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

The first doping statement specifies that the boron channel doping profile was created by a newer version of SUPREM-III (new.sup). The logical parameter boron specifies the dopant to be extracted from the SUPREM-III file. The SUPREM-III file name (inC) is given as n.exp. In the first doping statement, the implant window (x.lert, x.right) is not specified. Thus, it is the uniform blank implant. The channel doping profile is shown in Fig. 3.26(a). The peak channel implant is 5 x 1016 cm·3 and the substrate doping is 8 x 1014 em·3• The second and third doping statements specify the double diffused source doping profile. The second statement tells the program to extract the arsenic profile from the SUPREM-III file (n+.exp) and the uniform-implant window is from 0.0 (x.left) to 0.7 JJm (x.right). In this window, the doping profile is uniform in the x direction and only varies with y according to the 1-D SUPREM-III profile. Outside this window, the default lateral profile is the same shape as the vertical profile but it is scaled. The scale ratio (ratio) is 0.75. The third statement specifies the same information except the dopant is phosphorus. The fourth and fifth doping statements specify the double diffused drain doping profile. All the specifications are the same as those of the source except the implant window is from 2.3 JJ m to 3.0 JJ m. The specified doping profiles yield an effective channel length of 1.2 JJ m. The vertical doping profile of the source and drain regions is shown in Fig. 3.26(b). Due to the arsenic and phosphorus double diffusion, the profile is smoother than the conventional arsenic-only profile. The junction depth is about 0.27 JJ m. The end statement marks the end of the input file. The device structure specified by this input is shown in Fig. 3.27(a). The final mesh saved in n4msh3 is shown in Fig. 3.27(b). The total number of nodes is 939.

Electrical characteristics simulation

The next phase is the actual device simulation in the .subthreshold region. In this input, the first step is to load the device structure, a mesh and doping information from the mesh file n4msh3 using a mesh statement. Before solving the equations, several things should be specified.

116 Computer-Aided Design

title subthreshold & linear region characteristics : n4b.i

$

$ load the mesh me mesh inme =n4msh3

$

$ specify the symbolic factorization and parameters

In an n-channel MOS device, it is enough to solve the Poisson and electron continuity equations to calculate the channel current because the hole current is negligible. Thus, the number of carriers (carriers) is specified as 1 and the carrier type as electron (electrons) in the symbolic statement. In this input, the solution method is specified as the direct Newton method (newton) using an automated Newton-Richardson procedure (autonr) as shown in the symbolic and method statements.

The next thing is to specify the material types (or work function) of electrodes using the contact statement. The gate is the second electrode (number=2). It is n+ polysilicon (n.poly). Other electrodes are not specified. Thus, neutral contacts will be assigned as defaults. The physical models to be used in the simulation should be specified such as the mobility model, the recombination model, or statistics, etc. These models are specified by a models statement. The most important physical model is the mobility model in the MOS device simulation. In the subthreshold region, however, it is not critical so that the default constant mobility model is used. The absolute temperature is also set to 300 OK in the models statement. The logical parameter print directs the program to print out all the information on the physical models used in the simulation. Next, the initial solution will be solved.

Since there has been no solution before, the solution should start from the initial guess (initial) where all biases on the electrodes are equal to zero. In the first solve statement, all biases are set to zero by default and the solution will be saved in the file, n4slvO. Before proceeding further, a log file for the biases and currents of all electrodes is set up using a log statement. This log information will be saved in the file, n4b.IV. It will be used to plot I-V characteristics later. The next solve statement increases the bias of the first electrode (drain) to 0.1 V and calculates the solution. The gate voltage is ready to be stepped to generate the subthreshold and linear region I-V characteristics.

In the solve statement, the bias of any electrode can be set to a new constant value. If new values are not set, previous values will be used. The bias of the electrode can also be stepped with a uniform increment as shown on the third solve statement in the input file. Usually, the bias step should be less than 0.5 V. Otherwise, the convergence may be slow or non-convergence may occur in the worst case. In the bias stepping, the program needs the identification number ofthe electrode (electrode), the step voltage (vstep), and the number of steps (nsteps). In the third solve statement, the second

electrode (gate) is stepped by 0.2 V from 0 V to 1.8 V. The method of initial guess for the solution can also be specified in the solve statement.

The first bias point for a given structure must have the initial parameter specified. From then, the program will either use the previous (previous), or if there are two previous solution present and equivalent bias steps are taken on any electrodes that are changed, an extrapolation (project) from the preceding two solutions will be used to get an improved initial guess. After the initial bias point, the program will automatically use extrapolation wherever possible if no initial guess parameter is supplied. The extrapolated initial guess may reduce the number of iterations especially for bias stepping. The biases of the multiple electrodes can be stepped at the same time. If more than one electrode is to be stepped, electrode should be an n-digit integer, where each of the n-digits is a separate electrode number. If only the last bias solution is to be saved, the output file name should not be specified in the solve statement with bias stepping. Otherwise, the program will save each solution in separate files. Use a separate solve statement for the last bias point and specify the output file name as shown in the fourth solve statement. In summary, the four solve statements solve for the subthreshold and linear region characteristics of the n- channel MOS device for the drain bias of 0.1 V and the gate bias from 0 V to 2.0V.

The total input for the subthreshold characteristics is shown in Fig. 3.28(a). A typical output for a bias point is also illustrated in Fig. 3.28(b). For each bias point, the iteration information is first printed. The default termination criteria are that the maximum potential change is less than 1 x 10-5 kT/ q for the Poisson equation and that the maximum change relative to the local concentration is less than 10-5 for the current continuity equations. Both criteria must be satisfied. These criteria can be changed with the p.tol and c.tol parameters in the method statement. After convergence, the program calculates the conduction, displacement and total currents per micron width and prints out the results. For a DC simulation, the displacement current is zero and the conduction and total currents are the same. The cpu time is also printed out in seconds.

Graphical post-processing

The initial solution is saved in n4slvO. The last solution is saved in n4slvl. The I-V log information is saved in n4b.IV. The I-V characteristics are plotted using the following input file.

title plot I-V: n4piv.i

Although the mesh information is not used, the mesh file should be read first because the program prints an error message otherwise. The I-V information is read back from n4b.IV in the plot.ld statement. The x axis (x.axis) is assigned to VG (v2) andy axis (y.axis) to ID (it). As a default, the plot ranges ofx and y variables are determined by the maximum and minimum values ofx and y variables in the input file. Absolute and logarithm direct the program to take the absolute value and logarithm of the y variable. The I-V plot generated by this statement is shown in Fig. 3.29(a). From this plot, the subthreshold slope can be determined. The subthreshold slope, S is 98 mV/decade by simulation, which is close enough to the measured value of % mV/ decade. After this plot, the program stops and waits because the pause parameter is set. One can examine the plot or make a hard copy and continue the program by pushing the return key. The second plot.ld line plots the I-V characteristics on a linear scale. This plot is shown in Fig. 3.29(b). The extrapolated VT is 0.8 V for this short-channel device, which is comparable to the measured value of

0.75 ± 0.04 V.

The internal distributions of major variables can be plotted using ploUd and contour statement. The input for the potential contour plot is as follows.

title plot 2-D contour plot of potential: n4p2.i

$

$ load the mesh and solution mes

J

i

SUBSTRATE

Contour plot of potential when Va = 2 V and

VD = 0.1 V. Increment of Contour is 0.1 V.