ACUTE—Assembly for Computational Electronics
 Version 14
 by Dragica Vasileska
 Version 15
 by Dragica Vasileska
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2  
3  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.  
4  
5  [[Image(intro1.png, 250 class=alignleft)]]  
6  [[Div(start, class=clear)]][[Div(end)]]  
7  
8  Relationship between various transport regimes and significant lengthscales.  
9  
10  [[Image(intro2.png, 250 class=alignleft)]]  
11  [[Div(start, class=clear)]][[Div(end)]]  
12  
13  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.  
14  
15  [[Image(intro3.png, 250 class=alignleft)]]  
16  [[Div(start, class=clear)]][[Div(end)]]  
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  
21  == Energy Bands and Effective Masses ==  
22  
23  === PieceWise Constant Potential Barrier Tool – Open Systems ===  
24  
25  The [[Resource(4826)]] 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.  
26  
27  [[Image(pcpbt.png, 200 class=alignleft)]]  
28  [[Div(start, class=clear)]][[Div(end)]]  
29  
30  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.  
31  
32  [[Div(start, class=clear)]][[Div(end)]]  
33  
34  Exercises:  
35  
36  [[Div(start, class=clear)]][[Div(end)]]  
37  
38  * [[Resource(4831)]]  
39  
40  * [[Resource(4833)]]  
41  
42  * [[Resource(4853)]]  
43  
44  * [[Resource(4873)]]  
45  
46  * More on the energy bands formation: Cosine bands  
47  
48  * [[Resource(4849)]]  
49  
50  * [[Resource(5102)]]  
51  
52  * [[Resource(5130)]]  
53  
54  [[Div(start, class=clear)]][[Div(end)]]  
55  
56  
57  === Periodic Potential Lab ===  
58  
59  The [[Resource(3847)]] 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,  
60  
61  [[Image(ppl.png, 250 class=alignleft)]]  
62  [[Div(start, class=clear)]][[Div(end)]]  
63  
64  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).  
65  
66  Exercises:  
67  
68  * [[Resource(4851)]]  
69  
70  [[Div(start, class=clear)]][[Div(end)]]  
71  
72  
73  === Bandstructure Lab ===  
74  
75  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 [[Resource(1308)]] 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.  
76  
77  [[Image(bsl.png, 250 class=alignleft)]]  
78  [[Div(start, class=clear)]][[Div(end)]]  
79  
80  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.  
81  
82  Exercises:  
83  
84  * [[Resource(5201)]]  
85  
86  [[Div(start, class=clear)]][[Div(end)]]  
87  
88  
89  ==DriftDiffusion and Energy Balance Simulations==  
90  
91  
92  ===PADRE Simulator – Modeling of Sibased devices===  
93  
94  PADRE is a 2D/3D simulator for electronic devices, such as MOSFET transistors.  
95  
96  [[Image(padre.png, 250 class=alignleft)]]  
97  [[Div(start, class=clear)]][[Div(end)]]  
98  
99  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.  
100  For each electrical bias, PADRE 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).  
101  
102  Several example problems that utilize Padre are given below:  
103  
104  * [[Resource(229)]]  
105  
106  * [[Resource(4894)]]  
107  
108  * [[Resource(4896)]]  
109  
110  * [[Resource(452)]]  
111  
112  * [[Resource(4906)]]  
113  
114  * [[Resource(3984)]]  
115  
116  * [[Resource(5051)]]  
117  
118  A variety of supplemental documents are available that deal with the PADRE software and TCAD simulation:  
119  
120  * [[Resource(??)]]  
121  
122  * Abbreviated First Time User Guide  
123  
124  
125  A set of course notes on Computational Electronics with detailed explanations on bandstructure, pseudopotentials, numerical issues, and drift diffusion is also available.  
126  
127  * [[Resource(1516)]]  
128  
129  * [[Resource(980)]]  
130  
131  
132  ===SILVACO Simulator – Modeling of Sibased and IIIV devices===  
133  
134  In preparation.  
135  
136  
137  
138  == ParticleBased Simulators ==  
139  
140  
141  ===Bulk Monte Carlo Code===  
142  
143  The Bulk Monte Carlo Tool 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. 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  
144  
145  [[Resource(4843)]]  
146  
147  Available also is a voiced presentation  
148  
149  [[Resource(4439)]]  
150  
151  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:  
152  
153  [[Resource(4845)]]  
154  
155  Exercises:  
156  
157  * [[Resource(5047)]]  
158  
159  
160  ===QUAMC 2D – ParticleBased Device Simulator===  
161  
162  QuaMC (pronunciation: quamsee) 2D is effectively a quasi threedimensional quantumcorrected semiclassical Monte Carlo transport simulator for conventional and nonconventional MOSFET devices.  
163  
164  [[Image(quamc2d1.png, 250 class=alignleft)]]  
165  [[Div(start, class=clear)]][[Div(end)]]  
166  
167  Device structures that can be simulated.  
168  
169  [[Image(quamc2d2.png, 250 class=alignleft)]]  
170  [[Div(start, class=clear)]][[Div(end)]]  
171  
172  Phenomena that can be explained  
173  
174  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.  
175  
176  * [[Resource(4520)]]  
177  
178  * [[Resource(4543)]]  
179  
180  * [[Resource(4443)]]  
181  
182  * [[Resource(4439)]]  
183  
184  * [[Resource(5127)]]  
185  
186  Exercises:  
187  
188  
189  ===Thermal ParticleBased Device Simulator===  
190  
191  In preparation.  
192  
193  
194  
195  ==Inclusion of Quantum Corrections into SemiClassical Simulation Tools==  
196  
197  
198  ===Schred===  
199  
200  Schred 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.  
201  +  
202  +  [[Image(schred.png, 250 class=alignleft)]]


203  +  [[Div(start, class=clear)]][[Div(end)]]


204  +  
205  +  To better understand the operation of SCHRED tool and the physics of MOS capacitors please refer to:


206  
207  * [[Resource(4794)]]  
208  
209  * [[Resource(4796)]]  
210    
211    To better understand the operation of SCHRED tool and the physics of MOS capacitors please refer to:


212  
213  * [[Resource(5087)]]  
214  
215  * [[Resource(5127)]]  
216  
217  Exercises:  
218  
219  * [[Resource(4900)]]  
220  
221  * [[Resource(4902)]]  
222  
223  * [[Resource(4904)]]  
224  
225  
226  === 1D Heterostructure Tool ===  
227  
228  The [[Resource(5203)]] 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 [[Resource(5203)]] 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.  
229  
230  [[Div(start, class=clear)]][[Div(end)]]  
231  
232  [[Image(1dhet1.png, 120 class=alignleft)]]  
233  [[Image(1dhet2.png, 120 class=alignleft)]]  
234  
235  [[Div(start, class=clear)]][[Div(end)]]  
236  
237  Exercises:  
238  
239  * [[Resource(5231)]]  
240  
241  * [[Resource(5233)]]  
242  
243  
244  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.  
245  
246  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.  
247  
248  
249  
250  ==Quantum Transport==  
251  
252  
253  === Recursive Green's Function Method for Modeling RTD's===  
254  
255  in preparation.  
256  
257  
258  ===nanoMOS===  
259  
260  [[Resource(1305)]] 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. [[Resource(1305)]] 3.0 includes an improved treatment of carrier scattering. Some important information about NanoMOS 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  
273  ==Atomistic Modeling==  
274  
275  
276  ===NEMO3D===  
277  NEMO 3D 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.  
278  NEMO3D 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. 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.  
279  
280  Exercises:  
281  
282  * [[Resource(450)]  
283  
284  * [[Resource(2925)]] 