Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
1 Course Outline 1. Chapter 1: Signals and Amplifiers 2. Chapter 3: Semiconductors 3. Chapter 4: Diodes 4. Chapter 5: MOS Field Effect Transistors (MOSFET) 5. Chapter 6: Bipolar Junction Transistors (BJT) 6. Chapter 2 (optional): Operational Amplifiers EE 3110 Microelectronics I Suketu Naik 2 Chapter 3: Semiconductors EE 3110 Microelectronics I Suketu Naik Application of pn Junction: Diodes EE 3110 Microelectronics I 3 Suketu Naik Application of pn Junction: Solar Cells EE 3110 Microelectronics I 4 Suketu Naik Application of pn Junction: LEDs EE 3110 Microelectronics I 5 Suketu Naik 6 Objectives [1/2] The basic properties of semiconductors and, in particular, Silicon (Si) – the material used to make most modern electronic circuits How doping a pure silicon crystal dramatically changes its electrical conductivity – the fundamental idea in underlying the use of semiconductors in the implementation of electronic devices EE 3110 Microelectronics I Suketu Naik 7 Objectives [2/2] The two mechanisms by which current flows in semiconductors – drift and diffusion charge carriers. The structure and operation of the pn junction – a basic semiconductor structure that implements the diode and plays a dominant role in semiconductors. EE 3110 Microelectronics I Suketu Naik 8 3.1 Intrinsic Semiconductors Semiconductor – a material whose conductivity lies between that of conductors (copper) and insulators (glass). Single-element – such as Germanium (Ge) and Silicon (Si). Compound – such as Gallium-Arsenide (GaAs). Single-element crystal Compound crystal EE 3110 Microelectronics I Suketu Naik 9 3.1. Intrinsic Semiconductors What does a Semiconductor look like? Where is it used? SiO2 under SEM (Scanning Raw Silicon Si wafer Electron Microscope) Procesed Wafer and Electronics Components EE 3110 Microelectronics I Suketu Naik 10 3.1. Intrinsic Semiconductors Valence electron – is an electron that participates in the formation of chemical bonds. Lies in the outermost electron shell of an element The number of valence electrons that an atom has determines the kinds of chemical bonds that it can form. Covalent bond – is a form of chemical bond in which two atoms share a pair of electrons By sharing their outer most (valence) electrons, atoms can fill up their outer electron shell and gain stability EE 3110 Microelectronics I valence electron covalent bond Suketu Naik 3.1 Intrinsic Semiconductors 11 Why use Si? Cheap and abundant Thermally stable SiO2 is strong dielectric Si atom Has four valence electrons (Carbon group or group IV) Requires four more to complete outermost shell and form tetrahedral symmetry which is more stable Figure 3.1 Two-dimensional representation of the Each pair of shared forms a silicon crystal. The circles represent the inner core of silicon atoms, with +4 indicating its positive covalent bond charge of +4q, which is neutralized by the charge of Diamond cubic structure repeats the four valence electrons. Observe how the covalent bonds are formed by sharing of the valence and forms a lattice structure electrons. At 0K, all bonds are intact and no free electrons are available for current conduction. EE 3110 Microelectronics I Suketu Naik 12 Si Lattice Structure TEM (Transmission Electron Microscopy) Image of Si Lattice 3D View of the Si Lattice EE 3110 Microelectronics I Suketu Naik 13 3.1 Intrinsic Semiconductors Silicon at low temp all covalent bonds – are intact no electrons – are available for conduction conductivity – is zero Silicon at room temp some covalent bonds – break, freeing an electron and creating hole, due to thermal energy some electrons – will wander from their parent atoms, becoming available for conduction conductivity – is greater than zero The process of freeing electrons, creating holes, and filling them facilitates current flow… EE 3110 Microelectronics I Suketu Naik 14 Figure 3.2: At room temperature, some of the covalent bonds are 3.1: Intrinsic broken by thermal generation. Each broken bond gives rise to a free Semiconductors electron and a hole, both of which become available for current conduction. silicon at low temps: silicon at room temp: all covalent bonds are sufficient thermal energy intact exists to break some covalent bonds, freeing an no electrons are available electron and creating hole for conduction the process of freeing electrons, creating holes, a free electron may wander conductivity is zero and filling them facilitates current flow from its parent atom a hole will attract neighboring electrons EE 3110 Microelectronics I Suketu Naik 15 3.1 Intrinsic Semiconductors Intrinsic semiconductor – is one which is not doped One example is pure silicon. Generation – is the process of free electrons and holes being created. generation rate – is speed with which this occurs. Recombination – is the process of free electrons and holes disappearing. recombination rate – is speed with which this occurs Thermal generation – effects a equal concentration of free electrons and holes: electrons move randomly throughout the material. In thermal equilibrium, generation and recombination rates are equal. 