CN1322552C - Analog method for fluctuation of ionic injection - Google Patents

Abstract

The present invention provides an analog method for the fluctuation of ionic injection. The method is characterized in that after ion is injected N times according to an ionic injection analog method, and the ion is injected to the final three-dimensional position in a target material; then, the ion is divided into grids in the direction which is perpendicular to the surface of the target material, and the quantity of the staying ion in each grid after the ion is injected single time and the total quantity of the staying ion after the iron is injected N times are obtained; moreover, the fluctuation distribution of doping ion is obtained by a statistical method. The fluctuation analog method of the present invention has the advantages that the quantity of the doping ion influencing the doping fluctuation of a semiconductor is taken into consideration, and the factors of the depth of the doping ion are fully taken into consideration. The present invention can obtain the fine fluctuation of the doping that the ion is injected into the semiconductor is obtained on the basis of the existing analog data, and obtain the change relation of the doping fluctuation and the depth. The calibrating method for the doping fluctuation proposed by the present invention is good for the analysis of data and subsequent application.

Description

Ion implantation fluctuation simulation method

Technical Field

The invention relates to the field of manufacturing of integrated circuits, in particular to a method for simulating doping fluctuation of ion implantation in the manufacturing process of the integrated circuits.

Background

In the fabrication of integrated circuits, ion implantation is a well-established key process, in which an arsenic or boron plasma beam is incident into a silicon material, so that the ion beam and atoms or molecules in the silicon material undergo a series of physical and chemical interactions, and finally, the incident ions gradually lose energy and stay in the silicon material to form a P-type or N-type doped semiconductor.

Important specifications of semiconductor devices, such as threshold voltage and driving current, and critical performance of integrated circuits, such as maximum operating frequency, depend on the stability of each process step, i.e., the fluctuation of critical parameters in the process step, during the entire manufacturing process of the integrated circuits. Accurately predicting the fluctuation of the relevant parameters of the integrated circuit has great significance for the production of the integrated circuit. Overestimation of the fluctuations will lead to increased complexity of the integrated circuit design and may increase the design time period, the size of the design cells, and other disadvantages, and eventually make the produced integrated circuit less competitive in the market. On the other hand, an underestimation of the fluctuation will lead to underestimation of the product quality, excessive production, and other disadvantages. In summary, overestimation of fluctuations leads to increased difficulty in designing integrated circuits, and underestimation of fluctuations leads to increased difficulty in producing integrated circuits. The significance of accurately predicting fluctuations in parameters associated with an integrated circuit becomes increasingly significant. Fluctuations can be broadly divided into two categories: inter-cell (Dieto Die) fluctuation and intra-cell (within Die) fluctuation. The inter-unit fluctuation is fluctuation generated due to process instability between different batches, different wafers, and different units of the same wafer. The intra-cell fluctuation mainly includes fluctuation of lines and fluctuation of doping by ion implantation. The fluctuation of the lines is generated due to the uneven thickness of the photoresist material on the wafer, the uneven photoresist material and the unstable photoetching process; the doping fluctuation is derived from the nonuniformity of the spatial distribution of the doping ions after the ion implantation and the annealing, and the doping fluctuation is more obvious when the doping space is smaller. For integrated circuits manufactured by ion implantation, the in-mold fluctuation is mainly doping fluctuation.

At present, the feature size of integrated circuits is continuously reduced, and is expected to reach 50 nanometers before 2010, one of the key technologies for manufacturing ultra-deep submicron devices is the formation of ultra-shallow junctions, and low-energy ion implantation is the most effective and most feasible technical means for forming ultra-shallow junctions. For integrated circuits with larger feature sizes, inter-cell fluctuations are a major contributor to their performance fluctuations. As the feature size of the integrated circuit decreases, the influence of intra-cell fluctuation on the performance of the integrated circuit becomes more prominent, and the fluctuation of ion implantation is intrinsic, that is, the fluctuation inevitably exists as long as the ion implantation is used, and the fluctuation of ion implantation cannot be eliminated by improving the process. Therefore, it is necessary to fully recognize the characteristics of ion implantation doping fluctuation itself and study the effect of ion implantation doping fluctuation on the performance of the integrated circuit, thereby reducing the effect of intra-cell fluctuation in the integrated circuit manufacturing process.

