RU2545077C1 - Method for oriented modification of semiconductor device structures using pulse electromagnetic field - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method includes the determination of criterial parameters for devices, radiation in a passive mode of a limited survey sample of single-type semiconductor devices by a weak pulse electromagnetic field (PEMF) with variable parameters, including the pulse amplitude, its duration and repetition rate, processing of experiment data by statistic methods by comparing the criterial parameters of the semiconductor devices before and upon radiation by PEMF, in accordance with its results a positive effect of modification is detected and repeated radiation is performed for the untreated semiconductor device structures at PEMF generation modes optimal for the respective type of the device structures. At that the value of an integral parameter being the amplification coefficient is selected as the criterial parameter in the circuit with a common emitter of a bipolar transistor h_21E, while comparison of measurement results is made using a double-connected confidence S-interval, and according to the comparison results a conclusion is made about the influence degree of PEMF.

EFFECT: improved accuracy in the quantitative assessment of oriented modification of the semiconductor device structures using PEMF.

2 cl, 7 dwg

Description

The invention relates to the field of semiconductor electronics, in particular to the modification of the electrophysical properties of semiconductor device structures, and can be used to improve a number of electrophysical parameters of such structures.

In modern electronics, both bipolar and unipolar semiconductor transistor structures are widely used. First, the amplifying properties of semiconductor transistor structures are influenced by surface states at the interface between a passivating dielectric coating and a planar transistor structure [1], and second, the state of the gate insulator – MOS transistor (metal – oxide – semiconductor) interface [2] ].

Known methods for influencing non-magnetic semiconductor crystals of pulsed electromagnetic fields (IEMP) (for example, [3, 4]). Unlike ionizing radiation (II), which acts mainly on the dielectric layer and the insulator – semiconductor interface, ”IEMP act on the semiconductor crystal, changing the physicochemical properties of its surface layers. At the same time, in both cases, both as a result of the action of IEMP and under the influence of AI, long-term changes in the structure and properties of semiconductor crystals and transistor structures are observed, although these changes are realized and proceed by different mechanisms. The study of physical processes in semiconductor-based heterostructures under the action of IEMP is necessary to solve the problems of their possible use in technological processes to identify potentially unreliable elements of integrated circuits (ICs), to directionally modify materials and device structures, as well as to solve compensation problems intentional destabilizing effects of such factors.

Attempts are being made to establish the basic laws governing the effect of pulsed magnetic fields on the surface of semiconductors, the semiconductor – dielectric interface, and directly on the dielectric of bipolar structures and MOS structures.

The discovered effects of IEMP on semiconductors: low-temperature gettering in semiconductor crystals and modification of the physicochemical properties of the surface of semiconductor crystals by IEMP are the basis for the development of new technological processes, including the detection of latent technological defects in the IC of bipolar and MOS structures, low-temperature gettering in silicon, improving the quality of oxide films obtained on indium phosphide crystals, pre-treated IEMP.

In [5], a method for directional modification (solving a phase problem) was proposed by applying IEMP to non-magnetic semiconductor materials and technological methods were developed for using IEMP to detect latent defects in semiconductors and semiconductor materials.

In [5], the results of studies of the effects of IEMP on elementary semiconductors (Si, Ge), semiconductor compounds A ^III B ^V (GaAs, InP), and solid solutions of elements of groups III, IV, and V of the periodic table are presented. The effect of low-temperature gettering in semiconductor crystals was discovered, which is based on IEMP-induced decay of impurity-defective complexes (MPCs) in the crystal bulk, diffusion of the formed decomposition products with anomalously high mobility to the crystal surface, and the formation of new defective complexes in the surface layer. The movement of defects to the surface is stimulated by elastic stresses in the crystal. A method for low-temperature gettering in silicon is proposed, based on sequential processing of the crystal with alpha particles and IMEP. In this case, irradiation with alpha particles ensures the creation of outflows for point defects outside the working areas of the crystal, which are formed during the IEMP decay of the initial defect complexes. The principal advantage of the presented method is that it is implemented at T <520 K and can be used at any stage of the formation of the device, including the finish.

