Книги2 / 1988 Kit Man Cham, Soo-Young Oh, John L. Moll, Keunmyung Lee, Paul Vande Voorde, Daeje Chin (auth.) Computer-Aided Design and VLSI Device Development 1988

In SUPREM II, all high temperature anneals and oxidations are designated with the TYPE=OXID parameter; lines 12, 14, 18 and 22. The ambient is designated with the NITO, DRYO and WETO parameters.

After the poly doping operation (line 14) the channel and source/drain regions are treated differently. Therefore the structure is saved (line 16) in a file entitled CHNSD which will be used as the starting point for the source/drain simulation. The TYPE=B parameter specifies a binary file format.

The PRINT statement (line 20) instructs the program to print out some specified information. The HEAD =Y parameter indicates that the "header" should be printed. The "header" includes the thickness and integrated dopant content for the silicon and oxide layers. The PLOT statement (line 21) creates a log-linear plot of the doping profile. TOTL= Y indicates that the net doping level is plotted. The net doping is the absolute value of the n-type concentration minus the p-type concentration. The WIND parameter sets the depth of the plot. Oddly enough, the PRINT and PLOT statements apply to the result of the next process step. Therefore, to obtain the final profile, these two statements must appear before the final anneal cycle, line 22. The last SAVE statement (line 23) stores the final profile for future reference.

SUPREM In uses different statement names for each type of process step. For example, the oxide deposition is input with the deposit statement, line 4. The dx parameter specifies the grid spacing in the deposited layer. The channel implants are given in lines 6 and 7. The Pearson IV profile is used for these implants. The Pearson IV coefficients were selected to model channeling of the implanted boron and are different from the default parameters in SUPREMIII.

In SUPREM III, all high temperature anneals and oxidations are input with the diffusion statement, lines 11, 13, 17 and 18. The ambient is designated with the nit, dryo2 and weto2 parameters.

After the poly doping operation, the simulation structure is saved (line 15) in a binary file entitled chnsd which will be used as the starting point for the source/drain simulation. The structure parameter specifies the correct file format so that it can be read back into the SUPREM III program. The final results are output with the print and plot statements, lines 20 and 21. The layer parameter instructs the program to print the thicknesses and integrated dopant content of all the layers in the structure. The plot statement creates a

log-linear plot of the net active doping profile. For high doping levels the active concentration will be less than the chemical concentration. The final structure is saved (line 22) for future reference.

Fig. 2.5 shows the input files for the source/drain simulation. The structure created in the channel simulation, file CHNSD, is reloaded into SUPREM II with the LOAD statement, line 5. Then the source/drain implant is input in line 7. A two-side gaussian is used for this implant profile. The reoxidation and final drive-in are described in lines 9 and 14. The final structure is saved in line 15.

The simulation structure is loaded into SUPREM III in the initialize statement, line 3. The source/drain implant is specified in line 5. A Pearson IV profile is used for this implant. The reoxidation and final drive-in are input in lines 7 and 9. The final structure is saved in line 13.

The simulated doping profiles for the channel and source/drain regions are presented in Fig. 2.6. The differences between the predictions of SUPREM II and SUPREM III are due to the different implant profiles and the somewhat different default diffusion constants. In general the program user needs to adjust some of the model parameters to provide agreement with experimental observations. Chapter 6 goes into this issue in more detail.

IN SUPREM II the MODL statement is used to modify the model coefficients. For example, one could modify the parameters related to dry oxidation and designate the new coefficient set as model DRYl. This could then be input in a oxidation operation with the MODL=DRY1 parameter. In SUPREM II there is no way to save the new coefficient set for use in future simulations. Therefore any coefficient modifications must be repeated in each input file.

SUPREM III offers several statement types that can be used to modify the model coefficients. For example, the models related to an impurity such as boron may be modified in a boron statement. The model coefficients related to the silicon may be modified with a silicon statement. The segregation coefficients may be modified with a segregate statement. The modified coefficient set can be saved in a file and used in future simulations by specifying the coefficient file in the initialize statement.

(A)1 .... TITLE : SOURCE/DRAIN SIMULATION

2 .... SUBSTRATE ORNT=lOO,ELEM=B,CONC=6E14

3 .... GRID DYSI=O.Ol,YMAX=l.O

4 .... COMMENT : LOAD STRUCTURE FROM CHANNEL SIMULATION

5 .•.. LOAD FILE=CHNSD,TYPE=B

6 .... COMMENT: IMPLANT SOURCE/DRAIN

7 .... STEP TYPE=IMPL,ELEM=AS,DOSE=6E15,AKEV=80

(B)l .... title : source/drain profile simulation

2 .... comment : load structure from channel simulation

Fig.2.5. SUPREM Input Files for the Source/Drain Region Simulation (a) SUPREM II (b) SUPREM III

2.3 SUPRA: 2-D Process Simulator

SUPRA simulates the incorporation and redistribution of impurities in a two-dimensional (2-D) cross-section of a device as indicated in Fig. 2.1. Such two-dimensional structures are created by modeling actual lithographic patterning. A photoresist layer deposition in Fig. 2.7, for example, is formed by an ETCH card. Four parameters (START, CORNER, END and THICK) give enough freedom to create arbitrary etch profiles. However, re-entrant angles resulting from undercutting are not allowed because such a shape is difficult to express numerically with an array that represents a single value of a layer thickness at a horizontal position. Impurity concentrations are calculated only within the thermal oxide and substrate regions. The mask layers are used only as barriers against ion implantation and surface diffusion.

