Microelectronic Circuits Zhou Lingling Chapter 1 Diodes SJTU Zhou Lingling

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

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 current-voltage characteristics. Its use in rectifiers is the most common application. SJTU Zhou Lingling

Physical Structure The most important region, which is called pn junction, is the boundary between n-type and p-type semiconductor. SJTU Zhou Lingling

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

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

1.2 Basic Semiconductor Concepts Intrinsic Semiconductor Doped Semiconductor Carriers movement SJTU Zhou Lingling

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

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

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

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

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

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

Intrinsic Semiconductor(cont’d) Carrier concentration in thermal equilibrium At room temperature(T=300K) carriers/cm3 SJTU Zhou Lingling

Intrinsic Semiconductor(cont’d) Important notes: 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

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

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

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

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

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

Doped Semiconductor(cont’d) Carrier concentration for n type Thermal equilibrium equation Electric neutral equation SJTU Zhou Lingling

Doped Semiconductor(cont’d) Carrier concentration for p type Thermal equilibrium equation Electric neutral equation SJTU Zhou Lingling

Doped Semiconductor(cont’d) Because the majority is much great than the minority, we can get the approximate equations shown below: for n type for p type SJTU Zhou Lingling

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

Doped Semiconductor(cont’d) Doping compensation n type semiconductor is generated by donor diffusion, then injecting acceptor into the specific area(assuming ) 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. NA ND SJTU Zhou Lingling

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

Drift and Drift Current Drift velocities Drift current densities Where are the constants called mobility of holes and electrons respectively. SJTU Zhou Lingling

Drift and Drift Current Total drift current density Resistivity SJTU Zhou Lingling

Drift and Drift Current Resistivities for doped semiconductor * 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 For n type For p type SJTU Zhou Lingling

Drift and Drift Current Resistivity for intrinsic semiconductor * 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 . SJTU Zhou Lingling

Diffusion and Diffusion Current 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

Diffusion and Diffusion Current where 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

Einstein Relationship Einstein relationship exists between the carrier diffusivity and mobility: Where VT is Thermal voltage. At room temperature， SJTU Zhou Lingling

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

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

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

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: Diffusion Space charge region Drift Equilibrium SJTU Zhou Lingling

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

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

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

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

Junction Built-In Voltage The Junction Built-In Voltage It depends on doping concentration and temperature Its TC is negative. SJTU Zhou Lingling

Width of the Depletion Region Depletion region exists almost entirely on the slightly doped side. Width depends on the voltage across the junction. SJTU Zhou Lingling

I-V Characteristics The diode i–v relationship with some scales expanded and others compressed in order to reveal details SJTU Zhou Lingling

I-V Characteristic Curve Terminal Characteristic of Junction Diodes The Forward-Bias Region, determined by The Reverse-Bias Region, determined by The Breakdown Region, determined by SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions The pn junction excited by a constant-current 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

The pn Junction Under Forward-Bias 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

The pn Junction Under Forward-Bias Conditions Excess minority carrier concentration: Exponential relationship Small voltage incremental give rise to great incremental of excess minority carrier concentration. SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions Distribution of excess minority concentration: Where are called excess-minority-carrier lifetime. SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions The total current can be obtained by the diffusion current of majority carriers. SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions The saturation current is given by : SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions I-V characteristic equation: Exponential relationship, nonlinear. Is is called saturation current, strongly depends on temperature. or 2， in general VT is thermal voltage. SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions assuming V1 at I1 and V2 at I2 then: * For a decade changes in current, the diode voltage drop changes by 60mv (for n=1) or 120mv (for n=2). SJTU Zhou Lingling

The pn Junction Under Forward-Bias Conditions Turn-on voltage A conduction diode has approximately a constant voltage drop across it. It’s called turn-on voltage. Diodes with different current rating will exhibit the turn-on voltage at different currents. Negative TC, For silicon For germanium SJTU Zhou Lingling

The pn Junction Under Reverse-Bias 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

