PART II. THIN FILMS AND ION TECHNIQUES
1. Physical properties of thin films are different from the properties of bulk materials:
1. Electrical
2. Magnetic
3. Optical
4. Mechanical
5. Thermal, etc…
2. Substrate and its influence
3. Thickness dependence
Methods of deposition



PHYSICAL
o Evaporation
o Sputtering
o Printing
CHEMICAL
o CVD
o LPE
PHYSICO-CHEMICAL
o Electroplating
o Polymerization
vapor
vapor
liquid
vapor
liquids
2.1. Evaporation
Basic concept: melt the source and evaporate in vacuum.
Main problem: Interaction with residual gases (mean free path)
On the substrate:
K=Nd/Ng= K=
M 0T 1
N d Aρ
=
v dep
Ng Md
3.51*1022 p
Where: A - Avogadro number,  - specific mass of the deposit [g/m3], Md - molecular mass of the
deposit, vdep - speed of deposition [A/s], p – pressure [Tr].
Example: Residual gas N2, deposit Al, vdep= 1A/s
K= 1.6*10-3 @ 10-4 Tr; 1.6*10-1 @ 10-6 Tr, 1.6 *101 @ 10-8 Tr
Realistic pressures require minimum deposition speed of the order of 10 A/s
Thickness distribution of a source
Mass evaporated in a unit time:
dm
=f( )
dω
Two models for describing real sources:
 Isotropic source – point source : f(const.
 Planar source f(cos
Real source – a mixture of a number of plain and point sources
In real systems the thickness distribution does not depend only on the source characteristics but also on
the source-substrate geometry.
L1,L2, > L0
Averaging by rotation – see fig 21a
Sources
Resistive (fig 21 b)




Interaction between the source and the deposit
Wetting
Geometry
Sublimating materials
Electron beam sources
 Electrostatic
 Magnetic
Scanning sources
Needs careful cooling
X-ray emissions
Flash sources – flash evaporation
For materials with changing composition (eg 21 e)
Substrate cooling and heating


Resistive
Halogen lamp
Substrate preparation and cleaning




Mechanical
Chemical
AC glow discharge
Baking
2.2. Sputtering
Basic concept
1.
2.
3.
4.
DC and RF sputtering
Bias sputtering
Reactive sputtering
Chemical sputtering (ion etching)
Physical effects of ion bombardment on surfaces
1. Emission of neutral particles from the target.
The sputtering yield: the number of neutral particles emitted per an incident ion.
See table 1.
2. Emission of other particles
a.
b.
c.
d.
Secondary electrons.
The secondary electrons are accelerated away from the negative target with the energy of the
target potential. They help to maintain the discharge. Many get thermalized but still many
reach the substrate with the full energy.
Secondary ions.
The basics of SIMS(secondary ion mass spectroscopy). Most of the SIMS data deals with
positive ions. In sputtering, it is highly improbable that positive ions would escape the negative
target field. The negative ions result from sputtering of anionic species of compounds and high
electron affinity constituents of alloys. Negative ions are accelerated away from the target
toward the substrate. Due to interactions in the gas plasma arrive to the substrate as highly
energetic neutrals.
No negative ions while sputtering pure metals.
Reflected incident particles.
The basic of ISS (ion scattering spectroscopy). One more source of substrate bombardment.
These medium energy particles may be neutralized.
Desorption of gases.
Leave the surface as negative ions – problems with porous targets.
3. Radiation emission due to sputtering.
a.
b.
UV and visible photons. Close to the target there are Auger-like electron transitions in the
excited sputtered ions with subsequent emission of characteristic photons of the metal. These
electronic transitions do not apply to dielectrics and compounds.
X-rays. Something capable of damaging the film.
4. Ion implantation.
5. Altered surface layers and diffusion.
While sputtering a multi-component target the composition of the surface changes due to a
difference in the yield for various components. In the steady state the altered layer of a different
 , for
composition from the bulk is formed. For metals the thickness of the altered layer is ~ 10A
.
oxides ~ 1000A
Glow discharges
dc glow discharge
(see fig. on page 64)
Formation of the glow discharge under increasing power from the power supply in a form of a high
impedance sourceInsert fig p.64:
In subsequent steps one observes:

Small currents due to natural ionization (thermal, cosmic rays, etc)

More energy, current increases at a constant voltage due to the limit imposed by the output
impedance of the power supply (“Townsend discharge”)

Avalanche effect (due to secondary electrons). Voltage increases, but the current increases
much faster. - when the number of electrons is just enough to produce enough ions to regenerate
the same number of electrons – the discharge becomes self-sustaining – “normal glow”. The
current grows until the entire cathode surface is covered with the glow and there is a uniform
current density. This regime was used in voltage regulator tubes.

