ACUTE—Assembly for Computational Electronics
 Version 35
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 Version 36
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5  
6  The purpose of the ACUTE toolbased curricula is to introduce interested scientists from Academia and Industry in advanced simulation methods needed for proper modeling of stateoftheart nanoscale devices. The multiple scale transport in doped semiconductors is summarized in the figure below in terms of the transport regimes, relative importance of the scattering mechanisms and possible applications.  
7  
8  [[Image(intro1.png, 250 class=alignleft)]]  
9  [[Div(start, class=clear)]][[Div(end)]]  
10  
11  Relationship between various transport regimes and significant lengthscales.  
12  
13  [[Image(intro2.png, 250 class=alignleft)]]  
14  [[Div(start, class=clear)]][[Div(end)]]  
15  
16  We first discuss the energy bandstructure that enters as an input to any device simulator. We then begin with the discussion of simulators that involve the driftdiffusion model, and then move into simulations that involve hydrodynamic and energy balance transport and conclude the semiclassical transport modeling with application of particlebased device simulation methods.  
17  
18  Having discussed and utilized the semiclassical simulation tools and their applications, we then move into inclusion of quantum corrections into classical simulators. The final set of tools is dedicated to the farfrom equilibrium transport, where we will utilize the concept of pure and mixed states and the distribution function. Several tools that utilize different methods will be used for that purpose. We will utilize tools that use the recursive Green’s function method and its variant, the Usuki method. Also, we will utilize the Contact Block Reduction tool as the most efficient and most complete way of solving the quantum transport problem since this method allows one to simultaneously calculate sourcedrain current and gate leakage which is not the case, for example, with the Usuki and the recursive Green’s function techniques that are in fact quasi1D in nature for transport through a device. A table that shows the advantages and the limitation of various semiclassical and quantum transport simulation tools is presented below.  
19  
20  [[Image(intro3.png, 250 class=alignleft)]]  
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22  
23  
24  == Energy Bands and Effective Masses ==  
25  
26  === [/tools/acute/ PieceWise Constant Potential Barrier Tool in ACUTE]– Open Systems ===  
27  
28  The [/tools/acute/ PieceWise Constant Potential Barrier Tool in ACUTE] allows calculation of the transmission and the reflection coefficient of arbitrary five, seven, nine, eleven and 2nsegment piecewise constant potential energy profile. For the case of multiwell structure it also calculates the quasibound states so it can be used as a simple demonstration tool for the formation of energy bands.  
29  
30  [[Image(pcpbt.png, 200 class=alignleft)]]  
31  [[Div(start, class=clear)]][[Div(end)]]  
32  
33  Also, it can be used in the case of stationary perturbation theory exercises to test the validity of, for example, the first order and the second order correction to the ground state energy of the system due to small perturbations of, for example, the confining potential. The PCPBT tool can also be used to test the validity of the WKB approximation for triangular potential barriers.  
34  
35  [[Div(start, class=clear)]][[Div(end)]]  
36  
37  Exercises:  
38  
39  [[Div(start, class=clear)]][[Div(end)]]  
40  
41  * [[Resource(4831)]]  
42  
43  * [[Resource(4833)]]  
44  
45  * [[Resource(4853)]]  
46  
47  * [[Resource(4873)]]  
48  
49  * More on the energy bands formation: Cosine bands  
50  
51  * [[Resource(4849)]]  
52  
53  * [[Resource(5102)]]  
54  
55  * [[Resource(5130)]]  
56  
57  [[Div(start, class=clear)]][[Div(end)]]  
58  
59  
60  === [/tools/acute/ Periodic Potential Lab in ACUTE] ===  
61  
62  The [/tools/acute/ Periodic Potential Lab in ACUTE] solves the time independent Schroedinger Equation in a 1D spatial potential variation. Rectangular, triangular, parabolic (harmonic), and Coulomb potential confinements can be considered. The user can determine energetic and spatial details of the potential profiles, compute the allowed and forbidden bands, plot the bands in a compact and an expanded zone,  
63  
64  [[Image(ppl.png, 250 class=alignleft)]]  
65  [[Div(start, class=clear)]][[Div(end)]]  
66  
67  and compare the results against a simple effective mass parabolic band. Transmission is also calculated. This Lab also allows the students to become familiar with the reduced zone and expanded zone representation of the dispersion relation (Ek relation for carriers).  
