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ABACUS—Introduction to Semiconductor Devices

by Gerhard Klimeck, Dragica Vasileska

Version 58
by Lynn Zentner
Version 61
by Shawn Rice

Deletions or items before changed

Additions or items after changed

1 [[Image(abacus_ps_comp_2.gif, 600)]]
2
3 When we hear the term ''semiconductor device'', we may think first of the transistors in PCs or video game consoles, but transistors are the basic component in all of the electronic devices we use in our daily lives. Electronic systems are built from such components as transistors, capacitors, wires, light-emitting diodes and semiconductor lasers. These components are typically integrated into a single chip made of a semiconductor material.
4
5 Almost every college or university department of Electrical Engineering offers instruction in the fundamental concepts of semiconductor devices. These concepts typically include lattices, crystal structure, bandstructure, band models, carrier distributions, drift, diffusion, pn junctions, solar cells, light-emitting diodes, bipolar junction transistors (BJT), metal-oxide semiconductor capacitors (MOS-caps), and multi-acronym-device field-effect transistors (mad-FETs).
6
7 Advanced courses go more deeply into semiconductor theory, device physics, fabrication processes, as well as advanced and special purpose devices, such as heterostructure devices, power devices, and optoelectronic devices.
8
9 This nanoHUB "topic page" provides an easy access to selected nanoHUB educational material on semiconductor devices that is openly accessible.
10
11 We invite users to participate in this open source, interactive educational initiative:
12
13 -
*[/contribute/ Contribute content] by uploading it to the nanoHUB. (See "Contribute Content") on the nanoHUB mainpage.
+
*[/contribute/ Contribute content] by uploading it to the nanoHUB. (See "Upload your own content") on the nanoHUB mainpage.
14 * Provide feedback for the items you use on the nanoHUB through the review system. (Please be explicit and provide constructive feedback.)
15 * Let us know when things do not work by filing a ticket through the nanoHUB "Help" feature on every page.
16 -
* Finally, let us know what you are doing and[/feedback/suggestions/ submit your suggestions] for improving the nanoHUB by using the "Feedback" section, which you can find under "[/support/ Support]"
+
* If you have suggestions for improvements, [/wishlist/ submit a wish].
17
18 Thank you for using the nanoHUB, and be sure to [/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.
19
20 == Crystal Structures, Lattices ==
21
22 === [/tools/abacus Crystal Viewer] ===
23 -
[[Image(/site/resources/tools/crystal_viewer/buckyball.jpg, 120, class=align-right)]] [[Image(/site/resources/tools/crystal_viewer/si.jpg, 120, class=align-right)]] [[Image(/site/resources/tools/crystal_viewer/fcc.jpg, 120, class=align-right)]] [[Image(/site/resources/tools/crystal_viewer/bcc.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/crystal_viewer/buckyball.jpg, 120, right)]] [[Image(/site/resources/tools/crystal_viewer/si.jpg, 120, right)]] [[Image(/site/resources/tools/crystal_viewer/fcc.jpg, 120, right)]] [[Image(/site/resources/tools/crystal_viewer/bcc.jpg, 120, right)]]
24
25 The [/resources/5065 Crystal Viewer in ABACUS] enables the interactive visualization different Bravais lattices, crystal planes, and materials (diamond, silicon, indium arsenide, gallium arsenide, graphene, and buckyball).
26
27 First time use of the tool is supported by:
28 [[Resource(6788)]]
29
30 It is supported by a homework assignment in
31 [/site/resources/2008/01/03815/crystal_hw1.doc MS Word] and [/site/resources/2008/01/03816/crystal_hw1.pdf Adobe PDF] format.
32
33 [[Resource(5144)]]
34
35 [/topics/CrystalViewerPage Crystal Viewer Tool Learning Materials] - Comprehensive set of learning materials for the Crystal Viewer Tool.
