Andrey Shishkin

1. Methods of physical vapor deposition. Thermal evaporation. Adhesion. Role of vacuum. Monitoring of the deposition process. 2. Magnetron and RF-diod sputtering. 3. Electron-beam evaporation. 4. Engineering aspects of physical vapor deposition: vacuum chambers, pumps, cooling systems. 5. Monitoring and control of the deposition processes. 6. MBE based technologies.

Physical vapor deposition, PVD

Physical vapor deposition (PVD) systems deposit thin films and coatings by a process in which a target material is vaporized, transported in vacuum, and condensed on to a substrate. PVD processes include Sputtering, Electron beam, and Thermal Evaporation.

• Thermal evaporation • In-situ control of the film thickness. Estimations of the film uniformity. • Electron-beam physical vapor deposition • Sputtering deposition, magnetron sputtering deposition • Cathodic arc deposition. • Reactive deposition • Laser ablation • Role of vacuum conditions • Vacuum systems for the physical vapor deposition. Pumping systems. • Adhesion of coatings. • Types (modes) of thin film growth. • Several important examples of different coatings. Thermal evaporation Thermal evaporation is realized by thermal heating (usually resistive) of an evaporated material placed in an evaporation source. It is carried out in a vacuum at pressure P<10-5 torr. The thermal evaporation is the most gentle PVD method with evaporated particle energies ~1500 K (0.12 eV). This method is the simplest PVD method and needs comparatively low power consumption.

Main types of simple evaporation sources are metallic boats (1,2) and heaters made of refractory wires (3) (Wo, Mo,…) which can be covered by a passive material (2)

(Al2O3) More complicated effusion cells with a crucible made of passive material (e.g., boron nitride, BN) and an external heater are used for precision evaporation processes like the molecular beam epitaxy. A simple system for thermal evaporation

Vacuum chamber 1 is evacuated to pressure of the order of 10-6 Torr via the pumping line. The pressure is measured by vacuum gauge 2. A material 3 is evaporated from a metal boat 4 heated by an electric current. The current flows through an isolated vacuum tight lead 5, which is usually cooled by water (not shown in Fig.), and grounded lead 6. A substrate 7 is mounted on a holder 8. The holder may have options of rotating around vertical Pumping axis and tilting relative to it. The latter option line corresponds to the so named oblique evaporation. These options help to avoid undesirable shadows. The temperature of the holder may be varied and stabilized in a wide range. The thickness of evaporated film is controlled by a thickness monitor based on a quartz crystal microbalance 9 (QCM). QCM measures variation of a mass on a surface of a quartz crystal resonator. For a high accuracy measurements the crystal should stay at a constant temperature. The evaporation process is controlled by the current through the boat (i.e., the boat temperature) and the shutter 10 position. The shutter is closed till reaching the desired boat temperature and beginning of the material vaporization. It closes at the end of evaporation process. Thickness of deposited films: control and uniformity.

I. Thermal evaporation provides the best conditions for in-situ control of the average film thickness. A real – time film thickness monitor can use different sensors: (i) A quartz crystal microbalance, (ii) Reflection high-energy electron diffraction (RHEED) (in the molecular beam epitaxy), (iii) optical methods including ellipsometry. A simplified geometry of the quartz resonator, produced by a cylindrical quartz plate 1 and metallic films 2,3 on opposite sides of the plate. To excite the mechanical oscillations in the plate the ac voltage Vf is applied between films 2 and 3. The resonator is a part of an oscillator which frequency f is determined by the resonant frequency of the mechanical resonator (typical value ~5 MHz). The Q-factor of the mechanical resonance can be as high as 106. Evaporation of a thin film with mass  m shifts the resonant frequency by

Here f0  nN 0 / D is the resonance frequency without evaporated film, N0  1.661 MHz*mm for the quartz AT cut; n - is an integer numbering different resonant overtones, D-the plate thickness, S- active area of the resonator. 2 3 11 g/cm s - shear modulus for the AT cut 0  2.648 g/cm – density of the quartz , 0  2.947 *10 of a quartz crystal. . Quartz crystal microbalance For Au ( =19.3 g/cm3) film, one monolayer (d~3A) corresponds to  f=33 Hz. Temperature stabilization is important condition for precise measurements!

Equation (Q1) is valid for  f / f0  0.03

For a wide frequency range ( f/f0<~0.3) a more complicated equation is used:  f  f   m N 0  0  0  arctg Ztg  S Zf   f0 

  Here Z  0 0   and  are the density and shear modulus of evaporated film. 

Difficulties and ways to overcome them: 1. All geometries of evaporators are unique. Also we can have different positions of the substrate – the sensor needs often calibration. 2. Heating of the quartz resonator – we need cooling system which makes the system more complex. 3. Deposition of different materials on the same sensor – it can be eliminated by the use of several sensors: one for each material. Estimate for the thermal evaporation rate

, ma dm / dt  P(Tev ) 2kTev

Here dm/dt – the mass rate of evaporation from a unit area, ma – mass of evaporated particle, P(Tev) – the vapor pressure at evaporation temperature Tev . This formula is equivalent to the well known equation of the molecular kinetic theory for the particle flow Ns /t on a unit flat area: Ns /t=nV av /4 where n is the particle density and 1/2 Vav=(8kT/ma) is the average particle velocity determined from the Maxwell‘s distribution.