68  
69  Exercises:  
70  
71  * [[Resource(4851)]]  
72  
73  [[Div(start, class=clear)]][[Div(end)]]  
74  
75  
76  === [/tools/acute/ Bandstructure Lab in ACUTE] ===  
77  
78  In solidstate physics, the electronic band structure (or simply band structure) of a solid describes ranges of energy that an electron is "forbidden" or "allowed" to have. It is due to the diffraction of the quantum mechanical electron waves in the periodic crystal lattice. The band structure of a material determines several characteristics, in particular its electronic and optical properties. The [/tools/acute/ Bandstructure Lab in ACUTE] tool enables the study of bulk dispersion relationships of Si, !GaAs, !InAs. Plotting the full dispersion relation of different materials, students first get familiar with a bandstructure of direct bandgap (!GaAs, !InAs) and indirect bandgap semiconductors (Si). For the case of multiple conduction band valleys one has to determine first the Miller indices of one of the equivalent valleys and from that information it immediately follows how many equivalent conduction bands one has in Si and Ge, for example.  
79  
80  [[Image(bsl.png, 250 class=alignleft)]]  
81  [[Div(start, class=clear)]][[Div(end)]]  
82  
83  In advanced applications, the users can apply tensile and compressive strain and observe the variation in the bandstructure, bandgaps, and effective masses. Advanced users can also study bandstructure effects in ultrascaled (thin body) quantum wells, and nanowires of different cross sections. Bandstructure Lab uses the sp3s*d5 tight binding method to compute E(k) for bulk, planar, and nanowire semiconductors.  
84  
85  Exercises:  
86  
87  * [[Resource(5201)]]  
88  
89  * [[Resource(5031)]]  
90  
91  * [[Resource(4890)]]  
92  
93  * [[Resource(4880)]]  
94  
95  
96  [[Div(start, class=clear)]][[Div(end)]]  
97  
98  
99  ==DriftDiffusion and Energy Balance Simulations==  
100  
101  
102  === [/tools/acute/ PADRE Tool in ACUTE] – Modeling of Sibased devices===  
103  
104  [/tools/acute/ PADRE Tool in ACUTE] is a 2D/3D simulator for electronic devices, such as MOSFET transistors.  
105  
106  [[Image(padre.png, 250 class=alignleft)]]  
107  [[Div(start, class=clear)]][[Div(end)]]  
108  
109  It can simulate physical structures of arbitrary geometryincluding heterostructureswith arbitrary doping profiles, which can be obtained using analytical functions or directly from multidimensional process simulators such as Prophet.  
110  For each electrical bias, [/tools/acute/ PADRE Tool in ACUTE] solves a coupled set of partial differential equations (PDEs). A variety of PDE systems are supported which form a hierarchy of accuracy: (1) electrostatic (Poisson equation), (2) driftdiffusion (including carrier continuity equations), (3) energy balance (including carrier temperature) and (4) electrothermal (including lattice heating).  
111  
112  Several example problems that utilize [/tools/acute/ PADRE Tool in ACUTE] are given below:  
113  
114  * [[Resource(229)]]  
115  
116  * [[Resource(4894)]]  
117  
118  * [[Resource(4896)]]  
119  
120  * [[Resource(452)]]  
121  
122  * [[Resource(4906)]]  
123  
124  * [[Resource(3984)]]  
125  
126  * [[Resource(5051)]]  
127  
128  A variety of supplemental documents are available that deal with the PADRE software and TCAD simulation:  
129  
130  * [/site/resources/tools/padre/doc/index.html User Manual]  
131  
132  * [/site/resources/2006/06/01581/intro_dd_padre_word.pdf Abbreviated First Time User Guide]  
133  
134  
135  A set of course notes on Computational Electronics with detailed explanations on bandstructure, pseudopotentials, numerical issues, and drift diffusion is also available.  
136  
137  * [[Resource(1516)]]  
138  
139  * [[Resource(980)]]  
140  
141  
142  ===SILVACO Simulator – Modeling of Sibased and IIIV devices===  
143  
144  In preparation.  
145  
146  
147  
148  == ParticleBased Simulators ==  
149  
150  === [/tools/acute/ Bulk Monte Carlo Lab in ACUTE] ===  
151  
152  [[Image(mc.png, 250 class=alignleft)]]  
153  [[Div(start, class=clear)]][[Div(end)]]  
154  
155  The [/tools/acute/ Bulk Monte Carlo Lab in ACUTE] calculates the bulk values of the electron drift velocity, electron average energy and electron mobility for electric fields applied in arbitrary crystallographic direction in both column 4 (Si and Ge) and IIIV (GaAs, SiC and GaN) materials. All relevant scattering mechanisms for the materials being considered have been included in the model.  