The effect of revealing latent (latent) defects in the silicon structures of MOS as a result of IEMP was found. Local inhomogeneities that do not exhibit electrical activity in the initial structure can be converted into an electrically active state by the action of IEMP. The effect is explained by the IEMP decay of defective complexes in a silicon crystal and the subsequent capture of decay products (point defects capable of migration in the IEMP-treated crystal) on local structural inhomogeneities, including initially latent ones. The possibility of using IEMP as a testing effect for the detection of latent technological defects in the silicon structures of MOS is shown.

The effects of a long-term nonmonotonic change in the physicochemical properties of the surface of semiconductor crystals as a result of the action of IEMP were found. The effect of a long-term (hundreds of hours at room temperature) non-monotonic change in the topology of the surface of semiconductor crystals is manifested in a decrease in surface planarity at the first stage and its subsequent increase to a level exceeding the initial one (Fig. 1). The reconstruction of the crystal surface is caused by the emergence of flows of mobile point defects as a result of the decay of the initial defect complexes under the influence of IEMP. A change in the surface topology of semiconductors is also accompanied by a nonmonotonic change in its sorption ability. Using indium phosphide as an example, the possibility of using processing of IEMP semiconductor materials to increase the rate of chemical reactions occurring on their surface is shown. For indium phosphide crystals, a change was found in the rate of their low-temperature (T = 313 K) chemical oxidation. The change in the rate of the oxidation process is accompanied by a synchronous change in the dielectric strength of the oxide films (Figure 2). The effect of increasing the rate of chemical oxidation of indium phosphide as a result of preliminary processing of the IEMP crystal can be explained in terms of the mechanism responsible for the appearance of diffusion instability in crystals of semiconductor compounds A ^III B ^V [6].

As a result of studying the effect of IEMP on the defective subsystem of gallium arsenide single crystals by the study of deep level occurrence (DLTS), the effect of irreversible changes in the spectrum of deep levels corresponding to surface electronic states (TEC) as a result of processing the IEMP crystal was discovered. The effect is to change the temperature position of the peak PES (Figure 3). The positions and amplitudes of the peaks due to deep volume levels of EL6 and EL2 did not change as a result of IEMP, which indicates that only surface electronic states are sensitive to IMP. The DLTS spectra of gallium arsenide plates pretreated in selenium vapor did not change as a result of IEMP. The discovered effect can be explained from the standpoint of the concept of lattice magnetism induced by defects [7, 8]. At the same time, it is known that pulsed energy action on a solid causes more noticeable effects than the same pulsed, repeated action, but of a smaller magnitude or stationary. Models of such a manifestation of pulsed loading and possible causes were discussed in [9].

All this testifies in favor of the constructive effect of IEMP on solid-state semiconductor structures.

However, as follows from the above materials, quite specific parameters of semiconductor structures and materials are subject to change: optical, strength, morphological, etc. Integral parameters are of greatest information interest, such as, for example, the gain of bipolar transistors in a circuit with a common emitter - h _21E , which is characterized, in turn, by the emitter efficiency γ, recombination processes in the base (defective base material) and the electrical mode of the collector junction (the magnitude of the coefficient of avalanche multiplication of carriers).

However, the discovery of subtle effects of changes in the criterion parameters of semiconductor structures under the action of IEMP also requires more thorough processing of experimental data, especially in conditions of conducting expensive experiments with small samples. This problem is common both when performing experiments with IEMP, and for experiments with pulsed AI.

The closest (prototype) to the claimed method is the method described in [10]. A method for the formation of elements of semiconductor devices and IC structure of the MOSFET based on the use of IEMP is proposed.

In [10], α particles and IEMPs act sequentially on silicon crystals, which makes it possible to getter at a low temperature (300–500 K). Irradiation with α particles creates sinks outside the working regions of the crystal for rapidly diffusing point defects resulting from IEMF-induced decay of the initial impurity-defect complexes (MPC). The directed modification of semiconductor device structures as a result of such radiation-magnetic exposure is manifested, in particular, in an increase in the lifetime of minority carriers.

