Книги+1 / 2013 [Chandan_Kumar_Sarkar]_Technology_CAD

particular constant mobility is of no practical use because it leads to unrealistic high carrier velocity at high electric fields. Therefore, in order to achieve a successful prediction of a MOSFET device, it is necessary to use multiple non-conflicting mobility models simultaneously. It is also necessary to know which models are overriding others when conflicting mobility models are defined.

In ATLAS the mobility model to be used is specified in the MODEL statement. Detailed parameters associated with the chosen mobility models are specified on a separate MOBILITY statement.

For example, the ATLAS model statement shown below uses the constant voltage and temperature (CVT) Mobility Model for MOSFET in an ATLAS program. It is beyond the scope of this chapter to discuss in detail the parameters of the mobility model used.

models srh conmob fldnob b.electrons=2 b.holes=l evsatmod=0 hvsatmod=0 cvt boltzmann print numcarr=1 electrons temperature=300

mobility material=CVT parameter bn.cvt=4.75e+07 bp.cvt=9.92 5e÷06 cn.cvt=174000 cp.cvt=884200 taun.cvt=0.125 taup.cvt=0.0317 gamn.cvt=2.5 gamp.cvt=2.2 mu0n.cvt=52.2 mu0p.cvt=44.9 mu1n.cvt=43.4 mu1p.cvt=29 mumaxn.cvt=1417 mumaxp.cvt=470.5 crn.cvt=9.16e+16 crp.cvt=2.23e+17 csn.cvt=3 43e+20 csp.cvt=6.1e+20 alphn.cvt=0.68 alphp.cvt=0.71 betan.cvt=2 bctap.cvt=2 pcn.cvt=0 pcp.cvt=2.3e+15 deln.cvt=5.82e+14 delp.cvt=2.0546e+14

5.8  Benchmarking of MOSFET Simulations

Computer simulations allow modified devices to be tested within a few hours, although this can stretch out to days, and simulations also do not consume valuable raw materials or production time. However, the accuracy of computer models is always subject to question. This has led to the development of many different models for carrier mobility as well as different carrier transport models.

5.8.1  Method of Simulator Calibration

Typical TCAD tools, including both the process and the device simulators, are accurate, or predictive, but only for a sufficiently stable and mature technology, and after a lengthy calibration procedure [29]. This poses the issue of the relevance of device simulation for the development of a new technology

node, in which new processes and materials are introduced which are not under complete control until the technology is finally released, and for which doping profiles and geometry are not known with sufficient accuracy. However, although not fully predictive, the positive aspects of TCAD that make them useful are that they still provide optimization guidelines, explanations of the characterization results, and insights into the transport mechanisms. Therefore, it is extremely important to calibrate the process and device simulator tools not just to reproduce qualitative behaviors but also to obtain accurate device characterization.

5.8.2  Calibration of Process Simulator

Selection of the appropriate process coefficients and the process models of processes like diffusion, ion-implantation, etc., is the most critical part of the entire calibration procedure of a process simulator creating a virtual twodimensional device simulator. Thereafter the lengthiest task is to match the profiles of the actual device with the virtual device, for example, doping profile extraction from a physical device. The matching procedure effectively calibrates the simulator for a given process. It is a tedious task to tune the large number of undefined coefficients present in the empirical-based models in the process simulator considering the length of the subsequent process simulation runs.

The matching process is iterative. An exact match is rarely obtained. Generally there will be slight discrepancies between the structure generated by the process simulator and the physical fabricated device.

5.8.3  Calibration of Device Simulator

To calibrate a device simulator (ATLAS), the experimental I-V characteristics of the device obtained are set to best match the output of the DECKBUILD ATLAS program based on the same device dimension and structure. In order to obtain a match between the electrical characteristics of a real fabricated device and that with a simulated one, different advanced mobility models taking care of different scattering along with different doping profiles and different carrier transport models are analyzed iteratively, as shown in Figure 5.7.

5.9  Importance of Mesh Optimization

A mesh refers to a collection of volumetric elements whose union defines the interior and exterior of the device. The large number of small surface mesh elements allows finer geometrical resolution resulting in more accurate simulation.

FIGURE 5.7

Method for calibration.

In ATLAS, advanced nonlinear iterative solvers are employed for numerical solution of PDEs. Higher accuracy is correlated with the large number of nodes obtained from a dense mesh, but the tradeoff is between a longer elapsed time and memory. In order to obtain the desired accuracy and efficiency of solution, the mesh structure should be optimized. Very dense mesh is used in the region of interest of the device structure where the gradient of impurity and potential and current density is high. For example, in a MOSFET, very dense mesh is used in the channel region under the gateoxide interface and in the drain region where electric field is the highest. The tradeoff between the requirement of accuracy and computational time (complexity) dominated by the specification of the mesh structure causes problems for users. This problem always causes a dilemma for users. The time needed to complete a simulation run is roughly proportional to Na, where N is the number of nodes (grid points) and a is a constant that varies from 2 to 3 depending upon the complexity of the problem. Unfortunately, the size of the device pushes the number of nodes used close to 20,000—the maximum number of nodes permitted by ATLAS. The meshing procedure is thus extremely relevant to the way nodes are distributed throughout the device. ATLAS uses triangular meshes. It is shown that although optimal mesh generation is not exactly deterministic, guidelines and heuristics for defining satisfactory meshes with good triangulation scheme yield better results [30].

5.9.1  Strategy to Obtain a Satisfactory Mesh

1.Generate enough points to provide the required accuracy.