P(T) is usually described by the Clausius–Clapeyron equation

Q is the specific latent heat of the phase transition (vaporization)  V i s the specific volume change of the phase transition (the difference of specific volumes of a liquid and vapor). dP PQ Q  ln P    A  A  B / T For an ideal gas and dQ/dT=0 2 which gives (Q2) dT T R TR Temperature dependence of the vapor pressure

Temperature dependences of the vapor pressure P on the temperature T (horizontal scale is inversely proportional to T) for Au and Ti. Solid lines were calculated in accordance with Eq. (Q2) with the use of parameters 4 AAu=20.84 and BAu=4.26x10 K (liquid-vapor). 4 ATi=23.81 and Bti=5.67x10 K (solid-vapor). The solid signs are taken from handbook “Physical quantitites” edited by Grigor’eva and Meilikhov (1991).

The melting points Tm are marked by vertical by arrows.

Equilibrium vapor pressures of selected materials. The slashes indicate the melting points (MPs). Typical for the thermal deposition value of the vapor pressure 10-2 Torr is marked by the horizontal arrow. Some of the materials are evaporated and some are sublimated. Sublimation of metals is possible by their direct heating by passed current (e.g., Ti). Angular distribution of atomic flow

A general geometry of evaporation.  is the angle between the normal to the surface element dS1 of the evaporator and a direction R to the surface element dS2 of the substrate. R is a distance between these elements. The angle between R and a normal to dS2 is   Projection of the dS2 on the plane normal to R is dS0= dS2cos(   A part dw of a total flux w from a flat source into a small solid angle d in the direction determined by angle  is given by equation dw=(w/) cos( )d . This relation is the result of the maxwellian distribution and an analog of the Lambert law in the optics.

For evaporated mass m, the film thickness is d= m cos( )cos(  /R2 If the source is spherical, dw=(w/4) d and d= m cos(  /4R2

Coordinate dependence of the thickness of the deposited films

substrate Consider thermal vapor deposition from a small flat source on parallel substrate . This corresponds to  = , cos  =H/(H2+X2)1/2 , R2=H2+X2. m 2 m 1 d ( X )  H d   (H 2  X 2 )2 max  H 2 Flat source

m H m 1 d ( X )  2 2 3 / 2 d max  Spherical source 4 (H  X ) 4 H 2 source

Thickness distribution along the substrate for a small flat (black 1.0 Spherical sourc(ea)

lines) and spherical (red lines) sources. Panel b shows initial part of 0.8

x 0.6

panel a. ma These data show that condition of thickness uniformity leads to d/d 0.4 requirement of a large distance between the source and the substrate, 0.2 Flat source 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 i.e., to a large size of a vacuum system. 1.1 (b)

Theoretical calculations may be inaccurate due to a finite size of the 1.0

x

source and redistribution of the temperature along it. However some a 0.9

m d/d of these factors may even lead to a better film uniformity. In fact, in 0.8 practice the optimal conditions are chosen empirically and 0.7 0.0 0.2 0.4 reproduced from one evaporation cycle to another. X/H Advantages of the thermal evaporation method

• The most gentle PVD method, due to the lowest possible energy of evaporated particles (~1500 K~0.12 eV). • Atomic or molecular deposition from the vapor. • Appropriate for deposition of a large number of materials. • Appropriate for ultra-high vacuum conditions. • In-situ control of the deposited layer thickness. • Wide range of the evaporation rate. • Estimation of the film thickness uniformity.

About thermal evaporation of particular materials see 1. Thin Film Evaporation Guide http://www.vem-co.com/guide 2. Напыление пленок в вакууме (Physical vapor deposition, PVD) by С.И. Дорожкин, МФТИ (2012) Electron-beam physical vapor deposition (EBPVD) A focused electron beam is emitted from an electron gun and deflected to the evaporated material by magnetic field. Energy of electrons is determined by the acceleration voltage of 1-10 kV. The electron beam diameter is usually about several mm and the total power can reach 10 kW. At such conditions, local temperature of the evaporated material can be in excess of 3500 K, which allows for evaporation even very refractory materials. The crucible is kept rather cold due to the cooling by a water flow. High vacuum is necessary not only for evaporated atom transport but also for long life of the cathode of the electron gun. Typical pressure P<10-5 Torr. A local pressure at the heated surface may be rather high, so that the evaporated atoms first will move diffusively. Ballistic motion begins at some distance from the source surface. Electrons may also ionize the atoms of residual gas and of evaporated material. Magnetic field helps to avoid the direct flow of desorbed atoms from the electron gun area to the substrate and the appearance of the evaporated material and ions in the gun area.

Electron-beam physical vapor deposition (EBPVD)

Electron beam evaporators can be rather compact due to the use of the magnetic field H

The electron beam radius is given by formula 2m U c R  e R[cm]  1.8 U[kV ] / H[kG] | e | H

Features of the electron beam evaporation method. • A very wide range of evaporation rates (0.01 nm/s – 0.1 m/s) • A large number of metals including refractory ones. • Atomic deposition from the vapor. • Evaporation of source material only. • Appropriate for high vacuum conditions. • In-situ control of the evaporated layer thickness (small thicknesses). Deposition of a material sputtered by ions

Sputtering by ions is a very effective method due to high possible ion energy and a large mass. The sputtering normally leads to extraction of atoms from a source material. The extracted atoms may have energy of several eV.