Then, IEMP is affected, which leads to the decomposition of MPC in the bulk of the crystal, the diffusion of the products of this decay to the surface and the formation of new defective complexes in the surface layer. The surface of a dislocation-free crystal is a natural and main sink for mobile defects induced by IEMP processing. The role of preliminary (before the IEMP) irradiation of the crystal with α particles is the formation of a disturbed layer deep in the crystal, far from its working surface. The possibility of creating such a “buried” disturbed layer is due to the fact that the generation of radiation defects in a crystal, when high-energy α-particles are implanted, occurs locally, mainly at a depth corresponding to the mean free path of α-particles, where the main energy losses occur their braking. The penetration depth of α particles with an energy of ~ 5 MeV in Si, and hence the depth at which the disturbed layer is formed, is ~ 25 μm. This value significantly exceeds the thickness of the surface region of the crystal used to form semiconductor device structures. The result of gettering is, in particular, an increase in the LV lifetime and an improvement in the electrical characteristics of semiconductor device structures (for example, a decrease in the reverse currents of pn junctions of MOS and IC transistors) (Figure 4).

As a criterion electric parameter, which makes it possible to judge the degree of structural perfection of a crystal, the generation lifetime τ _g of charge carriers is chosen.

The disadvantage of the method [10] is that, firstly, to obtain a positive effect, preliminary irradiation of the MOS transistor structures with α-particles is required, which is not always possible to implement in the current production. Secondly, the positive effect of co-sequential processing of α-particles and IMEP is shown only for MOS structures containing a gate oxide and a dielectric “buried” layer (induced by α-particles in bulk MOS structures, the original in CMOS / KND structures (“complementary metal semiconductor oxide / silicon-on-dielectric ").

At the same time, in bipolar planar transistor structures there is a dielectric layer for creating a passivating coating, the maximum permissible concentration in the interface of which affects the surface leakage current collector-base and, therefore, the value of the integral parameter - the gain of the bipolar transistor in a circuit with a common emitter ( OE) - h _21E . Therefore, in these structures, irradiation with α particles to create a “buried” MPC can be excluded.

The technical result of the proposed method is to increase the accuracy of the quantitative assessment of directional modifications of semiconductor device structures using IEMP.

The technical result is achieved by the fact that in the method of directional modification of semiconductor device structures using IEMP, including determining the criteria for these devices, irradiating in a passive mode a limited sample of the same type of semiconductor device structures with a weak IEMP with variable parameters, including pulse amplitude, pulse duration and repetition rate, processing of experimental data by statistical methods by comparing the criteria of semiconductor devices Before and after irradiation of the IEMP, the results of which reveal the positive effect of modification and re-irradiate the untreated semiconductor device structures at the IEMP generation regimes optimal for this type of device structures, to establish the degree of influence of the electromagnetic field strength and distribution over time on the criterion parameters and to improve the accuracy of quantitative assessment of directional modification of semiconductor device structures using IEMP, as TBE criterial parameter selected value of the integral parameter - the gain in the common-emitter bipolar transistor - h _21E, and the comparison of measurement results is carried out using doubly connected confidence S-region [11] (Appendix), the results of which make a determination of the degree of PEMF influence.

, где $$\overline{x}$$

- среднее значение случайной величины h_21E в выборке, определяют в этом случае путем сравнения смещения «геометрического центра» S-областей $$\Delta \left(\overline{\nu },\overline{u}\right)$$

, построенных по результатам измерения экспериментальных данных «до» и «после» обработки полупроводниковых приборных структур ИЭМП, а координаты геометрического центра такой области определяются в виде $$\left(\overline{\nu },\overline{u}\right)$$

:For an unambiguous interpretation of the comparison results, the value of the significant effect $$\Delta \overline{x}$$

where $$\overline{x}$$

- the average value of the random variable h _21E in the sample, is determined in this case by comparing the displacement of the "geometric center" of S-regions $$\Delta \left(\overline{\nu },\overline{u}\right)$$

constructed from the results of measuring the experimental data “before” and “after” the processing of IEMP semiconductor device structures, and the coordinates of the geometric center of such an area are defined as $$\left(\overline{\nu },\overline{u}\right)$$

:

- среднее значение нижней допустимой границы критериального параметра, определенного в качестве случайной величины, u - нижнее выборочное значение этого параметра, s - минимальное нижнее допустимое значение критериального параметра, $$\overline{\nu }$$

- среднее значение верхней допустимой границы критериального параметра, ν - верхнее выборочное значение критериального параметра, t - максимальное верхнее значение критериального параметра, которые в свою очередь, определяют из соотношений:Where $$\overline{u}$$

is the average value of the lower permissible boundary of the criterion parameter defined as a random variable, u is the lower sample value of this parameter, s is the minimum lower permissible value of the criterion parameter, $$\overline{\nu }$$

is the average value of the upper permissible boundary of the criterial parameter, ν is the upper sample value of the criterial parameter, t is the maximum upper value of the criterial parameter, which, in turn, is determined from the relations:

and the parameter determining the half-width of the confidence interval, with ≤0.5, is calculated based on the numerical values of the degree of distrust α to the results, the numerical value of which is selected in the interval 0≤α≤1, and the sample size n.