36
37
38
39 == Band Models / Band Structure ==
40
41 === [/tools/abacus Piecewise Constant Potential Barriers Lab] ===
42
43 -
[[Image(/site/resources/2008/06/04826/801/B_T_O_04eV_2_6nm_931pix.gif, 120, class=align-right)]] [[Image(/site/resources/2008/06/04826/801/B_T_O_04eV_2_10nm_931pix.gif, 120, class=align-right)]] [[Image(/site/resources/2008/06/04826/801/B_T_O_011eV_2_6nm_933pix.gif, 120, class=align-right)]]
+
[[Image(/site/resources/2008/06/04826/801/B_T_O_04eV_2_6nm_931pix.gif, 120, right)]] [[Image(/site/resources/2008/06/04826/801/B_T_O_04eV_2_10nm_931pix.gif, 120, right)]] [[Image(/site/resources/2008/06/04826/801/B_T_O_011eV_2_6nm_933pix.gif, 120, right)]]
44
45 This tool computes the transmission and the reflection coefficient of a five, seven, nine, eleven and 2n-segment piecewise constant potential energy profile. It enables the rapid visualization of the formation of band structures in a finite superlattice.
46
47 First time use of the tool is supported by:
48 [[Resource(6794)]]
49
50 The materials below provide a detailed description of the physics required both to use this tool correctly and to interpret the results obtained:
51
52 * [/resources/4827 Open Systems]
53 * [/resources/4829 Double-Barrier Case Explained]
54
55 Exercises that illustrate the importance of quantum-mechanical reflections in state-of-the-art devices and the resonance width dependence upon the geometry in the double-barrier structure that is integral part of resonant tunneling diodes are given below:
56
57 * [/resources/4831 Quantum-Mechanical Reflections]
58 * [/resources/4849 Quantum-Mechanical Reflections in Nanodevices]
59 * [/resources/4833 Double-Barrier Structure]
60
61 The following assignments help to illustrate the formation of bands in periodic potentials and how the width and number of the energy bands changes by varying the geometry of the n-well potential:
62
63 * [/resources/4853 From one well, to two wells, to five wells, to periodic potentials]
64 * [/resources/4873 Bands as a function of the geometry of the n-well potential]
65
66 One can also use this tool to calculate the transmission coefficient through barriers that are approximated with Piece-Wise constant segments.
67
68 [/topics/PCPBTPage Piece-Wise Constant Potential Barriers Tool Learning Materials] - Comprehensive set of learning materials for the Piece-Wise Constant Potential Barriers Tool.
69
70
71
72 === [/tools/abacus Periodic Potential Lab] ===
73 -
[[Image(/site/resources/tools/kronig_penney/stepwell_ek_with_effmass_ek.png, 120, class=align-right)]] [[Image(/site/resources/tools/kronig_penney/expanded_ek_free_electron_ek_stepwell.png, 120, class=align-right)]] [[Image(/site/resources/tools/kronig_penney/stepwell_functional_with_energy.png, 120, class=align-right)]] [[Image(/site/resources/tools/kronig_penney/allowed_bands_step_well.png, 120, class=align-right)]]
+
[[Image(/site/resources/tools/kronig_penney/stepwell_ek_with_effmass_ek.png, 120, right)]] [[Image(/site/resources/tools/kronig_penney/expanded_ek_free_electron_ek_stepwell.png, 120, right)]] [[Image(/site/resources/tools/kronig_penney/stepwell_functional_with_energy.png, 120, right)]] [[Image(/site/resources/tools/kronig_penney/allowed_bands_step_well.png, 120, right)]]
74
75 The [/resources/5065 Periodic Potential Lab in ABACUS] solves the time independent Schrödinger Equation in a one-dimentional 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, and compare the results against a simple effective-mass parabolic band. Transmission is also calculated through the well for the given energy range.
76
77 Exercises:
78
79 * [[Resource(4851)]]
80
81 [/topics/PPLPage Periodic Potential Lab Learning Materials] - Comprehensive set of learning materials for the Periodic Potential Lab.