While the high energy ions can be produced by separate ion sources, usually a scheme with ionization of the incoming sputtering gas by high energy electrons directly in the coating chamber is used. Inert argon is frequently used as a sputtering gas.

The method is suitable for a reactive deposition of different compounds of the sputtered material with the use of an appropriate sputtering gas Sputtering process

One ion usually transfer its energy to many atoms of a solid target and can sputter many atoms if its energy Ei greatly exceeds the binding energy Et. It also leads to the fact that the threshold ion energy Ethr >> Et (Ethr~20-50 eV while Et~3-6 eV). The sputtering coefficient

 s p u t depends on the ion energy and mass.

+ for Ar at Ei=600 eV

Theoretical energy distribution of sputtered atoms has maximum at E=Et/2. Here  is the angle to the target normal. Magnetron evaporation

Schematic of the magnetron operation. The cathode is made substrate of evaporated material. It is bombarded by ions produced film anode due to collisions of a gas (usually Ar atoms) with electrons. + + e Both ions and electrons are accelerated by electric field E e + plasma applied between cathode and anode (typical electrical Ar e e H + A+r voltage is several hundred volts). The gas is supplied + through the fine control needle valve to a typical pressure cathode-source (-) N S N ~10-3 Torr. To enhance the probability of ionization of the S N S magnetic system gas atoms by electrons, the magnetic field (0.2 – 2 kG) is lines of electric Ar e -electrons -argon atoms E and magnetic applied which causes electrons to move along spiral orbits -sputtered atoms + -argon ions H fields centered on the magnetic field lines instead of along short straight lines parallel to the electric field. The magnetic field only slightly effects motion of ions due to their large mass. The plasma arises in the region with the largest magnetic field. The cathode material is sputtered by the ions. The atoms of the sputtered material move in different directions and, in particular, cover the substrate. Typical parameters of the process. •The gas pressure 10-3-10-1 Torr, •Electrical voltage applied between cathode and anode 300 – 1000 V; •Magnetic field at the cathode 0.2-2 kG; •Current density on the cathode up to 10 А/cm2; •The supplied electric power up to 10 kW. Uniformity of the film thickness produced by the magnetron deposition method

Coordinate dependence of the relative copper film thickness produced by the magnetron deposition method. Diameter of the source material on cathode is 76 mm. The data are obtained for two different depositions (different symbols) for two different distances (102 mm, red symbols) and 152 mm (blue symbols) between the cathode and the substrate. (Data from PVD Products Company) Features of the magnetron deposition method.

•A high evaporation rate. • Rather good adhesion of the coating due to high energy of sputtered atoms. •A large number of materials including refractory ones. Dielectrics are deposited with the use of the RF voltage. • Atomic deposition from the vapor. • Possibility of a reactive deposition with the use of an appropriate sputtering gas.

• (-) Inappropriate for high vacuum conditions. • (-) Not very clean coatings. • (-) Difficulty to control uniformity of the film thickness. • (+-) In-situ control of the evaporated layer thickness is problematic. • (-) Possible damage of the evaporated film or a substrate material by high-energy electrons. RF-magnetron High-frequency magnetron sputtering is used when it is necessary to apply dielectric films. Previously it was assumed that the sprayed material has good electrical conductivity. At the same time, the working gas ion hitting the cathode is neutralized on it and returns to the vacuum volume of the working chamber. Schematic representation of bipolar pulsed power If the sprayed material is a dielectric, then the positive ions are not neutralized and within a short period of time after the supply of a negative potential, the target is coated with a layer, creating a positive charge on its surface. The field of this charge compensates for the initial field of the cathode, which is under negative potential, and further sputtering becomes impossible, since the ions from the discharge are not attracted to the target. Therefore, dielectric targets cannot be sprayed in a constant electric field. To ensure sputtering of the dielectric target, it is necessary to neutralize the positive charge on its surface by applying a high-frequency alternating potential. When replacing a DC voltage with an alternating dielectric target, it is bombarded with ions only in the negative half-period of the supply voltage. In other words, the sputtering of the target does not occur continuously, as in cathode sputtering, but discretely with the frequency of the supply voltage (usually 13.56 MHz). At high frequency and the distance from the target to the substrate matched with it, the electrons in the middle part of the high-frequency discharge do not have time to reach the electrodes during the half-period, they remain in the discharge, making oscillatory movements and intensively ionizing the working gas. Cathodic arc deposition Steered cathodic arc source Electrical arc in a vacuum is a region of plasma produced by positive ions of a cathode material and electrons. The arc current is concentrated in small cathode spots about several microns in diameter . The current density in the spots is of order of 106 A/cm2. It produces local temperature up to 15000 K, which is accompanied by intensive material evaporation, emission of electrons and vapor ionization. The spots disappear in a one place of a cathode and appear in another shifting along the cathode. The arc starts by touching a cathode by an ignitor electrically connected to anode. A low pressure gas, if present in the chamber, is also ionized Random cathodic arc source and produces a compound with cathode material (Superhard (photo) coatings by nitrides like TiN, etc). Features of the cathodic arc deposition

•(+) Very high evaporation rate. • (+) Ability to produce extremely hard coatings in the reactive process. • (+) A large number of materials including refractory ones. • (-) Difficulty to control uniformity of the film thickness. • (-) In-situ control of the evaporated layer thickness is problematic.