156  
157  [[Image(scattering.png, 250 class=alignleft)]]  
158  [[Div(start, class=clear)]][[Div(end)]]  
159  
160  Detailed derivation of the scattering rates for most of the scattering mechanisms included in the model can be found on Prof. Vasileska personal website http://www.eas.asu.edu/~vasilesk (look under class EEE534 Semiconductor Transport). Description of the Monte Carlo method used to solve the Boltzmann Transport Equation and implementation details of the tool are given in the  
161  
162  [[Resource(4843)]]  
163  
164  Available also is a voiced presentation  
165  
166  [[Resource(4439)]]  
167  
168  that gives more insight on the implementation details of the Ensemble Monte Carlo technique for the solution of the Boltzmann Transport Equation. Examples of simulations that can be performed with this tool are given below:  
169  
170  [[Resource(4845)]]  
171  
172  Exercises:  
173  
174  * [[Resource(5047)]]  
175  
176  * [[Resource(5277)]]  
177  
178  * [[Resource(5275)]]  
179  
180  
181  === [/tools/acute/ Quamc2D Lab in ACUTE] ===  
182  
183  [/tools/acute/ Quamc2D Lab in ACUTE] (pronunciation: quamsee) 2D is effectively a quasi threedimensional quantumcorrected semiclassical Monte Carlo transport simulator for conventional and nonconventional MOSFET devices.  
184  
185  [[Image(quamc2d1.png, 250 class=alignleft)]]  
186  [[Div(start, class=clear)]][[Div(end)]]  
187  
188  Device structures that can be simulated.  
189  
190  [[Image(quamc2d2.png, 250 class=alignleft)]]  
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192  
193  Phenomena that can be explained  
194  
195  A parameterfree quantum field approach has been developed and utilized quite successfully in order to capture the sizequantization effects in nanoscale MOSFETs. The method is based on a perturbation theory around thermodynamic equilibrium and leads to a quantum field formalism in which the size of an electron depends upon its energy. This simulator uses different selfconsistent eventbiasing schemes for statistical enhancement in the MonteCarlo device simulations. Enhancement algorithms are especially useful when the device behavior is governed by rare events in the carrier transport process. A bias technique, particularly useful for small devices, is obtained by injection of hot carriers from the boundaries. Regarding the Monte Carlo transport kernel, the explicit inclusion of the longitudinal and transverse masses in the silicon conduction band is done in the program using the HerringVogt transformation. Intravalley scattering is limited to acoustic phonons. For the intervalley scattering, both g and fphonon processes have been included.  
196  
197  * [[Resource(4520)]]  
198  
199  * [[Resource(4543)]]  
200  
201  * [[Resource(4443)]]  
202  
203  * [[Resource(4439)]]  
204  
205  * [[Resource(5127)]]  
206  
207  Exercises:  
208  
209  
210  ===Thermal ParticleBased Device Simulator===  
211  
212  In preparation.  
213  
214  
215  
216  ==Inclusion of Quantum Corrections into SemiClassical Simulation Tools==  
217  
218  
219  === [/tools/acute/ SCHRED in ACUTE] ===  
220  
221  [/tools/acute/ SCHRED in ACUTE] calculates the envelope wavefunctions and the corresponding boundstate energies in a typical MOS (MetalOxideSemiconductor) or SOS (SemiconductorOxide Semiconductor) structure and a typical SOI structure by solving selfconsistently the onedimensional (1D) Poisson equation and the 1D Schrodinger equation.  
222  
223  [[Image(schred.png, 250 class=alignleft)]]  
224  [[Div(start, class=clear)]][[Div(end)]]  
225  
226  To better understand the operation of [/tools/acute/ SCHRED in ACUTE] tool and the physics of MOS capacitors please refer to:  
227  
228  * [[Resource(4794)]]  
229  
230  * [[Resource(4796)]]  
231  
232  * [[Resource(5087)]]  
233  
234  * [[Resource(5127)]]  
235  
236  Exercises:  
237  
238  * [[Resource(4900)]]  
239  
240  * [[Resource(4902)]]  
241  
242  * [[Resource(4904)]]  
243  
244  
245  === [/tools/acute/ 1D Heterostructure Tool in ACUTE] ===  
246  
247  The [/tools/acute/ 1D Heterostructure Tool in ACUTE] simulates confined states in 1D heterostructures by calculating charge selfconsistently in the confined states, based on a quantum mechanical description of the one dimensional device. The greater interest in HEMT devices is motivated by the limits that will be reached with scaling of conventional transistors. The [/tools/acute/ 1D Heterostructure Tool in ACUTE] in that respect is a very valuable tool for the design of HEMT devices as one can determine, for example, the position and the magnitude of the deltadoped layer, the thickness of the barrier and the spacer layer for which one maximizes the amount of free carriers in the channel which, in turn, leads to larger drive current. This is clearly illustrated in the examples below.  
