quantum electronics ii (tmu)

8/10/2019 Quantum electronics II (TMU)

http://slidepdf.com/reader/full/quantum-electronics-ii-tmu 1/12

Semiconductor Theory

The Course Outline

Fall 2014

Professor M K Moravvej-Farshi

Faculty of Electrical & Computer EngineeringTarbiat Modares University

P. O. Box 14115-194

Tehran, Iran

[email protected]

mailto:[email protected]

mailto:[email protected]



Semiconductor Theory Course Outline

Tarbiat Modares University (TMU) 1 Faculty of ECE

0. An Overview

1. The Quantum Foundation

2. Carrier Scattering

3. The Boltzmann Transport

4. Low –Field Transport

5.

Balance Equations

6. Monte Carlo Simulation

7.

High-Field Transport in BulkSemiconductors

8. Carrier Transport in Devices

9.

Transport in Mesoscopic

Structures

QC611.L86.2000



Fall 2014 2

An Overview

Until recently, Semiconductor devices were described well by

the drift and diffusion equation,

n n n J q qD nµ = + ∇E .

µ n and Dn had been measured carefully.

µ n and Dn did not need to be calculated exactly.

A deep understanding of electron transport was not essential to

the device engineers.





In the modern submicron devices: µ n and Dn are no longer

material- and field-dependent parameters.

µ n and Dn depend on microscopic physics, on the device

structure, and even on the applied bias.

Nowadays, we can engineer material properties, with modern

epitaxial technology.



Fall 2014 4

In this course, we begin at the microscopic level and progress

towards the macroscopic level of the devices.

The basic level: Electrons in semiconductors are quantum

mechanical waves propagating through the device under the

influence of the crystal, applied, and

scattering potentials, as shown in Fig. (a).





In Chapter 1, we begin at this level and

show that when the device is large

enough, the electron can be treated as a

classical particle, as Shown in Fig. (b).

Electron scattering, however, is the result of short-range forces.

Therefore, scattering must be treated quantum mechanically.

Calculation of scattering probabilities per unit time, for



Fall 2014 6

perturbing potentials encountered in common semiconductors is

the subject of Chapter 2.

At the macroscopic level, equations such as the drift-diffusion

result by averaging a great number of nearly chaotic trajectories

like that shown in Fig. (b).

One may ask, "What is the probability of finding an electron at r

with momentum p?" The answer is the distribution function,

f (r, p, t ), which defines the state of the device.





As shown in Fig. (c), f (r, p, t ) is a

probability density function. f (r, p, t )

completely defines the average state of

the system.

In chapter 3, we formulate and solve the Boltzmann transport

equation (BTE), an equation that determines f (r, p, t )

In chapter 4, a systematic treatment of low-field transport based

on solving the BTE is presented.



Fall 2014 8

A device engineer is mostly interested in quantities such as the

average carrier density, velocity, and energy.

These 3 quantities are the zeroth, first, and second moments of

the distribution function, respectively.

Chapter 5 presents a procedure for generating balance equations

for these quantities.

In the process, we will demonstrate how to derive drift-diffusion

equation from BTE.





At the drift-diffusion level, the quantities

of interest are the position-dependent

carrier and velocity profiles as illustrated

in Fig. (d)

Another approach for computing macroscopic transport

properties is to use Monte Carlo simulation technique to

simulate a large number of trajectories, like that in Fig. (b) on a

computer to average the results [see chapter 6].



Fall 2014 10

In chapter 7, both the balance equation approach and the Monte

Carlo simulation are applied to the problem analyzing high-field

carrier transport in bulk semiconductors.

Chapter 8 presents several of transport effects that occur in

modern devices. Devices contain both low- and high-field

regions, but spatial variations are strong, so some qualitatively

new transport features arise.





The course will be concluded by chapter 9, in which transport in

microscopic devices is examined.

Size of such devices lies between macroscopic and atomic

regimes.

quantum electronics ii (tmu)

Documents