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ACUTE—Assembly for Computational Electronics

by Dragica Vasileska, Gerhard Klimeck, Xufeng Wang, Stephen M. Goodnick, Margaret Shepard Morris, Michael Anderson, Philathia Rufaro Bolton, Cristina Leal Gonzalez, Craig Titus, Jamie E Hickner

Version 57
by Michael Anderson
Version 64
by Michael Anderson

Deletions or items before changed

Additions or items after changed

1 [[Image(picture_11.png, 700px, class=align-center)]]
2
3 This nanoHUB "topic page" provides an easy access to selected nanoHUB educational material on computational electronics that is openly accessible.
4
5 We invite users to participate in this open source, interactive educational initiative:
6
7 * [http://www.nanohub.org/contribute/Contribute content] by uploading it to the nanoHUB. (See "Contribute Content") on the nanoHUB mainpage.
8 * Provide feedback for the items you use on the nanoHUB through the review system. (Please be explicit and provide constructive feedback.)
9 * Let us know when things do not work by filing a ticket through the nanoHUB "Help" feature on every page.
10 * Finally, let us know what you are doing and [http://www.nanohub.org/feedback/suggestions/your suggestions] improving the nanoHUB by using the "Feedback" section, which you can find under "[http://www.nanohub.org/support/ Support]"
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12 Thank you for using the nanoHUB, and be sure to [http://www.nanohub.org/feedback/success_story/share your nanoHUB success stories] with us. We like to hear from you, and our sponsors need to know that the nanoHUB is having impact.
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14 [[Div(start, class=clear)]][[Div(end)]]
15
16 The purpose of the ACUTE tool-based curriculum is to introduce interested scientists from academia and industry to the advanced methods of simulation needed for the proper modeling of state-of-the-art 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.
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18 [[Image(intro1.png, 250px, class=align-left)]]
19 [[Image(intro2.png, 250px, class=align-left)]]
20 -
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21 ACUTE begins with a discussion of the energy band structure that enters as an input to any device simulator. The next section offers a discussion of simulators that involve the drift-diffusion model, and then simulations that involve hydrodynamic and energy-balance transport, and conclude the semi-classical transport modeling with application of particle-based device simulation methods.
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23 After the study and utilization of the semiclassical simulation tools and their applications, the next step includes quantum corrections into the classical simulators. The final set of tools is dedicated to the far-from equilibrium transport, where the concept of pure and mixed states and the distribution function is introduced. Several tools that utilize different methods will be used for that purpose, such as tools that use the recursive Green’s-function method and its variant, the Usuki method, as well as the Contact Block Reduction tool, as the most efficient and complete way of solving the quantum-transport problem because this method allows users to simultaneously calculate source-drain 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 quasi one-dimensional in nature for transport through a device). A table that shows the advantages and the limitation of various semi-classical and quantum-transport simulation tools is presented below.
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25 -
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26 +
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27
28 More details on the actual tool design and information on commercial tool usage can be found on the web pages:
29
30 [[Resource(4921)]]
31
32 [[Resource(5092)]]
33
34
35 == Energy Bands and Effective Masses ==
36
37 === [/tools/acute/ Piecewise Constant Potential Barrier Tool in ACUTE]– Open Systems ===
38 [[Image(pcpbt.png, 200px, class=align-left)]]
39 The [/tools/acute/ Piecewise Constant Potential Barrier Tool in ACUTE] allows users to calculate the transmission and the reflection coefficient of arbitrary five, seven, nine, eleven and 2n-segment piecewise constant potential energy profile. For the case of a multi-well structure, it also calculates the quasi-bound states. Thus the Piecewise Constant Potential Tool can be used as a simple demonstration tool for the formation of energy bands.
40
41 Other uses include: 1) in the case of stationary perturbation theory, as an exercise to test the validity of the first-order and the second-order correction to the ground state energy of the system due to small perturbations of the confining potential, and 2) as a test of the validity of the Wentzel–Kramers–Brillouin (WKB) approximation for triangular potential barriers.
