Modelling & Simulation of Semiconductor Devices - PowerPoint Presentation

Slide1

Modelling & Simulation of Semiconductor Devices

Lecture 7 & 8

Hierarchy of Semiconductor ModelsSlide2

Introduction

Nowadays, semiconductor materials are contained in almost all electronic

de-vices

.

Some

examples of semiconductor devices and their use are described in

the following.

Some examples of semiconductor devices and their use are described in

the following.

Photonic devices

capture light (photons) and convert it into an

electronic signal

. They are used in camcorders, solar cells, and light-wave

communication

systems as optical

fibers

.Slide3

Introduction

Optoelectronic

emitters

convert an electronic signal into light.

Examples are

light-emitting diodes (LED) used in displays and indication lambs

and semiconductor

lasers used in compact disk systems, laser printers, and

eye surgery.

Flat-panel

displays

create an image by controlling light that either

passes through

the device or is

reflected off

of it. They are made, for instance,

of liquid

crystals (liquid-crystal displays, LCD) or of thin semiconductor

films (

electroluminescent displays

).

In

field-effect

devices

the conductivity is modulated by applying an

electric field

to a gate contact on the surface of the device. The most

important field-effect

device is the MOSFET (metal-oxide semiconductor

field-effect transistor

), used as a switch or an

amplifier

. Integrated

circuits

are

mainly made

of MOSFETs.Slide4

Introduction

Quantum devices

are based on quantum mechanical phenomena, like

tunneling

of electrons through potential barriers which are impenetrable

classically

. Examples are resonant tunneling diodes,

super lattices

(

multi-quantum-well

structures), quantum wires in which the motion of carriers is

restricted

to one space dimension and

confined

quantum mechanically in

the other

two directions, and quantum dots

.

Clearly, there are many other semiconductor devices which are not

mentioned (

for instance, bipolar transistors, Schottky barrier

diodes

, thyristors).

Other new developments

are, for instance, nanostructure devices (

hetero-structures

) and

solar cells

made of amorphous silicon or organic semiconductor

materials.Slide5

Introduction

Usually, a semiconductor device can be considered as a device which needs

an input

(an electronic signal or light) and produces an output (light or an

electronic signal

).

The

device is connected to the outside world by contacts at which

a voltage

(potential

difference

) is applied

.

We are mainly interested in

devices which

produce an electronic signal, for instance the macroscopically

measurable electric

current (electron

flow

), generated by the applied bias

.

In this situation

, the

input parameter is the applied voltage and the output parameter is the

electric current

through one contact.Slide6

Introduction

The relation between these two physical quantities

is called

current-voltage characteristic. It is a curve in the two-dimensional

current-voltage

space.

The

current-voltage characteristic does not need to be a

monotone function

and it does not need to be a function (but a relation

).

The main objective of this

subject

is to derive mathematical models which

describe

the electron

flow

through a semiconductor device due to the application

of a

voltage.Slide7

Introduction

Depending on the device structure, the main transport phenomena

of the

electrons may be very

different

, for instance, due to drift,

diffusion

,

convection

, or quantum mechanical

effects

.

For

this reason, we have to devise

different mathematical

models which are able to describe the main physical

phenomena for

a particular situation or for a particular device

.

This leads to a hierarchy of semiconductor models.Slide8

Hierarchy of Semiconductor Models

Roughly speaking, we

can divide

semiconductor models in three classes

:

Quantum models

Kinetic

models

Fluid dynamical

(macroscopic)

models

In order to give some flavor of these models

and the methods used to derive them, we explain these three view-points

: quantum

, kinetic and

fluid dynamic

in a

simplified

situation.Slide9

Quantum Models

Consider a single electron of mass

m

and

elementary charge

q

moving in a vacuum under the action of an electric

field

E = E(x; t

)

.

The motion of the electron in space

and

time

t > 0

is governed by

the single-particle

Schrodinger equationWith some initial condition

 Slide10

Quantum ModelsSlide11

Quantum ModelsSlide12

Fluid Dynamic Model

In order to derive fluid dynamical

models,

for instance

, for the evolution of the particle density

n

and the current density

J

;

we assume

that the wave function can be decomposed in its amplitude

and

phase

.

 Slide13

Fluid Dynamic Model

The current density is now calculated asSlide14

Semiconductor Crystal

A solid is made of an

infinite three-dimensional

array of atoms arranged

according

to a latticeSlide15

Semiconductor Crystal

The state of an electron moving in this periodic potential is described

Schrodinger

equation:Slide16

Home Work

Apply Madelung Transform on above equation to obtain Fluid dynamical model of

electron moving in

periodic

potential

in semiconductor crystal. Slide17

End of Lectures 7-8

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