between the voltage domain oscillation quantum device pre-designed structure and the optimized device structure target, the subsequent adjustment of structure parameters and the optimization process are tedious and time-consuming, the volt-ampere characteristic simulation result curve is difficult to directly analyze and describe, and the voltage domain oscillation quantum device volt-ampere characteristic accurate model is inconvenient to directly use for circuit design and analysis.
Drawings
FIG. 1 is a linear coordinate curve of simulation test results of voltage-current characteristic curves of GaN-based quantum well voltage domain oscillating diodes in the embodiment of the invention;
FIG. 2 is a semilogarithmic coordinate curve of the simulation test result of the volt-ampere characteristic curve of the oscillating diode in the voltage domain of the quantum well in the embodiment of the invention;
FIG. 3 is a comparison of initial model peak envelope, valley envelope, balance current component and total current initial model curves for an embodiment of the present invention;
FIG. 4 is a plot of total current model results versus peak envelope and valley envelope curves for an embodiment of the present invention;
FIG. 5 is a comparison graph of the total current model result and the current-voltage characteristic curve simulation test result in the embodiment of the present invention;
FIG. 6 is a graph illustrating the effect of bias voltage on model amplitude in an embodiment of the present invention;
FIG. 7 is a graph illustrating the effect of bias voltage on the angular frequency of model oscillation according to an embodiment of the present invention;
FIG. 8 is a graph illustrating the effect of bias voltage on model weighting coefficients a and b according to an embodiment of the present invention;
FIG. 9(a) is a simulation test result of the influence of the GaN barrier width on the current-voltage characteristic of the GaN-based voltage domain oscillation diode in the embodiment of the invention;
FIG. 9(b) is a simulation test result of the effect of the quantum well width on the current-voltage characteristic of the GaN-based voltage domain oscillating diode in the embodiment of the invention;
FIG. 9(c) is a simulation test result of the effect of AlGaN barrier width on the current-voltage characteristic of GaN-based voltage domain oscillation diode in the embodiment of the present invention.
Detailed Description
The volt-ampere characteristic modeling of the GaN-based quantum well voltage domain oscillation diode is taken as an example.
Firstly, analog analysis is carried out on a simulation test curve of the volt-ampere characteristic of the similar device structure according to a current transport mechanism of the device, and curve decomposition is carried out by combining the current transport mechanism and the volt-ampere characteristic curve characteristic.
According to the current transport mechanism of the GaN-based quantum well diode, the current between the two poles under a given bias voltage is the electron dredging current corresponding to the superposition formula (1) after the electronic wave function is attenuated on the bound state energy level in the quantum well,
wherein the content of the first and second substances,
is a position vector of the phase space,
is the wave vector of the electronic wave function,
is a Bloch wave function, i is an imaginary unit,
electricity at a single bound state levelThe function of the wavelet is then calculated,
the transition attenuation factor is the wave function of the energy level corresponding to a single bound state.
As can be seen from the simulation test results of the voltage-current characteristic curve of the GaN-based quantum well voltage domain oscillating diode shown in fig. 1 and 2, the voltage-current characteristic curve is a continuous curve in a practical observable range, and the voltage domain oscillation thereof has the following characteristics: 1) at low bias voltage (V)bias2.5V) with the current being approximately zero in a linear coordinate system and similar to the characteristics of a common diode in a semilogarithmic coordinate system, however, the value of the parameter equivalent to the starting voltage of the common diode is higher; 2) in the medium bias voltage region (about 2.5 ≦ VbiasLess than or equal to 2.8V) is a starting oscillation stage, amplitude modulation waves with slowly increased amplitude and slowly increased balance current appear in a linear coordinate system, and balance current with slightly burrs and slowly increased appears in a semi-logarithmic coordinate system; 3) in the high voltage region (V)biasNot less than 2.8V), the current characteristic enters a stable oscillation area, the current characteristic looks like the superposition of the current oscillation waveform of the exponential amplitude modulation and weak frequency modulation voltage domain and the balance current which approximately increases exponentially in a linear coordinate system, and the current characteristic looks like the superposition of the current oscillation waveform of the approximate constant amplitude and weak frequency modulation voltage domain and the balance current which approximately increases linearly in a semilogarithmic coordinate system. 4) From the overall view of the curve, the peak envelope, the valley envelope and the balance current are similar to the characteristics of a common diode, and the whole curve can be approximately regarded as an amplitude modulation frequency modulation sine wave taking the balance current as a balance position.
According to the analysis, the simulation test result of the volt-ampere characteristic curve of the GaN-based quantum well voltage domain oscillating diode can be decomposed as follows: balancing current components equivalent to superposed corresponding electron currents of bound state electron wave function fundamental waves under given bias voltage after barrier attenuation; the oscillation current component is equivalent to superposition of bound state electron wave function harmonic waves under a given bias voltage after barrier attenuation.