Input commands and the internal organization of SUPRA are similar to those of SUPREM II. Specification of the two-dimensional device structures, however, requires the use of a coordinate system. The horizontal coordinate is defined as x and corresponds to variation parallel to the bottom surface of the device. The vertical coordinate is defined as y and corresponds to variation normal to the bottom surface of the device. The origin of coordinates is defined as the leftmost point of the original semiconductor/oxide interface, with positive x to the right and positive y downward into the substrate.

Finite-difference grids in two dimensions are easily generated by using X.GRID and Y.GRID statements for the x andy directions. Nonuniform grids are automatically generated, depending upon the number of nodes and spaces specified in the x and y directions. This allows fast computation as well as high resolution for regions where concentrations change rapidly. More details on the grid generation will be discussed in a following example section.

Two-Dimensional Process Models

Process models of the SUPRA program consist of two main parts. One is an analytical part containing closed forms of analytical equations, from which

PHOTORESIST ~_-THICK'---t i_

Xs: START

Xc: CORNER

XE:END

Fig.2.7. Structure definition in SUPRA. START, CORNER, and END represent the starting, comer, and ending positions. THICK is the thickness of the layer to be etched.

solutions are readily obtained at any position without numerical iterations. The other is a numerical part in charge of specific calculations for solving the nonlinear diffusion equation. Analytical solutions are used to model changes in the overall device structure (i.e. deposition/etch and oxide growth), ion implantation, and boron diffusion. This analytic technique is fast in computation and flexible in grid allocation. It is, however, limited to low-concentration diffusion. Inert drive-in involving high impurity concentration of arsenicimplanted source/drain regions is treated by the numerical solution.

a) Ion Implantation

The spatial distribution of implanted atoms is assumed to be a Gaussian function in the vertical and lateral direction when implanted through an infinitesimal mask window (actually a point source)[2.20]. When this Gaussian function is integrated for a finite window with a uniform thickness as shown in Fig. 2.8 from Xk to Xk +10 the profile is given below as

where I max is the peak concentration and erfc(x) is the complementary error function of x. The parameters Rp , t::.Rp and Ax are the projected range, and vertical and lateral standard deviations respectively. It should be noted that the

Fig. 2.8. Impurity distributions implanted through a small mask window after implantation (solid lines) and after inert drive-in (broken lines).

profile implanted through the window with a finite width becomes a Gaussian distribution multiplied by a complementary-error function in the lateral direction. The impurity profile, when implanted through an arbitrary mask as shown in Fig. 2.8, can be expressed by a summation of the profiles through all mask segments as

k=l

where k represents the kth mask segment.

b) Low Concentration Inert Drive-in

If the impurity concentration is lower than the intrinsic carrier concentration ni, as in the boron channel-stop region, the diffusivity can be assumed

constant. The diffusion Eq. (2.14) becomes linear when the drift term is ignored. The same superposition technique used for implantation can be applied to this inert drive-in condition. The inert drive-in solution for the profile described in Eq. (2.28) is given by

where the subscript i refers to inert ambient conditions. D is the impurity diffusivity, t is the time of the diffusion step, dk is the effective silicon thickness of the layers above the substrate through which the ion implantation is performed. The profile resulting from an inert drive-in of the implant through one mask segment is shown in Fig. 2.8 (broken lines). Once again, the complete drive-in profile is constructed by superposing the solution for each mask segment.

c) Moving Boundary Diffusion

The one-dimensional profile following oxidation is approximated by adding a correction factor to the inert drive-in concentration [2.21] as

(2.31)

where the correction factor Nc(y,t) is expressed by a term involving a complementary error function. In this approach the correction function basically subtracts an appropriate fraction of dopant to account for segregation and outdiffusion into the oxide. A boundary condition which properly determines the correction term has been found, and extensive analytical and numerical results

FIELD OXIDE

Fig.2.9. Cross-section of NMOSFET near the source and the channel-stop region simulated by SUPRA.

have been presented elsewhere [2.22]. For low concentration diffusion, this analytic method gives agreement typically better than 10% with numerical calculations, and it has a computation-time advantage of more than a factor of ten [2.23].

A quasi two-dimensional profile has been obtained by assuming that the oxide layer grows only in the vertical direction during a semi-recessed oxidation [2.22]. However, the effect of lateral oxide growth may not be negligible in a case such as fully-recessed oxidation. A more generalized boundary condition is given below as

volumetric ratio of silicon consumed in forming one unit of oxide (0.44). The quantity g(Xt, Yt, t) is the oxide growth rate, next, Yt) is a unit vector normal to the Si02 interface, and (Xt, Yt) is the final interface point closest to (x, y) as indicated in Fig. 2.9. Provided that No(x, y, t) can be separated in the x and Y variables, the above boundary condition is also separable in the vertical and lateral directions. The resulting 2-D profile is given by

where the subscripts 0 and i indicate oxidizing and inert conditions, respectively. The Dt terms implicit in Nix and N~ represent the diffusivity-time product for all high temperature steps including inert drive-in. The correction terms involve only the moving boundary and segregation effects, hence Dtox represents the diffusivity-time product for oxidation steps only.

The coefficient Ax andAy are obtained from Eq. (2.33) and the boundary condition Eq. (2.32) as

(2.34)

where z is either the x or y variable. Again gz is the oxide growth rate in either the vertical or lateral direction. The boron profile obtained by this analytical technique at the channel-stop region is shown in Fig. 2.9. The two-dimensional oxide shape resulted from LOCOS is approximated by empirically determined functions. More rigorous treatment of non-uniform oxidation is the topic of the next section.

d) High-Concentration Diffusion

If the impurity concentration is sufficiently large compared to the intrinsic electron concentration at the diffusion temperature, then diffusivity will no longer be constant throughout the simulation space. The diffusion equation then becomes nonlinear and must be solved numerically. Also, there may be several impurities present simultaneously which can interact by way of electric field or Fermi level effects. Also impurity clustering can become important.