At present, a great deal of work is focused on researching the influence of ion implantation doping fluctuation on the performance of an integrated circuit, and because the knowledge of the change of the ion implantation doping concentration along with the depth is not enough and the calculation capability is limited, a systematic method for describing the ion implantation doping fluctuation per se is not enough and accurate. In the experimental method, due to the limitations of experimental cost, stability of experimental conditions, sample testing and the like, doping fluctuation cannot be accurately obtained through the experimental method.

However, the existing fluctuation simulation methods, such as the simulation fluctuation method proposed by Hon-Sum Wong and Yuan Taur described in the document IEDM tech.dig., 7051993, are too coarse in simulation model and statistical technique, so that the obtained doping fluctuation data lacks sufficient accuracy and reliability. Fig. 1 is a schematic diagram of the doping fluctuation distribution obtained by the above simulation method, in which the abscissa represents the number of doping ions and the ordinate represents the relative frequency of occurrence of the number of doping ions. According to the method, the number of uniformly doped ions in a 150nm multiplied by 50nm multiplied by 80nm region is researched, the distribution of the doped ions of 1000 samples is counted, and the probability distribution of impurity ions in the region accords with Poisson distribution under the assumption of uniform doping. Since the doping region is assumed to be uniformly doped by the simulation method, only the overall fluctuation distribution can be given, and the result of the change of the doping fluctuation along with the depth cannot be given. In the actual ion implantation process, the distribution of doped impurity ions in the target material silicon is non-uniform, the non-uniformity of the distribution can obviously affect the performance (such as threshold voltage and the like) of the semiconductor device, and the influence of doping fluctuation at different depths on the performance of the device and the circuit is different due to different degrees of the influence of doping concentration at different depths on the performance of the semiconductor device and the circuit. Ion implantation doping fluctuations depend on variations in ion implantation depth and indirectly on the concentration distribution at different depths.

Disclosure of Invention

The invention aims to provide a simulation method of ion implantation fluctuation, which can obtain the change relation between the ion implantation fluctuation and the depth and accurately and reliably analyze the ion implantation fluctuation.

The invention relates to a simulation method of ion implantation fluctuation, which comprises the following steps: firstly, carrying out N times of ion implantation to obtain the final three-dimensional position of the implanted ions in a target material; secondly, grid division is carried out in the direction vertical to the surface of the target material, and the number of staying ions in each grid after single ion injection and the average number of staying ions in each grid after N times of ion injection are obtained; then, obtaining the fluctuation distribution of the doped ions by adopting a statistical method; and finally, obtaining the fluctuation distribution of the parameters of the semiconductor device and the integrated circuit according to the fluctuation distribution of the doping ions.

In other words, the method for simulating fluctuation of ion implantation according to the present invention includes obtaining a final three-dimensional position of implanted ions in a target material after N times of ion implantation according to an ion implantation simulation method, then performing grid division in a direction perpendicular to the surface of the target material to obtain the number of ions staying in each grid after a single ion implantation and the total number of ions staying after N times of ion implantation, further obtaining fluctuation distribution of doped ions by using a statistical method, and finally obtaining fluctuation distribution of parameters of a semiconductor device and an integrated circuit according to the fluctuation distribution of the doped ions.

The fluctuation simulation method not only considers the number of doped ions influencing semiconductor doping fluctuation, but also fully considers the factors of the depth of the doped ions.

Drawings

FIG. 1 is a schematic diagram of fluctuation distribution obtained by a conventional ion implantation fluctuation simulation method;

FIG. 2 is a flow chart of an ion implantation fluctuation simulation method according to the present invention;

FIG. 3 is a schematic view of the range distribution of 20keV ion-implanted single crystal silicon obtained by the method of the present invention;

FIG. 4 is a schematic view of the range distribution of 3keV ion-implanted single crystal silicon obtained by the method of the present invention;

FIG. 5 is a probability distribution plot of the number of particles at the peak depth of 3keV ion-implanted single crystal silicon obtained using the method of the present invention;

FIG. 6 is a probability distribution plot of the number of particles at the tail (18nm) of the range distribution for 3keV ion-implanted single crystal silicon obtained using the method of the present invention;

FIG. 7 is a schematic illustration of the standard deviation RMS of 3keV ion implanted single crystal silicon obtained using the method of the present invention as a function of depth;

FIG. 8 is a graphical representation of normalized standard deviation NRMS versus depth for 3keV ion implanted single crystal silicon obtained using the method of the present invention.