Step two, respectively establishing a mathematical model for the decomposed curve components, and fitting model parameters by adopting Matlab:
1. a mathematical model is established for the balance current component, and the specific method is as follows:
according to the voltammetry analysis in the first step, the peak envelope and the valley envelope of the voltammetry characteristic curve are similar to those of a common diode, and the voltammetry characteristic curve equation of the diode is as shown in formula (2):
wherein, JSIs reverse saturation current of a common diode, UTIs constant and thermoelectric for a common diode.
Respectively establishing a peak value envelope curve model and a valley value envelope curve model of the volt-ampere characteristic curve in the form of equation (2) as shown in equations (3) to (4):
wherein, UTeThe other variables have similar meanings to the formula (2) for the equivalent thermoelectric potential of the GaN-based quantum well voltage domain oscillating diode.
Then, the balance current model of the GaN-based quantum well voltage domain oscillating diode is obtained by carrying out weighted average on the formulas (3) to (4) as shown in the formula (5):
JDb＝aJSp+bJSv (5)；
where a and b are weighting coefficients, and the initial approximation is a-b-1/2.
2. Establishing a mathematical model for the oscillation current component, which comprises the following specific steps:
according to the analysis analogy of step one and the decomposition, the oscillation current component of the whole curve can be approximately regarded as the amplitude modulation frequency modulation sine wave taking the balance current as the balance position.
As is well known, a sine wave can be expressed in the form of equation (6):
wherein, A (V)bias) Is amplitude, ω (V)bias) In order to be the angular frequency of the frequency,
is the initial phase.
Setting initial phase according to the simulation test result curve in the step one
The amplitude A (V) is indicated by the amplitude modulation characteristic and the frequency modulation characteristicbias) And angular frequency ω (V)bias) Are all biased voltage VbiasAs a function of (c). By observing the characteristics of the change rule of the simulation test result curve in the first step, the amplitude A (V) can be approximately foundbias) The change rule of (2) is similar to the change rule of the current of a common diode, namely the amplitude changes approximately in an exponential rule along with the bias voltage, and the amplitude can be approximately expressed in a form of an equation (7) by taking a natural exponential function:
wherein the basic amplitude ASAnd pseudothermoelectric potential U0Is a fitting parameter; while the angular frequency omega is approximately seen as a constant that does not vary with the bias voltage.
And step three, superposing the respectively established curve component mathematical models to obtain an initial complete model of the volt-ampere characteristic of the device, and gradually adjusting the parameters of the fitting model by adopting Matlab simulation:
and (3) substituting the formula (7) into the formula (6), and then simplifying the formula and superposing the formula (5), so as to obtain an initial complete model of the volt-ampere characteristic of the device, wherein the initial complete model is as shown in the formula (8):
the initial models obtained after the Matlab preliminary simulation fitting are respectively expressed as the following formulas (9) to (12):
a comparison of the initial model curves corresponding to peak envelope, valley envelope, balance current component and total current versus the simulation test result curves is shown in fig. 3.
Comparing and analyzing the obtained initial complete model and a simulation test result of the volt-ampere characteristic curve, and further optimizing fitting parameters according to the regularity of errors;
comparing and analyzing the attached drawings 3 and 1, finding that the qualitative change regularity of the peak envelope and the valley envelope of the peak envelope and valley envelope curve model result and the simulation test result curve is similar, but the values of the valley envelope curve model result and the balance current component model result are obviously higher; the deviation between the total current initial model result and the simulation test result is also very obvious, wherein the peak value is higher, the valley value is lower, and the angular frequency omega (V) is higherbias) And are not constant. But changes approximately in a negative exponential law with the bias voltage, and the initial approximation can be approximately expressed in the form of equation (13) by taking a natural exponential function:
wherein, ω isrAnd UrAre fitting parameters. Further adjustments to the optimal fitting parameters are needed to reduce the bias.
Keeping the fitting parameters of the formulas (9) and (11) unchanged, optimizing the fitting parameters of the formula (14), and optimizing to obtain a result shown as the formula (15):
a comparison graph of the optimized total current model result and the peak envelope and valley envelope curve model result with the simulation test result curve is shown in fig. 4.
And fifthly, correcting the model parameters by adopting an error reduction method to ensure that the model result is matched with the simulation test result, thereby obtaining a voltage-domain oscillation quantum device volt-ampere characteristic model result with sufficient accuracy.
Comparing the model results curve shown in fig. 4 in step four with the simulation test results shown in fig. 1 in step one and the initial model results shown in fig. 3 in step three, it was found that the model results of equation (15) are relatively close to the simulation test results shown in fig. 1, but have obvious observable errors.
To obtain a more accurate model, A is eliminatedS、ωrAssuming that the bias voltage is constant, the bias voltage is taken as a piecewise function of the bias voltage, and the values of coefficients a and b are adjusted to describe the total current in a voltage domain in a piecewise way, so that a set of piecewise functions shown in formula (16) is obtained by changing the size of parameters:
the pair of the model result and the simulation test result of the corresponding equation (16) is shown in fig. 5. As can be seen from fig. 5, the model result of equation (16) matches well with the simulation test result, and can already meet the accuracy requirement of engineering application.