•(--) Presence of small drops in the ionized vapor of the cathode material. Needs special arrangement to be avoided. Laser ablation

Under high power laser irradiation the target injects a vapor formed by individual atoms, ions, atomic clusters and even small drops. A pulsed regime is usually used. For example: Nd:YAG laser (neodymium-doped yttrium aluminum garnet; Nd:Y3Al5O12) , ~10 nc pulse, ~1J/pulse, 10 Hz repetition. Particular composition depends on the evaporated material and laser power. The method is compatible with ultra-high vacuum conditions and allow to keep a complicated composition of a compound in the course of deposition Comparison of different PVD methods.

Thermal evaporation. Low energy atomic beams, compatibility with ultra-high vacuum conditions, stability and precision control of deposition rate, possibility of simultaneous deposition of several materials from different sources. Inappropriate for some refractory materials, special cautions to improve the adhesion to some substrates. Electron beam evaporation Appropriate for many materials including refractory ones, compatible with ultra-high vacuum conditions, wide range of deposition rate, heating of the evaporated material only. Inappropriate for films and substrates sensitive to the electric charge, problems with stabilization and control of the evaporation rate, limited target utilization. Ion sputtering. Appropriate for many materials including refractory ones, possibility of reactive deposition. Incompatible with high-vacuum conditions, possibility of undesirable contamination of the sputtering gas atoms in the deposited material, limited target utilization (~30% for magnetrons) Laser ablation. Appropriate for many materials including refractory and compound ones, compatible with ultra-high vacuum conditions. Complicated composition of the vapor: atoms, molecules, ions, droplets. Role of vacuum Flux of molecules Pressure, p, Torr Concentration of to the surface, I, Mean free path, Monolayer molecules n, cm-3 cm-2 s-1 λ formation time, τ

760 2x1019 3x1023 700 A 3 ns 1 3x1016 4x1020 50 μm 2 μs 10-3 3х1013 4х1017 5 cm 2 ms 10-6 3х1010 4х1014 50 m 2 s 10-9 3х107 4х1011 50 km 1 h

Table of characteristic values for nitrogen molecules at room temperature. The sticking coefficient is assumed to be 1. The surface concentration of one monolayer is assumed to be equal (which is close to the actual magnitudes for solid surfaces). To study the surface at the atomic level, it is absolutely necessary that during the experiment this surface should remained almost unchanged. This means that the flow of molecules from the surrounding volume to the surface should be very small. Pressure dependences of characteristic parameters (an estimate)

A unique line correspond to either P (left scales) or P-1 (right scales) dependences. Some absolute values depend on the molecular mass and cross-section. Measurements of the pressure Three main physical properties: 1. Mechanical deformation allows measurements of a differential pressure. If the reference pressure is known constant an absolute pressure is measured. 1000 bar – 0.1 bar – usual dial bourdon gauges with atmospheric reference pressure (1). 100 Torr – 10-1 Torr – precision mechanical manometers with evacuated reference volume. 1000 Torr – 10-3 Torr – precision capacitance manometers (2). 2. Measurements of the gas thermoconductivity allows for measurements in the range 1000 Torr -10-5 Torr. (Modern Pirani vacuum transducers (3)) 3. Measurements of ion current with the ion ionization being produced by a high-energy electrons allows measurements from 10-2 Torr down to 10-12 Torr. (4)

(1) (2) (3) (4) Adhesion

Adhesion is the tendency of dissimilar particles or surfaces to cling to one another (cohesion refers to the tendency of similar or identical particles/surfaces to cling to one another). The forces that cause adhesion and cohesion can be divided into several types. The intermolecular forces responsible for the function of various kinds of stickers and sticky tape fall into the categories of chemical adhesion, dispersive adhesion, Dew drops adhering to a spider web. and diffusive adhesion. In addition to the cumulative magnitudes of these intermolecular forces, there are also certain emergent mechanical effects.

Dependence of friction coefficient on the environment Adhesion of coatings.

Adhesion determines the quality of a mechanical contact between the substrate and the coating.

1. Inter-diffusion of materials in contact as well as chemical reactions between them provide the strongest adhesion. Corresponding energy usually exceeds 1 eV per particle. 2. Van der Waals forces lead to so-named physisorption (10-100 meV).

Vacuum cleaning and ion (electron) bombardment can remove adsorbed atoms/molecules from the substrate surface and highly improve the adhesion.

The best adhesion to a metallic substrate have metals producing alloys with the substrate material. A good adhesion to the oxide surfaces (e.g., glass) have an oxygen-active film materials such as Ti, Cr, Mo, or Zr. E.g., the Cr films are usually used in photo-masks for optical lithography. These materials are frequently used as an intermediate thin layer (~10 nm) between a substrate and a main film.

