Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1
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. Motion of charge carriers in electric and magnetic field. Non-equilibrium charge carriers. 5. Semiconductor structures - Semiconductor-semiconductor junction. Semiconductor-metal junction. Semiconductor-insulator junction. 6. Electronic devices - Bipolar diode. Schottky diode. Bipolar junction transistor. Field effect transistor 7. Optoelectronic devices - Photo-resistor and photo-diode. Solar cell. Light-emitting diode and semiconductor laser. 8. Principles of integrated circuit 9. Nanoelectronic devices 2
Goals of this course Two basic purposes of the course are: - 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
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 or/and applied to the structure from outside. AC current E, B DC current e.g. diode (rectification) current Amplified current e.g. transistor (amplification) E B 4
Electronic materials Electronic materials are those which support formation and operation of an electronic device structure: - Vacuum (medium for electron and ion beams) - Solids with mobile charge carriers (semiconductors, metals, insulators) - Large molecules (e.g. conjugated polymers) 5
Semiconductor versus metal Metals good conductors (σ~10 5 Scm -1 ). Concentration of mobile electrons ~ 10 21 cm -3 E= ρ/ε Penetration of electric field into metals is about 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 ~ 10 15 cm -3. Penetration of electric field into semiconductors well exceeds 1 micron. Typical semiconductors are nonmagnetic. Deep penetration of high frequency electromagnetic field. Skin depth vs. frequency for some materials Semiconductors are the most suitable materials for electronic devices 6
Semiconducting materials Major semiconductors in electronic industry: Si, Ge, GaAs 7
Quantum mechanics Quantum mechanics Probability P(x) Deterministic position in space: P x dx = 1 Classical mechanics Probability P(x) Deterministic position in space: P x 0 = 1 P x < 1 P x 0 = 1 P x > 0 P x > 0 P x < x 0 = 0 P x > x 0 = 0 x x x 0 x 0 Real distribution of object in space described by quantum mechanics f(x) = Simplified description of distribution of object in space by classical mechanics f(x)p x dx f(x) = f(x) 1 8
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. 9
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 10
Confined electrons Energy levels Wavefunctions Probability density functions 11
Tunneling through an energy barrier Transmission probability: T = exp 2 2m(U 0 E) ħ 12
Tunneling of an electron through a thin insulator layer 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 L = 0.5 nm. What is the transmission probability? ħ = 6.6e-16 ev.s T = exp 2L 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. 13
Electron in potential well of hydrogen atom 14
Electron orbitals in atom s P d f All atomic orbitals but s-orbitals are directional. 15