When the whole cathode surface is covered, further increase in power results in increase of both
voltage and current density in the discharge – “abnormal glow”. This is the regime, which is used
in sputtering.

If the cathode is not cooled then at about J~0.1 A/cm2 thermionic electrons are added to the
secondary ones, followed by a further avalanche. The output impedance of the power supply limits
the voltage and a low voltage, high current arc discharge forms.
Crucial to the formation of an abnormal glow is the breakdown voltage, V B. VB depends on the
mean free path of the secondary electrons and the distance d A-C between the anode and the cathode.
Each secondary electron must produce 10 to 20 ions for the avalanche to occur. Paschen’s low
describes the dependence of VB on the product pd A-C
Zone I:
VB increases as
pd A-C decreases, since there are
not enough collisions.
Zone III:
VB increases with increasing
pd A-C because due
to many collisions the secondary electrons are
too slow to ionize.
Most sputtering systems operate on the border between zone I and II. This requires relatively high
discharge starting voltages.
Solutions:

ignition electrode

ignition gas burst

ignition instantaneous shortening of the A-C distance

additional source, e.g. Tesla coil
Luminous regions of dc glow discharge
(See Fig. 22a)
1.
2.
3.
4.
Adjacent to the cathode –cathodic glow (very brilliant). In this region secondary electrons start
to accelerate and positive ions produced at the cathode are neutralized. The light is
characteristic of both the cathode material and the incident ion (gas).
Secondary electrons at high velocities start to make collisions with neutral gas atoms at a
distance away from the cathode corresponding to their mean free path. This leaves well-defined
dark space. Since electrons rapidly loose their energy in collisions, almost all of the applied
voltage appears across the dark space. Thus the darks space is the region in which positive ions
are accelerated towards the cathode. The mobility of electrons is much higher than the mobility
of ions, therefore, the predominant species in the dark space are ions.
The negative glow -- the region of ionizing collisions by accelerated secondary electrons.
Faraday dark and positive glow columns are nearly field free regions, solely connecting
electrically the negative glow to the anode. Both regions are not essential to the operation of a
glow discharge. In most systems the anode is located in the negative glow, and other regions do
not exist.
The length of unobstructed negative glow corresponds to the range of electrons accelerated from the
cathode. If the negative glow is truncated, higher voltages have to be applied to compensate for the ions
that would be generated in the part blocked by the anode. In general for uniform operation the anode
should be located at least 3 to 4 times the length of he cathode dark space (this distance is inversely
proportional to the pressure)
ac and rf glow discharge
ac – typically up to 50kHz where ions are mobile enough to follow the voltage and form a dc like
discharge on alternating both electrodes. When f >> 50kHz we deal with rf discharge where:
1.
electrons that oscillate in the glow space acquire sufficient energy to cause ionizing
collisions – lower breakdown voltage VB
2.
Electrodes no longer need to be electrical conductors since rf voltage can be coupled
through any type of impedance – possibility of sputtering dielectric materials!
How the sputtering occurs at all if ions at rf are relatively immobile (typical rf =13.56 MHz). The
answer: when rf bias is capacitively coupled to the electrode, pulsating negative voltage develops on the
cathode – sputtering effect.
Due to difference in mobilities of electrons and ions the I-V characteristics of a glow discharge
resembles that of leaky rectifier.
(Insert fig. From page 70)
After the first cycle there is a difference in ion and electron current. Since no charge can be transferred
through the capacitor the voltage on the electrode must self – bias it negatively until the net current
(averaged over the cycle) is zero.
In order to sputter from the target only one couples the target via a capacitor to the generator, and the
area of the capacitively coupled electrode must be small compared to the area of the dc-coupled
electrode because:
Vc  A d 