1) Generation can be effected by thermal energy (heat) 2) Both generation and recombination rates are functions of temperature. EE 3110 Microelectronics I Suketu Naik 3.1 Intrinsic Semiconductors (eq3.1) ni BT 16 3/ 2 Eg / 2 kT e equal to p and n ni = number of free electrons and holes in a unit volume for intrinsic semiconductor B = parameter which is 7.3E15 cm-3K-3/2 for silicon T = temperature (K) Eg = bandgap energy which is 1.12eV for silicon (energy between top of valence band and conduction band, see the figure above) k = Boltzman constant (8.62E-5 eV/K) EE 3110 Microelectronics I Suketu Naik 17 3.1 Intrinsic Semiconductors Q: Why can thermal generation not be used to effect meaningful current conduction? A: Silicon crystal structure described previously is not sufficiently conductive at room temperature. Additionally, a dependence on temperature is not desirable. Q: How can this “problem” be fixed? A: doping Doping – is the intentional introduction of impurities into an extremely pure (intrinsic) semiconductor for changing carrier concentrations. EE 3110 Microelectronics I Suketu Naik 3.2 Doped Semiconductors p-type semiconductor doped with trivalent impurity atom (e.g. Boron) 18 n-type semiconductor doped with pentavalent impurity atom (e.g. Phosphorus) EE 3110 Microelectronics I Suketu Naik 3.2 Doped Semiconductors p-type semiconductor Silicon is doped with element having a valence of 3. To increase the concentration of holes (p). One example is boron, which is an acceptor. 19 n-type semiconductor Silicon is doped with element having a valence of 5. To increase the concentration of free electrons (n). One example is phosphorus, which is a donor. EE 3110 Microelectronics I Suketu Naik 3.2 Doped Semiconductors 20 p-type doped semiconductor Concentration of acceptor atoms is NA If NA is much greater than ni … Then the concentration of holes in the p-type is defined as below. they will be equal... (eq3.6) (pp ) (NA ) number holes in p -type number acceptor atoms EE 3110 Microelectronics I Suketu Naik 21 3.2 Doped Semiconductors n-type doped semiconductor Concentration of donor atoms is ND If ND is much greater than ni … Then the concentration of electrons in the n-type is defined as below. they will be equal... (eq3.4) (nn ) (ND ) number free e-trons in n -type number donor atoms Important: now the number of free electrons (aka. conductivity) is dependent on doping concentration, not temperature… EE 3110 Microelectronics I Suketu Naik 22 3.2 Doped Semiconductors Free electrons in p-type semiconductor action: combine this with equation on previous slide pp np n 2 i number of holes in p -type number of free electrons in p -type number of free electrons and holes in thermal equil. 2 i n (eq3.7) np nA Holes in n-type semiconductor action: combine this with equation on previous slide pn nn n 2 i number of holes in n-type number of free electrons in n-type number of free electrons and holes in thermal equil. 2 i n (eq3.5) pn nD EE 3110 Microelectronics I Suketu Naik 23 3.2 Doped Semiconductors p-type semiconductor np will have the same dependence on temperature as ni2 the concentration of holes (pn) will be much larger than electrons holes are the majority charge carriers free electrons are the minority charge carriers n-type semiconductor pn will have the same dependence on temperature as ni2 the concentration of free electrons (nn) will be much larger than holes electrons are the majority charge carriers holes are the minority charge carriers EE 3110 Microelectronics I Suketu Naik 3.2 Doped Semiconductors 24 p-type or n-type semiconductor is electrically neutral by itself (as standalone unit) charge of majority carriers (holes in p-type and electrons in n-type) is neutralized by the bound charges associated with impurity atoms A bound charge (polarization charge) is charge of opposite polarity to free electron (proton) neutralizes the electrical