ECE 440 Lecture 2 : Semiconductors and Structure

Class Outline:

•Semiconductor Crystal Lattices •Miller Indices Semiconductor Crystal Growth Things you should know when you leave… Key Questions • Why is crystal order important? • How is a crystal defined? • What are the most common types of crystal lattices used in semiconductor devices? • What are Miller Indices?

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

What is the ?

Crystalline Polycrystalline Amorphous

• Crystal structures come in three basic kinds

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

What does it matter if it is crystalline or not?

Crystalline Amorphous • We can get a lot of information from the unit cell: – Density of – Distance between nearest atoms • Calculate forces between atoms – Perform simple calculations • Fraction of atoms filled in volume • Density of atoms M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

Since we care about crystalline lattices, let’s examine the periodic lattice… • In the periodic lattice:

+ =

2D lattice where the grey Basis balls denote lattice points 2D Crystal

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices In this section we consider some of the lattice types that will be important for our discussion of semiconductors…

• Examine the simple cubic structure:

a

z

y

x a1 = axˆ (2.1)

a2 = ayˆ (2.2)

a3 = azˆ (2.3)

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

A simple variant on the cubic lattice is the body-centered cubic lattice… • Examine the body-centered cubic lattice (bcc):

a a = [xˆ + yˆ − zˆ] (2.4) 1 2 z a a a = [− xˆ + yˆ + zˆ] (2.5) y 2 2

x a a = [xˆ − yˆ + zˆ] (2.6) 3 2 M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

A final variant is the face-centered cubic lattice… • Examine the face-centered cubic lattice (fcc):

a a = [xˆ + yˆ ] (2.7) 1 2

a a a = [yˆ + zˆ] (2.8) 2 2

z a a3 = [zˆ + xˆ] (2.9) y 2

x M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

But be careful… • There is a difference between unit cells and primitive cells.

IN THIS FIGURE THE DOTTED LINES INDICATE THE UNIT CELL OF THE FACE-CENTERED CUBIC LATTICE

a

THE GRAY REGION DENOTES THE PRIMITIVE CELL FOR THIS LATTICE WHOSE VOLUME CAN BE DETERMINED FROM THE PRIMITIVE VECTORS INTRODUCED IN Eqns. 2.7 - 2.9

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

Now let’s look at the silicon crystal… • To discuss the crystal structure of different semiconductors we will need to account for the basis unit that is added to each lattice point. – Elemental semiconductors such as silicon and germanium both exhibit the structure. – Named after one of the two crystalline forms of carbon.

• Here we display the silicon unit cell. • The balls each represent one silicon . • The solid lines represent chemical bonds. • Note how the bonds form a tetrahedron. • How many atoms per unit cell? M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

Looks confusing, but it’s not so bad… • It is really just two inter-penetrating fcc lattices with a diatomic basis. • It looks more complex because we do not show atoms extending beyond the unit cell by convention. • In the figure below, each different color represents pairs of atoms from the same basis. • The black balls represent atoms with one atom in their basis outside the unit cell.

a (xˆ,yˆ,zˆ) 4

(0,0,0)

LATTICE BASIS UNIT CELL

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Semiconductor Crystal Lattices

What about compound semiconductors? Gallium • Many compound Arsenide semiconductors such as Gallium Arsenide (GaAs) exhibit the zincblende crystal structure. – The atomic configuration is the same as diamond. – The difference lies in Useful questions to ask: that each successive •How many atoms per unit cell? atom is from a different chemical element. •How do you calculate density?

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Miller Indices

How do we classify these periodic atomic arrangements? • The periodicity could possibly be used to define a series of planes. • For any direction one could define many different equivalent planes. • For instance, consider the different equivalent crystal planes in a cubic lattice.

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Miller Indices

We can classify crystal planes through the use of Miller Indices. 1. Start with any arbitrary point in the crystal lattice. 2. Take the three primitive lattice vectors as axes. 3. Next we locate the intercepts of the desired with these coordinate axes. 4. Finally, we take the reciprocal of the intercepts and multiply each of these by the smallest factor required to convert them all to integers. – Indices which have no intercept have a Miller Index of zero.

LATTICE POINT AXIS INTERCEPT RECIPROCAL

a3

a1

a1 a2 LATTICE POINT a2

LATTICE POINT a3

TO CONVERT THE RECIPROCALS TO INTEGERS WE NEED TO MULTIPLY BY A FACTOR OF SIX THIS YIELDS

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Miller Indices

Applications of Miller Indices.

AXIS INTERCEPT RECIPROCAL MILLER INDEX

a1

a2

a3

AXIS INTERCEPT RECIPROCAL MILLER INDEX

a1

a2

a3

Notice how we denoted the miller index for a plane with a negative intercept

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Miller Indices

More Miller Indices: • Since we chose the origin arbitrarily when we began, Miller indices define a family of parallel planes. • To denote crystal planes with the same symmetry, we use {hkl}. • “h” is the x-axis intercept inverse, “k” is the y-axis intercept inverse, and “l” is the z-axis intercept inverse . z z z

(001)

(100) (010)

y y y x x x All three planes shown here are related by simple rotations, thus they represent {100} family. M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Miller Indices

We can also use Miller Indices to denote directions: • The direction Summary [hkl] is used A crystal plane: to denote the Equivalent crystal planes: directions perpendicular Crystal direction: to (hkl).

[001] [001]

[ h k l ]

( h k l )

[010] [010]

[100] [100] M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Crystal Growth - Silicon

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Crystal Growth – Compound Semiconductors

• Heterojunctions are typically produced by a process known as MOLECULAR-BEAM – This is performed in an ultra-high vacuum (UHV) evaporation chamber working at pressures of 10-11 Torr. – The materials to be grown are provided from heated KNUDSEN CELLS in which the individual elements are individually vaporized

ELECTRON- DIFFRACTION CHAMBER SOURCE WALLS COOLED WITH LIQUID NITROGEN

600 °C KNUDSEN CELLS CONTAINING Ga, Al, As & Si

ELECTRON- DIFFRACTION DETECTOR UHV PUMP

A SCHEMATIC DIAGRAM SHOWING THE KEY COMPONENTS OF A MOLECULAR-BEAM EPITAXY SYSTEM

M. J. Gilbert ECE 440 – Lecture 2 8/26/09 Crystal Growth – Compound Semiconductors

• Careful control of the deposition rates and the substrate temperature are required to realize heterojunctions with well- defined interfaces. – In order to achieve high uniformity the substrate is heated to approximately 600 ºC and is slowly rotated in the vacuum chamber. – The growth rate of the epitaxial layer is of order several MICRONS PER HOUR which allows for ATOMIC level resolution in the growth process. – The growth is monitored in situ using electron diffraction and mass spectroscopy.

TEM IMAGES OF EPITAXIALLY GROWN GaAs/AlGaAs

M. J. Gilbert ECE 440 – Lecture 2 8/26/09