Vd  A c 
4
Vc ,- Voltage between the glow space and the capacitively coupled electrode. A c - area of the
capacitively coupled electrode. Vd , A d - voltage, area of the direct coupled electrode. To minimize
the spurious sputtering from the dc coupled electrode Ad>>Ac is required. In practice the dc-coupled
electrode is constituted by the system (chamber walls + baseplate), so the ratio is high.
The disstribution of the potential in the system : (insert fig. on page 71)
Discharge support modes
 axial magnetic field, perpendicular to the target surface
 rf coil
 thermoionic support – triode system
Ions generated in a low voltage (~50V), high current (5-20A) arc discharge between a thermoionic
filament and a main anode. The target is located in the main discharge and ions are extracted from
it toward the target that can be powered either by dc or rf source. Triode systems are mainly used
for ion etching processes requiring large amounts of ions.
Equipment for sputtering
Schematic of an rf sputtering equipment – insert fig p.73 (see fig. on page 73)
Target




heat dissipation (water cooling)
electrical isolation and contacts (cooling water lines at high voltages!)
ground shielding (to prevent sputtering from target construction elements)
construction materials: Stainless steel, copper, aluminum (corrodes in water!)
Power supply
 dc source
output power depends on the target size. It should be capable of delivering 10W/cm2 at voltage
up to 5kV (this does not apply to magnetron sputtering which requires higher currents at lower
voltages)
 rf source
Set to one of the ISM (Industrial-Scientific-Medical) allocated frequencies. For the ISM
frequencies there is no limit on the radiated power. The often used ISM frequencies are: 13.56
MHz, 27.12 MHz, and 40.68 MHz
Output impedance of rf generators is usually 50 while that of the glow discharge is much higher matching network needed. We employ the solutions known from radio emitting generators
matching to the station antenna. Matching circuitry is located close to the target assembly.
Solution for a single ended sputtering:
Insert figure p.74
For bias sputtering power splitters are needed.
Power regulating and matching is done by variable coupling:
(see fig. on page 74)
Instrumentation and control
Parameters to monitor:
 dc voltage
 dc current
 power (in rf systems)
 pressure
In rf systems control also the matching by means of
 SWR meters
 Power split ratio
 Self bias meter
Film specific parameters:


Substrate temperature
Thickness and rate of deposition
Scale-up problems
From a lab system to a large industrial plant.
Each application must be treated as a special case.
Preparation and preconditioning of targets, substrates and systems for
deposition.
Targets



bonding the target to the electrode
presputtering (no change of sputter conditions are allowed afterwards)
target errosion problems
Substrate – sputter etch cleaning


organic contamination – best sputter in O2
contamination of the target while sputtering onto the shutter: use “catcher” shutters when
cleaning the substrate
Sputter gas
Work horse of the sputtering systems – Argon. Maintain constant flow and pumping to remove
contamination and to operate in a pure gas. Argon purifiers: Palladium filter.
Getter sputtering
To reduce the amount of background contamination, presputter on a cooled cylinder enclosing the
target, and only later open the shutter. Example: Nb, Ti, superconducting films.
Reactive sputtering:
Sputter in an active gas to obtain chemical modification of the target material.
 Sputtering in air (O2, H2O) – oxides
 Sputtering in N2, NH3 – nitrides
 Sputtering in O2 + N2 – oxynitrides
 Sputtering in H2S – sulfides
 Sputtering in C2H2, CH4 – carbides
 Sputtering in SiH4 - silicides, etc…
Bias sputtering
Any material body immersed in a glow discharge acquires (when not grounded) a floating potential
which is slightly negative with respect to the ground. Floating potential results from the difference in
mobility of electrons and ions, and can be shown to be
Vf =-
kTe πm
ln
2e 2M
Where m and Te stands for electron mass and electron temperature, respectively, M is the ion mass.
The substrate in glow discharge may be treated as floating plane Langumir probe of a characteristics:
(see fig. on page 78)
At the point Vp the probe is at the same potential as the plasma (plasma potential is
Vp ~kTln
 2/qi 
i
Where Ti and qi are the temperature and charge of the involved ions. The equations for Vp and Vf are
drown in the approximation of no magnetic field and they can be used to evaluate T i and Te.
N.B. If the substrate is dielectric and the holder is grounded then the substrate will be at V s and the
holder at Vs-Vf. In consequence there will be non-uniform bombardment resulting in variable thickness
and composition. Good rule is “Do not ground the substrate”.
To protect deposited films or to modify their properties – biased deposition. Positive bias results in
large electron current, hence heating. Negative bias enables ion implantation - e.g., deposition of TiN.
Magnetron Sputtering
Limitations of conventional sputtering:
 yield (rate of deposition)
 pressure limits (the yield is high between 50 to 150 mTorr, see graph p 80)
 high voltage requirement
The magnetron sputtering principle: magnetic field is used in concert with the cathode surface to form
electron traps that are so configured that E x B electron drift currents close on themselves. This method
is used also in microwave generators, also named magnetron. The method can work both with dc and rf,
at different configurations hollow, cylindrical, planar, or gun. (see fig 22 d,e)
Magnetron sputtering
V – 800 V
B – 150 G
p – 1 mTr
J – 20mA/cm2
r (Ar,Ni)– 2000 A/s (at the target 12000 A/s)
No plasma bombardment of the substrate
Classical sputtering
V – 3 kV
dca - 4 to 5 cm
p – 75 mTr
J – 1mA/cm2
r (Ar,Ni) – 360 A/s
Substrate exposed to plasma
Magnetron source is the best high rate source can be used in planar, circular or rectangular
configuration (Fig. 23b).
Problems: erosion profile – max usage of the target volume up to 20% only. Solution: Patents by Sloan
and Varian, the Sputter gun and the S-gun (Fig. 23 e,f)
Technical problems:
 The need for small and very strong magnets – almico alloys from the rare earth ferrites.
Magnetron magnets have to work in an “open” configuration and high coercion is required – no
loss of magnetic field is allowed (Fig. 23c).

