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Chapter 1 Diodes SJTU Zhou Lingling 1 Outline of Chapter 1 1.1 Introduction 1.2 Basic Semiconductor Concepts 1.3 The pn Junction 1.4 Analysis of diode circuits 1.5 Applications of diode circuits SJTU Zhou Lingling 2 1.1 Introduction • The diode is the simplest and most fundamental nonlinear circuit element. • Just like resistor, it has two terminals. • Unlike resistor, it has a nonlinear currentvoltage characteristics. • Its use in rectifiers is the most common application. SJTU Zhou Lingling 3 Physical Structure The most important region, which is called pn junction, is the boundary between n-type and p-type semiconductor. SJTU Zhou Lingling 4 Symbol and Characteristic for the Ideal Diode (a) diode circuit symbol; (b) i–v characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction. SJTU Zhou Lingling 5 Characteristics • Conducting in one direction and not in the other is the I-V characteristic of the diode. • The arrowlike circuit symbol shows the direction of conducting current. • Forward biasing voltage makes it turn on. • Reverse biasing voltage makes it turn off. SJTU Zhou Lingling 6 1.2 Basic Semiconductor Concepts • Intrinsic Semiconductor • Doped Semiconductor • Carriers movement SJTU Zhou Lingling 7 Intrinsic Semiconductor • Definition A crystal of pure and regular lattice structure is called intrinsic semiconductor. • Materials Silicon---today’s IC technology is based entirely on silicon Germanium---early used Gallium arsenide---used for microwave circuits SJTU Zhou Lingling 8 Intrinsic Semiconductor(cont’d) Two-dimensional representation of the silicon crystal. The circles represent the inner core of silicon atoms, with +4 indicating its positive charge of +4q, which is neutralized by the charge of the four valence electrons. Observe how the covalent bonds are formed by sharing of the valence electrons. At 0 K, all bonds are intact and no free electrons are available for current conduction. SJTU Zhou Lingling 9 Intrinsic Semiconductor(cont’d) At room temperature, some of the covalent bonds are broken by thermal ionization. Each broken bond gives rise to a free electron and a hole, both of which become available for current conduction. SJTU Zhou Lingling 10 Intrinsic Semiconductor(cont’d) • Thermal ionization Valence electron---each silicon atom has four valence electrons Covalent bond---two valence electrons from different two silicon atoms form the covalent bond Be intact at sufficiently low temperature Be broken at room temperature Free electron---produced by thermal ionization, move freely in the lattice structure. Hole---empty position in broken covalent bond,can be filled by free electron, positive charge SJTU Zhou Lingling 11 Intrinsic Semiconductor(cont’d) • Carriers A free electron is negative charge and a hole is positive charge. Both of them can move in the crystal structure. They can conduct electric circuit. SJTU Zhou Lingling 12 Intrinsic Semiconductor(cont’d) • Recombination Some free electrons filling the holes results in the disappearance of free electrons and holes. • Thermal equilibrium At a certain temperature, the recombination rate is equal to the ionization rate. So the concentration of the carriers is able to be calculated. SJTU Zhou Lingling 13 Intrinsic Semiconductor(cont’d) • Carrier concentration in thermal equilibrium n p ni 3 EG kT ni BT e 2 • At room temperature(T=300K) ni 1.5 10 10 SJTU Zhou Lingling carriers/cm3 14 Intrinsic Semiconductor(cont’d) Important notes: • • • ni has a strong function of temperature. The high the temperature is, the dramatically great the carrier concentration is. At room temperature only one of every billion atoms is ionized. Silicon’s conductivity is between that of conductors and insulators. Actually the characteristic of intrinsic silicon approaches to insulators. SJTU Zhou Lingling 15 Doped Semiconductor • Doped semiconductors are materials in which carriers of one kind predominate. • Only two types of doped semiconductors are available. • Conductivity of doped semiconductor is much greater than the one of intrinsic semiconductor. • The pn junction is formed by doped semiconductor. SJTU Zhou Lingling 16 Doped Semiconductor(cont’d) n type semiconductor • Concept