82
83
84 [[Div(start, class=clear)]][[Div(end)]]
85
86 === [/tools/abacus Band Structure Lab] ===
87 -
[[Image(/site/resources/tools/bandstrlab/bandstrlab.gif, 120, class=align-right)]] [[Image(/site/resources/tools/bandstrlab/composite1.jpg, 120, class=align-right)]] [[Image(/site/resources/tools/bandstrlab/composite2.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/bandstrlab/bandstrlab.gif, 120, right)]] [[Image(/site/resources/tools/bandstrlab/composite1.jpg, 120, right)]] [[Image(/site/resources/tools/bandstrlab/composite2.jpg, 120, right)]]
88
89 The [/tools/abacus Band Structure Lab in ABACUS] enables the study of bulk dispersion relationships of silicon, gallium arsenide, and indium arsenide. The users can apply tensile and compressive strain and observe the variation in the band structure, bandgaps, and effective masses. Advanced users can 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 E(k) for bulk, planar, and nanowire semiconductors.
90
91 Exercises:
92 * [[Resource(5201)]]
93 * [[Resource(5031)]]
94 * [[Resource(4890)]]
95 * [[Resource(4880)]]
96
97 [/topics/BSLPage Band Structure Lab Learning Materials] - Comprehensive set of learning materials for the Band Structure Lab.
98
99
100 [[Div(start, class=clear)]][[Div(end)]]
101
102
103 == Bulk Semiconductors ==
104
105 === [/tools/abacus Carrier Statistics Lab] ===
106 -
[[Image(/site/resources/tools/fermi/cd_carrierdensity.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/fermi/cd_carrierdensity.jpg, 120, right)]]
107 -
[[Image(/site/resources/tools/fermi/cd_fermi1.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/fermi/cd_fermi1.jpg, 120, right)]]
108
109 The [/tools/abacus Carrier Statistics Lab in ABACUS] demonstrates electron and hole-density distributions based on the Fermi-Dirac and Maxwell-Boltzmann equations. This tool shows the dependence of carrier density, density of states and occupation factor on temperature and fermi level. The user can choose between doped and undoped semi-conductors. silicon, germanium, and gallium arsenide can be studied as a function of doping or Fermi level, and temperature. The Carrier Statistics Lab is supported by a [/resources/3878/ homework assignment] in which students are asked to explore the differences between Fermi-Dirac and Maxwell-Boltzmann distributions, compute electron and hole concentrations, study temperature dependences, and the phenomenon of freeze-out.
110
111 First time use of the tool is supported by:
112 [[Resource(6443)]]
113
114 Exercises:
115
116 * [[Resource(5146)]]
117 * [[Resource(4892)]]
118 * [[Resource(5197)]]
119
120 [/topics/CarrierStatisticsPage Carrier Statistics Lab Learning Materials] - Comprehensive set of learning materials for the Carrier Statistics Lab.
121
122
123 === [/tools/abacus Drift Diffusion Lab] ===
124 -
[[Image(/site/resources/tools/semi/excess_carrier_intrinsic_slab_bias.png, 120, class=align-right)]] [[Image(/site/resources/tools/semi/excess_carrier_profile_light_left.png, 120, class=align-right)]] [[Image(/site/resources/tools/semi/excess_carrier_profile_light_top.png, 120, class=align-right)]]
+
[[Image(/site/resources/tools/semi/excess_carrier_intrinsic_slab_bias.png, 120, right)]] [[Image(/site/resources/tools/semi/excess_carrier_profile_light_left.png, 120, right)]] [[Image(/site/resources/tools/semi/excess_carrier_profile_light_top.png, 120, right)]]
125
126 The [/resources/5065 Drift Diffusion Lab in ABACUS] enables users to understand the basic concepts of the drift and diffusion of carriers inside a semiconductor slab using different kinds of experiments. Experiments like shining light onto the semiconductor, applying bias, as well as both processes simultaneously, can be performed. This tool provides important information about carrier densities, transient and steady state currents, Fermi-levels and electrostatic potentials. It is supported by two related homework assignments [/resources/4191/ #1] and [/resources/4188/ #2] in which students are asked to explore the concepts of drift, diffusion, quasi Fermi-levels, and the response to light.