The pn Junction Under Reverse-Bias Conditions I-V characteristic equation: Where Is is the saturation current, it is proportional to ni2 which is a strong function of temperature. Independent of voltage。 SJTU Zhou Lingling

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

The pn Junction In the Breakdown Region Supposing , 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

Breakdown Mechanisms Zener effect Avalanche 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

Breakdown Mechanisms Remember: pn junction breakdown is not a destructive process, provided that the maximum specified power dissipation is not exceeded. SJTU Zhou Lingling

Zener Diode Circuit symbol The diode i–v characteristic with the breakdown region shown in some detail. SJTU Zhou Lingling

Junction Capacitance Diffusion Capacitance Depletion 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

Diffusion Capacitance According to the definition: The charge stored in bulk region is obtained from below equations: SJTU Zhou Lingling

Diffusion Capacitance The expression for diffusion capacitance: Forward-bias, linear relationship Reverse-bias, almost inexistence SJTU Zhou Lingling

Depletion Capacitance According to the definition: Actually this capacitance is similar to parallel plate capacitance. SJTU Zhou Lingling

Depletion Capacitance A more general formula for depletion capacitance is : Where m is called grading coefficient. If the concentration changes sharply, Forward-bias condition, Reverse-bias condition, SJTU Zhou Lingling

Junction Capacitance Remember: Diffusion and depletion capacitances are incremental capacitances, only are applied under the small-signal circuit condition. They are not constants, they have relationship with the voltage across the pn junction. SJTU Zhou Lingling

1.4 Analysis of Diode Circuit Models Mathematic model Circuit model Methods of analysis Graphical analysis Iterative analysis Modeling analysis SJTU Zhou Lingling

The Diode Models Mathematic Model： The circuit models are derived from approximating the curve into piecewise-line. Forward biased Reverse biased SJTU Zhou Lingling

The Diode Models Circuit Model Simplified diode model The constant-voltage-drop model Small-signal model High-frequency model Zener Diode Model SJTU Zhou Lingling

Simplified Diode Model Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation. SJTU Zhou Lingling

The Constant-Voltage-Drop Model The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation. SJTU Zhou Lingling

Small-Signal Model Symbol convention: Lowercase symbol, uppercase subscript stands for total instantaneous qualities. Uppercase symbol, uppercase subscript stands for dc component. Lowercase symbol, lowercase subscript stands for ac component or incremental signal qualities. Uppercase symbol, lowercase subscript stands for the rms(root-mean-square) of ac. SJTU Zhou Lingling

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

Small-Signal Model(cont’d) Incremental resistance: *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

High-Frequency Model High frequency model SJTU Zhou Lingling

Zener Diode Model SJTU Zhou Lingling

Method of Analysis Load line Diode characteristic Q is the intersect point Visualization SJTU Zhou Lingling

Method of Analysis Iterative analysis Model Analysis Refer to example 3.4 Model Analysis Refer to example 3.6 and 3.7 SJTU Zhou Lingling

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

Half-Wave Rectifier Half-wave rectifier. Equivalent circuit of the half-wave rectifier with the diode replaced with its battery-plus-resistance model. SJTU Zhou Lingling

Half-Wave Rectifier (c) Transfer characteristic of the rectifier circuit. (d) Input and output waveforms, assuming that SJTU Zhou Lingling

Full-Wave Rectifier circuit transfer characteristic assuming a constant-voltage-drop model for the diodes SJTU Zhou Lingling

Full-Wave Rectifier (c) input and output waveforms. SJTU Zhou Lingling

The Bridge Rectifier (a) circuit SJTU Zhou Lingling

The Bridge Rectifier (b) input and output waveforms SJTU Zhou Lingling

Peak Rectifier Voltage and current waveforms in the peak rectifier circuit with . The diode is assumed ideal. SJTU Zhou Lingling

Voltage Regulator We define: SJTU Zhou Lingling

Limiter SJTU Zhou Lingling

Limiter Applying a sine wave to a limiter can result in clipping off its two peaks. SJTU Zhou Lingling

Soft Limiting SJTU Zhou Lingling