Doped silicon in which the majority of charge carriers are the negatively charged electrons is called n type semiconductor. • Terminology Donor---impurity provides free electrons, usually entirely ionized. Positive bound charge---impurity atom donating electron gives rise to positive bound charge carriers • Free electron---majority, generated mostly by ionized and slightly by thermal ionization. • Hole---minority, only generated by thermal ionization. SJTU Zhou Lingling 17 Doped Semiconductor(cont’d) A silicon crystal doped by a pentavalent element. Each dopant atom donates a free electron and is thus called a donor. The doped semiconductor becomes n type. SJTU Zhou Lingling 18 Doped Semiconductor(cont’d) p type semiconductor • Concept Doped silicon in which the majority of charge carriers are the positively charged holes is called p type semiconductor. • Terminology acceptor---impurity provides holes, usually entirely ionized. negatively bound charge---impurity atom accepting hole give rise to negative bound charge carriers • Hole---majority, generated generated mostly by ionized and slightly by thermal ionization. • Free electron---minority, only generated by thermal ionization. SJTU Zhou Lingling 19 Doped Semiconductor(cont’d) A silicon crystal doped with a trivalent impurity. Each dopant atom gives rise to a hole, and the semiconductor becomes p type. SJTU Zhou Lingling 20 Doped Semiconductor(cont’d) Carrier concentration for n type a) Thermal equilibrium equation nn 0 pn 0 ni 2 b) Electric neutral equation nn0 pn0 N D SJTU Zhou Lingling 21 Doped Semiconductor(cont’d) Carrier concentration for p type a) Thermal equilibrium equation p p 0 n p 0 ni 2 b) Electric neutral equation p p0 n p0 N A SJTU Zhou Lingling 22 Doped Semiconductor(cont’d) Because the majority is much great than the minority, we can get the approximate equations shown below: nno N D 2 ni pn 0 ND p p0 N A 2 for n type for p type ni n p 0 NA SJTU Zhou Lingling 23 Doped Semiconductor(cont’d) • Conclusion Majority carrier is only determined by the impurity, but independent of temperature. Minority carrier is strongly affected by temperature. If the temperature is high enough, characteristics of doped semiconductor will decline to the one of intrinsic semiconductor. SJTU Zhou Lingling 24 Doped Semiconductor(cont’d) • Doping compensation NA ND n type semiconductor is generated by donor diffusion, then injecting acceptor into the specific area(assuming N A N D ) forms p type semiconductor. The boundary between n and p type semiconductor is the pn junction. This is the basic step for VLSI fabrication technology. SJTU Zhou Lingling 25 Carriers Movement There are two mechanisms by which holes and free electrons move through a silicon crystal. • Drift--- The carrier motion is generated by the electrical field across a piece of silicon. This motion will produce drift current. • Diffusion--- The carrier motion is generated by the different concentration of carrier in a piece of silicon. The diffused motion, usually carriers diffuse from high concentration to low concentration, will give rise to diffusion current. SJTU Zhou Lingling 26 Drift and Drift Current • Drift Drift velocities vdrift p E vdrift n E Where p , n are the constants called mobility of holes and electrons respectively. Drift current densities J ndrift (qn) ( n E ) qnn E J p drift qp p E SJTU Zhou Lingling 27 Drift and Drift Current • Total drift current density J drift q(n n+p p ) E • Resistivity 1 q(n +p ) n p SJTU Zhou Lingling 28 Drift and Drift Current • Resistivities for doped semiconductor 1 For n type qN D n 1 q(n p ) n p 1 qN For p type A p * Resistivities are inversely proportional to the concentration of doped impurities. • Temperature coefficient(TC) TC for resistivity of doped semiconductor is positive due to negative TC of mobility SJTU Zhou Lingling 29 Drift and Drift Current • Resistivity for intrinsic semiconductor 1 q(n p ) 1 qn ( ) n p i n p * Resistivity is inversely proportional to the carrier concentration of intrinsic semiconductor. • Temperature coefficient(TC) TC for resistivity of intrinsic semiconductor is negative due to positive TC of ni . SJTU Zhou Lingling 30 Diffusion and Diffusion Current • diffusion A bar of intrinsic silicon (a) in