Review of Semiconductor Physics Lecture 3 – 4

Dr. Tayab Din Memon

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Electronic Materials

• The goal of electronic materials is to generate and control the flow of an electrical current.

• Electronic materials include: 1. Conductors: have low resistance which

allows electrical current flow 2. Insulators: have high resistance which

suppresses electrical current flow 3. Semiconductors: can allow or suppress

electrical current flow 2

Conductors

• Good conductors have low resistance so electrons flow through them with ease.

• Best element conductors include:

• Copper, silver, gold, aluminum, & nickel

• Alloys are also good conductors:

• Brass & steel

• Good conductors can also be liquid:

• Salt water

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Conductor Atomic Structure

• The atomic structure of good conductors usually includes only one electron in their outer shell. • It is called a valence electron.

• It is easily striped from the atom, producing current flow.

Copper Atom 4

Insulators

• Insulators have a high resistance so current does not flow in them.

• Good insulators include:

• Glass, ceramic, plastics, & wood

• Most insulators are compounds of several elements.

• The atoms are tightly bound to one another so electrons are difficult to strip away for current flow.

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Semiconductors

• Semiconductors are materials that essentially can be conditioned to act as good conductors, or good insulators, or any thing in between.

• Common elements such as carbon, silicon, and germanium are semiconductors.

• Silicon is the best and most widely used semiconductor. 6

Model of Semiconductor Physics

• Two complementary models are used in the discussion of semiconductor physics :

• Energy-band model

• Crystal – bonding model

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Energy band model

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Energy Band Model

• The main characteristic of a semiconductor element is that it has four electrons in its outer or valence orbit.

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Bond Model - Crystal Lattice Structure

• The unique capability of semiconductor atoms is their ability to link together to form a physical structure called a crystal lattice.

• The atoms link together with one another sharing their outer electrons.

• These links are called covalent bonds.

2D Crystal Lattice Structure

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3D Crystal Lattice Structure

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• At absolute temperature, all electrons are held in these bonds, and therefore none are free to move about the crystal in response to an electric field.

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Semiconductors can be Insulators

• If the material is pure semiconductor material like silicon, the crystal lattice structure forms an excellent insulator since all the atoms are bound to one another and are not free for current flow.

• Good insulating semiconductor material is referred to as intrinsic.

• Since the outer valence electrons of each atom are tightly bound together with one another, the electrons are difficult to dislodge for current flow.

• Silicon in this form is a great insulator.

• Semiconductor material is often used as an insulator. 13

Doping

• To make the semiconductor conduct electricity, other atoms called impurities must be added.

• “Impurities” are different elements.

• This process is called doping.

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Semiconductors can be Conductors

• An impurity, or element like arsenic, has 5 valence electrons.

• Adding arsenic (doping) will allow four of the arsenic valence electrons to bond with the neighboring silicon atoms.

• The one electron left over for each arsenic atom becomes available to conduct current flow.

Resistance Effects of Doping

• If you use lots of arsenic atoms for doping, there will be lots of extra electrons so the resistance of the material will be low and current will flow freely.

• If you use only a few boron atoms, there will be fewer free electrons so the resistance will be high and less current will flow.

• By controlling the doping amount, virtually any resistance can be achieved.

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Another Way to Dope

• You can also dope a semiconductor material with an atom such as boron that has only 3 valence electrons.

• The 3 electrons in the outer orbit do form covalent bonds with its neighboring semiconductor atoms as before. But one electron is missing from the bond.

• This place where a fourth electron should be is referred to as a hole.

• The hole assumes a positive charge so it can attract electrons from some other source.

• Holes become a type of current carrier like the electron to support current flow. 17

Types of Semiconductor Materials

• The silicon doped with extra electrons is called an “N type” semiconductor.

• “N” is for negative, which is the charge of an electron.

• Silicon doped with material missing electrons that produce locations called holes is called “P type” semiconductor.

• “P” is for positive, which is the charge of a hole.

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Current Flow in N-type Semiconductors

• The DC voltage source has a positive terminal that attracts the free electrons in the semiconductor and pulls them away from their atoms leaving the atoms charged positively.

• Electrons from the negative terminal of the supply enter the semiconductor material and are attracted by the positive charge of the atoms missing one of their electrons.

• Current (electrons) flows from the positive terminal to the negative terminal.

Current Flow in P-type Semiconductors

• Electrons from the negative supply terminal are attracted to the positive holes and fill them.