Detailed Description

The method of the present invention is described in further detail below with reference to the accompanying drawings and examples.

The basic idea of the invention is: the final three-dimensional position (x, y, z) distribution of the injected ions in the target material is obtained by an ion injection simulation method, then the grid is divided in the direction (z direction) vertical to the surface of the target material, the range distribution of the ion injection, namely the concentration distribution of the doped ions in the target material is obtained through the statistical analysis of the number of the ions staying in the grid, and the high-precision and high-reliability analysis of the ion injection fluctuation is realized.

In the invention, a mathematical statistic method is adopted to obtain the variation relation between the ion implantation fluctuation and the depth. The distribution of the implanted ions at different depths can be described by a discrete random variable, and the variation relation between the implanted ions and the depths is analyzed by calculating the mathematical expectation, variance and mean square error of the discrete random variable. The mathematical expectation of the random variables marks the average concentration of the ion implantation at a certain depth, and the variance and the mean square error can be used for characterizing the concentration fluctuation of the ion implantation.

The simulation method of the present invention as shown in fig. 2, first performs N ion implantation simulations, and for each ion implantation, obtains the final dwell position (x) of the implanted ions in the target material by means of monte carlo MC or molecular dynamics MD methods_i，y_i，z_i) And then, the flow of acquiring fluctuation is carried out.

Scanning the final staying positions of all the implanted ions after N times of ion implantation to obtain the maximum depth z of the implanted ions in the depth z direction_MAXAnd a minimum depth z_MIN. Defining the number of grids in the depth z-direction as m_divThe size z of the grid in the z direction_divComprises the following steps:

z_div＝(z_MAX-z_MIN)×(1+Δ/m_div)/m_div，

where Δ is a dimensionless value not greater than 0.01, and in this embodiment, Δ is in parts per million. For the size x of the grid in the x-direction_divAnd size y of the grid in the y-direction_divThe value is not easy to be too large, canTo take 20a where the size of a is the side length of a crystalline silicon cell, 5.432 angstroms. Thus, each grid has a size of (x)_div×y_div×z_div)。

According to the final staying position of each injected ion, calculating the grid (1 grid m)_div) Position, depth of grid_gridHas a size of z_MIN+z_divGrid-0.5. Then obtaining the number n of stay ions of a single ion implantation in each grid_grid ^tempAnd after N times of ion implantation, the average number of stay ions in each grid ${\stackrel{\‾}{n}}_{\mathrm{grid}}=\frac{1}{N}\mathrm{\Σ}{n}_{\mathrm{grid}}^{\mathrm{temp}}.$ When the doping concentration inside each grid is ${\stackrel{\‾}{c}}_{\mathrm{grid}}={\stackrel{\‾}{n}}_{\mathrm{grid}}/(x_{\mathrm{div}}\×y_{\mathrm{div}}\×z_{\mathrm{div}}).$ According to the average stay ion number in each gridThe average value of the number of implanted ions contained in each grid after N times of ion implantation, that is, the number of implanted ions is a certain numberA mathematical expectation of depth.

According to n obtained in the above process_grid ^tempAnd

recursively calculating the intermediate variable sigmalphaof fluctuation_grid， ${\mathrm{sigma}}_{\mathrm{grid}}={\mathrm{sigma}}_{\mathrm{grid}}+{(n_{\mathrm{grid}}^{\mathrm{temp}}{\sqrt{n}}_{\mathrm{grid}}-1)}^2,$ sigmα_gridThe initial value of (a) is taken as 0.