The invention is illustrated by the following graphic illustrations.

Figure 1 shows the STM image and the cross-sectional profile of the surface of the Cz-Si crystal: a - before exposure to IEMP (roughness parameter Rz = 1.34 nm); b and c - 200 and 400 hours after the treatment of IEMP, respectively (Rz = 5.81 nm and Rz = 0.92 nm); d is the cross-sectional profile (1 - before exposure to IEMP; 2 - 200 hours after processing IEMP, respectively) [5].

Figure 2 shows the time dependence after processing the IEMP of the substrate:

1) the difference in thickness Δd of oxide films of experimental and control samples;

2) the electric field E in the film, through the cross section of which a current of 1 μA flows, the oxidation time is 25 min [5].

In figure 3. The effect of IEMP processing on the DLTS spectra of Schottky Al-GaAs contacts is shown: 1 — initial; 2; 3 - 1 and 7 days after UTI, respectively. Spectra 4 and 5 were measured on samples pretreated with GaAs wafers in selenium vapor before and 3 days after exposure to IEMP. DLTS measurement mode: t ₁ / t ₂ = 10 ms / 210 ms [5].

Figure 4 shows the effect of combined radiation and IEMP treatments on non-stationary capacitance-voltage characteristics of MOS structures (a) and reverse currents of the pn junctions of MOS transistors (b). Characteristics: 1 - initial; 2 - after exposure to α particles; 3 - after exposure to α particles and IEMP [10].

Figure 5 shows a doubly connected trust S-region for GIS No. 4 with the coordinates of the boundary points u, ν, s, s ₁ , t, t ₂ (n = 16, s = 0.17).

Figure 6 shows a representation of a doubly connected confidence S-region in the form of "energy" levels, on which "energy transitions" correspond to the size of the confidence interval along the axes [θ ₁ , θ ₂ ] of the general population.

Figure 7 shows the displacement of the geometric center of the doubly connected confidence S-region after processing the IEMP samples. The projections of the upper and lower boundaries of confidence intervals are shown.

The proposed method is implemented as follows.

As a criterion integral parameter of semiconductor device structures, for example, bipolar transistor structures, the gain in the circuit with OE - h _{21E is} chosen as the most informative parameter, including information on the efficiency of the emitter - base and collector - base transitions.

Measure the values of the criterion parameter h _{21E of a} limited sample of transistor structures, including individual transistors in the IC, with a fixed electric mode before exposure to IEMP.

Then, a limited sample of semiconductor device structures in a passive (non-powered constant current source) mode is subjected to a series of weak IEMP pulses with varying characteristics (amplitude, duty cycle, repetition rate and pulse shape).

Next, measure the criteria parameters of these devices after IEMP exposure with the same electrical measurement mode as in the absence of IEMP effect.

Comparison of the measurement results is carried out using a doubly connected confidence S-region [11], the results of which make a conclusion about the degree of influence of the EMF (figure 5).

, где $$\overline{x}$$

- среднее значение случайной величины h_21E в выборке, определяют в этом случае путем сравнения смещения «геометрического центра» S-областей (фиг.5) $$\Delta \left(\overline{\nu },\overline{u}\right)$$

, построенных по результатам измерения экспериментальных данных «до» и «после» обработки полупроводниковых приборных структур ИЭМП (фиг.7), а координаты геометрического центра такой области определяются в виде $$\left(\overline{\nu },\overline{u}\right)$$

, где $$\overline{u}$$

- среднее значение нижней допустимой границы критериального параметра (1)? определенного в качестве случайной величины, u - нижнее выборочное значение критериального параметра, s - минимальное нижнее допустимое значение критериального параметра, $$\overline{\nu }$$

