Introduction

Labs and Course Multiple experiments

Prerequisites- Administrative drop General Approach

FETs and BJTs Analytical approach First Mid-Term

Syllabus Semiconductor fundamentals. Diodes and diode circuits. Field Effect Transistor (FET), FET Amplifiers and circuits. Bipolar Junction Transistor (BJT), BJT Amplifiers and circuits Exam 1 Frequency response. Output Stages and Power Amplifiers Ideal Operational Amplifier Integrated Circuit Biasing and Active Loads. Differential and Multistage Amplifiers. Operational Amplifier Circuits Exam 2 Nonideal Effects in Operational Amplifier Circuits Design of Integrated Circuits Feedback and Stability

Introduction to Semiconductors

Metals, Insulators, Semiconductors In SC we have 2 ‘types’ of carriers present.

Electrons Holes- Absence of electrons Separated in different energy bands The separation between these bands is the band gap of

the SC

Three types of solids, classified according to atomic arrangement: (a) crystalline and (b) amorphous materials are illustrated by microscopic views of the atoms, whereas (c) polycrystalline structure is illustrated by a more macroscopic view of adjacent single-crystalline regions, such as (a).

Unit cells for three types of cubic lattice structures.

Semiconductor Structure

The fundamental property that distinguishes SC from other materials is bonding. Ionic Bonding- Coulombic Interaction (localized

carriers) Metallic- Plenty of electrons that move around ‘freely’ Covalent [SC]- Electrons shared by atoms, rather

localized, but can be ‘freed’ to move around the lattice. The limited number of available carriers in SC

compared to metals is key to their behavior.

Different types of chemical bonding in solids (a) an example of ionic bonding in NaCl; (b) covalent bonding in the Si crystal, viewed along a <100> direction (see also Figs. 1–8 and 1–9).

Diamond lattice unit cell, showing the four nearest neighbor structure. (From Electrons and Holes in Semiconductors by W. Shockley, © 1950 by Litton Educational Publishing Co., Inc.; by permission of Van Nostrand Reinhold Co., Inc.)

Electronic structure and energy levels in a Si atom: (a) The orbital model of a Si atom showing the 10 core electrons (n = 1 and 2), and the 4 valence electrons (n = 3); (b) energy levels in the coulombic potential of the nucleus are also shown schematically.

Linear combinations of atomic orbitals (LCAO): The LCAO when 2 atoms are brought together leads to 2 distinct “normal” modes—a higher energy anti-bonding orbital, and a lower energy bonding orbital. Note that the electron probability density is high in the region between the ion cores (covalent “bond”), leading to lowering of the bonding energy level and the cohesion of the crystal. If instead of 2 atoms, one brings together N atoms, there will be N distinct LCAO, and N closely-spaced energy levels in a band.

Energy levels in Si as a function of inter-atomic spacing. The core levels (n = 1,2) in Si are completely filled with electrons. At the actual atomic spacing of the crystal, the 2 N electrons in the 3 s sub-shell and the 2 Nelectrons in the 3 p sub-shell undergo sp 3 hybridization, and all end up in the lower 4 Nstates (valence band), while the higher lying 4 Nstates (conduction band) are empty, separated by a bandgap.

Typical band structures at 0 K.

Relationship between band gap and lattice constant for alloys in the InGaAsP and AlGaAsSb systems. The dashed vertical lines show the lattice constants for the commer-cially available binary substrates GaAs and InP. For the marked example of InxGa1—xAs, the ternary composition x ~ 0.53 can be grown lattice-matched on InP, since the lattice constants are the same. For quaternary alloys, the compositions on both the III and V sub-lattices can be varied to grow lattice-matched epitaxial layers along the dashed vertical lines between curves. For example, In x Ga 1— x As y P 1— y can be grown on InP substrates, with resulting band gaps ranging from 0.75 eV to 1.35 eV. In using this figure, assume the lattice constant a of a ternary alloy varies linearly with the composition x.

Electron-hole pairs in a semiconductor.

Energy band model and chemical bond model of dopants in semiconductors: (a) donation of electrons from donor level to conduction band; (b) acceptance of valence band electrons by an acceptor level, and the resulting creation of holes; (c) donor and acceptor atoms in the covalent bonding model of a Si crystal.

Electron–hole pairs in the covalent bonding model of the Si crystal.

Direct and indirect electron transitions in semiconductors: (a) direct transition with accompanying photon emission; (b) indirect transition via a defect level.