Isolation, cooling, and cathode shielding (O’ ring protection) Fig. 23d.
Some amazing historical remarks comments:

US patent 1939 Penning (for a magnetron principle ion pump)

1939/40 microwave magnetron source for cm-wave radar

the first time used for deposition 1969 (!) Meissel

deposition patent 1974

commercially available 1975

full version (rf + bias) 1976
Ion Beam Deposition
Primary/Direct:
ion beam consists of the desired materials and is deposited at low energy (around 100 ev) directly onto
the substrate.
extractor
ion beam
ion source
substrate
Secondary
substrate
extractor
ion beam
ion source
target
Ion sources
Penning (Fig. 23e)
The opened cathode acts also as an extractor. The spread of ion energies is 10 - 50 eV.
Kaufman (Fig. 23f)
This is an extension of the Penning concept, which includes a thermionic cathode and a proper
extractor. Heated cathode allows operation at low pressures and voltages (50V). The spread of the ion
energy is 1 – 10 eV. Control the emission rate by controlling the electron emission rate. Output grid –
double-screen grid (~1400 holes of 0.21 mm diameter within the 10 cm dia) + accelerator grid. Density
of Ar ions from a 10 cm source: 1 – 2 mA/cm2 at a beam energy of 500 – 2000 ev. Ionization efficiency
~ 75%.
Duplasmatron (Fig. 23g)
For high intensity, narrow beams. The name reflects the dual manner of constricting the plasma in an
arc discharge by both electric and magnetic fields.
The filament supports 1-2A arc between the anode and the cathode (80V discharge voltage). There is
“in between” electrode “Zwischen” cathode at the intermediate potential of 40V. The canal-shaped
aperture in this electrode confines the discharge electrically and 0.1 – 0.3 T magnetic field between the
Zwischen electrode and the anode constrains the plasma axially.
The diverging magnetic field region shapes a plasma meniscus next in the anode aperture (Fig. 22h)
which becomes the emitting surface for ion extraction.
Ar ion currents above 2 mA are obtained at about 20 keV beam energy through 300 m dia aperture
with the energy spread of 10 – 50 eV.
BEAM EXTRACTION AND CONTROL
Ion extraction
Ions in the plasma diffuse to the boundary where they can get extracted by an electric field and form a
proper beam. The rate of extraction:
Child’s low of space charge limited current flow (as in a vacuum diode valve). For planer geometry –
two planes at a distance d and voltage V
j=
4 0
9
2q V3/2
m d2
This is the upper limit for any particle source. The determining factors are the voltage and the electrode
spacing.
For non-planar geometries the proportionality constant changes. It can be determined from the j/V 3/2
ratio.
Typically one has the extraction electrode at the ground potential and the entire source at high V.
The plasma meniscus adjusts itself to satisfy the Child’s low at the local electric field. Fig. 23i shows
normal extraction conditions and 23j shows excessive ion production resulting in the loss of the beam
collimation.
System requirements:
 materials: the cathode filaments and electrode apertures - sources of contamination. Grids
optimum material - molybdenum. Small distance between the grids – problems associated with
their thermal expansion.
 lifetime of the source: hot cathode burning out or buildup of the sputtered material in the
source. Typical lifetimes range from hours to months.
 vacuum and gas
 power supplies
Secondary ion deposition equipment
Veeco system with the 8 cm Kaufmen source, fig. 24a.
Beam diameter 7 cm, target dia. 13 cm, ion energy 200:2000 eV, beam current 30 mA.
Position 1: target presputter
Position 2: substrate precleaning
Position 3: deposition
Duplasmatron source with Einzel lens - General Louex Corp. USA. Fig. 24b:
20 keV Ar ions in 4 mm beam enables operation from very small targets, down to g amounts of the
sputtered material.