In general, the higher energy of evaporated (sputtered) particles leads to their better adhesion. As a result, one gets better adhesion in the cases of cathode arc deposition, magnetron sputtering and electron-beam evaporation. It may be related to desorption of extrinsical adsorbates from the substrate surface. Some materials (e.g., Zn, Cd) may have very poor sticking coefficients to many substrates. Pumping systems Two main mechanisms of the gas evacuation: (I) Compression and pumping out. (II) Adsorption . Usually applicable under high vacuum conditions in the absence of a gas flow.

Dry pumps

Wet pumps Rotary vane vacuum pump Leibold Trivac B The Principle of Operation is transfer of a mechanical pulse from oil vapor molecules to gas molecules resulting in their average motion from a pumed area to forevacuum area

100m3/h= 27.7 l/s; 1 mbar=0.75 Torr Oil diffusion pump The principle of operation is transfer of a mechanical pulse from oil vapor molecules to gas molecules resulting in their average motion from a pumped area to forevacuum area Dry preliminary pumps: diaphragm pump. Scroll pump Screw pump

Pump Model SP250 SP630

Disp. CFM @ 60 Hz 177 (250) 371 (630) (m3/hr @ 50 Hz)

Ult. Pressure Torr 7.5 x 10-3(1 x 10-2) 7.5 x 10-3(1 x 10-2) (mBar)

Motor HP (kW) 7.9 (5.9) 20 (15)

Dimensions 5.1 x 20.9 x 34.6 64.2 x 26 x 34.6 LxWxH - in. (mm) (1,350 x 530 x 880) (1,630 x 660 x 880)

Weight lbs (kg) 992 (450) 1,166 (530) Roots pumps

Roots pumps are usually used at the pressure range between 10-1 Torr and 10 Torr, where they are very effective Turbomolecular pumps The heart of a turbomolecular pump is a turbine rotating with a speed of the order of 50,000 rpm (turns per minute). The principle of operation is transfer of a mechanical pulse from turbine blades to gas molecules resulting in their average motion from a pumped area to the forevacuum area.

Turbomolecular pumps have very different rotor diameters covering pumping rate range from tens to several thousands l/s. Turbomolecular pums may have either mechanical or magnetic rotor suspension High vacuum turbomolecular pumps

The typical ultimate pressure of the turbomolecular pumps is 10-8 Torr but may be as low as 10-10 Torr. Sputter ion pumps The basic principle of operation is adsorption of residual gases by Ti film sputtered from Ti cathode due to the ion bombardment. Other mechanisms are also involved. Magnetic field increases probability of ionization by high-energy electrons. Pressure-current dependence

Dependence of the current through the ion pump is a measure of the pressure . However this dependence should be calibrated for a particular pump and is different for different residual gases. Titanium sublimation pump

The principle of operation is adsorption of residual gases by thermally evaporated Ti film. The pumping becomes very effective when Ti is evaporated onto a cooled (liquid nitrogen or helium) panel.

Model PGT-3F PGT-6F

Pumping speed *1 24m3/(s·m2) <20ºC> / 64m3/(s·m2) <-196ºC>

Applicable pressure range Ultra-high vacuum of between 10-1 to 10-9Pa Applicable gases H , N , O , H O, CO, CO Inapplicable gases 2 2 2 2 2 Leak volume He, Ne, Ar, CH4, C2H6 , other organic gases -11 3 Baking temperature 1.3 x 10 Pa·m /s max. Power consumption 250ºC Filament material 270W Titanium alloy Rated continuous operation time *2 : About 75 Filament life span hours/filament Continuous ON time : About 25 hours/filament Number of filaments 3 6 Connection flange *3 UFC070-FH UFC114-FH

Weight 1.0kg 2.5kg Cryo-pumps

The principle of operation is condensation and physisorption of residual gases on a surface cooled by liquid 4He (T>~4K). Porous materials (charcoal, zeolite, molecular sieves, etc) highly enhance the sorption capacity and allow effective sorption of light gases (H2, He, etc) at temperature ~4K.

Temperature (K)

Zeolites cooled with liquid nitrogen are frequently used as dry preliminary pumps (P=1000- 10-4 Torr). They should be backed up after each pumping circle. Elements of PVD systems 1.Vacuum chamber of a large volume to guarantee a uniform coating 2. Pumping systems. 3.Systems for evaporation (boats, electron beam guns, lasers, etc) and sputtering (regulated needle valves, ion sources, magnetrons, etc.)