42
43 Exercises:
44
45 * [[Resource(4831)]]
46
47 * [[Resource(4833)]]
48
49 * [[Resource(4853)]]
50
51 * [[Resource(4873)]]
52
53 * [[Resource(5319)]]
54
55 * [[Resource(4849)]]
56
57 * [[Resource(5102)]]
58
59 * [[Resource(5130)]]
60
61 [[Div(start, class=clear)]][[Div(end)]]
62
63 === [/tools/acute/ Periodic Potential Lab in ACUTE] ===
64 [[Image(ppl.png, 250px, class=align-left)]]
65
66 The [/tools/acute/ Periodic Potential Lab in ACUTE] solves the time-independent Schrödinger Equation in a one-dimensional 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 as well as an expanded zone, and compare the results against a simple effective-mass parabolic band. Transmission is also calculated. This lab also allows students to become familiar with the reduced-zone and expanded-zone representation of the dispersion relation (i. e. the E-k relation for carriers).
67
68 Exercises:
69
70 * [[Resource(4851)]]
71
72 [[Div(start, class=clear)]][[Div(end)]]
73
74
75 === [/tools/acute/ Band Structure Lab in ACUTE] ===
76 [[Image(bsl.png, 250px, class=align-left)]]
77
78 In solid-state 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/ Band Structure Lab in ACUTE] enables the study of bulk dispersion relationships of silicon (Si), gallium arsenide (GaAs), and indium arsenide (InAs). Plotting the full dispersion relation of different materials, students first get familiar with a band structure of direct bandgap (gallium arsenide and indium arsenide) and indirect band-gap semiconductors (silicon). In the case of multiple conduction band valleys, the user has first to determine the Miller indices of one of the equivalent valleys and then from that information it immediately follows, e. g., how many equivalent conduction bands one has in silicon and germanium (Ge).
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80 In advanced applications, the users can apply tensile and compressive strain and observe the variation in the band structure, bandgaps, and effective masses. Advanced users can also study band-structure effects in ultra-scaled (thin body) quantum wells, and nanowires of different cross sections. Band Structure Lab uses the ''sp3s*d5'' tight binding method to compute dispersion (E-k) for bulk, planar, and nanowire semiconductors.
81
82 Exercises:
83
84 * [[Resource(5201)]]
85
86 * [[Resource(5031)]]
87
88 * [[Resource(4890)]]
89
90 * [[Resource(4880)]]
91
92
93 [[Div(start, class=clear)]][[Div(end)]]
94
95
96 ==Drift-Diffusion and Energy Balance Simulations==
97
98
99 === [/tools/acute/ PADRE Tool in ACUTE]—Modeling of silicon-based devices===
100 [[Image(padre.png, 250px, class=align-left)]]
101
102 [/tools/acute/ PADRE Tool in ACUTE] is a two-dimensional/three-dimensional simulator for electronic devices, such as MOSFET transistors.
103
104 PADRE Tool in ACUTE is a 2D/3D simulator for electronic devices, such as MOSFETs. With PADRE, users can simulate physical structures of arbitrary geometry--including heterostructures--with arbitrary doping profiles, which can be obtained using analytical functions or directly from such multidimentional process simulators as Prophet
105 For each electrical bias, [/tools/acute/ PADRE Tool in ACUTE] solves coupled sets of partial differential equations (PDEs). The variety of PDE systems supported in PADRE form a hierarchy of accuracy: 1) electrostatic (Poisson equations), 2) drift-diffusion, including carrier continuity equations, 3) energy balance, including carrier temperature, and 4) electrothermal, including lattice heating.