Step six, continuously improving the precision of the model, and drawing the model according to the A in the obtained formula (16) by adopting Matlab or other curve drawing software with a fitting analysis functionS、ωrA and b with a bias voltage VbiasThe changing rule curves are respectively shown in fig. 6-8. According to pair AS、ωrA and b with a bias voltage VbiasThe analysis of the changed regularity curve establishes a mathematical model of the regularity and performs parameter fitting.
As can be seen from the analysis of FIGS. 6-8, the bias voltage points at which the coefficients begin to change are the same, and when the bias voltage is higher than the voltage at the point of beginning to change, the first parameter ASAnd a bias voltage VbiasThen approximately in a piecewise opening downward parabolic relationship, the second parameter ωrAnd a bias voltage VbiasIt approximates a parabolic relationship with the segmented opening facing upwards, while the last two parameters a and b are related to the bias voltage VbiasApproximately in a downwardly opening parabolic relationship; thus, these coefficients can be approximated to the bias voltage V using a parabolabiasAre respectively expressed by formulas (17) to (20):
wherein d1, e1, d2, e2, g, h, i, j, k, l, m, o, p, s, t, w are fitting coefficients of respective parabolic equations, VboneffTurn on bias voltage, V, for effective oscillationk1,2Is a basic amplitude ASWith variation of the bias voltage VbiasRespective apex bias voltages, A, varying approximately parabolically from the opening of the segments to the lower sideSk1,2Respectively corresponding to the peak basic amplitude value, V, of two segments of parabolasbt1,2Respectively, the bias voltage V at the respective bottom points of the upper parabola of the segment opening with the oscillation angular frequency changing along with the bias voltage(a,b)tCorresponding to the apex bias voltages of parameters a and b, respectively, which vary parabolically with bias voltage opening down.
By substituting expressions (17) to (20) for expression (14), a model result with further improved accuracy can be obtained.
Step seven, when a certain material structure parameter of the device is changed and other material structure parameters are kept unchanged, for example, taking the potential barrier/potential well width parameter as an example, simulation test results are respectively shown in fig. 9(a) to 9 (c). And (3) respectively establishing a model of the test curve under each group of parameter conditions by adopting the same method from the first step to the sixth step, fitting a functional relation between each model fitting parameter and the changed parameter, and then substituting the equations (17) to (20) and (14) according to the hierarchy to obtain the high-precision complete mathematical model of the volt-ampere characteristic curve of the GaN-based quantum well voltage domain oscillation diode, which comprises the influence of the material structure parameters.
Claims (1)
1. A modeling method for volt-ampere characteristics of a voltage domain oscillation quantum device is characterized by comprising the following steps: the method comprises the following steps:
firstly, analog analysis is carried out on a simulation test curve of the volt-ampere characteristic of the same device structure according to a current transport mechanism of a voltage domain oscillation quantum device, and the volt-ampere characteristic curve is decomposed into different characteristic components by combining the current transport mechanism and the volt-ampere characteristic curve characteristics: balancing the current component and the oscillating current component;
step two, respectively establishing mathematical models for the decomposed curve components, and fitting model parameters by adopting Matlab; respectively establishing a mathematical model for the balance current component and the oscillation current component according to the Voltan characteristic decomposition in the step one;
step three, superposing the mathematical model established for the balance current component and the mathematical model established for the oscillation current component in the step two to obtain an initial complete model of the volt-ampere characteristic of the voltage domain oscillation quantum device, and gradually adjusting the parameters of a fitting model by adopting Matlab simulation;
step four, comparing and analyzing the initial complete model obtained in the step three and the simulation test result of the volt-ampere characteristic curve obtained in the step one, and further optimizing fitting parameters according to regularity of errors;
obtaining a result curve of the optimized total current model and a comparison graph of a model result of a peak envelope curve and a valley envelope curve and a simulation test result curve;
step five, according to the comparison analysis of the total current model result curve in the step four, the initial complete model obtained in the step three and the volt-ampere characteristic curve simulation test result obtained in the step one, an error reduction method is adopted to correct model parameters, so that the model result is matched with the simulation test result, and an accurate volt-ampere characteristic model result of the voltage domain oscillation quantum device is obtained;
step six, drawing a regular curve of each parameter of the volt-ampere characteristic model of the voltage domain oscillation quantum device along with the change of the bias voltage in the step five by adopting Matlab or other curve drawing software with a fitting analysis function; establishing a mathematical model of the regularity according to the analysis of a regular curve of each parameter along with the change of the bias voltage, performing parameter fitting, and continuously improving the precision of the model;
step seven, when a certain material structure parameter of the voltage domain oscillation quantum device is changed and other material structure parameters are kept unchanged; and respectively establishing a model of the test curve under the condition of each group of parameters by adopting the same method as the first step to the sixth step, fitting a functional relation between the fitting parameters and the changed parameters of each model, and then substituting the functional relation into a high-precision integral model relational expression according to layers to obtain a high-precision complete mathematical model of the volt-ampere characteristic curve of the device, which contains the influence of the structural parameters.
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