• The positive terminal of the supply pulls the electrons from the holes leaving the holes to attract more electrons.

• Current (electrons) flows from the negative terminal to the positive terminal.

• Inside the semiconductor current flow is actually by the movement of the holes from positive to negative.

Semiconductor Devices Modeling and Simulation

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Semiconductor Devices

• Semiconductor devices form the foundation of modern electronics, being used in applications extending from computers to satellite communication systems.

• The most common devices includes:

• Diodes, Bipolar and field effect transistors, thyristors, triacs, and microwave optoelectronics

• Silicon is the most commonly used semiconductor material for both discrete and integrated devices

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Modeling of Semiconductor Devices

• In order to characterize a semiconductor device it is necessary to obtain suitable representation of the electrical and physical processes involved.

• It is also necessary to develop a description for the processes which cannot be directly observed.

• This is often achieved by implementing some form of analogy which follows the behavior of the device as closely as possible within the constraints of the defined operating environment.

• This process is called modeling.

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Modeling of Semiconductor Devices (Cont…)

• The process of modeling requires the analysis and/or simulation of the semiconductor device.

• The term ‘analysis’ in this context is usually taken to mean the method by which the complex problem of characterizing the device is resolved into simpler component parts which allow the required investigation to be achieved in a near exact manner.

• Simulation may be defined here as the process of imitating the operation of the device by considering the characteristics of a different analogous system, without resorting to direct practical experimentation on the device.

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Modeling of Semiconductor Devices (Cont…)

• Limitations of the model should be indicated

• In all device modeling work it is essential to appreciate the basis and limitations of the model in question.

• Role of modeling

• Modeling has an important role to play in the design, development and understanding of semiconductor devices

• Modeling process

• Traditionally the development of solid-state devices has involved a largely empirical design process with many iterations of the fabrications stage being required to achieve the desired specifications. Design rules are usually derived from this trail and error approach, which helps reduce the number of iterations required for future generations of devices.

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Categories of Solid-State Device Models

• Two broad categories

• Physical Device Model

• Equivalent Circuit Model

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Categories of Solid-State Device Models (Cont…)

• Equivalent circuit models • based on the electrical performance of the device, are a popular choice

for circuit design application and for circumstances where rapid evaluation is required

• Advantage of the Equivalent Circuit Model • Principle advantage of this technique is easy to implement • These models are frequently used in computer aided design (CAD)

packages intended for circuit design and ICs where multiple simulation is necessary

• Limitations of the Equivalent Circuit Model • These models are limited in their range of application because it is

often difficult to accurately relate the model elements to the physical parameters of the device (geometry, doping etc) and because of the bias, frequency dependence and non-linear behavior of most semiconductor devices.

• This means that this approach is not suitable for the predicting the characteristics of new devices and for modeling accurately large-signal operation, such as in oscillators or high speed logic circuits

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Categories of Solid-State Device Models (Cont…)

• Physical Device Models

• Physical device models are based on the physics of carrier transport, and can provide a greater insight into the detailed operation of the device

• Advantages of Physical Device Models

• Physical device models are not limited by the operating conditions and have been used successfully to analyze dc, transient, large-signal and high frequency operation.

• They may be used to predict the characteristics of new devices within the constraints of information available on the semiconductor material properties.

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Categories of Solid-State Device Models (Cont…)

• Limitation of Physical Device Models

• Major limitation of this technique is large memory and computation time;

• The analysis of physical device models is usually carried out using numerical techniques

• The derive towards smaller scale devices to achieve faster operating speeds has led to increasingly more complex device structures, where the operating characteristics depart from those predicted by classical models.

• Physical modeling allows these devices and other new structures to be rigorously characterized before fabrication.

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How Physical Device Models are Solved?

• Physical device models are solved using:

• Bulk carrier transport equation, Boltzmann transport models or quantum transport concepts

• Rigorous Boltzmann and quantum models have generally been restricted to providing detailed insight into carrier transport physics

• The trend towards sub-micron geometry devices, means that it is essential to consider non-equilibrium transport conditions and develop new models;

• This has led to increased interest in Boltzmann solution and quantum transport models;

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Physical Device Modeling History – Closed form analysis

• Before the advancement of digital computers, solid-state devices were theoretically characterized using closed-form analytical techniques based on approximation solutions to the carrier transport processes.