127
128 Exercises:
129 * [[Resource(5181)]]
130
131 [/topics/DriftDiffusionPage Drift-Diffusion Lab Learning Materials] - Comprehensive set of learning materials for the Drift-Diffusion Lab.
132
133
134 == PN Junctions ==
135
136 === [/tools/abacus/ PN Junction Lab] ===
137
138 -
[[Image(/site/resources/tools/pntoy/pntoy3.gif, 120, class=align-right)]] [[Image(/site/resources/tools/pntoy/pntoy2.gif, 120, class=align-right)]] [[Image(/site/resources/tools/pntoy/pntoy1.gif, 120, class=align-right)]] [[Image(/site/resources/tools/pntoy/pnjunction.gif, 120, class=align-right)]]
+
[[Image(/site/resources/tools/pntoy/pntoy3.gif, 120, right)]] [[Image(/site/resources/tools/pntoy/pntoy2.gif, 120, right)]] [[Image(/site/resources/tools/pntoy/pntoy1.gif, 120, right)]] [[Image(/site/resources/tools/pntoy/pnjunction.gif, 120, right)]]
139
140 [/tools/abacus/ PN-Junction Lab in ABACUS] is everything users need to explore and teach the basic concepts of P-N junction devices. Edit the doping concentrations, change the materials, tweak minority-carrier lifetimes, and modify the ambient temperature. Then, see the effects in the energy band diagram, carrier densities, net charge distribution, current-voltage (I/V) characteristic, and other phenomena.
141
142 There is a significant set of associated resources available for this tool.
143 * a [/site/resources/tools/pntoy/pnjunction.swf demo of this tool]
144 * a [/resources/980/ Primer on Semiconductor Device Simulation].
145 * a Learning Module entitled [/resources/68/ PN Junction Theory and Modeling] that walks students through the PN-junction theory and let's them verify concepts through on-line simulation.
146 * Homework assignment on the [/resources/893/ depletion approximation (on the undergraduate level)]
147 * Homework assignment on the [/resources/932/ depletion approximation (at the graduate level)]
148
149 Exercises:
150
151 * [[Resource(4894)]]
152 * [[Resource(4896)]]
153 * [[Resource(4898)]]
154 * [[Resource(5177)]]
155 * [[Resource(5179)]]
156 * [[Resource(5183)]]
157
158 [/topics/PNDiode PN Junction Lab Learning Materials] - Comprehensive set of learning materials for the PN Junction Lab.
159
160
161 [[Div(start, class=clear)]][[Div(end)]]
162
163 == Bipolar Junction Transistors (BJT) ==
164
165 === [/tools/abacus/ Bipolar Junction Lab] ===
166
167 -
[[Image(/site/resources/tools/bjt/3npn_gummel.gif, 120, class=align-right)]] [[Image(/site/resources/tools/bjt/1npn_input.jpg, 120, class=align-right)]] [[Image(/site/resources/tools/bjt/2npn_output.gif, 120, class=align-right)]]
+
[[Image(/site/resources/tools/bjt/3npn_gummel.gif, 120, right)]] [[Image(/site/resources/tools/bjt/1npn_input.jpg, 120, right)]] [[Image(/site/resources/tools/bjt/2npn_output.gif, 120, right)]]
168
169 The [/tools/abacus/ Bipolar Junction Lab in ABACUS] allows Bipolar Junction Transistor (BJT) simulation using a 2D mesh. It allows users to simulate either the npn- or pnp-type of device. Users can specify the emitter, base and collector region depths and doping densities. Also the material and minority-carrier lifetimes can be specified by the user. The tool is supported by a [/resources/4185/ homework assignment] in which students are asked to find the emitter efficiency, the base transport factor, current gains, and the Early voltage. Also, students are requested to provide a qualitative discussion.
