Textbook:

1. EE3406 Microelectronics Materials Part II A/P Vivian Ng elengv@nus.edu.sg E4-08-10 6516 2573 http://courses.nus.edu.sg/course/elengv/ee3406/ Textbook: S.O. Kasap, “Principles of Electrical Engineering Materials and Devices,” McGraw Hill, 3rd edition, 2006.

2. ANNOUNCEMENTS • 1 lab and 1 HW, exam 60% (4 compulsory questions) • Lab timing and expectations • Consultation-email for appointment • Lecture and Tutorial timing-will announce about tutorial timing • Conference week-30 Oct. Will be used for tutorial of part 1. Will arrange make-up for lectures. • Go explore course website • Feel free to give feedback on pace, contents and anything related to course ANYTIME • Ask questions! If you ask, you may ‘look stupid’ once. If you don’t ask, you will be in the dark forever.

3. Syllabus Outline Learning Outcomes 1) Surfaces and interfaces Thermionic emission, Schottky effect, Schottky barriers, ohmic contacts. 2) Dielectric Materials Polarisation, mechanisms of polarisation; Dielectric relaxation, losses and frequency response; dielectric breakdown. Piezoelectric and ferroelectric properties. 3) Magnetism Magnetization of matter; magnetic material classification; anisotropy; soft and hard materials; magnetic domains; applications of magnetism. • understand different conduction mechanisms and be able to draw energy band diagrams for ohmic and Schottky contacts • differentiate polarization effects and mechanisms in dielectric materials • differentiate different classes of magnetic materials and analysehysteresis loops

4. Applications of electron emission Schottky diode Field emission display Thermionic emission Si wafer /integrated circuits in microelectronics industry: contacts, dielectrics, etc Scanning Electron Microscopy

5. Atomic Force Microscopy Applications of Dielectrics & Piezoelectrics Dielectric breakdowns in nature & in semiconductor Hot spots Film thickness monitor, pressure sensors electrical tree Dielectric aging Water tree

6. Applications of magnetism Hard disk Magnetic sensors Magnetic Resonance Imaging MRAM

7. Surfaces and Interfaces • Pre-requisites • Electron Emission • Contacts/Junctions

8. electrons outside the metal States (empty) Electron energy Electron energy vacuum level Ф+EFO eV vacuum level (EO) electrons inside the metal ФM work function Ф work function Fermi level EFO eV Fermi level (EFM) EFO Bottom energy level 0 eV (reference energy level) Distance States (filled) Distance Pre-req: Metal Energy Band Diagram Note: Metal has a partially filled band with available energy levels above Fermi level so electrons are free to move and conduct.

9. Work-function of metal, ФM  Energy difference between the vacuum level and the Fermi level  Invariant fundamental property (mainly depends on metal type)  Equivalent to minimum energy required to free an electron from the metal vacuum level (EO) ФM work function Fermi level (EFM) Work-Function of Metal

10. Electron energy vacuum level (EO) χ electron affinity ФSC work function EC Fermi level (EFS) Ei EV Distance Energy Band Diagram for Semiconductor Electron energy States (empty) electrons outside semiconductor Vacuum level EC + χ Conduction band edge EC Band-gap (Eg) Valence band edge EV Bottom energy level 0 (reference energy level) Distance States (filled) No states Semiconductor: conduction band with available energy levels separated from the filled valance band—electrons need to overcome bandgap

11. EO ФSC work function χ electron affinity EC EFS Ei EV Electron Affinity & Work Function of Semiconductor • Work-function, ФSC • Energy difference between the vacuum level and the Fermi energy •  Relates with χ via • ФSC = χ+(EC-EFS) • depends on doping concentration • Electron affinity, χ •  Energy difference between the conduction band and the vacuum level in semiconductor • χ is an invariant fundament property of the semiconductor Note: Energy band diagrams refer to ELECTRON energy levels.

12. Electron Distribution and Concentration X Fermi-Dirac distribution What is EF? How about holes? Available density of states per unit energy interval Probability of states at energy level E to be occupied by electrons Volume density of electrons per unit energy interval between E and E+dE Average number of electrons Analogy: seats in class

13. Types of Electron Emission Thermionic Emission Schottky Effect Field Emission Secondary Electron Emission Electron Emission

14. Types of Electron Emission 1st 2nd Depending on how energy is provided to the system, electron emission can be grouped: A: Thermionic emission B: Photoemission (addressed in the first part) C: Secondary electron emission D: Field emission

15. Thermionic Emission: Definition • When the temperature of a metal is increased, some of the bound electrons gain enough energy to overcome the binding forces in the solid and appear as free electrons outside the solid. This is known as thermionic emission. • This basic principle operation (electrons emitted from a heated cathode) still finds applications in CRT (Cathode Ray Tube) and various microwave tubes. • Emitted electrons leave behind a net positive charge on the metal which in turn attracts the emitted electrons. Hence, the process is self-limiting.