Reactive ion beam sputtering
possible configurations (insert fig. on page 87)
Primary ion beam deposition
e.g. diamond films by means of a Penning source with carbon electrodes and Argon gas. The beam
consists of C ions, C neutrals, Ar ions and neutrals. (see fig. on page 88)
Chemical methods
Typically deposition from solutions, the most popular aqueous solutions.
Deposition by a chemical reaction
e.g. Ag films for silver mirrors:
Solution of silver salt (usually AgNO3) in one solution and a reducing agent in the second solution. Two
solutions are sprayed on the surface that has been "sensitized", e.g. by dipping in a solution of SnCl2
acidified with HCl.
Most common deposits Cu, Ag, Au, PbS (for coloring brass), and Ni. Deposition also on nonconduction surfaces.
Autocatalytic chemical reduction (“electroless plating”)
Deposition of a metallic coating by a controlled chemical reaction catalyzed by the metal or the alloy
being deposited
( Mn+ + ne -> M0 ) only on catalytic surfaces
After the initiation of the reaction it becomes self-sustaining.
Example, Ni:
2H2PO2 + 2H2O + Ni2+  Ni0 + H2 + 4H+ + 2HPO32The reaction goes as follows:
HPO2 + H2O (cat.surf HPO3- + 2H+ + H2H- + Ni2+  Ni0 + H2
The efficiency may be decreased by a spurious reaction H+ + H-  H2.
Possible catalytic surface: Ni, Co, Rh, Pd, steel…Non-catalytic surface can be activated simply by
touching with a catalytic agent.
Typical electroless deposits: Ni, Co, Pd, Pt, Cn, Au, Ag.
Conversion coating
1.
2.
3.
Oxides
Chromates
Phosphates
Displacement deposition ("immersion plating")
Used more for recovery of the metal than for the actual plating. Known also as “cementation”.
Electro-deposition by electrochemical reactions
Faraday's laws (1833):
1. The amounts of chemical charge produce by the current is proportional to the quantity
of electricity that passes
2. The amounts of different substances liberated by a given quantity of electricity are
proportional to their electrochemical equivalent weights
Electrochemical equivalent weight :
e=
atomic (molecular) weight
valence change (number of electrons involved in the reaction)
For example, if Fe is being deposited from Fe2+ solution (valence change 2), e=55.85/2=27.93.
If Fe3+ would be used, then e=18.62.
N.B. an old definition of Coulomb unit: ! C is the amounts of electricity that deposits 0.001118 g of Ag
from a solution.
It follows from the Faraday's law that the amounts of electricity needed to deposit 1 g electrochemical
equivalent weight of any element is one Faraday
atomic weight of Ag
= 96.483 C = 1F
0.001118
The mass of the reacting substance is
G 
Iet
96500
where G is mass in [g], I is current in [A], e is elect. eq. weight and t is time [s].
Important factors is electroplating
1.
2.
3.
4.
5.
pH
J
T
agitation
bath composition
Chemical Vapor Deposition ("CVD")
Reaction from the gas phase to form solid on the surface. There are many types of reaction:
1. Pyrolisis,
SiH4(g)  Si(s) + 2H2(g)
2. Reduction,
SiCl4(g) + 2H2(g)  Si(s) + 4HCl(g)
3. Oxidation,
SiH4(g) + O2(g) SiO2(s) + 2H2(g)
4. Hydrolysis,
Al2Cl6(g) + 3CO2(g) + H2(g)  Al2O3(s) + 3HCl(g) + 3CO(g)
5. Nitride formation,
3SiH4(g) + 4NH3(g)  Si3N4(s) + 12H2(g)
6. Carbide formation,
TiCl4(g) + CH4(g) TiC(s) + 4HCl(g)
7. Disproportionation,
2GeI2(g) (lower temp)  Ge(s) + GeI4(g)
8. Synthesis,
(CH3)3Ga(g) + AsH3(g)  GaAs(s) + 3CH4(g)
9. Chemical transport,
6GaAs(g) + 6HCl(g)  As4(g) + As2(g) + GaCl(g) + 3H2(s)
The reaction goes forward at high temperature and backwards at lower. Lowering the
temperature in the down-stream part of the reactor initiates the deposition of GaAs(s)
10. All possible combinations of the above reactions.
Thermodynamics for calculating temperature of reaction and optimizing the chemistry. Kinetics of the
reaction - all processes determine the rate.
High pressure and low pressure CVD