The PRO Line PVD 75 is compatible with the following techniques: Thermal Evaporation (up to four 4" individual boats, or six 2" boat assemblies) Torus® Magnetron Sputtering sources (up to six 2" or 3" sources) Electron Beam Evaporation Source (4 pocket 8cc, 8 pocket 12cc, 6 pocket 20cc) LTE10 Organic deposition sources (up to two) Combinations of the above techniques are also available. Pumping system

Pfeiffer 790 l/s turbomolecular pump with KJLC RV212 oil sealed roughing pump. Base pressure for a properly conditioned chamber is 5 x 10-7 torr (6.7 × 10-7 mbar). Wide range gauge reads from atmosphere to 10-9 Torr. Magnetron system

Assembly of three magnetrons 0 to 800V @ 0 to 2.5A Output 0 to 400V @ 0 to 5A Evaporation Sources

Tungsten tapered helix coil. Wire diam.=0.76 mm; Max diam 20 mm; 2.5 V, 23 A , 1800oC

Tungsten flat trough 0.25mm thick; 19 mm wide; 3 mm deep 1.47 V, 158 A, 1800oC

Boron Nitride Crucible inner Diam.=11.7 mm

Molibdenium heat shielded crucible heater 1.24 V, 273 A, 1600oC Quartz sensors

Control quartz crystal, plano-convex, 6 MHz, 0.55 inches (1.4 cm) diameter. Compatible with all 6MHz crystal sensors. Choice of coating, silver, gold, or alloy determined by the application. Gold recommended for low film stress deposition, such as Aluminum, Gold, Silver, etc. Silver or Alloy recommended for high film stress deposition, such as Chromium, Nickel, Inconel, etc. Alloy recommended for dielectric material deposition, such as Magnesium Twelve crystals contained in one sensor Fluoride, Silicone Monoxide, etc. Thickness controller

A controller measures deposition rate and thickness like a monitor, but also provides an Radio-frequency oscillator output signal to control source power supply and deposition rate.

A monitor measures only deposition rate and thickness. Film growth modes

There are three primary modes of thin-film growth for mutually insoluble materials: (a) Volmer–Weber (VW: island formation), (b) Frank–van der Merwe (FM: layer-by- layer), and (c) Stranski–Krastanov (SK: layer-plus-island). For each mode, the layers are shown for three values of surface coverage characterized by number of monolayers (ML) Θ with the same mass.

In the most common VW mode, individual islands coalescence into a continuous polycrystalline film above some threshold thickness which depends on the substrate material. E.g., a gold film on a glass substrate gets continuous at average thickness about 7 nm. Nanotechnology: metallization in the fabrication of integrated circuits and photomasks Metallization is usually the final step in the fabrication of integrated circuits.

(1) Electrical connections of all components of a circuit. (2) Producing of bonding pads Thin aluminum films are usually used for the metallization.

Simple photomasks are usually made of glass covered by chromium.

(2) (1)

Thin metal films in superconducting logic elements Examples of large-area coatings. Thin-film solar cells belong to a second generation of photovoltaic solar sells. This is one of examples of the largest area thin-film coatings. Modern thin-film semiconductor materials for solar cells: Amorphous silicon (a-Si) Cadmium telluride (CdTe) Copper indium gallium diselenide (CIGS) Thin-film silicon laminates being installed onto a roof.

CIGS solar cell on a flexible plastic substrate

p-type

n-type CdTe panels mounted on a supporting structure

Produced mainly by methods based on the chemical vapor deposition. Hard and decorative coatings (TiN,…) are mainly produced by the cathodic arc deposition and magnetron sputtering

Several additional examples

1. Molecular beam epitaxy of semiconductor structures for lasers, high electron mobility transistors (HEMTs), etc. To be considered in more detail in following lectures. 2. Optical coatings. 3. …. Molecular beam epitaxy (MBE)

MBE is the layer by layer growth of a high quality single crystal by physical vapor deposition in ultra- high vacuum. The method is the most widely used for growth of layered semiconductor materials constituted by layers with different chemical composition (heterostructures). (‘semiconductor engineering’) . The grown material is used in production of semiconductor lasers, high-electron-mobility transistors (HEMTs), … This method, in fact, is the technological culmination of the physical vapor deposition technique. The most strict requirements are met in growing of the material for HEMTs. Here we consider growth of the GaAs/AlGaAs heterostructures with a two- dimensional electron channel. The following main conditions should be met: (i) Ultra clean materials (Ga, Al, As) with impurity concentrations significantly below 1x1014 atoms/cm3. (ii) Ultra-high vacuum P<~10-11 Torr. (iii) Great experience (‘know how’) in growth technology.

MBE of GaAs/AlGaAs heterostructures: vacuum

Standard ultra-high vacuum systems manufactured by several companies are usually adapted for a particular consumer. Most frequently a set of closed cycle helium cryopumps is added. One example of pumping system of growth chamber: (i) three helium cryopumps with pumping rate 3000 l/s each (9000 l/s together) (ii) a liquid nitrogen–cooled titanium sublimation pump, (iii) a liquid nitrogen–filled panel which surrounds the sample area. The pressure in the growth chamber is kept below 10-11 Torr several years after initial charging of effusion cells with necessary materials, long-term backing and evacuation. The system consists of three ultra-high-vacuum chambers: a growth chamber, a preparation chamber and loading chamber (the latter two are not shown in the Fig.). Grown heterostructures are transported to the preparation chamber and exchanged by new substrates (GaAs wafers) by a manipulator. MBE -machine Peculiarities of the GaAs/AlGaAs growth

AlxGa1-xAs Crystal structure - Zinc Blende Lattice constant - 5.6533+0.0078x A lattice mismatch between AlAs and the GaAs is ~0.1%

To avoid the formation of the Ga droplets there should be excess flux of As. Then the growth rate is determined by the Ga flux. Typical growth parameters

Cell temperatures: As – 350o C Ga – 850o C Al – 980o C Substrate (wafer) temperature can lie in a rather wide temperature range ~500o C – 650o C with typical value ~635o C The growth rate is determined by the Ga flux, depends on a layer and is typically ~1 A/s Growth interruptions are extensively used to facilitate interface smoothness. At 350o C As sublimes in a form of tetramer

As4. Sometimes an additional thermal cracker cell is used to decompose As4 into dimmers As2.

