Simulation of Transient Diffusion Enhancement of Boron with VICTORY Process in 3D, with the Plus-One Implantation Damage Model and the Five-Stream Diffusion Model

 

1. Introduction

VICTORY Process is a 3D process simulation tool which allows for an accurate simulation of the doping distributions in semiconductor devices. It is able to simulate both the insertion of the doping atoms by ion implantation and their subsequent redistribution by thermal treatment.

During thermal treatment the motion of the doping atoms is assisted by point-defects in semiconductor material. When the point-defects are in thermal equilibrium and hence the point-defect concentrations are rather low, the effective diffusivity of the doping atoms is also low. In this case a significant redistribution of doping atoms can only be observed after annealing for several minutes and only when the annealing temperature is high. On the other hand, in the presence of high point-defect concentrations, the effective diffusivity of the doping atoms can be dramatically enhanced so that a significant redistribution of doping atoms can be observed after just a few seconds of annealing and at relatively low annealing temperatures. Diffusion enhancement caused by the presence of high concentrations of point-defects can only be simulated by means of diffusion models which take point-defects into account in the problem formulation [1][2][3].

 

2. Five-stream Diffusion Model

In semiconductor materials there are two types of point-defects:

  • Interstitials
  • Vacancies

Each of these two point defects may form a pair with dopant atoms (the probability of such defect-dopant pair formation depends both on the type of the point-defect and on the doping species). The five-stream model assumes that diffusion of the doping atoms is dominated by the spreading of such fast-diffusing dopant – point-defect pairs. The model includes equations for:

  • diffusion and recombination of point defects (two equations),
  • diffusion, formation and re-combination of both types of dopant – point-defect pairs (two equations per doping species) and
  • diffusion of the un-paired doping species (one equation per doping species).

In the case of a single species the model consists of 5 reaction-diffusion equations, hence the name ‘five-stream model’. The model is defined by means of the Open Model Library and is therefore extendable by the user.

The implementation of the five-stream model used for the analysis in this paper (supplied with VICTORY Process version 3.12.1) also includes the following effects:

  • Interstitial trap model – it was activated for this analysis.
  • Electrical activation models – empirical activation was used here.
  • <311> interstitial clustering model – it was deactivated for this analysis.

 

2.1 Running the five-stream model in VICTORY Process
In order to run a specific, non-default, diffusion model with VICTORY Process:

  1. Assign this model to the material of interest (for other materials default models will be used) by means of the deck statement :
    Method material=<material_name> model=<model_name>

  2. Start the diffusion simulation by means of the statement :
    Diffuse temperature=<temp.in Celsius> time=<value> [options]

Note that once model is set, it is used for all subsequent Diffuse statements unless it is changed via another Method statement.

The deck name of the five-stream model in VICTORY Process is ‘five_stream’. The results in this study were obtained by assigning it to silicon as follows:

Method material=silicon model=five_stream

Diffusion was run with default settings (no optional parameters were set).

2.2 Other diffusion models available in VICTORY Process
VICTORY Process version 3.12.1 also includes the following diffusion models:

  • Fick model (model = direct) – “classic” diffusion with atoms moving according to Fick law. For the analysis in this paper this model was applied to silicon-dioxide (default for all non-semiconductor materials in VICTORY Process version 3.12.1).

  • Fermi model (model = fermi) – assumes that point-defects are close to their equilibrium concentration and do not require explicit modeling. For the analysis in this paper this model was applied to poly-silicon (default for all semiconductor materials in VICTORY Process version 3.12.1).

  • Fully coupled mode (model=fullCpl) – assumes that there is an equilibrium between:

    • the dopant – point-defect pair concentration
    • the dopant concentration
    • the defect concentrations

Similar to five-stream model, it includes explicit simulation of point-defects movement. However, it does not simulate explicitly the formation and diffusion of the dopant – point-defect pairs. Instead, it calculates effective diffusion coefficients based on the local point-defects concentration.

  • Single-pair model (model=single_pair) – very similar to the five-stream model, but takes into account only one type of the two possible types of dopant – point-defect pairs, because the concentration of the other pair is considered as too low to have a significant influence on the effective diffusivity.

It follows from the above that the five-stream model used in this paper is the most advanced of all diffusion models listed above. However, the single-pair model and fully coupled model may also be used for simulation of transient diffusion enhancement effects.

 

3. Ion Implantation Induced Damage for Transient Enhanced Diffusion Simulation

In order to observe any transient diffusion enhancement effects the point-defect concentration must exceed the thermal equilibrium concentration, because the term enhancement refers to an enhanced diffusion in comparison to the situation when the point-defects are in their thermal equilibrium. Ion implantation, which normally precedes the thermal treatment, is one possible source for the formation of a supersaturation of interstitials. During an ion implantation process, a lot of atoms are displaced from their crystal lattice positions by the implanted ions. After rapid recombination, an excess concentration of interstitials as well as extended defects remain, while the vacancies return to the thermal equilibrium.

