CZ processing

Ingot diameter varies inversely with pull rate:

r

T

LNV mmp 3

21 5

max

L = latent heat of fusion

N = density

= Stephan-Boltzman constant

m = thermal conductivity at Tm

Tm = melt temperture (1417 oC for Si)

o = Cs/Co increases as ingot grows

The dopant concentration is given by:

IL=Io(1-Vs/Vo)ko and

Cs = -dIL/dVs = Coko(1-f)(o-1)

C, I and V are concentration, number of impurities and volume when

o: initial L: liquid and s: solid

Float Zone Processing

L

xk

oos

o

CxC exp11)(

In Float Zone refining, solid concentration varies with initial concentration as follows:

Concentration

Liquid

Tem

pera

ture

Solid

CoCs CL

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4-point probeOuter probe forces current through wafer; inner probes measure voltage drop

Used to measure sheet resistivity

= 1/q(nn+pp) -cm

us. n>>p or p>>n, so only one term is of interest

= 2s V/I

Typically, 0.5-mm< s <1.5-mm

When s = 1.588 mm, 2s = 1 cm

If t is not >>s, use correction factor:

r = t/ln(2)*V/I

If xj is the dopant depth, we measure square resistivity: s = /xj

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2-point probe

Useful to determine material type (n- or p-type)

•Apply two probes, one 25 – 100 oC hotter than other

•Thermally excited electrons flow away from hot probe, leaving holes and build up around cold electrode

•Measure Seebeck voltage using high impedance volt meter

•If material is p-type polarity will be reversed

We can measure either short circuit current or open circuit voltage. Current for an n-type material is:

Jn = qnnPndT/dx

Pn is thermoelectric power, either (-) for e- or (+) for h+

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Hall effect

Using Hall effect, we can determine material:

•Type

•Carrier concentration

•Carrier mobility

1. Current, Ix, is forced through sample

2. Results in measurable voltage drop, Vx

= wt/s Vx/Ix

3. Applying a magnetic field, B, deflects electrons: F = q( + v x B)

electrons will be forced in –y direction

Where v = electron velocity

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Hall effect

Since no current flows in the y-direction, an electric field e must build to offset magnetic force:

Fy = q(y + vxBz) = 0

→ y = -vxBz

Since vx = Ix/qwtn,

y = Bz Ix/qwtn,

or

Vy = Bz Ix/qtn

Define the Hall Coefficient:

RH = tVy/BzIx = 1/qn

→ n = ± 1/qRH

The “Hall mobility”, H is

H = ׀RH׀/ = ׀RH׀ Hall mobility is typically ~2 x e- or h+ mobility

Consistent units for calculating Hall effect:

V = volts A = Amps length = meters

B = Tesla (1T = 104 Gauss = 1 V-s/m2) RH = m3/C

Typical defects in crystalsTypical defects are:

Point defects – vacancies & interstitials

Line defects – dislocations

Volume defects – stacking faults, precipitates

The equilibrium number of vacancies varies with temperature:

nv = noexp(-Ev/kT)

Thermal stresses cause dislocations. Thermal stress is: = ET

= stress, E = Young’s modulus, = thermal expansion coefficient (m/m/oC)

O and C are also defects with concentrations of 1017-1018 cm-3 and 1015-1016 cm-3

Other impurities are in the ppb range

Where do defects come from?

• Naturally occurring vacancies and interstitials

• Thermal stresses inducing dislocations and stacking faults

• Precipitation of second phases inducing dislocations and stacking faults

• Impurities

• Process damage (e.g, ion implantation)

Precipitates and Dislocations

Precipitates usually do not fit into the host lattice. The growing particle causes considerable stress that can be reduced by plastic deformation.

If the precipitate fits in one lattice direction, but not in others (a precipitate with an hexagonal lattice, e.g., may fit relatively well on the {111} planes of an fcc lattice) a compromise between a non-spherical shape of the precipitate and a system of dislocation loops in some direction may produce least strain energy. The precipitate-dislocation system then has a very specific structure; the process is known as "prismatic loop punching". An example is shown below on the left (taken under kinematic bright field conditions).

Precipitate with prismatic loops. An arrangement like that accounts for the peculiar etch features shown before

Plate-like precipitate (the dark grey feature) with dislocations relieving parts of the stress.

The oval shaped area with a lighter contrast is the emitter of a bipolar transistor. In preferential etching this would look similar to what was shown as an illustration for etching.

Some of these small stacking faults have a peculiar, "sailing-boat" like shape (marked by "S" in the picture above). Below, a detailed view of a "sailing boat stacking fault":

• Oxidation of Silicon produces interstitials in supersaturation. These surplus interstitials tend to agglomerate in discs - i.e. stacking fault loops. The difficult part is the nucleation; it determines what will happen. We have to consider two ways of oxidizing Si, we first consider Surface oxidation: The surface oxidizes homogeneously by exposing it to an oxidizing atmosphere at high temperatures. This is the normal oxidation process. The emission of interstitials occurs at the interface; the interstitials diffuse into the bulk; the supersaturation decreases with the distance from the surface. There is no easy nucleation for an interstitial type dislocation loop as long as the interface is defect free. If defects are present, most prominent small precipitates of metal impurities (Fe, Ni, Cu) may serve as nucleation centers for the interstitials; a stacking fault penetrating in a semicircular fashion into the bulk is formed. If many precipitates are available, a large density of small stacking faults may be observed: 

The name "swirl" comes from the spiral "swirl-like" pattern observed in many cases by preferential etching as shown on the right.Close inspection revealed two types of etch features which must have been caused by different kinds of defects. Lacking any information about the precise nature of the defects (which etching can not give), they were termed "A-" and "B-swirl defects".

Looking at the etch pattern with a microscope at high magnifications shows that there are a lot of small defects (the B-swirls; white dots) and a much smaller number of larger defects (A-swirls; the black-white contrasts). Quantitative evaluation of the micrograph shows that the B-swirls are delineated as small and shallow pits whereas the A-swirls are delineated as hillocks.

Swirl defects are generated by the agglomeration of point defects while the crystals cools. The Si crystal growing industry soon learned how to grow crystals without swirl defects - without ever understanding precisely what they were.

But that did not mean that the crystals were defect free - it only meant that the methods

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Imaging Defects

Dislocations and stacking faults introduced during processing and nucleated by oxygen, thermal stress and oxidation processes

Chemical etchants reveal density, size and location of defects. Etchants attack areas with high chemical or strain energy and are visible with a microscope

Etch Composition

Sirtl Cr2O3 (5M): HF

1:1

Secco K2Cr2O7 (1.5M):HF or Cr2O3 (.15M):HF

1:2

Dash HF:HNO3:acetic acid

1:3:10

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FTIR: Fourier Transform Infrared Spectroscopy

Used to measure concentrations of O and C (down to ~1015/cm3)

Molecules absorb energy at characteristic wavelengths

E = h= hc/

Si-O-Si absorbs at wave number 1106/cm

C absorbs at wave number 607/cm

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1. IR beam split & follows two separate paths to sample and detector

2. Moving mirror causes two beams to interfere constructively or destructively in a sinusoidal manner

3. The Fourier transform of the signal will be a delta function proportional to incident beam intensity

4. If the frequency of the source is swept, the FT of the resulting transform will produce an intensity spectrum

5. If we insert a sample, the intensity spectrum will change because of absorption of specific wavelengths

6. Scan of sample is compared to a baseline scan to identify absorbed frequencies