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 injects the analogy method of fluctuation

Technical field

The present invention relates to the manufacturing field of integrated circuit, specifically, relate to the method that the doping fluctuation of ic manufacturing process intermediate ion injection is simulated.

Background technology

In the manufacturing of integrated circuit, it is a kind of critical process of maturation that ion injects, it is that arsenic, boron beam-plasma are incided in the silicon materials, make atom in ion beam and the silicon materials or molecule that a series of physics and interaction chemistry take place, final incident ion is off-energy gradually, rest in the silicon materials, form the doped semiconductor of P type or N type.

The important indicator of semiconductor device, as threshold voltage and drive current, and the key performance of integrated circuit, as maximum operating frequency, all depend on the stability of each processing step in the whole manufacturing process of integrated circuit, the fluctuation of key parameter in the established technology step.Accurately the fluctuation of prediction integrated circuit relevant parameter has huge meaning for the production of integrated circuit.To cause the increase of integrated circuit (IC) design complexity to the too high estimation of fluctuation, and might increase the time cycle of design, size and other unfavorable factors of design cell, and the final integrated circuit of producing that makes lacks enough competitiveness on market.On the other hand, for the low excessively estimation of fluctuation, will cause the underestimating of product quality, excessive production waits other adverse factors.In a word, over-evaluate design difficulty increase, the underestimating of fluctuation that can cause integrated circuit of fluctuation cause the difficulty of integrated circuit production to increase.Therefore become all the more great of the meaning of predicting the fluctuation of integrated circuit relevant parameter accurately.Fluctuation can be divided into two kinds substantially: (within Die) fluctuation in (Dieto Die) fluctuation and the unit between the unit.Fluctuation is between different batches, different chips, the same wafer different units between the unit, owing to the unstable fluctuation that produces of technology.Fluctuation then mainly comprises the fluctuation of lines and the doping fluctuation that ion injects in the unit.The fluctuation of lines be owing to the photoresist material on wafer in uneven thickness, photoresist material itself is inhomogeneous, photoetching process is unstable produces; The doping fluctuation is after being derived from ion injection and annealing, the inhomogeneities that dopant ion spatially distributes, and the doping space is more little, and the doping fluctuation is just obvious all the more.For the integrated circuit that adopts ion injection method to make, fluctuation mainly is the doping fluctuation in its mould.

The characteristic size of integrated circuit is constantly dwindled at present, just can reach 50 nanometers before and after expecting 2010, and one of key technology of making the sub-micro device is exactly the formation of super shallow junction, and the low energy ion injection is the most effective and the technological means of the super shallow junction of formation that feasibility is the highest.For the bigger integrated circuit of characteristic size, fluctuation is the major influence factors that constitutes its performance fluctuation between the unit.And reducing along with the integrated circuit characteristic size, fluctuation becomes outstanding all the more to the influence of performance of integrated circuits in the unit, and the fluctuation that ion injects has intrinsic, promptly as long as use ion to inject, just certainly exist this fluctuation, can't eliminate the fluctuation that ion injects by improving technology.Therefore, need fully realize the characteristic of ion implantation doping fluctuation itself, and study the influence of ion implantation doping fluctuation, thereby reduce the influence of fluctuation in the unit in the ic manufacturing process performance of integrated circuits.

At present, a large amount of work all concentrates in the influence of research ion implantation doping fluctuation to performance of integrated circuits, because it is not enough with the understanding of change in depth to ion implantation doping concentration, and the restriction of computing capability, never the way of comparison system itself is enough described accurately to the ion implantation doping fluctuation.On experimental technique because experimental cost, the restriction of all many-sides such as the stability of experiment condition, sample test, make the doping fluctuation by experiment method accurately obtain.