106
107 Listed below are tools, exercises, and sets of problems that utilize the [/tools/acute/ PADRE Tool in ACUTE]:
108
109 * [[Resource(229)]]
110
111 * [[Resource(4894)]]
112
113 * [[Resource(4896)]]
114
115 * [[Resource(452)]]
116
117 * [[Resource(4906)]]
118
119 * [[Resource(3984)]]
120
121 * [[Resource(5051)]]
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123 Supplemental documentation:
124
125 * [/site/resources/tools/padre/doc/index.html User Manual]
126
127 * [/site/resources/2006/06/01581/intro_dd_padre_word.pdf Abbreviated First Time User Guide]
128
129 A set of course notes on computational electronics with detailed explanations on band structure, pseudopotentials, numerical issues, and drift diffusion is also available.
130
131 * [[Resource(1516)]]
132
133 * [[Resource(980)]]
134
135
136 ===SILVACO Simulator—Modeling of Silicon-Based and III-V Devices===
137
138 In preparation.
139
140
141 == Particle-Based Simulators ==
142
143 === [/tools/acute/ Bulk Monte Carlo Lab in ACUTE] ===
144 [[Image(scattering.png, 250px class=align-left)]]
145 [[Image(mc.png, 250px, class=align-right)]]
146
147 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 (silicon and germanium) and III-V (gallium arsenide, silicon carbide and gallium nitride) materials. All relevant scattering mechanisms for the materials being considered have been included in the model.
148
149 Detailed derivation of the scattering rates for most of the scattering mechanisms included in the model can be found on Prof. Vasileska personal web-site (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
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151 [[Resource(4843)]]
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153 An A/V presentation is also available:
154
155 [[Resource(4439)]]
156
157 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:
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159 [[Resource(4845)]]
160
161 Exercises:
162
163 * [[Resource(5047)]]
164
165 * [[Resource(5277)]]
166
167 * [[Resource(5275)]]
168
169 * [[Resource(5321)]]
170
171 * [[Resource(5323)]]
172
173
174 === [/tools/acute/ Quamc2D Lab in ACUTE] ===
175 [[Image(quamc2d1.png, 250px, class=align-left)]] [[Image(quamc2d2.png, 250px, class=align-left)]]
176
177 [/tools/acute/ Quamc2D Lab in ACUTE]
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179 QuaMC 2D (pronounced "quam-see") is a quasi three-dimensional quantum-corrected semi-classical Monte-Carlo transport simulator for conventional and non-conventional MOSFET devices.
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181 A parameter-free quantum field approach has been developed and utilized quite successfully in order to capture the size-quantization 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 self-consistent event-biasing schemes for statistical enhancement in the Monte-Carlo 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 realized in the program using the Herring-Vogt transformation. Intravalley scattering is limited to acoustic phonons. For the intervalley scattering, both g- and f-phonon processes have been included.
182
183 * [[Resource(4520)]]
184
185 * [[Resource(4543)]]
186
187 * [[Resource(4443)]]
188
189 * [[Resource(4439)]]
190
191 * [[Resource(5127)]]
192
193 Exercises:
194
195 ===Thermal Particle-Based Device Simulator===
196
197 In preparation.
198
199 Exercises and Other Resources:
200
201 * [[Resource(5350)]]
202
203
204 ==Inclusion of Quantum Corrections in Semiclassical Simulation Tools==
205
206
207 === [/tools/acute/ Schred in ACUTE] ===
208 [[Image(schred.png, 250px, class=align-left)]]
209 [/tools/acute/ Schred in ACUTE] calculates the envelope wavefunctions and the corresponding bound-state energies in a typical MOS (Metal-Oxide-Semiconductor) or SOS (Semiconductor-Oxide- Semiconductor) structure and a typical SOI structure by solving self-consistently the one-dimensional Poisson and Schrödinger equations.