The substrate rotation is used to improve the layer uniformity while it complicates the real- time control of the thickness by RHEED. Dots show the melting points Control of layer by layer growth by reflection high-energy electron diffraction (RHEED)



RHEED pattern Similar to a diffraction grating d(cos  cos )  n o   2 / p  2 / 2mE  0.39 / E[keV][A] Example of the MBE-grown structure

Main growth steps: 1. Preparation of a GaAs substrate wafer (i) Removal of the water by heating in the introduction chamber (ii) outgassing in the buffer chamber at a temperature about 400o C (iii) oxide removal in the growth chamber at a temperature about 600o C under As flux 2. Growth of a short period GaAs/AlGaAs superlattice to minimize effects of the GaAs wafer surface imperfections. 3. Growth of the main layers, including doped ones. Transmission electron microscope image of a 7-nm AlAs, 5-nm GaAs 50-period superlattice.

The best growth conditions are usually reached by trial and error. Modification of electron energy spectrum

AlxGa1-xAs GaAs

2 Eg=(1.424+1.155x+0.37x ) eV (static) =12.90-2.84x  (high frequency)=10.89-2.73x

There no strong requirements to the quality of layers in such lasers. Such heterostructures can be even grown by liquid-phase epitaxy. Double heterostructure laser

Lasers utilizing transitions between subbands

In a quantum well laser, motion of electrons and holes in the growth direction is quantized.  22n2 p2  p2 E e,h ( p , p )   x y n x y 2me,ha2 2me,h

In a quantum cascade laser electron transitions occur between different subbands  22 h  [(n 1)2  n2 ] 2m*a2

AlInAs/GaInAs multiple quantum well Selective doping as a method to produce high-electron mobility systems (single heterojunction)

Electron motion in Z direction is quantized

Profile of the conduction band minimum for selectively doped AlGaAs-GaAs heterojunction

At small voltages between source and drain, HEMT is similar to a plane capacitor ens  C0Vg

C0   / 4d0   / 4 (c  d  s)

2 R(Vg )  m*/ ns (Vg )e  High electron mobility transistor (HEMT) High electron mobility transistor (HEMT) = heterostructure FET (HFET) = modulation-doped FET (MODFET)

Such transistors can be produced on other semiconductior materials: InGaAs/AlGaAs, AlGaN/InGaN, etc. However the modulation doping is the common method to produce high electron mobility.

Example of a static I-V charachteristic. At small voltages between drain and source 2 R(Vg )  m*/ ns (Vg )e  I-V nonlinearity is the result of the potential drop along the current carrying channel, which leads to coordinate dependence of the electron density ns. High frequency HEMTs HEMTs are used in high-frequency circuits and can operate at frequencies ~ 1 THz.

In such transistors, the channel length Lsd should be well below 1mm. Two- dimensional electron systems (2DESs)

Two-dimensional electron systems arise in many selectively doped semiconductor heterostructures as a result of size quantization of electron motion in the growth direction (normal to the heterostructure layers) and free degenerate 2DES electron motion along the layer. Energy spectrum for electrons in an infinite quantum well of a width a  22n2 p2  p2 E ( p , p )   x y (electrons with isotropic effective mass m*) n x y 2m*a2 2m*

Two-dimensional electron systems correspond to situation when all electrons reside in the lowest subband 3 22 p2 E  E   F  kT 2 1 2m*a2 2m* Classical electron dynamics in a magnetic field (2D)

Electron orbit Jx=jH=nseVd=nsecEy/H Hall resistance RH=H/nsec E H Current along the electric field is the result of 2 2 2 electron scattering Jy=nse  /(1+wc  )Ey

Less probable scattering jx   xx Ex  xy Ey

jy   xy Ex  xx Ey

More probable scattering  nsec 2  ~   (w  )  1 0 H c   2   1 (w  ) nsec 2 c  (w  )    H c 0  E H  1 H     E   j   j ~ 0 x xx x xy y  nsec  drift V =cE/H   d  H 1  Ey  xy jx  xx jy   0   nsec  In the absence of scattering n e2 electrons drift along equipotential   s conductivity at H=0 lines. 0 m*

wc  eH / m*c cyclotron frequency Two- dimensional electron systems in a quantizing magnetic field

(wc>>1) D(e) At H=0 D(e)  m*/2  const Landau levels Unique property of 2DES is a discrete energy spectrum in quantizing magnetic field H normal to 2DES  22n2 E   (k 1/ 2)w e n,k 2m*a2 c wc eH is the cyclotron frequency of electrons where wc  m*c with effective mass m*

Remarkably, degeneracy of a spin-split Landau level N0=eH/hc is independent of the electron energy spectrum (effectve mass e m*, spin-orbit splitting, etc).