And existing fluctuation analogy method, as document IEDM Tech.Dig., simulation fluctuation method 705 1993 records, that propose by Hon-Sum Wong and Yuan Taur, because simulation model and statistical technique are too coarse, make the doping fluctuating date that obtains lack enough accuracy and reliability.Fig. 1 is the doping fluctuation distribution schematic diagram that adopts above-mentioned analogy method to obtain, and its abscissa is represented the dopant ion number, and ordinate is represented the relative frequency that the dopant ion number occurs.The ion populations of this method by evenly mixing in research 150nm * 50nm * 80nm zone added up the distribution of the dopant ion of 1000 samples, finds under the hypothesis of evenly mixing, and the Probability Distribution of the inner foreign ion of above-mentioned zone meets Poisson distribution.Because this analogy method is assumed to even doping with doped region, therefore can only provide overall fluctuation and distribute, can't provide the result of variations of doping fluctuation with the degree of depth.In the ion implantation process of reality, the distribution of foreign ion in target material silicon of mixing is heterogeneous, the heterogeneity of this distribution can obviously influence the performance (as threshold voltage etc.) of semiconductor device, because the different depth doping content is different to the influence degree of semiconductor device and circuit performance, the doping fluctuation of different depth is different for the Effect on Performance of device and circuit simultaneously.The ion implantation doping fluctuation depends on the variation that ion injects the degree of depth, and depends on the distribution of different depth place concentration indirectly.

Summary of the invention

Technical problem to be solved by this invention is to propose the analogy method that a kind of ion injects fluctuation, can obtain the variation relation that ion injects the fluctuation and the degree of depth, analyzes ion accurately and reliably and injects fluctuation.

Ion of the present invention injects the analogy method of fluctuation, may further comprise the steps: at first carry out the N secondary ion and inject, obtain to inject the final three-dimensional position of ion at target material; Secondly carry out grid division in direction, obtain the stop ion populations and the N secondary ion of single ion injection back in each grid and inject average stop ion populations in each grid of back perpendicular to target surfaces; The fluctuation of adopting statistical method to obtain dopant ion then distributes; Obtain the fluctuation distribution of the parameter of semiconductor device and integrated circuit at last according to the fluctuation distribution of dopant ion.

In other words, ion of the present invention injects the analogy method of fluctuation, after the injection of ion injection simulation method acquisition N secondary ion, inject the final three-dimensional position of ion at target material, carry out grid division in direction then perpendicular to target surfaces, obtain the single ion and inject the number of the stop ion of back in each grid and the number that the N secondary ion injects the total stop ion in back, and then the fluctuation distribution of the method acquisition dopant ion of employing statistics, obtain the fluctuation distribution of the parameter of semiconductor device and integrated circuit at last according to the fluctuation distribution of dopant ion.

Fluctuation analogy method of the present invention not only considers to influence the dopant ion number of semiconductor doping fluctuation, and taken into full account the factor of the residing degree of depth of dopant ion, by the present invention, based on existing analogue data, can obtain the careful fluctuation that ion-implanted semiconductor mixes, obtain the variation relation of the doping fluctuation and the degree of depth, the scaling method to the doping fluctuation that the present invention proposes helps the analysis of data and follow-up application more.

Description of drawings

Fig. 1 is that existing ion injects the fluctuation distribution schematic diagram that the fluctuation analogy method obtains;

Fig. 2 is the flow chart that ion of the present invention injects the fluctuation analogy method;

Fig. 3 is the range distribution schematic diagram that adopts the 20keV ion injection monocrystalline silicon of the inventive method acquisition;

Fig. 4 is the range distribution schematic diagram that adopts the 3keV ion injection monocrystalline silicon of the inventive method acquisition;

Fig. 5 is that the 3keV ion that adopts the inventive method to obtain injects the probability distribution graph of monocrystalline silicon in the number of particles at peak depth place;

Fig. 6 is the probability distribution graph that the 3keV ion that adopts the inventive method to obtain injects the number of particles that monocrystalline silicon locates in range distribution tail (18nm);

Fig. 7 is that the 3keV ion that adopts the inventive method to obtain injects the schematic diagram of the standard variance RMS of monocrystalline silicon with change in depth;

Fig. 8 is that the 3keV ion that adopts the inventive method to obtain injects the schematic diagram of the normalization standard variance NRMS of monocrystalline silicon with change in depth.

Embodiment

Below in conjunction with drawings and Examples, the inventive method is described in further detail.