170
171 [[Div(start, class=clear)]][[Div(end)]]
172
173 Exercises:
174
175 * [[Resource(5199)]]
176 * [[Resource(5193)]]
177 * [[Resource(5083)]]
178
179 [/topics/BJTLabPage BJT Lab Learning Materials] - Comprehensive set of learning materials for the BJT Lab.
180
181
182 == MOS Capacitors ==
183
184 === [/tools/abacus/ MOScap] ===
185
186 -
[[Image(/site/resources/tools/moscap/moscap2.gif, 120, class=align-right)]] [[Image(/site/resources/tools/moscap/moscap3.gif, 120, class=align-right)]] [[Image(/site/resources/tools/moscap/moscap.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/moscap/moscap2.gif, 120, right)]] [[Image(/site/resources/tools/moscap/moscap3.gif, 120, right)]] [[Image(/site/resources/tools/moscap/moscap.jpg, 120, right)]]
187
188 The [/tools/abacus/ MOScap Tool in ABACUS] enables a semi-classical analysis of metal-oxide-semionductor (MOS) capacitors. It simulates the capacitance of bulk- and dual-gate capacitors for a variety of different device sizes, geometries, temperature, and doping profiles.
189
190 First time use of the tool is supported by:
191 [[Resource(6546)]]
192
193 Exercises:
194
195 * [[Resource(4855)]]
196 * [[Resource(5185)]]
197 * [[Resource(5187)]]
198 * [[Resource(5189)]]
199 * [[Resource(5087)]]
200
201 [/topics/MOSCAPPage MOSCap Learning Materials] - Comprehensive set of learning materials for the MOSCap Tool.
202
203
204 [[Div(start, class=clear)]][[Div(end)]]
205
206 == MOSFETs ==
207
208 === [/tools/abacus/ MOSfet Lab] ===
209
210 -
[[Image(/site/resources/tools/mosfet/1mosfet.gif, 120, class=align-right)]] [[Image(/site/resources/tools/mosfet/mosfet.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/mosfet/1mosfet.gif, 120, right)]] [[Image(/site/resources/tools/mosfet/mosfet.jpg, 120, right)]]
211
212 The [/tools/abacus/ MOSfet Lab in ABACUS] tool enables a semi-classical analysis of current-voltage (I/V) characteristics for bulk and SOI Field-Effect Transistors (FETs) for a variety of different device sizes, geometries, temperature, and doping profiles.
213
214 Exercises:
215
216 * [[Resource(4906)]]
217 * [[Resource(5104)]]
218 * [[Resource(5191)]]
219 * [[Resource(5085)]]
220
221 [/topics/MOSFETLabPage MOSFet Learning Materials] - Comprehensive set of learning materials for the MOSFet Tool.
222
223
224
225 == About ABACUS Constituent Tools ==
226
227 The Assembly of Basic Applications for Coordinated Understanding of Semiconductors (ABACUS) has been put together from individual tools to provide educators and students with a one-stop-shop in semiconductor education. It therefore benefits tremendously from the hard work that the contributors of the individual tool builders have put into their tools.
228
229 As a matter of credit, simulation runs that are performed in the ABACUS tool are also credited to the individual tools, which help the ranking of the individual tools. We do also count the number of usages of the individual tools in the ABACUS tool set, to measure the ABACUS impact and possibly also improve the tool.
230
231 In the description above, we do not refer to the individual tools since we want to guide the users to the composite ABACUS tool. We cite the individual tools here explicitly so they are being given the appropriate credit and on their respective tool pages are being linked to this ABACUS topic page.
232
233 [[Resource(crystal_viewer)]],
234 [[Resource(pcpbt)]],
235 [[Resource(kronig_penney)]],
236 [[Resource(bandstrlab)]],
237 [[Resource(fermi)]],
238 [[Resource(semi)]],
239 [[Resource(pntoy)]],
240 [[Resource(bjt)]],
241 [[Resource(moscap)]],
242 and
243 [[Resource(mosfet)]].