Thus, the normalized variance NRMS_gridIs composed of

${\mathrm{NRMS}}_{\mathrm{grid}}=\sqrt{{\mathrm{sigma}}_{\mathrm{grid}}/(N-1)},$

Variance RMS of doping concentration of each grid_gridThe calculation formula of (2) is as follows: ${\mathrm{RMS}}_{\mathrm{grid}}={\mathrm{NRMS}}_{\mathrm{grid}}\·{\stackrel{\‾}{c}}_{\mathrm{grid}}.$ finally, the output grid is largeSmall (x)_div，y_div，z_div) Depth coordinate depth of each grid_gridDoping concentration ofSign normalized variance NRMS of fluctuation_gridAnd the variance RMS_grid。

The data is input into the simulation software of the semiconductor device to obtain the fluctuation of the key parameters (such as threshold voltage) of the semiconductor device, and then the fluctuation data is input into the simulation software of the integrated circuit to obtain the further fluctuation of the parameters of the integrated circuit.

FIG. 3 is a graph of 20keV energy 1e13cm obtained using the method of the present invention^-2Range profile after dose arsenic implantation into crystalline silicon, with the abscissa representing depth in nanometers (nm) and the ordinate representing concentration of implanted ions in cm^-3. It can be seen from the graph that the peak position of the curve is at a depth of 17.17nm, and the arsenic ion concentration at the peak is: 1e18.58cm^-3(ii) a At depths after the peak position, the concentration of the implanted ions decreases rapidly.

FIG. 4 is a 3keV 5e13cm obtained by the method of the invention^-2Range profile of dose ion implantation into single crystal silicon, with the abscissa representing depth in nanometers (nm) and the ordinate representing concentration of implanted ions in cm^-3. It can be seen from the graph that the peak position of the curve is at a depth of 4.47nm, and the arsenic ion concentration at the peak is: 6e19cm^-3(ii) a At depths after the peak position, the concentration of the implanted ions decreases rapidly.

FIG. 5 is a 3keV 5e13cm obtained by the method of the invention^-2Dose ion implantation the probability distribution of the number of implanted ions of single crystal silicon at the peak depth (4nm) is plotted with the abscissa as the number of ions and the ordinate as the probability of occurrence of the corresponding number of ions. As can be seen from the figure, the probability distribution of the number of ions at the peak depth conforms to the normal distribution.

FIG. 6 is a graph obtained by the method of the present inventionResulting 3keV 5e13cm^-2The probability distribution of the number of ions implanted into the dose ion-implanted monocrystalline silicon at the tail (18nm) of the range distribution is shown on the abscissa, the number of ions is shown on the abscissa, and the probability of the occurrence of the corresponding number of ions is shown on the ordinate. As can be seen from the figure, the probability distribution of the number of ions at the peak depth is more in line with the binomial distribution than the normal distribution.

FIG. 7 is a 3keV 5e13cm obtained using the method of the invention^-2Standard deviation RMS distribution plot of dose ion implanted single crystal silicon, with depth in nanometers (nm) on the abscissa and variance RMS value of implanted ion fluctuations in cm on the ordinate^-3. It can be seen from the graph that the peak position of the curve is at a depth of 4.47nm, and the arsenic ion concentration at the peak is: 2.8e19cm^-3. The peak depth of the fluctuating RMS value and the peak depth of the range distribution of the ion implantation are substantially the same. At depths after the peak position, the fluctuation of the implanted ions is rapidly reduced.

FIG. 8 is a 3keV 5e13cm obtained using the method of the invention^-2Dose ion implanted single crystal silicon normalized variance NRMS distribution plot with the abscissa representing depth in nanometers (nm) and the ordinate representing NRMS of implanted ion fluctuation in dimensionless units. It can be seen from the figure that the minimum position of the NRMS profile is at a depth of 4.47nm, and the magnitude of the minimum is: 0.47. the minimum depth of the fluctuating NRMS value and the peak depth of the range distribution of ion implantation are substantially the same. At depths after the minimum position, the NRMS of the implant ion fluctuation increases rapidly after a slow smoothing period.

Finally, it should be noted that the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.

Claims (6)

1. A simulation method of ion implantation fluctuation is characterized by comprising the following steps: firstly, carrying out N times of ion implantation to obtain the final three-dimensional position of the implanted ions in a target material; secondly, grid division is carried out in the direction vertical to the surface of the target material, and the number of staying ions in each grid after single ion injection and the average number of staying ions in each grid after N times of ion injection are obtained; then, obtaining the fluctuation distribution of the doped ions by adopting a statistical method; and finally, obtaining the fluctuation distribution of the parameters of the semiconductor device and the integrated circuit according to the fluctuation distribution of the doping ions.