- среднее значение верхней допустимой границы критериального параметра, ν - верхнее выборочное значение этого параметра (1), s - минимальное нижнее значение критериального параметра (2), t - максимальное верхнее значение критериального параметра (3) (фиг.5). Параметр, определяющий полуширину доверительного интервала, с≤0,5, вычисляют, исходя из численных значений степени недоверия α к полученным результатам, численное значение которой выбирают в интервале 0≤α≤1, и объема выборки n (Приложение).For an unambiguous interpretation of the interpretation of the results of comparison, the value of the significant effect of the increment $$\Delta \overline{x}$$

where $$\overline{x}$$

- the average value of the random variable h _21E in the sample, is determined in this case by comparing the displacement of the "geometric center" of the S-regions (figure 5) $$\Delta \left(\overline{\nu },\overline{u}\right)$$

based on the results of measuring the experimental data “before” and “after” processing the semiconductor device structures of the IEMP (Fig. 7), and the coordinates of the geometric center of such an area are defined as $$\left(\overline{\nu },\overline{u}\right)$$

where $$\overline{u}$$

- the average value of the lower permissible boundary of the criterion parameter (1)? defined as a random variable, u is the lower sample value of the criterial parameter, s is the minimum lower acceptable value of the criterion parameter, $$\overline{\nu }$$

is the average value of the upper permissible boundary of the criterion parameter, ν is the upper sample value of this parameter (1), s is the minimum lower value of the criterion parameter (2), t is the maximum upper value of the criterion parameter (3) (Fig. 5). The parameter that determines the half-width of the confidence interval, with ≤0.5, is calculated based on the numerical values of the degree of distrust α to the obtained results, the numerical value of which is chosen in the interval 0≤α≤1, and the sample size n (Appendix).

According to the results of processing data with variable IEMP parameters, the IEMP generation modes optimal for this type of semiconductor device structures are revealed, in which a positive modification effect is revealed.

Repeated irradiation of untreated semiconductor device structures is performed at the IEMP generation regimes optimal for this type of device structure.

An example of a specific implementation.

We studied hybrid integrated circuits (GIS), consisting of 16 parallel-connected bipolar transistors according to a circuit with OE, in which the amplification factors h _21E (integrated radiation-critical parameter (RPC)) were measured.

At the preliminary stage of the study of the integral characteristics of the optical properties of silicon-on-sapphire (SPS) heterostructures and changes in the surface roughness of the instrument layer, no significant changes were revealed after IEMP exposure.

Then, the changes in the gain h _{21E of the} transistors in the GIS were studied with the aim of:

- increase sample statistics of measurements;

- attracting new methods for processing experimental data;

- use of the parameter - gain factors h _21E as the most informative integral parameter (influence of emitter efficiency, collector junction voltage - impact ionization coefficient, recombination coefficient in the base, etc.).

To increase the reliability of research results:

- The results of measurements “before” and “after” the impact of the IEMP were not compared in advance with its parameters until the experiments were completed (principle of “anonymity”);

- Used 4 pcs. GIS as samples for research (4 × 16, a total of 64 transistors);

- The statistical processing technique “the method of biconnected domains” was used (Appendix and Fisher criterion [12]).

Gain of semiconductor transistor structures of well logs was measured "before" and "after" the impact of IEMP.

The instrumental measurement error was 3.5% for the selected measuring instruments according to the technical specifications per microcircuit (calculated value).

Covers were removed from all well logs, the semiconductor instrument structures were placed in a cylindrical inductor so that their working surface was perpendicular to the lines of force of the magnetic field of the inductor, which was a multilayer inductor. The magnetic field intensity was measured with a G77 milliteslameter. Processing time was fixed. The duration of the magnetic pulse was measured using an S1-68 oscilloscope connected to a G77 milliteslameter. Processing was carried out for 10 minutes. in the frequency range 2–16 Hz by pulses of duration from 2 to 5 ms, the field induction was in the range of 40–150 mT. Power consumption of the installation - no more than 250 W, average current ~ 1 A.

The results of measurements of the gain h _21E for all transistors in the sample before and after exposure to the IEMP are given in Table A.1 of the Appendix. The results of processing the source data using the Fisher test are summarized in table 1.

They show that the conditions for deciding on the significance of the results

, $$F_{n,v}^{\mathrm{uh}\mathrm{to}\mathrm{from}PeR.}<F_{n,v}^{te\mathrm{about}R.}$$

,

where n is the sample size (16 pcs. for each well logging unit, ν is the number of degrees of freedom, are performed only for transistors of groups “1” and “2.” In this case, the term “significance” means the reliability of the result of the IEMF obtained by statistical processing limited sample (finding the arithmetic mean value, standard deviation, Pearson criterion χ ² , etc.).