• A well know example of this type of analysis was described by Shockley in his paper on unipolar field effect transistors in 1952

• This approach usually proceeds by dividing the device into regions in which simplified linearized approximations are applied, joined by appropriate boundary conditions.

• This technique offers one – two dimensional models

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Physical Device Modeling History – Closed Form Analysis Merits and Demerits

• Advantages of Closed-form analysis technique

• Closed-form analysis technique has proved effective in characterizing large geometry unipolar devices and has continued to be used in many applications which take advantage of the relative simplicity and ease of programming inherent in this approach

• Limitations of closed-form analysis techniques

• It is unsuitable for modeling devices where the transport process is other than largely one-dimensional and where the electric field varies rapidly throughout the device

• In results, modeling sub-micron devices and many planar devices, such as field-effect transistors (FETs) found in a wide range of discrete and integrated forms can’t be modeled using closed-form technique.

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Physical Device Modeling History – Numerical simulation techniques development

• Development of Numerical Simulation Techniques

• Numerical simulation of semiconductor devices, using physical device models, began in 1964 with one-dimensional steady-state models and has been extended towards 2 – 3 dimensional numerical simulations to obtain a more realistic representation of planar and three terminal devices.

• Advantages of two dimensional numerical simulations includes:

• Current crowding (?) and high level injection in bipolar junction transistors (BJTs) and short and thin channels in FET’s to be investigated, which is not possible for one-dimensional models.

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Current Crowding

• Current crowding (also current crowding effect, or CCE) is a nonhomogeneous distribution of current density through a conductor or semiconductor, especially at the vicinity of the contacts and over the PN junctions.

• Current crowding is one of the limiting factors of efficiency of light emitting diodes. Materials with low mobility of charge carriers, e.g. AlGaInP, are especially prone to current crowding phenomena. It is a dominant loss mechanism in some LEDs, where the current densities especially around the P-side contacts reach the part of the emission characteristics with lower brightness/current efficiency. [Source : Wikipedia]

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Physical Device Modeling History – development of three dimensional simulation

• Three-dimensional Simulation

• Initiated to investigate small devices with narrow widths and non-uniformities in the active regions.

• Small geometry VLSI MOSFET’s with channel widths of the order of the gate length cannot be accurately modeled using two-dimensional models and three-dimensional simulations have been used to characterize these devices.

• These types of models has been used to investigate, fringing field effects (?), breakdown voltage and threshold voltage variations

• Fringing Fields Leakage flux particularly associated with edge effects in a magnetic circuit [source: http://www.phoenixamerica.com/technical-resources/glossary/default.html]

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Physical Device Modeling History – Limitations of traditional transport equations

• The majority of modern low-dimensional semiconductor devices are subject to regions of high electric fields, carrier gradients and current densities which give rise non-equilibrium (hot electron) transport conditions.

• The traditional transport equations, based on field dependent carrier mobility (often known as ‘drift-diffusion’ models), do not account for the process by which carriers gain energy from the transport conditions (carrier heating), and are not capable of modeling accurately sub-micron VLSI and other high frequency devices.

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Physical Device Modeling History – Development of Monte Carlo Methods

• Classical modeling techniques based on drift-diffusion equations have been extended to include momentum and energy relaxation effects (the ‘semi-classical’ approach), and provide a relatively easily evaluate model.

• Monte Carlo methods have been used extensively to characterize transport processes in short samples of semiconductor material and in simplified device structures. The carrier transport characteristics obtained from Monte Carlo techniques are frequently used in semi-classical models.

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Physical Device Modeling History – Simulation Packages

• Many simulations based on classical and more recently semi classical semiconductor equations have reached a high level of development and are available commercially and as public domain software.

• For example MINIMOS, GEMNI, PISCES, CADDET, HFIELD, WATMOS, SEDAN, BIPLE and LUSTRE etc.

• More recently, interest in developing flexible simulations with a choice of solution algorithms has led to the introduction of new generation software packages for example – PSPICE and etc

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Importance of Quantum Transport Theory

• QTT has been used in semiconductor theory to verify the range of validity of Boltzmann transport models. It has not widely used for device modeling because of the difficulty of implementation.

• However, quantum transport theory has been more recently used to analyze novel device structures where genuine quantum transport phenomena occur.

• QTT is also important to understand the operation of the device operating in the optical frequency regime, where it has been shown that Boltzmann transport theory is not valid.

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END OF LECTURES 3-4 40