3.1 The plus-one implantation damage model
In order to model the excess concentration of interstitials following an ion implantation process, VICTORY Process offers the plus-one ion implantation damage model [4]. This model assumes that:

  • an excess concentration of interstitials is created,
  • vacancies return to their thermal equilibrium concentration after the rapid recombination which follows ion implantation.

The profile of the interstitial concentration is assumed to be nearly identical to the as-implanted profile of the doping atom.

For calibration purposes the interstitial profile may be scaled by a factor specified by means of the parameter dam.factor of the Implant statement. This parameter is typically of the order of 1. Within a VICTORY Process simulation flow the plus-one model can be activated as part of the ion implantation statement using the plus.one parameter:

Implant boron energy=20.0 dose=4.0e13 tilt=7.0 dam.factor=2.0 plus.one

This statement simulates the implantation of boron ions and creates an excess concentration of interstitials which is derived from the as-implanted distribution of the boron atoms scaled by a factor of 2.0 as used later on in this paper. The boron as well as the interstitial concentration are shown in Figure 1. The vacancies are not shown in Figure 1 since the plus-one model assumes that those have returned to their thermal equilibrium concentration as mentioned at the beginning of this section.


Figure 1. Boron and interstitial profile after ion implantation with the plus-one model being activated (dam.factor=2).

 

4. Simulation of Transient Diffusion Enhancement Due to Point-Defect Supersaturation

Starting from the initial condition described in section 3 we have performed an annealing simulation where the five-stream model was selected for silicon as described in section 2.1 . Therefore the following statements in the VICTORY Process flow were used :

Method material=silicon model=five_stream

Diffuse time=0.001 sec temperature=950

This was followed by a sequence of Diffuse statements with different annealing times to analyze the various stages of the transient process.

In the early stages of annealing, a rather high concentration of boron-interstitial-pairs are formed due to the excess concentration of interstitials. The distribution of the boron-interstitial-pairs after 1 ms of annealing is shown in Figure 2. A significant amount of boron atoms has formed pairs with the interstitials.


Figure 2. Boron-Interstitial-pair distribution and Interstitial distribution after 1 ms of annealing.

 

Since the diffusivity of the boron-interstitial pairs is rather high, the diffusion of boron is dominated by the diffusion via boron-interstitial pairs and hence the effective diffusivity of boron is enhanced in comparison to the case without point-defect supersaturation. This effect is shown in Figure 3 where the boron distribution after 100 ms of annealing is shown. These results were obtained by calling another Diffuse statement :

Diffuse time=0.099 sec temperature=950

Note, that once the five-stream model is activated for diffusion, it stays activated. Hence it is not necessary to use the Method statement for each individual diffusion step.


Figure 3. Comparison of the boron profile after 100 ms of annealing for a simulation with the five-stream model without implantation damage (blue curve) and with plus-one implantation damage (dam.factor=2.0) (red curve). Note that the as-implanted profile (black curve) is hardly visible since the blue curve is plotted on top of it.

While the simulation without implantation damage, where all point-defects are at their thermal equilibrium concentration, does not show any visible diffusion of boron, the simulation with the five-stream model shows a significant diffusion due to the enhancement as a result of the supersaturation of the interstitials.

As the annealing time progresses, the interstitials tend towards their thermal equilibrium and hence the concentrations of the boron-interstitial-pairs also decreases. Figure 4 shows that the peak concentration of the boron-interstitial-pair distribution has already decreased by more than 1 order of magnitude after 100 ms of annealing.

 


Figure 4. Comparison of boron-interstitial-pair distributions after 1 ms and after 100 ms of annealing.

 

4.1 Transient characteristic of the diffusion enhancement
As a decreasing boron-interstitial-pair concentration also decreases the contribution of the boron-interstitial-pairs diffusivity to the effective diffusivity of boron, the enhancement of the effective diffusivity decreases and finally disappears. This is why this enhancement due to the supersaturation of point-defects induced by ion implantation is a transient effect. Figure 5 shows the transient characteristic of this enhancement effect by showing the position of the junction over time.


Figure 5. Position of the junction between the boron doping and the substrate arsenic doping of 1e16 cm-3 over time as the annealing time progresses.

 

For the analysis in Figure 5 a series of Diffuse statements like,

Diffuse time=0.001 sec temperature=950

were executed within the VICTORY Process flow to obtain a sequence of time samples. In order to visualize the transient characteristic the position of the junction (see Figure 6) with arsenic substrate doping of 1e16 cm-3 was extracted for every time sample by means of Extract statements like :

Extract name=”j(1)” xj material=silicon x.val=0. y.val=0.

Doing so at the end of the simulation, a functional representation of the junction position over time can be found in the file ‘results.final’ where each individual Extract statement records its extraction result.

