Solid State Device Fundamentals

Transcription

1 Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev Tel: Office 4N101b 1

2 Outline - Goals of the course. What is electronic device? Quantum mechanics. 2. Atoms - Hydrogen atom. Periodic table. 3. Crystals - Periodic atomic structure. Defects. 4. Charge carriers in solids - Energy bands. Electrons and holes. Non-equilibrium charge carriers. Motion of charge carriers in electric and magnetic fields. 5. Semiconductor structures - Semiconductor-semiconductor junction. Semiconductor-metal junction. Semiconductor-insulator junction. 6. Basic electronic devices - Bipolar diode. Bipolar junction transistor. Field-effect transistor. 2

3 Goals of this course - to give students the basic knowledge of the properties of materials used for fabrication of solid state electronic devices. - to give students the basic knowledge of physical principles of operation of solid state electronic devices. - to provide students with a sound understanding of operation of basic semiconductor devices, so that their studies of electronic circuits will be meaningful. 3

4 What it is, an electronic device? Electronic device is a structure, in which the passing electric current is controlled by electric/magnetic fields. The electric/magnetic fields are created permanently inside this structure and/or are applied to the structure from outside. AC current E DC current e.g. diode (rectification) current Amplified current e.g. transistor (amplification) E 4

5 Materials and media for electronic devices Electronic materials/media are those which support propagation of charge carriers and are suitable for formation and operation of an electronic device structure: - Vacuum (medium for electron and ion beams) - Solids with mobile/stationary charge carriers (semiconductors, metals, insulators) - Large molecules (e.g. conjugated polymers) 5

6 Semiconductor versus metal Metals good conductors (σ~10 5 Scm -1 ). Concentration of mobile electrons ~ cm -3 E= /ε E = ρ ε E/ x Penetration of electric field into metals is less than 1Å. Many metals are magnetic materials: Poor penetration of high frequency electromagnetic field (skin effect). Semiconductors poor conductors (σ~10-1 S*cm -1 ). Concentration of mobile electrons ~ cm -3. Penetration of electric field into semiconductors may well exceed 1 micron. Typical semiconductors are nonmagnetic. Deep penetration of high frequency electromagnetic field. Semiconductors are the most suitable materials for electronic devices Skin depth vs. frequency for some materials 6

7 Homework 1 Penetration of electric field into silicon 1. Calculate penetration depth of electric field into intrinsic silicon (charge carrier concentration of 10 8 cm -3 ) and highly doped silicon (charge carrier concentration of cm -3 ). 2. To what concentration of donors/acceptors a 300 micron thick silicon wafer must be doped in order to allow penetration of electric field through its whole thickness? 7

8 Semiconducting materials Major A4 semiconductors in electronic industry is Si A4 semiconductors 8

9 Semiconducting materials Major A3B5 semiconductors in electronic industry is GaAs A3B5 semiconductors 9

10 Semiconducting materials A2B6 semiconductors 10

11 Quantum mechanics Classical mechanics Probability P(x) Deterministic position in space: P x 0 = 1 Quantum mechanics Probability P(x) Deterministic position in space: P x dx = 1 P x 0 = 1 P x < 1 P x < x 0 = 0 P x > x 0 = 0 x x 0 Simplified description of distribution of object in space by classical mechanics f(x) = f(x) 1 P x > 0 P x > 0 Real distribution of object in space described by quantum mechanics f(x) = x 0 f(x)p x dx x 11

12 Quantum operators Associated with each measurable parameter in a physical system is a quantum mechanical operator. Such operators arise because in quantum mechanics you are describing nature with waves (the wavefunction) rather than with discrete particles. Part of the development of quantum mechanics is the establishment of the operators associated with the parameters needed to describe the system. Some of those operators are listed below. It is part of the basic structure of quantum mechanics that functions of position are unchanged in the Schrodinger equation, while momenta take the form of spatial derivatives. The Hamiltonian operator contains both time and space derivatives. 12

13 Schrodinger equation The time dependent Schrodinger equation for one spatial dimension is of the form: For a free particle where U(x) =0 the wavefunction solution can be put in the form of a plane wave For other problems, the potential U(x) serves to set boundary conditions on the spatial part of the wavefunction and it is helpful to separate the equation into the timeindependent Schrodinger equation and the relationship for time evolution of the wavefunction 13

14 Confined electrons Wavefunctions Energy levels Probability density functions 14

15 Homework 2 Confined electrons 1. Calculate energy of 5 first levels of electrons in a 1x1x1 mm 3 piece of silicon. Binding energy of electrons in silicon is about 4 ev. 2. Calculate energy of 5 first levels of valence electrons in silicon atom. Ionization energy of silicon atom is about 8 ev, size of silicon atom is about 0.1 nm. 3. Compare average energies between the energy levels in piece of silicon and silicon atom. Compare these values with the energy barriers confining electrons in piece of silicon and in silicon atom. 15

16 Quantum tunneling P x = 1 P x < 1 P x = 0 x x 0 x 0 P x > 0 x Classical particle is localized in a point, that is why it cannot get through potential barrier. Quantum particle is localized all over the space, that is why potential barrier cannot stop it. 16

17 Tunneling through energy barrier 0 d Transmission probability: T = exp 2 2m(U 0 E) ħ 17

18 Tunneling through MOS capacitor Metal gate Si substrate SiO 2 insulator An electron with kinetic energy E = 1 ev tunnels through a barrier with U 0 = 10 ev and width d = 0.5 nm. What is the transmission probability? T = exp 2d 2m U 0 E ħ = 10 7 The probability is small, even for a light particle and a thin barrier. However it can be experimentally observed and used in some electronic devices, e.g. tunnel diodes. ħ = 6.6e-16 ev.s 18

19 Homework 3 Tunneling of electrons Calculate tunneling probability through 1 nm SiO 2 gate insulator and 3 nm HfO 2 gate insulator of an field-effect transistor. Energy barriers of penetration of electron through and are 8 and 6 ev respectively. Calculate tunneling leakage current through the gates of an area of 0.1 mm 2. 19

20 Electron in potential well of hydrogen atom 20

21 Electron orbitals in atom s p d f All atomic orbitals but s-orbitals are directional. 21