244
245 == Additional Reading and Tools ==
246
247 === Solar Cells ===
248
249 ==== [/tools/adept/ ADEPT] ====
250 -
[[Image(/site/resources/tools/adept/adept2.png, 120, class=align-right)]]
+
[[Image(/site/resources/tools/adept/adept2.png, 120, right)]]
251
252 [/tools/adept/ ADEPT] is not supported within ABACUS because it is a research-oriented tool that enables the study of solar cells for various material systems. A [/site/resources/2007/05/02659/adoc.pdf Reference Manual] and a [/site/resources/2007/05/02660/adept_heterostruct_tutorial.pdf ADEPT Heterostructure Tutorial] are available. The interface is not a simple point-and-click interface, as for example the PN junction lab, but simulation commands are entered via a command line.
253
254 === MOS Capacitors with Quantum Corrections===
255 ==== [/tools/schred/ Schred] ====
256 -
[[Image(/images/tool/schred/schred.jpg, 120, class=align-right)]]
+
[[Image(/images/tool/schred/schred.jpg, 120, right)]]
257 [/tools/schred/ Schred] is not formally supported in ABACUS. It contains more advanced quantum mechanical concepts and is a nanoHUB contributed tool. It calculates the envelope wavefunctions and the corresponding bound-state energies in a typical metal-oxide semiconductor (MOS) or semiconductor-oxide-semiconductor (SOS) structure and a typical SOI structure by solving self-consistently the one-dimensional (1D) Poisson equation and the 1D Schrödinger equation.
258
259 [[Div(start, class=clear)]][[Div(end)]]
260
261 Exercises:
262 * [[Resource(4900)]]
263 * [[Resource(4902)]]
264 * [[Resource(4904)]]
265 * [[Resource(4794)]]
266 * [[Resource(4796)]]
267
268 === madFETs—more Field Effect Transistors ===
269 -
[[Image(/site/resources/tools/nanomos/nanomos2.gif, 120, class=align-right)]] [[Image(/site/resources/tools/nanomos/nanomos3.gif, 120, class=align-right)]]
+
[[Image(/site/resources/tools/nanomos/nanomos2.gif, 120, right)]] [[Image(/site/resources/tools/nanomos/nanomos3.gif, 120, right)]]
270 -
[[Image(/site/resources/tools/nanofet/nanofet2.gif, 120, class=align-right)]]
+
[[Image(/site/resources/tools/nanofet/nanofet2.gif, 120, right)]]
271 -
[[Image(/site/resources/tools/fettoy/1-fettoy.gif, 120, class=align-right)]]
+
[[Image(/site/resources/tools/fettoy/1-fettoy.gif, 120, right)]]
272 -
[[Image(/site/resources/tools/fettoy/fettoy1.gif, 120, class=align-right)]]
+
[[Image(/site/resources/tools/fettoy/fettoy1.gif, 120, right)]]
273
274 The Field-Effect Transistor has been proposed and implemented in many physical systems, materials, and geometries. A multitude of acronyms have developed around these concepts. The "Many-Acronym-Device-FET" (madFET) was born. The author of this document was able to trace an attribute to the acronym madFET from [http://www.utdallas.edu/~frensley/ Bill Frensley] to [http://en.wikipedia.org/wiki/Herbert_Kroemer Herbert Kroemer].
275
276 nanoHUB.org hosts a variety of tools that enable the simulation of field effect transisors for a variety of different geometries in a variety of different levels of approximations. There is a [/topics/madfets madFETs topics page] that provides an overview of many of the nanoHUB.org madFET tools.
277
278 === Technology Computer Aided Design—TCAD ===
279 -
[[Image(/site/resources/tools/padre/padre.jpg, 120, class=align-right)]]
+
[[Image(/site/resources/tools/padre/padre.jpg, 120, right)]]
280 Once students have mastered the basics of semiconductors they may be quite interested in venturing into TCAD. There is a [/topics/atcadlab topics page for aTCADlab] and associated single [/tools/atcadlab aTCADlab] tool that assembles various TCAD tools available on the nanoHUB. Process, device, and circuit simulation is represented in [/tools/atcadlab aTCADlab].

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.