2. The method of claim 1, wherein after said N times of ion implantations, the final three-dimensional position (x) of the implanted ions in the target material is determined₁，y₁，z₁) Is obtained by means of Monte Carlo or molecular dynamics methods.

3. The method of claim 1, wherein the step of performing the grid division in the direction perpendicular to the surface of the target material further comprises: obtaining the maximum value z of the implanted ions in the direction z vertical to the surface of the target material according to the final staying positions of all the implanted ions after N times of ion implantation_MAXAnd minimum value z_MIN(ii) a Determining the number m of grids in the z-direction_div(ii) a Calculating the value z of each grid in the z-direction_divComprises the following steps:

z_div=(z_MAX-z_MIN)×(1+Δ/m_div)/m_div，

wherein Δ is a dimensionless value of not more than 0.01; each grid has a volume of (x)_div×y_div×z_div) Wherein x is_divIs the size of the grid in the x-direction on the surface of the target material, y_divIs the size of the grid in the y-direction on the surface of the target material.

4. The method of claim 3, wherein the value of Δ is one part per million; said x_divAnd y_divHas a value of 20a, where α represents the side length of the crystalline silicon cell.

5. The method according to claim 1, wherein the obtaining of the number of ions staying in each grid after a single ion implantation and the average number of ions staying in each grid after N ion implantations are: according to the final stay position of each injected ion, the position of the grid where the ion is located is calculatedDepth of grid from origin in z-direction_gridHas a size of z_MIN+z_div(grid-0.5); then obtaining the number n of stay ions of a single ion implantation in each grid_grid ^lempAnd after N times of ion implantation, the average number of stay ions in each grid ${\stackrel{-}{n}}_{\mathrm{grid}}=\frac{1}{N}\mathrm{\Σ}{n}_{\mathrm{grid}}^{\mathrm{temp}};$ Finally obtaining the doping concentration in each grid as ${\stackrel{-}{c}}_{\mathrm{grid}}={\stackrel{-}{n}}_{\mathrm{grid}}/(x_{\mathrm{div}}\×y_{\mathrm{div}}\×z_{\mathrm{div}}),$ Wherein z is_MINIs the minimum of the implanted ions in the z-direction perpendicular to the surface of the target material, z_divFor each grid value in the z direction, x_divIs the size of the grid in the x-direction on the surface of the target material, y_divIs the size of the grid in the y-direction on the surface of the target material.

6. The method of claim 1, wherein the obtaining the fluctuation distribution of the doped ions by using the statistical method further comprises: according to the number n of stay ions inside each grid after single ion implantation_grid ^lempAndaverage number of stay ions in each grid after N times of ion implantationWherein ${\stackrel{-}{n}}_{\mathrm{grid}}=\frac{1}{N}\mathrm{\Σ}{n}_{\mathrm{grid}}^{\mathrm{temp}},$ Mean variable sigma for recursively calculating fluctuation_gridIs of the formula ${\mathrm{sigma}}_{\mathrm{grid}}={\mathrm{sigma}}_{\mathrm{grid}}+{(n_{\mathrm{grid}}^{\mathrm{temp}}/{\stackrel{-}{n}}_{\mathrm{grid}}-1)}^2,$ Wherein sigma_gridThe initial value of (a) is taken as 0; calculating normalized variance NRMS_gridIs of the formula

${\mathrm{NRMS}}_{\mathrm{grid}}=\sqrt{{\mathrm{sigma}}_{\mathrm{grid}}/(N-1)};$

Calculating the variance RMS of the doping concentration of each grid_grid(ii) a Is given by the formula ${\mathrm{RMS}}_{\mathrm{grid}}={\mathrm{NRMS}}_{\mathrm{grid}}\·{\stackrel{-}{c}}_{\mathrm{grid}},$ Wherein,

for the doping concentration inside each grid, ${\stackrel{-}{c}}_{\mathrm{grid}}={\stackrel{-}{n}}_{\mathrm{grid}}/(x_{\mathrm{div}}\×y_{\mathrm{div}}\×z_{\mathrm{div}}),$ z_divfor each grid value in the z direction, x_divIs the size of the grid in the x-direction on the surface of the target material, y_divIs the size of the grid in the y-direction on the surface of the target material.

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