离子注入中硼在Rp缺陷的析出模型

摘要：建立了一种析出模型用来模拟硼在硅中的扩散现象，描述了硼原子与离子注入引起的Rp缺陷之间的相互作用，解释了非活性硼峰形成的原因，与实验结果能够较好的吻合，为研究硼的扩散机理提供了很好的依据，为超浅结工艺模拟提供了基本模型，对于开发下一代集成电路研制的工艺模拟程序有着非常重要的意义。

关键词：Rp缺陷；硼峰；聚集析出；增速扩散

1 Introduction

Boron diffusion after ion implantation is an active topic of resear-ch.However,many details concerning the interactions between boron atoms and ion implantation damage are still not understood.An interesting observation is that for boron implantation to medium doses,the peak portion of the boron profile is not electrically activated and has remained immobile during annealing for a long time,though the peak concentration is lower than the boron solubility in silicon.Several models have been proposed to explain this result.According to the Fermi-level model,boron diffuses mainly via positively charged Si interstitials once its concentration exceeds the intrinsic carrier concentration.The diffusion via positively charged Si interstitials is assumed to be much slower than that via neutral Si interstitials[1].In the clustering model,the immobile boron peak is associated with the formation of electrically inactive boron interstitials clusters[2].In this work,we attribute the limited activation and mobility of the dopant to be the segregation on the extended defects[3,4]and present a model in which the immmobile boron peak is explained with boron segregation to Rp defects.

2 Experiment

Ion implantation produces extended defects or dislocation loops such as Rp (the projected range) defects,EOR and clamshell defects upon anneal-ing,depending on the dose and species[5].Rp defects form during annealing at a depth corresponding approximately to Rp when the dose exceeds the critical value of 1×1014cm-2 and simultaneously no amorphous layer is formed.[4]To produce Rp defects,boron was implanted into n-type Si wafers at 15 keV and 30keV with a dose of 2×1014cm-2 at 800℃.Fig.1 shows the immobile boron peak dissolves with increasing annealing time.The depth range of hump of the boron concentration peak was found to be in the same depth range of Rp defects.Rapid diffusion occurs at low concentrations compared to the diffusion found at higher concentrations.The transition between these two regimes occurs at a concentration which is typically ten times lower that the B solubility limit.The boron solubility at 800 ℃ is around 4×1019cm-3[6].

3 Segregation model for boron pile-up

The model implemented in this work uses kinetic reactions that lead to the segregation of boron.Because of the difference of potential energy between boron atoms in the matrix and those at the periphery of Rp defects,boron segregates to Rp defects.The segregated boron atoms are released from Rp defects at a rate determined by the hopping frequency of boron atoms and the boron segregation energy.The change of concentration of the boron atoms segregated to Rp defects with time is given by the difference between the segregation rate and the release rate,that is

Here CRp represents the concentration of interstitials contained in Rp defects.Fig.2 indicates the immobile boron amount decreases exponentially with a characteristic decay time,which is approximately equal to the characteristic decay time of segregated boron.This boron segregation to Rp defects and the characteristic decay time of segregated boron is determined by the dissolution of Rp defects.

The segregation process of boron atoms is assumed to bi limited by diffusion,so the segregation rate constant is given by

Here DB=D0exp(-ΔE/kT)is the boron diffusivity;T is the annealing temperature;a is the average interatomic spacing;a is the capture radius expressed in units of a.Determined by the hopping frequency and the segegation energy,the release rate constant of boron atoms is given by

Here Es is the boron segregation energy to Rp defects.Adding the segregation terms into Fick’s second law of diffusion.

One obtains

To compute boron profiles with the boron segregation effect,we only need to solve the following two differential equations

Due to the non-conservative nature of the implantation process,the boundary conditions for above two differential equations are

Here kf represents the flux constant toward surface of boron atoms,and is given by kf=JB/B(0),JB is the boron diffusive flux of boron atoms to the surface and can be approximately obtained by experimental data.

In the first thermal step following implantation of impuritees into silicon,there is an initial rapid displacement of the impurity known as TED (transient enhancement diffusion).The time for cluster evaporation is found to be similar to the duration of transient diffusion over the temperature range 670-815℃ and the measured dose of interstitials in the clusters is consistent with the doses required to match simulations of TED with data.It has also been observed[3] that the enhanced diffusivity in TED is nearly constant for the duration of the transient,before dropping abruptly to its equilibrium value.In this work,the enhancement can be estimated[8]by Ie/I*,Ie is a fixed interstitial concentration when the enhancement in diffusivity is constant during transient diffusion which means a balance between cluster evaporation and growth.Ie is found and has the value,Ie=(NS/4πα)exp(-Eb/kT).I* is interstitial equilibrium concentration,also,the time for TED is given by[8]

Here Rw is the implanted range;Q is the implant dose;Ns=a-3 is the number of lattice sites per cubic centimeter;DI=D0exp(-Em/kT) is the interstitial diffusivity.The activation energy Eb is taken to be 1.8eV,and Em is 1.77eV.Applying this model to the 15keV,2×1014cm-2 boron implants,assuming a=1,and using experimental values from metal diffusion studies [9,10].Parameter values used in the calculations are listed in Table 1.The boron segregation energy to Rp defects is assumed to be 0.57 eV.We solved these equations with Flex PDE3.10.We obtained τ=155s at 800 ℃,and the enhancement is about 4.3×103.

4 Comparison to data

The model parameters are optimized to fit a wide range of data.A comparison between experimental and simulated boron profiles is shown in Figs.3,4,5,6 for samples annealed at 800 ℃ for different time and implanted with dose of 2×1014cm-2 at 15keV and 30keV,respectively.The profiles show enhanced diffusion for concentrations lower than about 5×1018cm-3,in good agreement with the simulations.For times beyond TED,a large fraction of boron atoms is still not allowed to move,even if at a concentration lower than the solubility[3].An annealing time longer than 8h is necessary to free the dopant for the diffusion.Slow boron diffusion and slow defect annealing in the crystalline Si samples indicate that the defect annealing process is closely related to boron diffusion in the boron peak region [11].