Basic thought of the present invention is: obtain to inject ion by ion injection simulation method and distribute at the final three-dimensional position (x, y, z) of target material, divide grid in direction (z direction) then perpendicular to target surfaces, through statistical analysis to stop ion populations in the grid, obtain the range distribution that ion injects, be the CONCENTRATION DISTRIBUTION of dopant ion in target material, realize ion is injected high accuracy, the high reliability analysis of fluctuation.

In the present invention, adopt the method for mathematical statistics, obtain the variation relation that ion injects the fluctuation and the degree of depth.Injecting the distribution of ion on different depth can describe with discrete random variable, injects the variation relation of the ion and the degree of depth by mathematic expectaion, variance and the variance analysis that calculates this discrete random variable.The mathematic expectaion sign of stochastic variable ion be infused in mean concentration on a certain degree of depth, variance and mean square deviation then can be used for characterizing the concentration fluctuation that ion injects.

Analogy method of the present invention is as shown in Figure 2 at first carried out the N secondary ion and is injected simulation, and the ion injection for each time all obtains to inject the final stop place (x of ion at target material by Monte Carlo MC or molecular dynamics MD method _i, y _i, z _i), obtain the flow process of fluctuation then.

After the scan N secondary ion injects all are injected the final stop place of ion, obtain to inject the depth capacity z of ion in the depth z direction _MAXWith minimum-depth z _MINThe grid number of definition depth z direction is m _Div, the big or small z of z direction grid then _DivFor:

z _div＝(z _MAX-z _MIN)×(1+Δ/m _div)/m _div，

Wherein Δ is a nondimensional value of 0.01 that is not more than, in the present embodiment, the value of Δ is 1,000,000/.Big or small x for x direction grid _DivBig or small y with y direction grid _Div, its value is difficult for excessive, can be taken as 20 α, and wherein the size of α is the length of side of crystalline silicon primitive unit cell, i.e. 5.432 dusts.Therefore, the size of each grid is (x _Div* y _Div* z _Div).

According to each final stop place of injecting ion, calculate the residing grid grid (1≤grid≤m of this ion _Div) position, the depth d epth of grid _GridSize be z _MIN+ z _Div(grid-0.5).Obtain the stop ion populations n that the single ion is infused in each grid inside then _Grid ^TempAnd after the injection of N secondary ion, the inner average ion populations that stops of each grid ${\stackrel{\‾}{n}}_{\mathrm{grid}}=\frac{1}{N}\mathrm{\Σ}{n}_{\mathrm{grid}}^{\mathrm{temp}}.$ This moment, the doping content of each grid inside was ${\stackrel{\‾}{c}}_{\mathrm{grid}}={\stackrel{\‾}{n}}_{\mathrm{grid}}/(x_{\mathrm{div}}\×y_{\mathrm{div}}\×z_{\mathrm{div}}).$ According to the inner average ion populations that stops of each grid Can obtain mean value, promptly inject the mathematic expectaion of ion populations in a certain degree of depth through the contained injection ion populations of each grid after the injection of N secondary ion.

According to the n that obtains in the said process _Grid ^TempWith

The intermediate variable sigm α of recursive calculation fluctuation _Grid, ${\mathrm{sigma}}_{\mathrm{grid}}={\mathrm{sigma}}_{\mathrm{grid}}+{(n_{\mathrm{grid}}^{\mathrm{temp}}{\sqrt{n}}_{\mathrm{grid}}-1)}^2,$ Sigm α _GridInitial value be taken as 0.

Therefore, the variance NRMS after the normalization _GridFor

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

The variance RMS of the doping content of each grid _GridComputing formula be: ${\mathrm{RMS}}_{\mathrm{grid}}={\mathrm{NRMS}}_{\mathrm{grid}}\·{\stackrel{\‾}{c}}_{\mathrm{grid}}.$ At last, the size (x of output grid _Div, y _Div, z _Div), the depth coordinate depth of each grid _Grid, doping content The sign amount normalization variance NRMS of fluctuation _Grid, and variance RMS _Grid

Simulation softward with above-mentioned data input semiconductor device, can obtain the fluctuation of the key parameter (as threshold voltage) of semiconductor device, in the simulation softward with these fluctuating date input ics, can obtain the fluctuation of further integrate circuit parameter again.