charge of these majority carriers However if you put p-type and n-type together, electron flow happens... EE 3110 Microelectronics I Suketu Naik 3.3 Current Flow in Semiconductors 25 Summary Holes (absence of electrons, p) and free electrons (n): p-type semiconductor: holes are majority carriers ( pp ), free electrons (np) are minority carriers n-type semiconductor: free electrons are majority carriers (nn), holes are minority carriers ( pn ) Two distinct mechanisms for current flow (movement of charge carriers) Drift Current (IS) Diffusion Current (ID) EE 3110 Microelectronics I Suketu Naik 26 3.3.1 Drift Current Q: What happens when an electrical field (E) is applied to a semiconductor crystal? A: Holes are accelerated in the direction of E, free electrons are repelled. Q: How is the velocity of these holes defined? p hole mobilityPpp n electron mobilityPpp (eq3.8) vpdrift pE (eq3.9) vndrift nE E electric fieldPpp E electric fieldPpp Electrons move faster than holes! .E (V/ cm), μp (cm2/Vs) = 400 for doped Si,.μn (cm2/Vs) = 1110 for doped Si EE 3110 Microelectronics I Suketu Naik 27 3.3.1 Drift Current (IS) Assume that, for the single-crystal silicon bar on previous slide, the concentration of holes is defined as p and electrons as n. Q: What is the current components attributed to the flow of holes (Ip) and electrons (In)? Ip current flow attributed to holes A cross-sectional area of siliconp q magnitude of the electron chargep p concentration of holesp vpdrift drift velocity of holesp (eq3.10) Ip Aqpvpdrift Ip In IS = Ip+In EE 3110 Microelectronics I Suketu Naik 28 3.3.1 Drift Current (IS) Conductivity (s.) – relates current density (J=Is/A) and electrical field (E) Resistivity (r.) – Inverse of conductivity Example 3.3 - FYI: how to calculate resistivity of a substrate Ohm's Law 1 (eq3.14) J s E q(pp nn ) (eq3.16) s q(pp nn ) q(p 1 (eq3.15) J E / r q(p p nn ) 1 (eq3.17) r q(pp nn ) 1) Resistivity of the intrinsic silicon is reduced significantly when it is doped (see example 3.3) 2) Also, doping reduces carrier mobility EE 3110 Microelectronics I Suketu Naik Doping and Mobility 29 1) For low doping concentrations, the mobility is almost constant 2) At higher doping concentrations, the mobility decreases due to ionized impurity scattering with the ionized doping atoms EE 3110 Microelectronics I Suketu Naik 30 Mobility Holes have less mobility than free electrons Why? Free electrons are loosely tied to the nucleus and are closer to the conduction band (higher orbits, see slide 19) Holes are absence of electrons in the covalent bond between Si atoms and B Holes are locked or subjected to the stronger atomic force pulled by the nucleus than the electrons residing in the higher shells or farther shells So, holes have a lower mobility EE 3110 Microelectronics I Suketu Naik 31 3.3.2 Diffusion Current (ID) Example of Diffusion Process Inject holes – By some unspecified process, one injects holes in to the left side of a silicon bar. Concentration profile arises – Because of this continuous hole injection, a concentration profile arises. Diffusion occurs – Because of this concentration gradient, holes will flow from left to right. inject holes EE 3110 Microelectronics I diffusion occurs concentration profile arises Suketu Naik 3.3.2 Diffusion Current (ID) 32 Carrier diffusion – is the flow of charge carriers from area of high concentration to low concentration. It requires non-uniform distribution of carriers. Diffusion current – is the current flow that results from diffusion. Current flow due to mobile charge diffusion is proportional to the carrier concentration gradient. The proportionality constant is the diffusion constant. dp J p qD p dx EE 3110 Microelectronics I Suketu Naik 3.3.2 Diffusion Current (ID) Diffusion Current Density Jp current flow density attributed to holesJpp q magnitude of the electron chargeJpp Dp diffusion constant of holes (12cm2 /s for silicon)Jpp p( x ) hole concentration at point xJpp dp / dx gradient of hole concentrationJpp 33 Current through Area A dp(x) (eq3.19) hole diffusion current density : Jp qDp dx dn(x) (eq3.20) electron diffusion current density : Jn qDn dx Jn current flow density attributed to free electronsJpp Dn diffusion constant of electrons (35cm2 /s for silicon)Jpp n( x ) free electron concentration at point xJpp dn / dx gradient of free electron concentrationJpp Diffusion Current I p J p A; I n J n A ID I p In EE 3110 Microelectronics I Suketu Naik 3.3.3 Relationship Between D and .? 