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Transcript
전자 회로 1 Lecture 4 (Diode) 2009. 03. 임한조 아주대학교 전자공학부 [email protected] 이 강의 노트는 전자공학부 곽노준 교수께서 08.03에 작성한 것으로 노트제공에 감사드림. Overview Ideal Diode model (Intrinsic) Semi-conductor characteristic Doping Majority/minority Carrier (Electrons & holes) PN-junction Thermal ionization Current components (Drift + Diffusion) Bulti-in voltage (Barrier voltage) Depletion region Biasing (Reverse, Breakdown, Forward) March, 2008 Nojun Kwak 2 The Ideal Diode Diode symbol i-v characteristic Reverse direction March, 2008 Forward direction Nojun Kwak 3 Simple application: Rectifier March, 2008 Nojun Kwak 4 Another application: Logic gates Y = AB C Y = A + B + C March, 2008 Nojun Kwak 5 Example Start from an appropriate assumption on a diode mode. March, 2008 Whether D1 is conducting or insulating. Nojun Kwak 6 Nonlinear Elements (Semi-conductor) What is SEMI-conductor? Acts as a conductor in a situation. Acts as an insulator in other situation. In what situation? Depends on the input voltage or currents (and output) Input-output characteristic curve. (voltage-current / current-current / voltage-voltage …) How to make a semi-conductor? Silicon (Si), Germanium (Ge) March, 2008 column 4 (covalent bonds) + impurities (column 3 or 5) Nojun Kwak 7 Different types of solid March, 2008 Nojun Kwak 8 Intrinsic silicon (Si) Silicon: our primary focus Atom number = 14 14 electrons in 3 shells: 2 ) 8 ) 4 March, 2008 i.e., 4 electrons in outer “bonding” shell Silicon forms a strong covalent bonds with 4 neighbors. Nojun Kwak 9 Thermal ionization At room temperature, some of the covalent bonds are broken by thermal ionization. Free electrons & holes current conduction ni = # of free electrons/holes = 1.5*10^10 carrier/cm^3 (at 300K) Cf) # of atoms = 5*10^22 atoms/cm^3 only very small number is ionized. n p ni Temperature dependency ni2 BT 3e EG / kT March, 2008 (3.36) Nojun Kwak 10 Current (moving carriers) Diffusion Diffusivity dp J p qDp dx dn J n qDn dx (3.37) (3.38) Drift: by electric field drift p E Mobility (3.39) J p drift qp p E (3.40a) J n drift qnn E (3.40b) J drift q( p p nn )E (3.40c) Dn/Dp = un/up ~= 2.5 March, 2008 Resistivity 1/ q( p p nn ) Dn n Dp p VT (3.41) (3.42) Electrons are easier to move than holes Nojun Kwak 11 Charge Drift Current In thermal equilibrium, carriers are not stand still Brownian motion = collision Mean free time btw collision But it goes nowhere (on average) with no electric field Application of E-field F=±qE March, 2008 Holes: +, Electrons: - v(t) = at = ±qEt/m m: mass of a charge Nojun Kwak 12 Velocity randomization by collision Average velocity & Drift current March, 2008 Nojun Kwak 13 Doped (extrinsic) semiconductor Donor (Group 5) – phosphorus N-type ND: concentration of donor atoms Majority carrier: By recombination: Minority carrier: Majority carrier concentration is constant, while minority carrier concentration does depend on temperature. Acceptor (Group 3) – boron March, 2008 P-type NA: concentration of acceptor atoms Nojun Kwak 14 pn- Junction (Diode) Electrons diffuse from the N-side to the P-side and recombine with holes at the boundary. Holes diffuse from the P-side to the N-side and recombine with electrons at the boundary. There is a region at the boundary of charged atoms – called the space-charge region (also called the depletion region; no mobile carriers in this region) An electric field is created which results in a voltage drop across the region – called the barrier voltage or built-in potential In equilibrium, diffusion current (ID) is balanced by drift current (IS): ID = IS Drift current comes from (thermal) generation of electron-hole pair. March, 2008 Nojun Kwak 15 E-field and Built-in potential March, 2008 Nojun Kwak 16 Junction Built-in voltage With no external biasing, the voltage across the depletion region is March, 2008 Typically at room temperature, V0 ~= 0.6~0.8 V Note that there is no measurable potential difference between the n-type and p-type materials of pn junction when in equilibrium. The electrochemical potentials (Fermi levels) are the equal. Nojun Kwak 17 Width of depletion region March, 2008 Nojun Kwak 18 PN-junction Real Diode March, 2008 Nojun Kwak Abrupt PN-junction Separate view 19 Diffusion starts and then balanced by drift Depletion approx. March, 2008 Nojun Kwak 20 Space charge density & E-field • Gauss equation March, 2008 Nojun Kwak 21 Potential (Voltage) • It is known that (we do not derive here) Reference point @ n0 = p0 = ni • Voltage barrier March, 2008 Nojun Kwak 22 • Can also be calculated by March, 2008 Nojun Kwak 23 Depletion width Overall charge neutrality: Potential continuity at x = 0: Depletion width: March, 2008 Nojun Kwak 24 Contact potential Potential difference across structure must be zero!!! March, 2008 Nojun Kwak 25 Reverse-Bias Reverse-bias Increase the built-in potential: V0 V0+VR Increased depletion region Decrease in diffusion current (ID) while drift current (Is) remains the same. I = IS – ID : almost constant Wdep 2 s 1 1 V0 VR q NA ND March, 2008 Nojun Kwak (3.52) 26 Breakdown (large reverse bias) Zener breakdown (Vz < 5V) Increased depletion region larger electric field break covalent bonds electron-hole pair Avalanche breakdown (Vz > 7V) March, 2008 Minority carrier with large kinetic energy collide with atoms break covalent bonds electron-hole pair Nojun Kwak 27 Forward-Bias March, 2008 Nojun Kwak 28 March, 2008 Nojun Kwak 29 Very important!!! March, 2008 Nojun Kwak 30 Summary: Forward-Bias Decrease the built-in potential Increase the number of carriers able to cross the barrier Diffusion current (ID) increase While drift current (Is) remains the same Current flows from p to n March, 2008 Nojun Kwak 31 Review Open circuit: ID = IS Reverse-bias: I = IS - ID ~= IS Breakdown (large reverse-bias): almost constant V Forward-bias: I = ID – IS ~=ID March, 2008 Current exponentially increases Nojun Kwak 32 Reference: Constants Thermal voltage Boltzmann constant (k) PV = NkT = nRT k = 1.38×10−23 joule/kelvin = 8.62×10−5 eV/kelvin. = 1.38×10−16 erg/kelvin. Magnitude of electron charge VT = kT/q = 0.25mV q = 1.6×10-19 C Permittivity of silicon March, 2008 Nojun Kwak 33