1 Scattering frequency  ~D(eF) has minima in the minima of D(eF). 2 2 nse  nse This leads to minima of the dissipative conductivity  xx  2 2  2 m*(1 wc ) m*wc

 xx  xx and resistivity xx  2 2  2 since xy/xx=wc>>1  xx  xy  xy

Condition of the minima is occupation of integer number n of Landau levels: ns=nN0=neHn/hc, i.e. positions of the minima are periodical in the inverse magnetic field (Shubnikov- de Haas oscillations : 1 where  is an additional degeneracy of the Landau level Hn  ne / hcns Integer quantum Hall effect

Hall resistance in the minima of the Shubnikov – de Haas oscillations has a universal quantized value 2 RH  xy  H / nsec  H / ec(neH / hc)  h /ne

When xx~xx tends to zero, the Hall resistance stays quantized in a range of parameters ns or H Resistance standard h/e2 = 25812.807557(18) W

K. von Klitzing (1980), Nobel prize of 1985 2DES in Si MOSFET: ns~(Vg-Vg0) Explanation in terms of localized and extended states Fractional quantum Hall effect (1982) Nobel winners 1998 R.B. Laughlin, H.L. Stoermer, D.C. Tsui h m h n Many-body effect, RQu  Main fractions: RQu  H e2 n H e2 (2n 1) quasiparticles with a fractional charge e/(2n+1)

2DES in GaAs/AlGaAs Graphene

  8 e  VF | p  pi | VF=10 cm/s 2 2 D(e)   s v |e | / 2 VF

v=2 – valley degeneracy s=2 – psevdospin degeneracy Integer quantum Hall effect in graphene

N0=eH/hc en  VF 2eH | n | / c

2 Qu Qu h Qu 2e (2n 1) RH  xy    2e2 (2n 1) xy h

Nobel winners 2010 A. Geim and K. Novoselov Microwave induced resistance oscillations (MIRO) and Zero-resistance states (ZRS)

MIRO (Zudov et.al., 2001) ZRS (Mani et.al., 2002)

MIRO show extremely large amplitude The oscillation period is determined by relation w=nwc with xx tending to zero in the minima Oscillations of the magnetoresistance and conductivity are connected by the normal

relations, so that simultaneously xx 0 and xx 0

C.L. Yang, M.A.Zudov, T.A. Knuuttila, R.R. Du, L.N.Pfeiffer, and K.W. West, Phys. Rev.Lett. 91, 096803 (2003). Two mechanisms: indirect inter-Landau-level transitions and non-equlibrium electron energy distribution function f(e)

Ryzhii, 1969

Dorozhkin, 2003 Dmitriev, et al 2003, 2005

Durst et.al, 2003

w/ wc Instability of a homogeneous state with xx<0 or xx<0 A.V. Andreev, I. L. Aleiner, and A. J. Millis. Phys. Rev. Lett. 91, 056803 (2003) I.G. Finkler and B.I. Halperin, Phys. Rev. B 79, 085315 proposed spontaneous separation of the system into domains (2009) carrying non-dissipative Hall current of density j0

Spontaneous symmetry breaking implies equal probability of states with opposite electric field directions.

This is valid independently of particular domain geometry Fragment of a sample with 2DES at a GaAs/AlGaAs heterojunction

0.6 мм

Fragment of a Hall bar sample (a strip of 0.6 mm width) with internal (60x60 mm2) and external alloyed contacts (Au/Ge/Ni), bonding pads (Cr/Au) and wiring (gold wires with 25 mm diameter). Irregular correlated switching of the MW photo-voltages S.I. Dorozhkin, L.N. Pfeiffer, K. W. West, K. von Klitzing, and J.H. Smet, Nature Physics 7, 336 (2011)

-1 2 -1 fsw~10 s fsw~10 s

B = -95 mT, f = 48.1 GHz, P = -2 dBm B = +97 mT, f = 50.0 GHz, P = -1 dBm Quasi-periodical switching Irregular switching Wafer 2 The essence of the switching effect are flips of spontaneous electric field in domains Temperature dependence of the average switching frequency

Wafer 1

1.66 K

1.50 K

1.15 K ZRS

Microwave induced resistance oscillations Signals of the microwave photo-voltage measured at different temperatures Temperature dependence of conductivity of the doped layer

Wafer 1

The sample layout and a measurement circuit. (c) Schematic of the HEMT layers. (d) lateral geometry of the transistor. D1=162 nm, d2=79 nm L=2.8 mm, W=0.5 mm

Experimental dependencies of the measured capacitance on the modulation frequency for a set of temperatures (symbols). Results of calculations in accordance with Equations (1) are shown as solid   fC 2 /LW(C  C ) lines for different values of fitting parameter  2 2 1

  fC1C2 /LW(C2  C1 )

Similar temperature dependences of the conductivity and the

switching frequency.

Thermally activated temperature dependences

 ~ exp( /T )

fsw ~ exp( f /T )

Close values of activation energies  and f1 imply proportionality between conductivity of the doped layer and the switching frequency, ~fsw, which is the basis of an idea of the spontaneous electric field screening by charges in the doped layer as a physical origin of the dynamical domain structure.