 


Figure 6. Position of the junction after ion implantation.

 

For the example shown in this paper, the diffusion velocity is temporarily enhanced by a factor of more than 1e5 and gradually decreases with time. According to Figure 5 a significant diffusion enhancement can be observed only up to 500 ms.

As shown in Figure 7 the enhancement strongly depends on the amount of interstitial supersaturation induced by ion implantation. For the analysis shown in Figure 7 the concentration of the interstitials is varied by changing the parameter dam.factor of the plus-one model, which is specified in the Implant statement (see section 3. ). Alternatively, the amount of interstitial supersaturation induced by implantation can also be varied by changing the implantation dose and keeping the parameter dam.factor constant.


Figure 7. Position of the junction as a function of time while the annealing progresses. The parameter dam.factor of the plus.one implantation model is varied. (0=surface, a negative value means inside the bulk).

 

4.2 3D effects on transient enhancement
In order to demonstrate the importance of taking into account the 3D geometry of the structure for transient enhanced diffusion simulation we have considered two similar structures shown in Figure 8. Since the enhancement of the effective diffusivity is driven by the point-defects, any material interface which is a sink for the point-defects influences the enhancement. Hence a feature like the trench isolation in an MOS device does influence the effective diffusivity in the gate area if point-defect supersaturation is induced by implantation within the source or drain area.


Figure 8. 2D type (left) and 3D (right) type structure where the diffusion enhancement is compared. The vertical lines on the domain’s wall (located 100and 300from the edge of the poly-silicon region) are the cut-lines along which junction positions were extracted.

 

The diffusion enhancement was analyzed when the trench sidewalls are not considered as in a 2D simulation (Figure 8 - left) and was compared with the simulation of a full 3D structure (Figure 8 - right) where the trench side wall is taken into account explicitly. For the analysis the substrate was doped with arsenic with a concentration of 1e16 cm-3 and implanted with boron before any other features were formed. This gives a junction depth of 221 nm (from the silicon/oxide interface) (position = -0.221 um) after ion implantation which is initially constant along the direction of the arrow (see Figure 8). After forming the features shown in Figure 8, arsenic was implanted and the plus.one model was switched on for this implantation step. Due to this ion implantation step, interstitial supersaturation was established within the silicon region which is not covered by poly-silicon. During subsequent annealing the interstitial supersaturation spreads underneath the poly-silicon and enhances the diffusion of boron there. Therefore, even after short time annealing (too short for the implanted arsenic doping to spread out), the junction depth underneath the poly-silicon varies depending on the distance from the poly-silicon edge as shown in Figure 9.


Figure 9. Boron distribution in the 2D like structure (left) and in the full 3D type structure (right) after annealing for 500 ms at 950 C.

 

Figure 10 shows the change of the location of the junction, extracted along the vertical cut-lines shown on Figure 8, as diffusion progresses. You can see that the diffusion enhancement is less in the 3D case. This is due to the fact that more interstitials are consumed by interface recombination at the trench side wall, and hence less interstitials can contribute to enhance boron diffusion. Normally, for a 2D simulation, the influence of such 3D effects can be accounted for only by careful structure-specific calibration.


Figure 10. Position of the junction as a function of time while the annealing progresses, within the structures shown in Figure 8 for two positions along the arrows shown in Figure 8. (0=silicon/oxide interface, a negative value means inside the bulk).

 

Also note that the blue line in Figure 10 (transient position of the junction at a cut-line 300 nm away from the poly edge) also nicely indicates the retarded onset of the diffusion enhancement for points which are further away from the poly-silicon edge, because the interstitials need some time to reach those points.

 

5. Conclusions

This paper demonstrates the importance of the inclusion of all three dimensions when simulating diffusion in three-dimensional structures. With the simulator VICTORY Process it is possible to simulate transient diffusion enhancement effects in such structures. All three-dimensional effects like recombination on side walls are rigorously taken care of without the need for device size specific calibration. Several models capable of simulating of transient diffusion enhancement are available in VICTORY Process:

  • Fully coupled
  • Single-pair
  • Five-stream

among which the five-stream model is the most advanced. All diffusion models are set-up via the Open Modeling library which can be amended and extended by the user.

 

References

  1. D. Mathiot and J. C. Pfister. “Dopant diffusion in silicon: A consistent view involving nonequilibrium defects”. Journal of Applied Physics 55(10), 3518 (1984).
  2. S. T. Dunham. “A quantitative model for the coupled diffusion of phosphorus and point defects in silicon”. Journal of Electrochemical Society 139, 2628 (1992).
  3. S.T. Dunham, A.H. Gencer, and S. Chakravarthi, “Modeling of Dopant Diffusion in Silicon”, IEICE Trans. Electron., 82(1), 800 (1998).
  4. M.D. Giles, “Transient phosphorus diffusion below the amorphization threshold”, J. Electrochem. Soc. 138, 285 (1991).

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