34 Q: What is the relationship between diffusion constant (D) and mobility ()? A: thermal voltage (VT) Q: What is this value? A: at T = 300K, VT = 25.9mV the relationship between diffusion constant and mobility is defined by thermal voltage (eq3.21) Dn n Dp p VT D kT q Where, VT = kT EE 3110 Microelectronics I Suketu Naik 35 Summary Drift current density (Jdrift) effected by – an electric field (E). Diffusion current density (Jdiff) effected by – concentration gradient in free electrons and holes. A cross-sectional area of silicon, q magnitude of the electron charge,Jpp p concentration of holes, n concentration of free electrons,Jpp p hole mobility, n electron mobility, E electric fieldJpp drift current density : Jdrift Jpdrift Jndrift q(pp nn )E diffusion current density : Jdiff Jpdiff Jndiff dp(x) dn(x) qDp qDn dx dx Dp diffusion constant of holes (12cm2 / s for silicon), Dn diffusion constant of electrons (35cm2 /s for silicon),Jpp p( x ) hole concentration at point x , n ( x ) free electron concentration at point x ,Jpp dp / dx gradient of hole concentration, dn / dx gradient of free electron concentrationJpp Drift current IS = Jdrift A ; Due to electric field Diffusion current ID = Jdiff A ; Due to concentration gradient EE 3110 Microelectronics I Suketu Naik 36 Example 3.2: Doped Semiconductor Consider an n-type silicon for which the dopant concentration is ND = 1017/cm3. Find the electron and hole concentrations at T = 300K. EE 3110 Microelectronics I Suketu Naik Example 3.3: Resistivity of Intrinsic and Doped Semiconductor 37 Q(a): Find the resistivity of intrinsic silicon using following values: μn = 1350cm2/Vs, μp = 480cm2/Vs, ni = 1.5E10/cm3. Q(b): Find the resistivity of p-type silicon with NA = 1016/cm2 and using the following values: μn = 1110cm2/Vs, μp = 400cm2/Vs, ni = 1.5E10/cm3 EE 3110 Microelectronics I Suketu Naik 38 Exercise 3.4: Find drift current n-type silicon: length = 2 μm, Vd = 1 V, ND=1016/cm3, μn=1350 cm2/Vs Find the drift current in the silicon across cross sectional area A=0.25μm2 EE 3110 Microelectronics I Suketu Naik 3.4.1 Physical Structure 39 pn junction (diode) structure p-type semiconductor n-type semiconductor metal contact for connection EE 3110 Microelectronics I Suketu Naik Creating a pn junction EE 3110 Microelectronics I 40 Suketu Naik SEM (Scanning Electron Microscopy) Images: pn junction 41 Zener Diode LED EE 3110 Microelectronics I Suketu Naik 42 pn junction: modes of operation In order to understand the operation of pn junction (diode), it is necessary to study its behavior in three operation regions: equilibrium, reverse bias, and forward bias. VD = 0 VD VD < 0 VD > 0 p + - n EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals 43 Step #1: The p-type and n-type semiconductors are joined at the junction. p-type semiconductor filled with holes p-n junction EE 3110 Microelectronics I n-type semiconductor filled with free electrons Suketu Naik 3.4.2 Operation with Open Circuit Terminals 44 Step #1A: Bound charges are attracted (within the material) by free electrons and holes in the p-type and n-type semiconductors, respectively. They remain weakly “bound” to these majority carriers; however, they do not recombine. negative bound charges positive bound charges EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals 45 Step #2: Diffusion begins.Those free electrons and holes which are closest to the junction will recombine and, essentially, eliminate one another. Diffusion: 1) Concentration of holes is higher in p-type than in n-type (thermally generated holes): holes travel from p-type to n-type 2) Concentration of electrons is higher in n-type than in p-type (thermally generated electrons): electrons travel from n-type to p-type EE 3110 Microelectronics I Suketu Naik 46 Movement of Holes and Electrons Holes are absence of electrons in covalent bond which travels across the lattice Donor atoms have extra electrons, which are loosely bound to the donor nuclei, and travel the other way EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals 47 Step #3: The depletion region begins to form – as diffusion occurs and free electrons recombine with holes. The depletion region is filled with “uncovered” bound charges – who have lost the majority carriers to which they were originally linked. EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals 48 Q: Why does diffusion occur even when bound charges neutralize the electrical attraction of majority carriers to one another? A: Diffusion current, as shown in (3.19) and (3.20), is effected by a gradient in