## ABACUS—Introduction to Semiconductor Devices

## Introduction to Semiconductor Devices with ABACUS

When we hear the words, 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 components such as transistors, capacitors, wires and other electronic devices such as light emitting diodes and semiconductor lasers. These components are typically integrated into a single chip made of a semiconductor material.

Almost every Electrical Engineering department teaches 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-cap), and multi-acronym-device field effect transistors (mad-FETs).

Advanced courses go more deeply into semiconductor theory, device physics, fabrication processes, and advanced and special purpose devices, such as heterostructure devices, power devices, and optoelectronic devices.

This nanoHUB “topic page” provides an easy access to selected nanoHUB Semiconductor Device Education Material that is openly accessible and usable by everyone around the world.

We invite you to participate in this open source, interactive educational initiative:

- Contribute your content by uploading it to the nanoHUB. (See “Contribute Content”) on the nanoHUB mainpage.
- Provide feedback for the items you use on the nanoHUB through the review system. (Please be explicit and provide constructive feedback.)
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- Finally, let us know what you are doing and your suggestions improving the nanoHUB by using the “Feedback” section, which you can find under “Support“

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### Crystal Structures, Lattices

#### Crystal Viewer

The Crystal Viewer in ABACUS tool enables the interactive visualization different Bravais lattices, and crystal planes, and materials (diamond, Si, InAs, GaAs, graphene, buckyball). It is supported by homework assignment in MS Word and Adobe PDF format.

### Band Models / Band Structure

#### Piece-Wise Constant Potential Barriers Lab

#### Periodic Potential Lab

The Periodic Potential Lab in ABACUS solves the time independent Schroedinger Equation in a 1-D 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.

Exercises:

#### Bandstructure Lab

The Bandstructure Lab in ABACUS enables the study of bulk dispersion relationships of Si, GaAs, InAs. The users can apply tensile and compressive strain and observe the variation in the bandstructure, bandgaps, and effective masses. Advanced users can study bandstructure effects in ultra-scaled (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.

Exercises:

#### StrainBands

StrainBands in ABACUS uses first-principles density functional theory within the local density approximation and ultrasoft pseudopotentals to compute and visualize density of states, E(k), charge densities, and Wannier functions for bulk semiconductors. Using this tool, you can study and learn about the bandstructures of bulk semiconductors for various materials under hydrostatic pressure and under strain conditions. Physical parameters such as the bandgap and effective mass can also be obtained from the computed E(k). We note here that the bandgaps obtained with DFT-LDA are underestimated, by about a factor of two for some semiconductors (including Si and GaAs), as is well known.

Exercises:

### Bulk Semiconductors

#### Carrier Statistics Lab

The 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. User can choose between doped and undoped semi-conductors. Silicon, Germanium, and GaAs can be studied as a function of doping or Fermi level, and temperature. It is supported by a 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 study freeze-out.

Exercises:

#### Drift Diffusion Lab

The Drift Diffusion Lab in ABACUS enables a user to understand the basic concepts of DRIFT and DIFFUSION of carriers inside a semiconductor slab using different kinds of experiments. Experiments like shining light on the semiconductor, applying bias and both 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 #1 and #2 in which Students are asked to explore the concepts of drift, diffusion, quasi Fermi levels, and the response to light.

Exercises:

### Semiconductor Process Modeling

Semiconductor process modeling is a vast field in which several commercial products are available and in use for production in industry and to some extent in education. nanoHUB is serving a few applications that are primarily geared towards education. The four tools entitled ‘Process Lab …’Oxidation, Oxidation Flux, Concentration Dependent Diffusion, and Point Defect Coupled Diffusion are all educational front-ends to the general Prophet tool in ABACUS.

#### Process Oxidation Lab

The Oxidation Lab in ABACUS simulates the oxidation process in integrated circuit fabrication. It is supported by a supplemental document that describes the theory and potential experiments that can be conducted.

#### Process Oxidation Flux Lab

The Process Oxidation Flux Lab in ABACUS simulates the oxidation flux in the oxide growth process in integrated circuit fabrication. It is supported by a supplemental document that describes the theory and potential experiments that can be conducted.

#### Concentration Dependent Diffusion Lab

The Concentration Dependent Diffusion Lab in ABACUS simulates the oxidation flux in the oxide growth process in integrated circuit fabrication.

#### Point Defect Coupled Diffusion Lab

The Point Defect Coupled Diffusion Lab in ABACUS the point-defect-coupled diffusion process in integrated circuit fabrication.

#### PROPHET

PROPHET in ABACUS was originally developed for semiconductor process simulation. Device simulation capabilities are currently under development. PROPHET solves sets of partial differential equations in one, two, or three spatial dimensions. All model coefficients and material parameters are contained in a database library which can be modified or added to by the user. Even the equations to be solved can be specified by the end user. It is supported by an extensive set of User Guide pages and a seminar on Nano-Scale Device Simulations Using PROPHET.