Fig. 3 is the 20keV energy 1e13cm that adopts the inventive method to obtain ^-2Dosage arsenic is injected into the later range distribution map of crystalline silicon, and abscissa is represented the degree of depth, and unit is nanometer (nm), and ordinate represents to inject the concentration of ion, and unit is cm ^-3As we can see from the figure, the peak of curve is at 17.17nm degree of depth place, and the arsenic ion concentration at peak value place is: 1e18.58cm ^-3At the later degree of depth place of peak, the concentration of injecting ion reduces rapidly.

Fig. 4 is the 5e13cm that adopts the 3keV of the inventive method acquisition ^-2Dose ion is injected the range distribution map of monocrystalline silicon, and abscissa is represented the degree of depth, and unit is nanometer (nm), and ordinate represents to inject the concentration of ion, and unit is cm ^-3As we can see from the figure, the peak of curve is at 4.47nm degree of depth place, and the arsenic ion concentration at peak value place is: 6e19cm ^-3At the later degree of depth place of peak, the concentration of injecting ion reduces rapidly.

Fig. 5 is the 5e13cm that adopts the 3keV of the inventive method acquisition ^-2Dose ion is injected the probability distribution of the injection ion populations that monocrystalline silicon locates at peak depth (4nm), and abscissa is the number of ion, and ordinate is the probability that corresponding ion populations occurs.As we can see from the figure, the probability distribution at the peak depth ion populations meets normal distribution.

Fig. 6 is the 5e13cm that adopts the 3keV of the inventive method acquisition ^-2Dose ion is injected the probability distribution of the injection ion populations that monocrystalline silicon locates in range distribution tail (18nm), and abscissa is the number of ion, and ordinate is the probability that corresponding ion populations occurs.As we can see from the figure, the probability distribution at the peak depth ion populations meets binomial distribution more with respect to normal distribution.

Fig. 7 is the 5e13cm that adopts the 3keV of the inventive method acquisition ^-2Dose ion is injected the standard variance RMS distribution map of monocrystalline silicon, and abscissa is represented the degree of depth, and unit is nanometer (nm), and ordinate represents to inject the variance RMS value of ion fluctuation, and unit is cm ^-3As we can see from the figure, the peak of curve is at 4.47nm degree of depth place, and the arsenic ion concentration at peak value place is: 2.8e19cm ^-3The peak depth that the range that the peak depth of fluctuation RMS value and ion inject distributes is basic identical.At the later degree of depth place of peak, the fluctuation of injecting ion reduces rapidly.

Fig. 8 is the 5e13cm that adopts the 3keV of the inventive method acquisition ^-2Dose ion is injected the normalization variance NRMS distribution map of monocrystalline silicon, and abscissa is represented the degree of depth, and unit is nanometer (nm), and ordinate represents to inject the NRMS of ion fluctuation, dimensionless unit.As we can see from the figure, the minimum value position of NRMS distribution curve is at 4.47nm degree of depth place, and the size of minimum value is: 0.47.The peak depth that the range that the minimum value degree of depth of the NRMS value of fluctuation and ion inject distributes is basic identical.The later degree of depth place in the minimum value position, the NRMS that injects the ion fluctuation increases rapidly through a level and smooth slowly after date.

It should be noted last that, above embodiment is only unrestricted in order to technical scheme of the present invention to be described, although the present invention is had been described in detail with reference to preferred embodiment, those of ordinary skill in the art is to be understood that, can make amendment or be equal to replacement technical scheme of the present invention, and not breaking away from the spirit and scope of technical solution of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (6)

1, a kind of ion injects the analogy method of fluctuation, it is characterized in that, may further comprise the steps: at first carry out the N secondary ion and inject, obtain to inject the final three-dimensional position of ion at target material; Secondly carry out grid division in direction, obtain the stop ion populations and the N secondary ion of single ion injection back in each grid and inject average stop ion populations in each grid of back perpendicular to target surfaces; The fluctuation of adopting statistical method to obtain dopant ion then distributes; Obtain the fluctuation distribution of the parameter of semiconductor device and integrated circuit at last according to the fluctuation distribution of dopant ion.