concentration of majority carriers – not an electrical attraction of these particles to one another. In other words the bound charges can not effectively neutralize the majority carriers while the pn junction seeks equilibrium EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals 49 Step #4: The “uncovered” bound charges effect a voltage differential across the depletion region. The magnitude of this barrier voltage (V0) differential grows, as diffusion continues. voltage potential No voltage differential exists across regions of the pn-junction outside of the depletion region because of the neutralizing effect of positive and negative bound charges. barrier voltage (Vo) location (x) EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals pn-junction built-in voltage (V0) – is the equilibrium value of barrier voltage. Vo ~ 0.7 V for Si, Vo ~ 0.3 V for Ge 50 V0 barrier voltage VT thermal voltage NA acceptor doping concentration ND donor doping concentration ni concentration of free electrons... ...in intrinsic semiconductor This voltage is applied across depletion region, not terminals of pn junction. NA ND (eq3.22) V0 VT ln 2 Power cannot be drawn from V0 ni It can not be measured EE 3110 Microelectronics I Suketu Naik 3.4.2 Operation with Open Circuit Terminals 51 Step #5: The barrier voltage (V0) is an electric field whose polarity opposes the direction of diffusion current (ID). As the magnitude of V0 increases, the magnitude of ID decreases. diffusion current (ID) drift current (IS) EE 3110 Microelectronics I Suketu Naik 52 The Drift Current IS In addition to majority-carrier diffusion current (ID), a component of current due to minority carriers, i.e. drift current (IS) exists. Specifically, some of the thermally generated holes in the n-type material and thermally generated electrons in p-type material move toward and reach the edge of the depletion region. There, they experience the electric field (V0) in the depletion region and are swept across it. Electrons moved by drift from p to n and holes moved by drift from n to p: add together to form combined drift current IS. EE 3110 Microelectronics I Suketu Naik The Drift Current IS 53 Drift current (IS) – is due to the movement of these minority carriers. electrons from p-side to n-side holes from n-side to p-side determined by number of minority carriers that make it to the depletion region Because these holes in n-type and electrons in p-type are produced by thermal energy, IS is heavily dependent on temperature Any depletion-layer voltage, regardless of how small, will cause the transition across junction. Therefore IS is independent of V0. EE 3110 Microelectronics I Suketu Naik 54 The Drift Current IS and Equilibrium Step #6: Equilibrium is reached, and diffusion ceases, once the magnitudes of diffusion and drift currents equal one another – resulting in no net flow. Once equilibrium is achieved, no net current flow exists (Inet = ID – IS) within the pn-junction while under open-circuit condition. diffusion current drift (ID) p-type depletion region current (IS) n-type EE 3110 Microelectronics I Suketu Naik The Drift Current IS and Equilibrium diffusion current drift (ID) 55 current (IS) Note that the magnitude of drift current (IS) is unaffected by level of diffusion and / or V0. It will be, however, affected by temperature. EE 3110 Microelectronics I Suketu Naik Depletion Region 56 The depletion region is not symmetrical Typically NA > ND More holes can travel from p-type to n-type than electrons can travel from ntype to p-type The width of depletion layer differs on two sides The depletion region will extend deeper in to the “less doped” material, a requirement to uncover the same amount of charge. EE 3110 Microelectronics I Suketu Naik 57 With of the Depletion Region W width of depletion regionPpp S electrical permiability of silicon (11.7 0 1.04 E12 F / cm)Ppp q magnitude of electron chargePpp NA concentration of acceptor atomsPpp ND concentration of donor atomsPpp V0 barrier / junction built-in voltagePpp 2 S 1 1 (eq3.26) W xn x p V0 q NA ND NA (eq3.27) xn W NA ND (eq3.28) x p W EE 3110 Microelectronics I ND NA ND Suketu Naik Summary 58 The pn junction is composed of two silicon-based semiconductors, one doped to be p-type and the other ntype Majority carriers: holes are present on p-side, free electrons are present on n-side Bound charges: charge of majority carriers are neutralized electrically by bound charges Diffusion current ID: majority carriers close to the junction will diffuse across, resulting