Table 1 The results of processing the source data using the Fisher test

Table 2 shows the results of processing experimental data using the method of constructing a doubly connected confidence S-region.

From the analysis of these data it follows:

(1).Using the distribution parameters A (s) and d (s) does not give reliable results on the nature of the IEMP effect, since they determine the allowable geometric field of a possible change in a random variable in the region with coordinates [θ ₂ , θ ₁ ]. It is much more reasonable to determine the coordinates of the "geometric center" of such an area in the form $$\left(\overline{\nu },\overline{u}\right)$$

(one).

table 2 Results of processing experimental data using the method of constructing a doubly connected confidence S-region.

определяют в этом случае путем сравнения смещения «геометрического центра» S-областей, построенных по результатам измерения экспериментальных данных «до» и «после» обработки полупроводниковых приборных структур ИЭМП (фиг.7). При анализе результатов выявлена тенденция положительного изменения $$\Delta \overline{x}$$

- коэффициента усиления после воздействия ИЭМП (увеличение исходных значений).Significant effect $$\Delta \overline{x}$$

in this case, it is determined by comparing the displacement of the "geometric center" of S-regions constructed from the results of measuring the experimental data "before" and "after" processing the semiconductor device structures of the IEMP (Fig. 7). An analysis of the results revealed a trend of positive change. $$\Delta \overline{x}$$

- gain after exposure to IEMP (increase in initial values).

The magnitude of the changes exceeds the error in the estimation of the RCP.

The result obtained in this way clearly indicates an increase in the gain after processing the IEMP. It should be noted that the installation used to generate the IEMP had limited possibilities for induction, pulse duration, and frequency range.

Thus, the use of the proposed method allows quite simply to modify the basic electrophysical parameters of semiconductor structures.

APPENDIX

Biconnected Trust Area

To describe the samples with the number of samples (measurements) n <50, S-distributions (having two characteristic break points on the graph of the integral distribution law of a random variable) are best adapted. These S-distributions include:

- S - normal distribution (or Gauss);

- lognormal distribution;

- Weibull distribution.

Such data are not reliable for checking the model along the so-called Easterling line. It is much easier to set the upper and lower boundaries of the distribution. For this, it is necessary to determine a doubly connected S-confidence region with a confidence probability γ = 1-α. Let (U, V) be large-order statistics (general population) and (u, ν) be small-order statistics (sample), U, u be the lower minimum values of a random variable in these statistics, and V, ν be upper maximum values random variable in these statistics. Assuming that these boundary values are randomly distributed along two independent axes for a number of independent samples, we can define A (s) as the area of the confidence region, and d (s) as the maximum diagonal (variance) of the confidence region.

Let X be a random variable. Based on the Shannon-Brillouin information theory, information I can be determined by the relation

where k is the Boltzmann constant, S is the thermodynamic entropy.

The following distributions satisfy this "non-entropic" principle in order to reduce the uncertainty of convergence of the theoretical and experimental laws of distribution of a random variable:

- uniform;

- exponential;

- Poisson;

- normal distribution (or Gauss).

For the worst result from the point of view of convergence of the theoretical and experimental distribution laws, we choose a uniform (rectangular) law inside the interval [θ ₁ , θ ₂ ]

It is required to determine the γ = 1-α confidence s-region for sample values of the pair boundaries [θ ₁ , θ ₂ ], for a sample of size n of the distribution density pdf (x). Then, for the lower bound u and the upper bound ν for a random variable, the integral distribution function takes the form

For n independent implementations of samples of a random variable, we can write

Then the joint probability density will be equal to

for θ ₁ <u <ν <θ ₂ and 0 for all other values of x.

For a fixed value α≥2 ^{-m + 1} (a decrease in the degree of distrust in the result with an increase in the sample size + one degree of freedom), which ensures that with≤1 / 2 the probability of the coefficient taking into account the restrictions made will be equal to

The meaning of this expression is that: 1) the boundaries of the population [U, V] are actually located inside the measured boundaries [θ ₁ , θ ₂ ]; 2) the possible boundaries of the change in the values of U and V cannot overlap; therefore, the coefficient c, which determines the width of the interval of change in the values of U and V, does not exceed ½; 3) the confidence probability of these realizations of a random variable is γ.