which the hole concentration profile shown in (b) has been created along the x-axis by some unspecified mechanism. SJTU Zhou Lingling 31 Diffusion and Diffusion Current dp ( x) dx dn( x ) J n qDn dx J p qD p where D p , Dn are the diffusion constants or diffusivities for hole and electron respectively. * The diffusion current density is proportional to the slope of the the concentration curve, or the concentration gradient. SJTU Zhou Lingling 32 Einstein Relationship Einstein relationship exists between the carrier diffusivity and mobility: Dn Dp kT VT n p q Where VT is Thermal voltage. At room temperature,VT 25mv SJTU Zhou Lingling 33 1.3 pn Junction • The pn junction under open-circuit condition • I-V characteristic of pn junction Terminal characteristic of junction diode. Physical operation of diode. • Junction capacitance SJTU Zhou Lingling 34 pn Junction Under Open-Circuit Condition • Usually the pn junction is asymmetric, there are p+n and pn+. • The superscript “+” denotes the region is more heavily doped than the other region. SJTU Zhou Lingling 35 pn Junction Under Open-Circuit Condition Fig (a) shows the pn junction with no applied voltage (open-circuited terminals). Fig.(b) shows the potential distribution along an axis perpendicular to the junction. SJTU Zhou Lingling 36 Procedure of Forming pn Junction The procedure of forming pn the dynamic equilibrium of drift and diffusion movements for carriers in the silicon. In detail, there are 4 steps: a) Diffusion b) Space charge region c) Drift d) Equilibrium SJTU Zhou Lingling 37 Procedure of Forming pn Junction • diffusion Both the majority carriers diffuse across the boundary between p-type and n-type semiconductor. The direction of diffusion current is from p side to n side. SJTU Zhou Lingling 38 Procedure of Forming pn Junction • Space charge region Majority carriers recombining with minority carriers results in the disappearance of majority carriers. Bound charges, which will no longer be neutralized by majority carriers are uncovered. There is a region close to the junction that is depleted of majority carriers and contains uncovered bound charges. This region is called carrier-depletion region or space charge region. SJTU Zhou Lingling 39 Procedure of Forming pn Junction • Drift Electric field is established across the space charge region. Direction of electronic field is from n side to p side. It helps minority carriers drift through the junction. The direction of drift current is from n side to p side. It acts as a barrier for majority carriers to diffusion. SJTU Zhou Lingling 40 Procedure of Forming pn Junction • Equilibrium Two opposite currents across the junction is equal in magnitude. No net current flows across the pn junction. Equilibrium conduction is maintained by the barrier voltage. SJTU Zhou Lingling 41 Junction Built-In Voltage The Junction Built-In Voltage N AND Vo VT ln 2 ni It depends on doping concentration and temperature Its TC is negative. SJTU Zhou Lingling 42 Width of the Depletion Region Width of the Depletion Region: Wdepo Wdep 2 1 1 ( )Vo q N A ND 2 1 1 ( ( ) Vo-V ) q N A ND Depletion region exists almost entirely on the slightly doped side. Width depends on the voltage across the junction. SJTU Zhou Lingling 43 I-V Characteristics The diode i–v relationship with some scales expanded and others compressed in order to reveal details SJTU Zhou Lingling 44 I-V Characteristic Curve Terminal Characteristic of Junction Diodes • The Forward-Bias Region, determined by v o • The Reverse-Bias Region, determined by VZK v 0 • The Breakdown Region, determined by v VZK SJTU Zhou Lingling 45 The pn Junction Under ForwardBias Conditions The pn junction excited by a constantcurrent source supplying a current I in the forward direction. The depletion layer narrows and the barrier voltage decreases by V volts, which appears as an external voltage in the forward direction. SJTU Zhou Lingling 46 The pn Junction Under ForwardBias Conditions Minority-carrier distribution in a forward-biased pn junction. It is assumed that the p region is more heavily doped than the n region; NA >>ND. SJTU Zhou Lingling 47 The pn Junction Under ForwardBias Conditions Excess minority carrier concentration: p n ( xn ) p n 0 e v VT n p ( x