2.Do not generate many unnecessary points that impair accuracy.

3.Minimize or avoid generation of obtuse triangles and long, thin triangles which tends to impair accuracy, convergence, and robustness.

206Technology Computer Aided Design: Simulation for VLSI MOSFET

4.Transition from a region with larger-sized triangles to a region with small triangles must be smooth (i.e., avoid abrupt discontinuity).

5.Generate dense mesh in critical areas where the movements of electrons and holes are rapid in order to prevent information loss and accuracy.

6.Use coarse mesh density for non-critical areas.

7.For a symmetrical structure, simulators allow simulation of one-half of the structure and then reflection of the results on the other half to save computational time and memory.

5.9.2  Mesh Re-Gridding

Re-gridding is used for refinement of regions of the initial/base mesh according to some specified criterion. If the value of the specified solution variable (such as carrier concentration, doping concentration, electric field, etc.) exceeds a certain value or when the change in the value within a mesh triangle exceeds a certain value, then mesh refinement will take place. ATLAS supports mesh re-gridding based upon doping or a wide range of suitable solution variables as the basis for mesh refinement. Regrid algorithms will search for the triangle that satisfies the criteria specified for refinement. Once they are identified, those triangles will be divided into four congruent sub-triangles. Grid solution quantities (electric field potential, carrier concentration, etc.) are interpolated into the new nodes using linear or logarithmic interpolation. The initial or base mesh is referred to as “level 0,” and new triangles are referred to as “level 1.” After all level 0 triangles are examined, level 1 triangles will be examined by the same procedure. Therefore, sub-triangles of level 1 become level 2 triangles. This process continues until no more triangles meet the refinement criterion. It is possible to specify the “maximum level” which is the limiting factor for amount of refinement and size of the grid after refinement. Re-gridding can produce obtuse triangles causing inaccurate results. Therefore, smoothing should be performed on both the initial grids and subsequent re-grids.

5.10  Introduction to Other Tools from Silvaco Used in Conjunction with ATLAS

Virtual Wafer Fab (VWF) is a suite of software programs used to create a multifunctional environment for the simulation of semiconductor technology. VWF of Silvaco allows cost and yield estimation as well as comprehensive parametric analysis of semiconductor processing

amorphous and polycrystalline materials. MixedMode provides the ability to simulate circuits using a combination of SPICE models and ATLAS devices. Luminous and Laser support general optoelectronic and semiconductor laser devices, respectively.

Mixed-mode simulations with mesh-based device structures within a circuit defined by SPICE models are also supported in order to enhance the capability. For the transient mode of simulation, the device properties are re-solved at any increment of time. In addition to the device design, the mixed device/circuit simulation environment allows users to evaluate the device performance in a real circuit, and there is no limitation as to whether a compact model ever exists or not for the device under test. By examining the simulation results for the new structure, designers can make tradeoffs among design parameters to achieve optimal device characteristics. MIXEDMODE is a circuit simulator of Silvaco to provide mixed-mode circuit simulation of multiple device structures simulated using device simulation and compact circuit models.

Device 3D, INTERCONNECT3D, and THERMAL3D provide support for three-dimensional device capabilities for three-dimensional simulation, parasitic extraction, and three-dimensional thermal analysis.

5.10.1  Process Simulation Tools

Semiconductor process simulation involves the numerical solution of equations describing the physics of dopant diffusion, silicon oxidation, lithography, ion implantation, etching, and deposition steps resulting in geometry and doping profiles that define a device. A number of programs each specialized to solve a specific set of equations are used to simulate the entire process flow. However, the various programs use different solution strategies.

ATHENA is a framework program that integrates several smaller programs into a more complete process simulation tool. This program focuses upon the simulation of fabrication processes. In ATHENA, devices are created through simulation of the fabrication process. To optimize the device characteristics, changes in process parameters supplied to the ATHENA process simulator environment are required, as certain process parameters change the device characteristics. ATHENA consists of four primary and several secondary tools. The primary tools are SSuprem4 for simulating ion implantation, diffusion, oxidation, and silicidation process for silicon; Flash for simulating implantation and diffusion for advanced materials; Elite for topography simulation; and Optolith for lithography simulation. ATHENA also provides options for modeling silicides, Monte Carlo modeling of ion implantation, etc.

y.mesh loc=0 spac=0.0004 y.mesh loc=0.03 spac=0.008 y.mesh loc=0.10 spac=0.01

#1.3 region definition region num=1 y.min=0 silicon region num=2 y.max=0 oxide

#1.4 electrode declaration

electrode name=gate number=1 x.min=0.05 x.max=0.13 top electrode name=source number=2 left length=0.05 y.min=0 y.max=0 electrode name=drain number=3 right length=0.05 y.min=0 y.max=0 electrode name=substrate number=4 bottom

#1.5 doping specification of distribution, type doping uniform conc=2e18 p.type region=1

doping uniform conc=1e20 n.type x.left=0 x.right=0.05 y.min=0 y.max=0.03

doping uniform conc=1e20 n.type x.left=0.13 x.right=0.18 y.min=0 y.max=0.03

#1.6 contact specification

#n.poly sets n+ doped polysilicon as contact material with workfuction=4.17eV

contact name=gate n.poly contact name=source neutral contact name=drain neutral contact name=substrate neutral

#Step 2: Set the material model models mos print

#Step 3: Set the specific method used to do the calculation method newton trap

#Step 4: generate initial solution at zero bias solve init

# ramp gate bias with a specific drain bias solution load infile=solve_vdrain1