High pressure - fig 24 c
Normal pressure – flow CVD – fig 24 d
Low pressure, vacuum CXVD fig 24 e.
types of CVD reactors: examples: 24f pedestal, 24g horizontal, 24h barrel and 24j pancake
Fig 25 a – epitaxial GaAs CVD
Physical-chemical methods.



plasma deposition
polymerization
plasma spraying.
Nucleation and growth of thin films
Film growth stages:
1. Nucleation 25 c
2. Nucleus growth
3. Coalescence 25 b
The growth kinetics, which determines the structure, texture and the state of the film surface, depends
on the deposition rate and the substrate temperature.
The mechanism of condensation:
V – L – S, when the substrate is hot
V – L, when the substrate is at low temperature T<T m/3, see 25 d, e.
Films quenched at very low temperatures have amorphous structure. This is the way to achieve metallic
glasses.
Pattern definition
1.


2.
3.
Master mask fabrication
coordinate table
digital techniques
Photoreduction (two stages: X 10 and X 30)
Chromium working maskes
Photoresists.
Negative photoresists (Fig 26a):
a) KMER - Kodak metal etch
b) KPR - Kodak photo-resist
c) KTFR - Kodak thin film
d) KPL - Kodak photo-resistive lacquer
Resolution increases from a) to d). Chemical resistance increases from d) to a
Positive photoresists.
AZ 1350
AZ 1350 H (hard)
AZ 1350 J (electron sensitive resist)
Photoresit processing:
1. Spinning
2. Drying – sensitive.
3. Exposing
4. Developing
5. Rinsing
6. Drying
7. Hardening
Lift-off techniques
Fig 26 b,c,d. Projection exposure through the transparent substrate to avoid undercuts (fig. 26e)
Equipment
(Carl Suss - Switzerland)
Exposition and mask aligner (Fig. 27a)
Substrate table (Fig. 27b) and table movement system (Fig. 27c)
Infrared alignment (Fig. 27d)
Laser alignment and exposition (Fig. 27e,f)
Etching process





Chemical
Plasma
Ion
Reactive
Reactive ion etch
“undercut” issue
Thickness measurements
Optical methods
1)
Optical - interferometry (on the step edge (Fig. 28a,b))
N λ = 2 n d cosθ
Where N is the order, n is the refraction index of the film and d is thickness. Opaque films needs a step
in the thickness down to the substrate.
 Fringes of the equal thickness - Fizeau
 Fringes of equal chromatic order (parallel plate but white and nonmonochromatic light) - watch for minimum as a function of the wavelength.
2)
Optical VAMFO - variable angle monochromatic fringe observation.
3)
Elipsometry (Fig. 28c) - measure relative amplitudes and phase of parallel and
perpendicular components.
Non-optical methods
a)
Stylus - down to 10Å Computer aided. Dektac, Alphastep, etc
d=a
D1 -D 2
H
(Fig. 28d).
b) Precision weight - mass measurement (Fig. 28e,f). Quartz weight – needs
calibration for a given system-source-substrate arrangment (Z-factor)
c) X-ray fluorescence (compare intensity with standards)
d) Scattering - as c) but much simpler (Fig. 28g)