Saturation of electron drift velocity at high electric fields for Si.

Properties of an equilibrium p-n junction: (a) isolated, neutral regions of p-type and n-type material and energy bands for the isolated regions; (b) junction, showing space charge in the transition region W, the resulting electric field % and contact potential V0, and the separation of the energy bands; (c) directions of the four components of particle flow within the transition region, and the resulting current directions.

Space charge and electric field distribution within the transition region of a p-n junction with Nd > Na: (a) the transition region, with x = 0 defined at the metallurgical junction; (b) charge density within the transition region, neglecting the free carriers; (c) the electric field distribution, where the reference direction for % is arbitrarily taken as the +x-direction.

Examples of contact potential for a heavily doped p-n junction: (a) at equilibrium; (b) approaching the maximum forward bias V = V0

Effects of a bias at a p-n junction; transition region width and electric field, electrostatic potential, energy band diagram, and particle flow and current directions within W for (a) equilibrium, (b) forward bias, and (c) reverse bias.

I–V characteristic of a p-n junction.

The Zener effect: (a) heavily doped junction at equilibrium; (b) reverse bias with electron tunneling from p to n; (c) I–V characteristic.

Reverse breakdown in a p-n junction.

Saturation of electron drift velocity at high electric fields for Si.

Forward and reverse current-voltage characteristics plotted on semi-log scales, with current normalized with respect to saturation current, I0; (a) the ideal forward characteristic is an exponential with an ideality factor, n = 1 (dashed straight line on log-linear plot). The actual forward characteristics of a typical diode (colored line) have four regimes of operation; (b) ideal reverse characteristic (dashed line) is a voltage-independent current = 2 I0. Actual leakage characteristics (colored line) are higher due to generation in the depletion region, and also show breakdown at high voltages.

Ideal forward-biased I-V characteristics of pn junction diode, with thecurrent plotted on a log scale for Is = 10-14 A and n = 1

The ideal diode: (a) I-V characteristics, (b) equivalent circuit under reverse bias, and (c) equivalent circuit in the conducting state

I–V characteristics of heavily doped p-n junction diodes at 77 K, illustrating the effects of contact potential on the forward current: (a) Ge, Eg . 0.7 eV; (b) Si, Eg . 1.4 eV; (c) GaAs, Eg . 1.4 eV; (d) GaAsP, Eg . 1.9 eV.

Piecewise-linear approximations of junction diode characteristics: (a) the ideal diode; (b) ideal diode with an offset voltage; (c) ideal diode with an offset voltage and a resistance to account for slope in the forward characteristic.

AC circuit analysis: (a) circuit with combined dc and sinusoidal input voltages, (b) sinusoidal diode current superimposed on the quiescent current, (c) sinusoidal diode voltage superimposed on the quiescent value, and (d) forward-biased diode I-V characteristics with a sinusoidal current and voltage superimposed on the quiescent values

The diode and load line characteristics for the circuit shown in

Figure 1.24

The diode rectifier: (a) circuit, (b) sinusoidal input signal,

(c) equivalent circuit for vI> 0, (d) equivalent circuit for vI < 0, and

(e) rectified output signal

The diode equivalent circuit (a) in the “on” condition when VD Vy, (b) in the “off” condition when VD < Vy, and (c) piecewise linear approximation when rf = 0

A breakdown diode: (a) I–V characteristic; (b) application as a voltage regulator.

Space charge and electric field distribution within the transition region of a p-n junction with Nd > Na: (a) the transition region, with x = 0 defined at the metallurgical junction; (b) charge density within the transition region, neglecting the free carriers; (c) the electric field distribution, where the reference direction for % is arbitrarily taken as the +x-direction.

Effects of a step turn-off transient in a p+-n diode: (a) current through the diode; (b) decay of stored charge in the n-region; (c) excess hole distribution in the n-region as a function of time during the transient.

Effects of storage delay time on switching signal: (a) switching voltage; (b) diode current.

A Schottky barrier formed by contacting an n-type semiconductor with a metal having a larger work function: (a) band diagrams for the metal and the semiconductor before joining; (b) equilibrium band diagram for the junction.

Ohmic metal–semiconductor contacts: (a) Fm < Fs for an n-type semiconductor, and (b) the equilibrium band diagram for the junction; (c) Fm < Fs for a p-type semiconductor, and (d) the junction at equilibrium.