in their elimination (concentration gradient) Depletion region: carriers disappear and release bound charges and uncovered bound charges create a voltage differential V0 EE 3110 Microelectronics I Suketu Naik Summary 59 Depletion-layer voltage: as diffusion continues, the depletion layer voltage (V0) grows, making diffusion more difficult and eventually bringing it to halt Minority carriers Are generated thermally (due to heat) Free electrons are present on p-side, holes are present on n-side Drift current IS The depletion-layer voltage (V0) facilitates the flow of minority carriers to opposite side Open circuit equilibrium ID = IS Drift current IS = Jdrift A ; Due to minority charge carriers generated by heat and electric field in the depletion region Diffusion current ID = Jdiff A ; Due to majority charge carriers generated by doping and nonuniform concentration profile EE 3110 Microelectronics I Suketu Naik pn junction: modes of operation 60 (a) Open-circuit:voltage drop across depletion region = V0 , ID = IS (b) Reverse bias:voltage drop across depletion region = V0 +VR, ID < IS (c) Forward bias:voltage drop across depletion region = V0 -VF, ID > IS EE 3110 Microelectronics I Suketu Naik 61 Reverse-Bias Case Observe that increased barrier voltage will be accompanied by… W width of depletion regionPpp S electrical permiability of silicon (11.7 0 1.04 E12 F / cm)Ppp q magnitude of electron chargePpp NA concentration of acceptor atomsPpp ND concentration of donor atomsPpp V0 barrier / junction built-in voltagePpp VR externally applied reverse-bias voltagePpp 2 S 1 1 (1) Increase in (eq3.31) W xn x p (V0 VR ) q NA ND action: stored uncovered replace V charge on both with V V sides of junction (2) wider depletion NA ND (eq3.32) QJ A 2 S q region (V0 VR ) 0 NA ND 0 R action: replace V0 with V0 VR QJ magnitude of charge stored on either side of depletion regionPpp EE 3110 Microelectronics I Suketu Naik Reverse-Bias Case 62 ID reduces to nearly zero, Why? Recall that ID is the result of diffusion of Holes from p type to n type and diffusion of Electrons + from n type to p type + + Holes (absence of an electron in the covalent + bond in Si atoms in order to create covalent bond between B and Si) have to overcome higher potential barrier In other words, the electrons being supplied by the external supply now enter p region and fill up the holes in Si atoms which uncovers more bound charges (Boron, negative): this makes it harder for the holes to move across the depletion region Similarly, holes supplied by external supply enters the n region and combine with free electrons here which uncovers more bound charges (Phospohorus, positive): this makes it harder for free electrons to move EE 3110 Microelectronics I Suketu Naik 63 Forward-Bias Case Observe that decreased barrier voltage will be accompanied by W width of depletion regionPpp S electrical permiability of silicon (11.7 0 1.04 E12F / cm )Ppp q magnitude of electron chargePpp NA concentration of acceptor atomsPpp ND concentration of donor atoms Ppp V0 barrier / junction built-in voltagePpp VF externally applied forward-bias voltagePpp (1) Decrease in stored uncovered charge on both sides of junction (2) Smaller depletion region 2 S 1 1 W xn x p (V0 VF ) q NA ND action: replace V0 with V0 VF NA ND QJ A 2 S q NA ND (V0 VF ) action: replace V0 with V0 VF QJ magnitude of charge stored on either side of depletion regionPpp EE 3110 Microelectronics I Suketu Naik pn junction: current vs voltage EE 3110 Microelectronics I 64 Suketu Naik 3.5.2. The Current-Voltage Relationship of the Junction 65 Step #1: Initially, a small forward-bias voltage (VF) is applied. Due to its polarity, it pushes majority (holes in pregion and electrons in n-region) carriers toward the junction and reduces width of the depletion zone. Note that, in VF this figure, the smaller circles represent minority carriers and not bound charges – which are not considered here. EE 3110 Microelectronics I Suketu Naik 3.5.2. The Current-Voltage Relationship of the Junction 66 Step #2: As the magnitude of VF increases, the depletion zone becomes thin enough such that the barrier voltage (V0 – VF) cannot stop diffusion current VF EE 3110 Microelectronics I Suketu Naik 3.5.2. The Current-Voltage Relationship of the Junction 67 Step #3: Majority carriers (free electrons in n-region and holes in p-region) cross the junction and become minority charge carriers at boundary of the depletion region. VF diffusion current (ID) drift current (IS) EE 3110 Microelectronics