248  
249  [[Image(1dhet1.png, 180 class=alignleft)]]  
250  [[Image(1dhet2.png, 180 class=alignleft)]]  
251  [[Div(start, class=clear)]][[Div(end)]]  
252  
253  Exercises:  
254  
255  * [[Resource(5231)]]  
256  
257  * [[Resource(5233)]]  
258  
259  
260  The most commonly used semiconductor devices for applications in the GHz range now are !GaAs based MESFETs, HEMTs and HBTs. Although MESFETs are the cheapest devices because they can be realized with bulk material, i.e. without epitaxially grown layers, HEMTs and HBTs are promising devices for the near future. The advantage of HEMTs and HBTs is a factor of 2 to 3 higher power density compared to MESFETs which leads to significantly smaller chip size.  
261  
262  HEMTs are field effect transistors where the current flow between two ohmic contacts, Source and Drain, and it is controlled by a third contact, the Gate. Most often the Gate is a Schottky contact. In contrast to ion implanted MESFETs, HEMTs are based on epitaxially grown layers with different band gaps Eg.  
263  
264  
265  
266  ==Quantum Transport==  
267  
268  
269  === Recursive Green's Function Method for Modeling RTD's===  
270  
271  in preparation.  
272  
273  
274  === [/tools/acute/ nanoMOS in ACUTE] ===  
275  
276  [/tools/acute/ nanoMOS in ACUTE] is a 2D simulator for thin body (less than 5 nm), fully depleted, doublegated nMOSFETs. A choice of five transport models is available (driftdiffusion, classical ballistic, energy transport, quantum ballistic, and quantum diffusive). The transport models treat quantum effects in the confinement direction exactly and the names indicate the technique used to account for carrier transport along the channel. Each of these transport models is solved selfconsistently with Poisson's equation. Several internal quantities such as subband profiles, subband areal electron densities, potential profiles and IV information can be obtained from the source code.  
277  
278  [[Image(nanomos.png, 250 class=alignleft)]]  
279  [[Div(start, class=clear)]][[Div(end)]]  
280  
281  [[Resource(1305)]] 3.0 includes an improved treatment of carrier scattering. Some important information about [/tools/acute/ nanoMOS in ACUTE] can be found on the following links:  
282  
283  * [[Resource(2845)]]  
284  
285  * [[Resource(1533)]]  
286  
287  
288  ===CBR===  
289  
290  in preparation.  
291  
292  
293  
294  ==Atomistic Modeling==  
295  
296  
297  === [/tools/acute/ NEMO3D in ACUTE] ===  
298  
299  [/tools/acute/ NEMO3D in ACUTE] calculates eigenstates in (almost) arbitrarily shaped semiconductor structures in the typical column IV and IIIV materials. Atoms are represented by the empirical tight binding model using s, sp3s*, or sp3d5s* models with or without spin. Strain is computed using the classical valence force field (VFF) with various Keatinglike potentials.  
300  
301  [[Image(modeling_agenda5.gif, 250 class=alignleft)]]  
302  [[Div(start, class=clear)]][[Div(end)]]  
303  
304  [/tools/acute/ NEMO3D in ACUTE] has been used to analyze quantum dots, alloyed quantum dots, long range strain effects on quantum dots, effects of wetting layers, piezoelectric effects in quantum dots, quantum dot nuclear spin interactions, quantum dot phonon spectra, coupled quantum dot systems, miscut Si quantum wells with SiGe alloy buffers, coreshell nanowires, allyed nanowires, phosphorous impurities in Silicon (P:Si qbits), bulk alloys.  
305  
306  [[Image(qdot.png, 250 class=alignleft)]]  
307  [[Div(start, class=clear)]][[Div(end)]]  
308  
309  Boundary conditions to treat the effects of (surface states have been developed. Direct and exchange interactions and interactions with electromagnetic fields can be computed in a postprocessing approach based on the NEMO 3D single particle states.  
310  
311  Exercises:  
312  
313  * [[Resource(450)]]  
314  
315  * [[Resource(2925)]]  
316  
317  
318  == Collection of tools that comprise ACUTE ==  
319  
320  [[Resource(4826)]]  
321  
322  [[Resource(3847)]]  
323  
324  [[Resource(1308)]]  
325  
326  [[Resource(941)]]  
327  
328  [[Resource(4438)]]  
329  
330  [[Resource(1092)]]  
331  
332  [[Resource(221)]]  
333  
334  [[Resource(5203)]]  
335  
336  [[Resource(1305)]]  
337  
338  [[Resource(450)]] 