p ) n p 0 e v VT Exponential relationship Small voltage incremental give rise to great incremental of excess minority carrier concentration. SJTU Zhou Lingling 48 The pn Junction Under ForwardBias Conditions Distribution of excess minority concentration: pn ( x) pno [ pn ( xn ) pn 0 ]e ( x-xn ) n p ( x) n p 0 [n p ( x p ) n p 0 ]e Where Lp D p p Ln Dn n Lp ( x+x p ) Ln n , p are called excess-minority-carrier lifetime. SJTU Zhou Lingling 49 The pn Junction Under ForwardBias Conditions The total current can be obtained by the diffusion current of majority carriers. I I pD I nD A( J pD J nD ) dp ( x ) A( q dx Aq( D p pn 0 Lp SJTU x xn dn( x) q ) dx x x p Dn n p 0 Ln Zhou Lingling V )( e VT 1) 50 The pn Junction Under ForwardBias Conditions The saturation current is given by : I s qA( D p pn 0 Lp Dn n p 0 Ln ) Dp Dn qAni ( ) L p nD Ln n A 2 SJTU Zhou Lingling 51 The pn Junction Under ForwardBias Conditions I-V characteristic equation: i I( s e • • • • v nVT 1) Exponential relationship, nonlinear. Is is called saturation current, strongly depends on temperature. n 1 or 2, in general n 1 VT is thermal voltage. SJTU Zhou Lingling 52 The pn Junction Under ForwardBias Conditions assuming V1 at I1 and V2 at I2 then: V2 V1 nVT ln I 2 I1 2.3nVT lg I 2 I1 * For a decade changes in current, the diode voltage drop changes by 60mv (for n=1) or 120mv (for n=2). SJTU Zhou Lingling 53 The pn Junction Under ForwardBias Conditions • Turn-on voltage A conduction diode has approximately a constant voltage drop across it. It’s called turn-on voltage. VD ( on) 0.7V For silicon VD ( on) 0.25V For germanium • Diodes with different current rating will exhibit the turn-on voltage at different currents. • Negative TC, TC 2mv / C SJTU Zhou Lingling 54 The pn Junction Under ReverseBias Conditions The pn junction excited by a constant-current source I in the reverse direction. To avoid breakdown, I is kept smaller than IS. Note that the depletion layer widens and the barrier voltage increases by VR volts, which appears between the terminals as a reverse voltage. SJTU Zhou Lingling 55 The pn Junction Under ReverseBias Conditions I-V characteristic equation: i Is Independent of voltage。 Where Is is the saturation current, it is proportional to ni2 which is a strong function of temperature. D p pn 0 Dn n p 0 I s qA( ) Lp Ln Dp Dn qAni ( ) L p nD Ln n A 2 SJTU Zhou Lingling 56 The pn Junction In the Breakdown Region The pn junction excited by a reverse-current source I, where I > IS. The junction breaks down, and a voltage VZ , with the polarity indicated, develops across the junction. SJTU Zhou Lingling 57 The pn Junction In the Breakdown Region • Supposing I I s , the current source will move holes from p to n through the external circuit. • The free electrons move through opposite direction. • This result in the increase of barrier voltage and decrease almost zero of diffusion current. • To achieved the equilibrium, a new mechanism sets in to supply the charge carriers needed to support the current I. SJTU Zhou Lingling 58 Breakdown Mechanisms • Zener effect Occurs in heavily doping semiconductor Breakdown voltage is less than 5v. Carriers generated by electric field---field ionization. TC is negative. • Avalanche effect. Occurs in slightly doping semiconductor Breakdown voltage is more than 7v. Carriers generated by collision. TC is positive. SJTU Zhou Lingling 59 Breakdown Mechanisms Remember: pn junction breakdown is not a destructive process, provided that the maximum specified power dissipation is not exceeded. SJTU Zhou Lingling 60 Zener Diode Circuit symbol The diode i–v characteristic with the breakdown region shown in some detail. SJTU Zhou Lingling 61 Junction Capacitance • Diffusion Capacitance Charge stored in bulk region changes with the change of voltage across pn junction gives rise to capacitive effect. Small-signal diffusion capacitance • Depletion capacitance Charge stored in depletion layer changes with the change of voltage across pn junction gives rise to capacitive effect. Small-signal depletion capacitance SJTU Zhou Lingling 62 Diffusion Capacitance According to the definition: Cd dQ dV Q The charge stored in bulk region is obtained from below equations: Q Aq [ p ( x ) p ]dx p xn n no Aq [ pn ( xn ) pno ] L p pI p Qn n I n SJTU Zhou Lingling 63 Diffusion Capacitance The expression for diffusion capacitance: V d Cd [ T I s e VT ] dV ( T VT )IQ T )IQ ( VT 0 Forward-bias, linear relationship Reverse-bias, almost inexistence SJTU Zhou Lingling 64 Depletion Capacitance According to the definition: C j dQ dVR V R VQ Actually this capacitance is similar to parallel plate capacitance. A A Cj = Wdep 2 1 1 [ ( )(V0 vR ) q N A NB C j0 (1 VR SJTU Vo ) Zhou Lingling 65 Depletion Capacitance • A more general formula for depletion capacitance is : C j0 Cj (1 VR ) m V0 1 1 • Where m is called grading coefficient. m ~ 3 2 1 • If the concentration changes sharply, m 2 • Forward-bias condition, C j 2C j 0 • Reverse-bias condition, C j C d SJTU Zhou Lingling 66 Junction Capacitance Remember: a) Diffusion and depletion capacitances are incremental capacitances, only are applied under the small-signal circuit condition. b) They are not constants, they have relationship with the voltage across the pn junction. SJTU Zhou Lingling 67 1.4 Analysis of Diode Circuit • Models Mathematic model Circuit model • Methods of analysis Graphical analysis Iterative analysis Modeling analysis SJTU Zhou Lingling 68 The Diode Models Mathematic Model: i I s (e v nVT v I s e nVT I s 1) Forward biased Reverse biased The circuit models are derived from approximating the curve into piecewise-line. SJTU Zhou Lingling 69 The Diode Models Circuit Model a) Simplified diode model b) The constant-voltage-drop model c) Small-signal model d) High-frequency model e) Zener Diode Model SJTU Zhou Lingling 70 Simplified Diode Model Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation. SJTU Zhou Lingling 71 The Constant-Voltage-Drop Model The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation. SJTU Zhou Lingling 72 Small-Signal Model Symbol convention: iD (t ) Lowercase symbol, uppercase subscript stands for total instantaneous qualities. I D Uppercase symbol, uppercase subscript stands for dc component. id (t ) Lowercase symbol, lowercase subscript stands for ac component or incremental signal qualities. I d (t ) Uppercase symbol, lowercase subscript stands for the rms(root-mean-square) of ac. SJTU Zhou Lingling 73 Small-Signal Model Development of the diode small-signal model. Note that the numerical values shown are for a diode with n = 2. SJTU Zhou Lingling 74 Small-Signal Model(cont’d) Incremental resistance: V rd T I DQ *The signal amplitude sufficiently small such that the excursion at Q along the i-v curve is limited to a short, almost linear segment. SJTU Zhou Lingling 75 High-Frequency Model High frequency model rs rd SJTU Zhou Lingling cj 76 Zener Diode Model VZ VZ 0 I Z rZ SJTU Zhou Lingling 77 Method of Analysis Load line Diode characteristic Q is the intersect point Visualization SJTU Zhou Lingling 78 Method of Analysis • Iterative analysis Refer to example 3.4 • Model Analysis Refer to example 3.6 and 3.7 SJTU Zhou Lingling 79 1.5 The Application of Diode Circuits • Rectifier circuits Half-wave rectifier Full-wave rectifier • Transformer with a center-tapped secondary winding • Bridge rectifier The peak rectifier • Voltage regulator • Limiter SJTU Zhou Lingling 80 Half-Wave Rectifier (a) Half-wave rectifier. (b) Equivalent circuit of the half-wave rectifier with the diode replaced with its battery-plus-resistance model. SJTU Zhou Lingling 81 Half-Wave Rectifier (c) Transfer characteristic of the rectifier circuit. (d) Input and output waveforms, assuming that rD R SJTU Zhou Lingling 82 Full-Wave Rectifier (a) circuit (b) transfer characteristic assuming a constant-voltage-drop model for the diodes SJTU Zhou Lingling 83 Full-Wave Rectifier (c) input and output waveforms. SJTU Zhou Lingling 84 The Bridge Rectifier (a) circuit SJTU Zhou Lingling 85 The Bridge Rectifier (b) input and output waveforms SJTU Zhou Lingling 86 Peak Rectifier Voltage and current waveforms in the peak rectifier circuit with CR T . The diode is assumed ideal. SJTU Zhou Lingling 87 Voltage Regulator We define: Lineregula tion Vo Loadregulation Vo SJTU Zhou Lingling Vs I L 88 Limiter SJTU Zhou Lingling 89 Limiter Applying a sine wave to a limiter can result in clipping off its two peaks. SJTU Zhou Lingling 90 Soft Limiting SJTU Zhou Lingling 91