I Suketu Naik 3.5.2. The Current-Voltage Relationship of the Junction 68 Step #4: The concentration of minority charge carriers increases on either side of the junction. They diffuse and recombine with majority charge carriers. minority carrier concentration VF location (x) EE 3110 Microelectronics I Suketu Naik 3.5.2. The Current-Voltage Relationship of the Junction 69 Step #5: Diffusion current is maintained – in spite low diffusion lengths (e.g. microns) and recombination – by constant flow of both free electrons and holes towards the junction by the external supply recombination VF flow of diffusion current (ID) flow of holes flow of electrons EE 3110 Microelectronics I Suketu Naik Diffusion Current 70 Dp Dn V / VT 2 V / VT (eq3.40) I Aqni ( e 1) I ( e 1) S L N L N p D n A IS Saturation current (IS) (drift current): maximum reverse current which will flow through pn-junction. Proportional to cross-section of junction (A). Typical value is 10-18A. Is depends on ni2 which depends strongly on temperature T (recall that ni=BT3/2e-Eg/2kT) EE 3110 Microelectronics I Suketu Naik 71 Summary Reverse bias case the externally applied voltage VR adds to (aka. reinforces) the barrier voltage V0 (increases barrier) this reduces rate of diffusion, reducing ID if VR > 1V, ID will fall to 0A the drift current IS is unaffected, but dependent on temperature result is that pn junction will conduct small drift current IS Forward bias case the externally applied voltage VF subtracts from the barrier voltage V0 (decreases barrier) this increases rate of diffusion, increasing ID the drift current IS is unaffected, but dependent on temperature result is that pn junction will conduct significant current ID - IS Minimal current flows in reverse-bias case Significant current flows in forward-bias case EE 3110 Microelectronics I Suketu Naik Reverse Bias: Breakdown 72 As V decreases to VZ, dramatic increase in reverse current occurs: this is known as junction breakdown Breakdown is not destructive: pn junction can still be operated Can operate with a max value (set by resistor) Why does breakdown occur? (1) Zener effect: when VZ < 5 V (2) Avalanche effect: when Vz > 7 V (3) Either effect when 5 V< Vz < 7 V EE 3110 Microelectronics I Suketu Naik Reverse Bias: Breakdown 73 Why does breakdown occur? 1) Zener effect: when VZ < 5 V As electric field increases, covalent bonds begin to break: new hole-electron pairs are created Electrons are swept into n side and holes into p side At V=VZ very large number of carriers are generated and large reverse current appears We can control over the value of reverse current Voltage is capped at V=VZ 2) Avalanche effect: when Vz > 7 V Ionizing collision: under electric field minority charge carriers (electrons in p side and holes in n side) collide with atoms and break covalent bonds Resulting carriers have high energy to cause more carriers to be liberated in further ionizing collision Process keeps repeating as avalanche We can control over the value of reverse current Voltage is capped at V=VZ EE 3110 Microelectronics I Suketu Naik Junction Capacitance 74 A reverse-biased pn junction can be viewed as a capacitor The depletion width (Wdep) hence the junction capacitance (Cj) varies with VR. EE 3110 Microelectronics I Suketu Naik Capacitance: Voltage Dependence Cj Cj C j0 75 si Wdep C j0 VR 1 V0 si q N A N D 1 2 N A N D V0 si 10-12 F/cm is the permittivity of silicon. EE 3110 Microelectronics I Suketu Naik 76 Reverse Biased pn Junction: Application A very important application of a reverse-biased pn junction is in a voltage controlled oscillator (VCO) By changing VR, we can change C, which changes the oscillation frequency f res EE 3110 Microelectronics I 1 2 1 LC Suketu Naik Important Equations 77 Table 3.1 on p. 159 EE 3110 Microelectronics I Suketu Naik 78 Example 3.6: Current in pn-Junction Consider a forward-biased pn junction conducting a current of I = 0.1mA with following parameters: NA = 1018/cm3, ND = 1016/cm3, A = 10-4cm2, ni = 1.5E10/cm3, Lp = 5um, Ln = 10um, Dp (n-region) = 10cm2/s, Dn (p-region) = 18cm2/s Q(a): Calculate IS . Q(b): Calculate the forward bias voltage (V). Q(c): Component of current I due to hole injection and electron injection across the junction EE 3110 Microelectronics I Suketu Naik Exercise 3.11 : Change in Current due to Change in Carriers 79 Forward-biased pn junction:V = 0.605 V with same parameters as Example 3.6 ND = 0.5 x 1016/cm3 Q(a): Calculate IS . Q(b): Calculate current I EE 3110 Microelectronics I Suketu Naik