210
211 To better understand the operation of [/tools/acute/ Schred in ACUTE] and the physics of MOS capacitors please refer to:
212
213 * [[Resource(4794)]]
214
215 * [[Resource(4796)]]
216
217 * [[Resource(5087)]]
218
219 * [[Resource(5127)]]
220
221 Exercises:
222
223 * [[Resource(4900)]]
224
225 * [[Resource(4902)]]
226
227 * [[Resource(4904)]]
228
229
230 === [/tools/acute/ 1D Heterostructure Tool in ACUTE] ===
231 [[Image(1dhet1.png, 180px, class=align-left)]] [[Image(1dhet2.png, 180px, class=align-left)]]
232
233 The [/tools/acute/ 1D Heterostructure Tool in ACUTE] simulates the confined states in one-dimentional heterostructures by self-consistently calculating their charge based on a quantum-mechanical description of the one-dimensional device. Increased interest in high electron mobility transistors (HEMTs) is due to the eventual limitations reached by scaling conventional transistors. The 1D Heterostructure Tool in ACUTE is a very valuable tool for the design of HEMTs because the user can determine such components as the position and the magnitude of the delta-doped layer, the thickness of the barrier, and the spacer layer, for which the user can maximize the amount of free carriers in the channel, which, in turn, leads to a larger drive current.
234
235 Exercises:
236
237 * [[Resource(5231)]]
238
239 * [[Resource(5233)]]
240
241
242 The most commonly used semiconductor devices for applications in the GHz range now are gallium arsenide 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 compared to MESFETs is a higher power density (by a factor of two to three), which leads to a significantly smaller chip size.
243
244 HEMTs are field-effect transistors wherein the flow of the current between two ohmic contacts, known as the source and the drain, is controlled by a third contact, the gate. Such gates are usually Schottky contacts. In contrast to ion-implanted MESFETs, HEMTs are based on epitaxial layers with different band gaps.
245
246
247 ==Quantum Transport==
248
249
250 === Recursive Green's Function Method for Modeling RTD's===
251
252 in preparation.
253
254
255 === [/tools/acute/ nanoMOS in ACUTE] ===
256 [[Image(nanomos.png, 250px, class=align-left)]]
257
258 [/tools/acute/ nanoMOS in ACUTE] is a two-dimensional simulator for thin body (less than 5 nm), fully depleted, double-gated n-MOSFETs. Five transport models is available (drift-diffusion, 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 self-consistently with Poisson's equation. Several internal quantities such as subband profiles, subband areal electron densities, potential profiles, and current-voltage (I/V) information can be obtained from the source code.
259
260 [[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:
261
262 * [[Resource(2845)]]
263
264 * [[Resource(1533)]]
265
266
267 ===CBR===
268
269 in preparation.
270
271
272 ==Atomistic Modeling==
273
274
275 === [/tools/acute/ NEMO3D in ACUTE] ===
276 [[Image(modeling_agenda5.gif, 250px, class=align-left)]] [[Image(qdot.png, 250px, class=align-left)]]
277
278 [/tools/acute/ NEMO3D in ACUTE] calculates eigenstates in (almost) arbitrarily shaped semiconductor structures in the typical column IV and III-V 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 Keating-like potentials.
279
280 Users of [/tools/acute/ NEMO3D in ACUTE] can analyze quantum dots, alloyed quantum dots, long-range strain effects on quantum dots, the effects of wetting layers, piezo-electric effects in quantum dots, quantum-dot nuclear-spin interaction, quantum-dot phonon spectra, coupled quantum-dot systems, miscut silicon quantum wells with silicon-germanium alloy buffers, core-shell nanowires, alloyed nanowires, phosphorous impurities in silicon (P:Si qubits), and buck alloys.
281
282 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 post-processing approach based on the NEMO 3D single particle states.
283
284 Exercises:
285
286 * [[Resource(450)]]
287
288 * [[Resource(2925)]]
289
290 == Collection of tools that comprise ACUTE ==
291
292 [[Resource(4826)]]
293
294 [[Resource(3847)]]
295
296 [[Resource(1308)]]
297
298 [[Resource(941)]]
299
300 [[Resource(4438)]]
301
302 [[Resource(1092)]]
303
304 [[Resource(221)]]
305
306 [[Resource(5203)]]
307
308 [[Resource(1305)]]
309
310 [[Resource(450)]]

nanoHUB.org, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.