Optimization of annealing to decrease quantity of radiation defects in a bipolar transistor

E. L. Pankratov 0 0 E. L. Pankratov (&) Nizhny Novgorod State University of Architecture and Civil Engineering , 65 Il'insky street, Nizhny Novgorod 603950, Russia It has recently been shown that manufacturing of diffusive- and implanted-junction bipolar transistors in semiconductor heterostructure and optimization of annealing give us possibility to increase compactness of dopant distributions. In this paper, we analyze the possibility of decreasing the quantity of radiation defects by choosing regimes of annealing. - One of the intensive solving problems of solid-state electronics is decreasing the dimensions of elements of integrated circuits (IC) (Gusev and Gusev 1991; Grebene 1983; Lachin and Savelov 2001; Gotra 1991). Another intensive solving problem is increasing the performance of such elements of IC as p-n-junctions and their systems (bipolar transistors and thyristors). To fabricate p-n-junctions and their systems, some approaches can be used. One of the approaches is implantation of ions of dopant in a semiconductor sample or epitaxial layer (EL) of a heterostructure (H). It has been recently shown (see Pankratov 2008a, b) that implantation of dopant in a two-layer (TwL) H or in a three-layer (ThL) H at appropriately chosen energy of ions, thickness and materials of layers of H and optimal value of annealing time gives us the possibility to increase homogeneity of dopant distribution in doped area and sharpness of the p-n-junctions. Increasing the homogeneity gives us the possibility to decrease local overheats in the doped area during operation of the p-njunction or to decrease the depth of the p-n-junction at fixed tolerance on the value of the local overheats. A disadvantage of ion implantation is radiation damage of H. The main aim of the present paper is determination of the conditions to decrease the radiation damages or to decrease the influence of the damages on the characteristics of devices. Statement of the problem In this paper we consider a ThLH, which consists of a substrate (S) and two epitaxial layers EL1 and EL2 (see Fig. 1). The type of conductivity of S and other parameters (thickness, dopant diffusion coefficient, etc.) are known. Thicknesses and other parameters of EL1 and EL2 are known. A dopant has been implanted in the EL1 to produce the type of conductivity, which is reverse to the type of conductivity of S. Another dopant has been also implanted in EL2 to produce the type of conductivity, which coincides with the type of conductivity of S. Further annealing of radiation defects was done. After appropriate choosing of the thicknesses of the epitaxial layers and energies of ions, the dopants achieve the interfaces between EL1 and S and also EL1 and EL2. If the interfaces were not achieved by the dopants, additional annealing to shift the p-n-junctions to the interfaces attracted interest. If the dopants achieved the interface, maximal compromise between increasing the homogeneity of dopant distribution and sharpness of the p-n-junctions was obtained. Let us consider an alternative approach to annealing. In the framework of the alternative approach, the first dopant was implanted in EL1. Further Fig. 1 Heterostructure, which consist of a substrate and two epitaxial layers radiation defects were annealed. After that, another dopant was implanted in EL2 and new defects were annealed. The main aim of the present paper is comparison of restoring abilities of ThLH in the situations. oJIx;t ox >>> oVoxt;t oox hDV x; T oVoxx;ti > > : kI;V x; TIx; tVx; t kI;V x; TIx; tVx; t kI;V x; TIx; tV x; t kI;V x; TIx; tV x; t Method of solution Let us determine the spatiotemporal distribution of dopant concentration to solve our aim. We determine the distribution by solving the second Ficks law (Gusev and Gusev 1991; Grebene 1983; Lachin and Savelov 2001; Gotra 1991) with boundary and initial conditions Ckx; 0 fCkx: Here, Ck(x, t) is the spatiotemporal distribution of the kth type dopant concentration; JCk(x, t) is the spatiotemporal distribution of the kth type dopant flow; DCk is the dopant diffusion coefficient. The value of dopant diffusion coefficient depends on the properties of materials of layers in H, on the rate of heating and cooling of SH and on spatiotemporal distributions of dopant and defect concentrations. The concentration dependence of the diffusion coefficient could be approximated by the following functions (Gotra 1991; Zorin et al. 1975) Here, Pk(x, T) is the limit of solubility of the kth type dopant in H; DLk(x, T) is the diffusion coefficient of the kth type dopant for low level of doping; parameter ck, which depends on the properties of materials of H, can be the integer usually in the interval ck 2 1; 3 (Gotra 1991); T is the temperature of annealing; V(x, t) is the spatiotemporal distribution of concentration of vacancies; V* is the equilibrium distribution of concentration of vacancies. Spatiotemporal distributions of concentration of defects were determined by the following system of equations (Zorin et al. 1975, Fahey et al. 1989) with boundary and initial conditions JI L; t 0; Ix; 0 fI x; JV L; t 0; Vx; 0 fV x: Here I(x, t) is the spatiotemporal distribution of concentration of interstitials; DI(x, T) and DV(x, T) are diffusion coefficients of vacancies and interstitials; quadratic terms in Eq. 4 correspond to generation of divacancies and diinterstitials (see, for example Pankratov 2008c and appropriate references in the paper); kI,V(x, T) is the recombination parameter; kI,I(x, T) and kV,V(x, T) are parameters of generation of diinterstitials and divacancies, respectively. In this paper, in comparison with Pankratov (2008a, b), generation complexes of radiation defects have been accounted for. Let us transform Eqs. 14 to the following integral form 8 t 1 < Z Ckx; t Ckx; t L :FCk DLkx; TWx; s Ckck x; s oCkx; s ds 1 nk Pckk x; T ox 8 1 Z t Z t >>> Ix;t Ix;t L 0 DIx;ToIoxx;sds 0 kI;Vv;TIv;sVv;sdvds FIx > > <>>>>>>> ZLx Iv;tdv Z0t kI;Iv;TI2v;sdvds 1 Z t Z t L2 0 L 1 Z t Z x h L2 0 L kIIv;T F0I 2Xn11 FnIcnvenIsi2dvds F0I F0I Lx p2Xn11 FnnI snxenIt kIVv;T F0I 2Xn11 FnIcnvenIsihF0V 2Xn11 FnVcnvenVsidvds FIx h i 1 Z t >>>>>>>>>> V1x;t L1 h1F0ZV tZ2xXn11 FnVcnxenVt L 2Lp2 Xn11 nFnVsnx 0 DVx;TenVsds > > > > > > > > > > > > : L2 0 L 1 Z t Z x h L2 0 L kVVv;T F0V 2Xn11 FnVcnvenVsi2dvds F0V F0V Lx p2 Xn11 FnnV snxenVt ; Let us to determine the approximations of dopants and radiation defects concentrations with the higher order by using the standard procedure of the method of averaging of function corrections (Pankratov 2008c; Sokolov 1955), i.e., by substitution of the functions q (x, t) in the right side of Eqs. 6 and 7 in the following sum aiq ? qi-1(x, t), where i is the order of approximation. The substitution gives us the possibility of obtaining the second-order approximations of concentrations in the following form 0 t 1 C2kx; t a2Ck C1kx; t L @FCkx C1kv; tdvA; 0 L 1 Z t (...truncated)