The constant c can be determined from the relation

Carrying out the calculations, we obtain the transcendental ratio

α = 2 (1-c)

The solution (A.7) by the numerical Newton method allows us to calculate the values of the constant c as a function of the sample size n and probability α. The results of calculating the constant c as a function of the sample size of a random variable x and probability α are summarized in Table A.1. These data can be used to predict confidence intervals for changing the criterial parameters of newly created products in the case when a priori information is missing.

For large n, relation (A.7) takes the form

which transforms into

$$nc\approx -\ln (\mathrm{one}-\sqrt{\mathrm{one}-\alpha )=-\ln (\mathrm{one}-\sqrt{\gamma .}}\left(P.9\right)$$

In the above analysis, the symmetric boundaries of the changes in the quantities U and V are considered. In principle, the option of considering asymmetric boundaries is not excluded.

When replacing a variable in (A.7)

c⇒c-d for one boundary;

c⇒c-d for the second border. The value of d is a characteristic of asymmetry.

With this in mind (A.7) will take the form

The value 1-P (s, d) is stationary along c and this stationarity corresponds to the condition 0≤c≤1. It is difficult to expect any progress along this path. The following definition of the probability of distribution of the constant c

P ^* (s) = Pr {(U-θ ₁ ) ² + (V-θ ₂ ) ² } ≤c.

Integration of g (u, v) over this region should establish wider boundaries and, accordingly, a larger area A (s) than previously determined. Area S is bounded by lines

θ ₁ = u;

θ ₂ = ν.

Table A.1 The calculated values of the coefficient c depending on the sample size n and confidence probability α

1) The data contains the product nc for n⇒∞. (1-c) θ ₁ + cθ ₂ = u; cθ ₁ + (1-s) θ ₂ = ν.

Using the equations of analytical geometry, it is possible to describe in the format (u, ν) 4 boundary points on a doubly connected confidence s-region (see Table PA.2);

1) Upper left (s, t);

;2) Bottom Left $$\left(s_{{\mathrm{one}}_{\mathrm{one}}}u\right)$$

;

3) Upper right (u, t ₂ );

4) Lower right (u, ν).

This allows us to represent these points on the "energy" diagram of Fig. A.1.

The distances between the corresponding energy levels determine the width of the confidence interval from the set of confidence intervals enclosed within the biconnected S-region.

Table A.2 Coordinates of the boundary points of the S-region Short designation. The name of the boundary point on the plane S-region point coordinates one 2 3 max ↓ Max bottom

$$s_{\mathrm{one}}=\frac{u-c\nu }{\mathrm{one}-c}$$

min ↑ Minimum top $$t_2=\frac{\nu -cu}{\mathrm{one}-c}$$

one 2 3 min ↓ Minimum bottom

$$s=\frac{u-c(u+\nu )}{\mathrm{one}-2c}$$

max ↑ Max upper $$t=\frac{(\mathrm{one}-c)(u+\nu )}{\mathrm{one}-2c}$$

min Minimum u max Maximum v

Then A (s) is the area of the confidence region, and d (s) is the maximum diagonal (lispersion), which determines the distance between the points (u, v) and (s, t). Using the relations of analytic geometry, we can determine

$$d\left(s\right)=\sqrt{2c}\frac{\left(\nu -u\right)}{\left(\mathrm{one}-2c\right)}/\left(P.12\right)$$

It is possible to construct confidence intervals in the range

(ν-u) ≤R≤ (ν-u) / α,

obtained directly from the distribution in the range V-U, where α is the largest root in the range {0,1] for equality

Literature

1. Bakerenkov A.S. A conversion model of the low-intensity effect in bipolar integrated circuits for space applications / Diss. for a job. student Art. Ph.D. // M.: NRNU MEPhI, 2013.

2. CERN Training / April 11, 2000 / Radiation Effects on Electronic Component and Circuits, part 1 on 2 / Martin DENTAN, p. 77.

3. Golovin Yu.I. Magnetoplasticity of solids / Yu.I. Golovin // FTT. - 2004 .-- T.46, issue 5. - S.769-803.

4. Morgunov RB Spin-dependent reactions between structural defects and their effect on the plasticity of crystals in a magnetic field / RB. Morgunov // UFN. - 2004. - T.174, No. 2. - S.131-159.