#### TSuprem4

TSuprem4 simulates the processing steps used in the manufacture of silicon integrated circuits and discrete devices. The types of processing steps modeled by the current version of the program include ion implantation, inert ambient drive-in, silicon and polysilicon oxidation and silicidation, epitaxial growth, and low temperature deposition and etching of various materials.

Because of the way TSUPREM-4 is licensed, it is available only to users on the West Lafayette campus of Purdue University. Note that you must use a network connection on campus, or else you will get an 'access denied' message.### PN Junctions

#### /tools/abacus/ PN Junction Lab]

PN-Junction Lab in ABACUS: Everything you 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, I/V characteristic, etc.

There is a significant set of associated resources available for this tool.

- a demo of this tool
- a Primer on Semiconductor Device Simulation.
- a Learning Module entitled PN Junction Theory and Modeling which walks students through the PN junction theory and let’s them verify concepts through on-line simulation.
- Homework assignment on the depletion approximation
- Homework assignment on the depletion approximation

Exercises:

### Solar Cells

#### ADEPT

ADEPT in ABACUS is a research-oriented tool that enables the study of solar cells for various material systems. A Reference Manual and a 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 in a command-like fashion.

### Bipolar Junction Transistors (BJT)

#### Bipolar Junction Lab

(Image(/site/resources/tools/bjt/5_BJTenergy_nonequil.gif, 120 class=align-left) failed - File not found) The Bipolar Junction Lab in ABACUS allows Bipolar Junction Transistor (BJT) simulation using a 2D mesh. It allows user to simulate 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. It is supported by a homework assignment in which Students are asked to find the emitter efficiency, the base transport factor, current gains, and the Early voltage. Also a qualitative discussion is requested.

Exercises:

### MOS Capacitors

#### MOScap

The MOScap Tool in ABACUS tool enables a semi-classical analysis of MOS Capacitors. Simulates the capacitance of bulk and dual gate capacitors for a variety of different device sizes, geometries, temperature and doping profiles.

Exercises:

#### Schred

(Image(/images/tool/schred/schred.jpg, 120 class=align-right) failed - File not found) Schred Tool in ABACUS 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 (1D) Poisson equation and the 1D Schrodinger equation.

Exercises:

### MOSFET / mad-FET

The Field-Effect-Transistor has been proposed and implement in many physical systems, materials, and geometries. A multitude of acronyms have developed around these concepts. The “Many-Acronym-Device-FET” or “madFET” was born.

#### MOSfet Lab

The MOSfet Lab in ABACUS tool enables a semi-classical analysis of current-voltage characteristics for bulk and SOI Field Effect Transistors (FETs) for a variety of different device sizes, geometries, temperature and doping profiles.

Exercises:

#### nanoMOS

The nanoMOS tool in ABACUS enables a 2D simulation for thin body MOSFETs, with transport models ranging from drift-diffusion to quantum diffusive for a variety of different device sizes, geometries, temperature and doping profiles.

#### nanoFET

The nanoFET in ABACUS simulates quantum ballistic transport properties in two-dimensional MOSFET devices for a variety of different device sizes, geometries, temperature and doping profiles.

#### FETtoy

[FETtoy] is a set of Matlab scripts that calculate the ballistic I-V characteristics for a conventional MOSFETs, Nanowire MOSFETs and Carbon NanoTube MOSFETs. For conventional MOSFETs, assumes either a single or double gate geometry and for a nanowire and nanotube MOSFETs it assumes a cylindrical geometry. Only the lowest subband is considered, but it is readily modifiable to include multiple subbands. Additional related documents are: FETToy Detailed Description, Theory of Ballistic Nanotransistors, Learning Module on FETToy, Homework Exercises for FETToy.

### TCAD Simulators

#### PADRE

PADRE in ABACUS is a 2D/3D simulator for electronic devices, such as MOSFET transistors. It can simulate physical structures of arbitrary geometry—including heterostructures—with arbitrary doping profiles, which can be obtained using analytical functions or directly from multidimensional process simulators such as . A variety of supplemental documents are available that deal with the PADRE software and TCAD simulation:

- User Guide
- Abbreviated First Time User Guide
- FAQ
- A set of course notes on Computational Electronics with detailed explanations on bandstructure, pseudopotentials, numerical issues, and drift diffusion.
- Introduction to DD Modeling with PADRE
- Description and Semiclassical Simulation With PADRE
- A Primer on Semiconductor Device Simulation

Exercises:

#### PROPHET

PROPHET was originally developed for semiconductor process simulation. Device simulation capabilities are currently under development. PROPHET solves sets of partial differential equations in one, two, or three spatial dimensions. All model coefficients and material parameters are contained in a database library which can be modified or added to by the user. Even the equations to be solved can be specified by the end user. It is supported by an extensive set of User Guide pages and a seminar on Nano-Scale Device Simulations Using PROPHET.

## About

The Assembly of Basic Applications for Coordinated Understanding of Semiconductors (ABACUS) has been put together from individual disjoint tools to enable educators and students to have 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.

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.

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 rspective tool pages are being linked to this ABACUS topic page.