16. Thermionic Emission: Experimental Observation NB: Open circuit but I flows in ext circuit. At certain T, I increases with anode V until Vsatat which rate of electron emission stays constant. The anode collects the thermally-emitted e- from the cathode A battery replenishes the cathode e- and provides a positive bias to the anode The vacuum of the tube ensures e- emitted do not collide with the air molecules and become dispersed The cathode, heated by a filament, emits e-

17. Assume NO external fields E EO=EF+Ф Ф: barrier height EF Metal Vacuum Thermionic Emission: Analysis (I) Physical picture Energy representation Metal surface Only electrons with energy greater than EF+Ф (Fermi energy + work function) which are moving towards the metal surface can leave the metal Barrier height No. of electrons leaving metal depends on T or thermal energy

18. Electron concentration distribution along electron energy with increased temperature, shifts more and more to higher energies Thermionic Emission: Analysis (II) T3>T2>T1 Number of electrons with energy greater than EF+Ф increases with increasing temperature

19. Barrier height: work-function (Ф)of metal Number of e- with energy larger than EF+Ф: mainly depends on temperature (T) E Few e- has energy larger than EF+Ф EO=EF+Ф Some e- have energy lower than EF+Ф Ф: barrier height EF Most e- have energy lower than EF n Vacuum Metal Thermionic Emission: Analysis (III) ZOOM IN: Whole picture of thermionic emission

20. Thermionic Emission: Current Density • Barrier height: work-function of metal • Number of electrons leaving the metal depends on the temperature or how much thermal energy is supplied. • Thermionic emission can be described by the Richardson-Dushman equation • where Bo= 4emek2/h3 = 1.2 x 106 A m-2 K-2 • Jthis the thermionic emission current density. B0is Richardson-Dushman constant. B0 value has been calculated theoretically.* • Factors such as surface forces, material processes and surface roughness may cause the value to differ in actual solids. * by considering FD distribution and integrating over 3D space, assuming infinite crystal lattice and perfect crystal

21. Thermionic Emission: Final Model • Emitted electrons may reflect back from the surface into the metal •  wave nature of electron (wave-particle duality from Quantum Mechanics) • Taking this effect into account, the emitted current • can be modified to • where Be = (1-R)Bois the emission constant and R is the reflection coefficient. • A plot of ln(J/T2) vs 1/kT is always used to confirm the mechanism and extract some parameters 1 2

23. Motivation: In thermionic emission: considered how an electron can overcome the work function of a solid due to the thermal energy associated at a given temperature How will this process be affected in the presence of an electric field or a potential difference (usually present)? Common sense: when a positive voltage is applied to the anode, the overall potential barrier which electron has to overcome to leave the metal cathode is changed. Schottky Effect: Definition Schottky effect: when a positive voltage is applied to the anode with respect to cathode, the electric field at the cathode helps the thermionic emission process by lowering the potential barrier

24. Consider theorem of image charge x x electron hole Metal Vacuum Schottky Effect: Image Force (I) 1st contribution • Consider the potential energy (PE) of the electron just outside the surface of the metal. The electron is pulled in by the effective positive charge left in the metal. • Image force: the coulombic force between the emitted electron and the induced (image) hole • Formula for image force • Potential energy due to the image force • Boundary condition used for this definition: Electron energy x

25. Schottky Effect: Image Force (II) Our boundary conditions: E Metal Vacuum 1 EO=EF+Ф Electron energy Energy equals to EO at x approaches infinity EO=EF+Ф + x 2 Electron energy x E=0 at x=0 x Shift up the potential curve in vacuum side by EO (EF+Ф)

26. Schottky Effect: Image Force (III) • Considering the effect of image force, we shift up ФS to ensure ФSapproaches EO at x approaches to infinity • thus, the PE becomes: • Note: Valid for x>0 E EO=EF+Ф x 0

27. Schottky Effect: Electric Field 2nd contribution Consider effect of applied electrical field Electron energy • Apply external electric field (ξ) with positive V applied to anode • Electron will experience an attractive force due to the electric field applied. • Hence, the electron will experience an additional potential energy given by x

28. Schottky Effect: Electric Field • Thus, the total PE of the electron outside the metal can be given as • Notes: • (i) the PE outside the metal is reduced from EF+Ф to EF+Фeff, where Фeff is • (ii) Фeff is the effective work function of the electron or the effective barrier that the electron needs to overcome. E EO=EF+Ф EF+Фeff x 0 Prove this! Hint: Look at the curve. ***What if higher field?