5. Tatarintsev A.V. The effect of ionizing radiation and pulsed magnetic fields on the surface properties of semiconductors / Diss. for a job. student Art. Dr. Ph.D. / Voronezh: Voronezh State University, 2000. - P.323.

6. Levin M.N. The effect of magnetically induced diffusion instability in semiconductor compounds A ^III B ^V / M.N. Levin, G.V. Semenova, T.P.Sushkova // DAN. - 2003 .-- T.388, issue 5. - S. 608-610.

7. Belyavsky V.I. Spin effects in defect reactions / V.I. Belyavsky, M.N. Levin // Phys. Rev. B. - 2004. - V.70. - P.104101 (8).

8. Belyavsky V.I. Defect-induced Iattice magnetism: Phenomenology of magnetic-field-stimulated defect reactions in nonmagnetic solids / V.I. Belyavsky, M.N. Levin, N.J. Olson // Phys. Rev. B. - 2006. - V.73. - P.054429 (6).

9. Kachemtsev A.H., Kiselev V.K., Pyaterikova I.V., Skupov V.D. Relaxation processes in solid-state semiconductor devices when exposed to pulsed ionizing radiation / Sat. doc. VIII intersectoral conference on radiation resistance, Sarov, October 16-19, 2007 // Sarov: RFNC-VNIIEF, 2007, p.5-23.

10. Levin M.N., Ivankov Yu.V. Impact of pulsed magnetic fields on metal-dielectric-semiconductor / Voronezh structures: Ministry of General and Professional Education of the Russian Federation, Voronezh State University, department. Nuclear Physics, 1999. - P. 24.

11. Salvia Anthony A. / IEEE Transactions on Reliability, vol. R-29. - No.5. - p. 397-400.

12. David Hudson. Statistics for physicists. M.: Mir, 1964 .-- P.164.

Claims (2)

1. The method of directional modification of semiconductor device structures using pulsed electromagnetic fields, including
determination of criteria parameters of semiconductor device structures,
irradiation in a passive mode of a limited sample of the same type of semiconductor device structures with a weak pulsed electromagnetic field (IEMP) with variable parameters, including the amplitude of the pulse, its duration and repetition rate,
processing of experimental data by statistical methods by comparing the criterial parameters of semiconductor device structures before and after irradiation of IEMP,
the results of which reveal the positive effect of the modification and re-irradiate the untreated semiconductor device structures at optimal generation conditions for pulsed electromagnetic fields for this type of semiconductor device structures,
characterized in that as a criterion parameter, the value of the integral parameter is chosen - the gain in the circuit with the common emitter of the bipolar transistor - h _21E , and the comparison of the measurement results before and after irradiation is carried out using a doubly connected confidence S-region, based on which the conclusion on the degree of the effects of IEMP. 2. The method according to claim 1, characterized in that the value of the significant effect of the increment $$\Delta \overline{x}$$

where $$\overline{x}$$

- the average value of the random variable h _21E in the sample, is determined in this case by comparing the displacement of the "geometric center" of S-regions $$\Delta \left(\overline{\nu },\overline{u}\right)$$

constructed from the results of measuring the experimental data “before” and “after” the processing of IEMP semiconductor device structures, and the coordinates of the geometric center of such an area are defined as $$\left(\overline{\nu },\overline{u}\right)$$

where
$$\overline{u}=(\frac{u-s}{2})+s$$

; $$\overline{\nu }=(\frac{t-\nu }{2})+\nu$$

,
Where $$\overline{u}$$

is the average value of the lower permissible boundary of the criterion parameter defined as a random variable, u is the lower sample value of the criterial parameter, s is the minimum lower permissible value of the criterion parameter, $$\overline{\nu }$$

is the average value of the upper admissible boundary of the criterial parameter, ν is the upper sample value of the criterial parameter, t is the maximum upper value of the criterial parameter, which in turn is determined from the relations
$$s=\frac{u-c(u+\nu )}{\mathrm{one}-2c}$$

;
$$t=\frac{(\mathrm{one}-c)(u+\nu )}{\mathrm{one}-2c}$$

,
and the parameter determining the half-width of the confidence interval, with ≤0.5, is calculated based on the numerical values of the degree of distrust α to the obtained results, the numerical value of which is chosen in the interval 0≤α≤1, and the sample size n.

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