2, ion according to claim 1 injects the analogy method of fluctuation, it is characterized in that, after described N secondary ion injects, injects the final three-dimensional position (x of ion at target material ₁, y ₁, z ₁) obtain by Monte Carlo or molecular dynamics method.

3, ion according to claim 1 injects the analogy method of fluctuation, it is characterized in that, describedly further comprise carrying out grid division perpendicular to the direction of target surfaces: all after injecting according to the N secondary ion are injected the final stop place of ions, obtain to inject ion at the maximum z perpendicular to the direction z direction of target surfaces _MAXWith minimum value z _MINDetermine the grid number m of z direction _DivCalculate the value z of each grid in the z direction _DivFor:

z _div=(z _MAX-z _MIN)×(1+Δ/m _div)/m _div，

Wherein Δ is a nondimensional value of 0.01 that is not more than; The volume of each grid is (x _Div* y _Div* z _Div), x wherein _DivBe the size of target surfaces x direction grid, y _DivSize for target surfaces y direction grid.

4, ion according to claim 3 injects the analogy method of fluctuation, it is characterized in that, and the value of described Δ is 1,000,000/; Described x _DivAnd y _DivValue be 20a, wherein α represents the length of side of crystalline silicon primitive unit cell.

5, ion according to claim 1 injects the analogy method of fluctuation, it is characterized in that, the described single ion that obtains injects stop ion populations and the N secondary ion of back in each grid and injects that the average ion populations that stops is in each grid of back: inject the final stop place of ion according to each, calculate the position of the residing grid grid of this ion, grid is at the depth d epth of z direction apart from initial point _GridSize be z _MIN+ z _Div(grid-0.5); Obtain the stop ion populations n that the single ion is infused in each grid inside then _Grid ^LempAnd after the injection of N secondary ion, the inner average ion populations that stops of each grid ${\stackrel{-}{n}}_{\mathrm{grid}}=\frac{1}{N}\mathrm{\Σ}{n}_{\mathrm{grid}}^{\mathrm{temp}};$ The doping content that obtains each grid inside at last is ${\stackrel{-}{c}}_{\mathrm{grid}}={\stackrel{-}{n}}_{\mathrm{grid}}/(x_{\mathrm{div}}\×y_{\mathrm{div}}\×z_{\mathrm{div}}),$ Wherein, z _MINFor injecting ion at the minimum value perpendicular to the direction z direction of target surfaces, z _DivBe the value of each grid in the z direction, x _DivBe the size of target surfaces x direction grid, y _DivSize for target surfaces y direction grid.

6, ion according to claim 1 injects the analogy method of fluctuation, it is characterized in that, the fluctuation distribution that described employing statistical method obtains dopant ion further comprises: inject the stop ion populations n of back in each grid inside according to the single ion _Grid ^LempAnd the N secondary ion injects the average ion populations that stops in each grid of back Wherein ${\stackrel{-}{n}}_{\mathrm{grid}}=\frac{1}{N}\mathrm{\Σ}{n}_{\mathrm{grid}}^{\mathrm{temp}},$ The intermediate variable sigma of recursive calculation fluctuation _Grid, formula is ${\mathrm{sigma}}_{\mathrm{grid}}={\mathrm{sigma}}_{\mathrm{grid}}+{(n_{\mathrm{grid}}^{\mathrm{temp}}/{\stackrel{-}{n}}_{\mathrm{grid}}-1)}^2,$ Sigma wherein _GridInitial value be taken as 0; Variance NRMS after the calculating normalization _Grid, formula is

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

Calculate the variance RMS of the doping content of each grid _GridFormula is ${\mathrm{RMS}}_{\mathrm{grid}}={\mathrm{NRMS}}_{\mathrm{grid}}\·{\stackrel{-}{c}}_{\mathrm{grid}},$ Wherein,

Be the doping content of each grid inside, ${\stackrel{-}{c}}_{\mathrm{grid}}={\stackrel{-}{n}}_{\mathrm{grid}}/(x_{\mathrm{div}}\×y_{\mathrm{div}}\×z_{\mathrm{div}}),$ z _DivBe the value of each grid in the z direction, x _DivBe the size of target surfaces x direction grid, y _DivSize for target surfaces y direction grid.

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