29. Schottky Effect: Current Density • Since now the PE is EF+Фeff, the Schottky emission can be modified through the thermionic emission equation as: where, βS is called Schottky coefficient and its value is given as

30. Some discussions of factors determining Schottky emission Temperature Work function Electric field A plot of ln(J/T2) vssqrt(ξ) is always used to confirm its mechanism and extract some parameters Schottky emission vs thermionic emission: Schottky emission depends on temperature, work function, and electric field Thermionic emission mainly depends on temperature, work function. Schottky Effect: Some Discussions

31. Motivation When the applied field becomes very large (e.g. >107 V/cm), electrons can leave the metal without increasing their energy Potential energy, PE(x), outside metal surface may bend sufficiently steeply to give rise to a narrow PE barrier Instead of climbing over energy barrier, there is a distinct probability that electron at energy EF will tunnel through the barrier and escape into vacuum. This is a totally quantum mechanical phenomena and the emission process is termed field emission. Field Emission: Definition • Likelihood of tunneling depends on • effective barrier height of the barrier above EF; • width of the barrier xF at energy level EF (ie, the process depends on external field)

32. Field Emission: Tunneling High field, sharp barrier  rectangular barrier • The transmission probability through a rectangular barrier is • where • and a is the barrier width • In this case • To can be taken as 1, a = xF, E = EF (since electrons are tunneling with EF) and hence • Vo-E = Φeff • Then, probability of an electron the metal at EF tunneling out from metal or be emitted is given by Hint: Using following equation to calculate xF when PEtotal=EF:

33. Field Emission: Current Density • Furthermore, it is also possible for electrons at E<EF to tunnel out (though with lower probability), taking that into account, the field emission current density is given by the Fowler-Nordheim equation: • where, C and ξC are temperature-independent constants depends on the work function of the metal.

34. Field Emission: VG dependence • Since field emission from a sharp pointed source is usually controlled by a gate voltage, the field emission current density is given by aand b are constants which depend on the field emitting structure and cathode material.

35. Field Emission: Applications • Application examples: • Field emission can be generated by applying moderate voltage to metal needle-like tips thinned to a radius of curvature of 100nm or less. This occurs commonly in scanning tunneling, field ion and electron microscopes • In a scanning electron microscope, field emission occurs from a sharp tip (eg. LaB6 or W tip) producing electrons which impinge on sample. The secondary electrons from the surface of the materials give rise to images.

36. Field vs Thermionic Emission • More power efficient than thermionic (requires heating cathode to high T) • Can be operated at high frequencies • Potential applications: field emission microscopy, microwave amplifiers, nanolithography, FEDs (field emission displays) • Typical materials used as field emission tip materials: molybdenum, LaB6, tungsten, hafnium, carbon nanotubes! Nanotechnology 13, 2002

37. Field Emission vs Tunneling Field emission refers to electrons escaping from a material through a narrow (potential) barrier induced by a field. In a sense, the electron also tunnels through a PE barrier to be emitted. However, it may not tunnel into another material but may become free. Tunneling refers generally to the probability of finding an electron across a certain (physical) barrier—ie. electron tunnels from one conductor across a thin insulator to another conductor. The barrier needs to be sufficiently thin in order for a finite probability of tunneling. • Both are quantum mechanical phenomena. Difference is subtle.

38. Secondary Electron Emission: Definition • Experimental observation: When electrons are incident on a solid, bound electrons in the solid can gain enough energy through collisions with the incoming electrons to overcome the binding surface potentials and emerge as free electrons. This is known as secondary electron emission. • Secondary electrons: Electrons which have low energies of a few to tens of eV and emanated from only the upper most atomic layers near the surface are called secondary electrons. • One important feature: Surface conditions of solid have a marked effect on secondary electron emission • Example: Presence of monolayer of adsorbed gas changes the emission yield drastically; yield also decreases as the surface roughness increases.

39. Secondary Electron Emission: Applications Applications: Scanning electron microscopy by capturing secondary electron emitted in response to an impinging high energy (~30kV) electron beam  allows high resolution images to be obtained.