ndian nstitute of echnology Jodhpur, Year 2017 Analog lectronics (ourse ode: 314) Lecture 5 7: Junction contd, J ourse nstructor: Shree Prakash iwari mail: sptiwari@iitj.ac.in Webpage: http://home.iitj.ac.in/~sptiwari/ Note: he information provided in the slides are taken form text books for microelectronics (including Sedra & Smith,. Razavi), and various other resources from internet, for teaching/academic use only 1 Reverse reakdown As the reverse bias voltage increases, the electric field in the depletion region increases. ventually, it can become large enough to cause the junction to break down so that a large reverse current flows: breakdown voltage 1
Reverse reakdown Mechanisms a) Zener breakdown occurs when the electric field is sufficiently high to pull an electron out of a covalent bond (to generate an electron hole pair). b) Avalanche breakdown occurs when electrons and holes gain sufficient kinetic energy (due to acceleration by the field) in between scattering events to cause electronhole pair generation upon colliding with the lattice. onstant oltage Diode Model f D < D,on : he diode d operates as an open circuit. i f D D,on : he diode operates as a constant voltage source with value D,on. 2
xample: Diode D ias alculations X X X X R 1 D X R1 2.2mA for 0.2mA for X X 3 1 ln X S his example shows the simplicity provided by a constant voltage model over an exponential model. Using an exponential model, iteration is needed to solve for current. Using a constant voltage model, only linear equations need to be solved. Small Signal Analysis Small signal analysis is performed at a D bias point by perturbing the voltage by a small amount and observing the resulting linear current perturbation. f two points on the curve are very close, the curve inbetween these points is well approximated by a straight line: e x 1 x 2 x 2! 3 x 3! D D d d s D D e D D1 / D1 D1 3
Diode Small Signal Model Since there is a linear relationship between the small signal current and small signal voltage of a diode, d the diode d can be viewed as a linear resistor when only small changes in voltage are of interest. Small-Signal Resistance (or Dynamic Resistance) rd D Small Sinusoidal Analysis f a sinusoidal voltage with small amplitude is applied in addition to a D bias voltage, the current is also a sinusoid that varies about the D bias current value. D ( t ) 0 p cos t D ( t) 0 p cos t s exp 0 p cos t / 0 4
ause and ffect n (a), voltage is the cause and current is the effect. n (b), current is the cause and voltage is the effect. Summary urrent flowing in a semiconductor is comprised of drift dn dp and diffusion components: Jtot qp p qnn qdn qdp dx A region depleted dof mobile charge exists it at the junction dx between P type and N type materials. A built in potential drop ( 0 ) across this region is established by the charge density profile; it opposes diffusion of carriers across the junction. A reverse bias voltage serves to enhance the potential drop across the depletion region, resulting in very little (drift) current flowing across the junction. he width of the depletion region (W dep ) is a function of the bias voltage ( D ). W dep 2 1 1 si q N A N D 0 D 0 k q N AN ln 2 n i D 5
Summary: PN Junction Diode Under forward bias, the potential barrier is reduced, so that carriers flow (by diffusion) across the junction urrent increases exponentially with increasing forward bias he carriers become minority carriers once they cross the junction; as they diffuse in the quasi neutral regions, they recombine with majority carriers (supplied by the metal contacts) injection of minority carriers D S D / Underreverse reverse bias, the potentialbarrier is increased, so that negligible carriers flow across the junction e 1 f a minority carrier enters the depletion region (by thermal generation or diffusion from the quasi neutral regions), it will be swept across the junction by the built in electric field collection of minority carriers Appendix P-N Junction-Under quilibrium Depletion approximation areer depletion within space charge region harge neutrality outside space charge Dipole about the junction must have an equal number of charges on either side qax p0n A qaxn0nd Poisson's equation : Relates the gradient of the electric field to the local space charge at any point x d q p n N D N A dx 9/5/2017 12 6
Appendix P-N Junction-Under quilibrium d q p n N D N A dx d q q N D ND 0 x xn0 dx d q q N A NA xp0 x0 dx x 0 p 0 q d NA dx xp0 x0 0 0 lectric field x n 0 0 q d ND dx 0 x x n0 0 0 q q 0 N Axp0 NDxn0 9/5/2017 13 Appendix P-N Junction-Under quilibrium lectric field x n 0 d ( x) ( x ) bi ( x ) dx dx x p0 1 1 q 1 q bi W0 NAxp0W NDxn0W 2 2 2 WN x 0 0 ; 0 0; A p NA xn ND W xp xn xn0 ( NA ND) Potential 1 q NAN D 2 bi W 2 ( NA ND) 1/2 2bi 1 1 W q NA ND 9/5/2017 14 7
Appendix P-N Junction-Under quilibrium 1/2 2bi 1 1 W q NA ND 1/2 WND 2 bi ND x p0 ( NAND) q NA( NAND) he space charge/depletion region extends deep into the side with the lighter doping q q 0 NAxp0 NDxn0 1 q NAN 2 D bi W 2 ( NA ND) 1/2 2bi 1 1 W q NA ND lectric field Potential 9/5/2017 15 oltage Dependent urrent Source A voltage dependent current source can act as an amplifier. f KR L is greater than 1, then the signal is amplified. A out in KR L 8
oltage Dependent urrent Source with nput Resistance he magnitude of amplification is independent of the input resistance r in. xponential oltage Dependent urrent Source deally, a bipolar junction transistor (J) can be modeled as a three terminal exponential voltage dependent current source: 9
Reverse iased PN Junction as a urrent Source PN junction diode current is ~independent of the reverse bias voltage. t depends only on the rate at which minority carriers are introduced into the depletion region. We can increase the reverse current by injecting minority carriers near to the depletion region. J Structure and ircuit Symbol A bipolar junction transistor consists of 2 PN junctions that form a sandwich of three doped semiconductor regions. he outer two regions are doped the same type; the middle region is doped the opposite type. 10
NPN J Operation (Qualitative) n the forward active mode of operation: he collector junction is reverse biased. he emitter junction is forward biased. current gain: J urrents Sedra and Smith 11
ase urrent he base current consists of two components: 1) njection of holes into the emitter, and 2) Recombination of holes with electrons injected from the emitter. J Design mportant features of a well designed J (large ): njected minority carriers do not recombine in the quasi neutral base region. Make a quasi neutral base width small compared to minority carrier diffusion length, W 0.1m mitter current is comprised almost entirely of carriers injected into the base (rather than carriers injected into the emitter). Dope emitter more heavily than base. 12
arrier ransport in the ase Region Since the width of the quasi neutral base region (W = x 2 x 1 ) is much smaller than the minority carrier diffusion length, very few of the carriers injected (from the emitter) into the base recombine before they reach the collector junction depletion region. Minority carrier it i diffusion i current is ~constant in the quasi neutral base he minority carrier concentration at the edges of the collectorjunction depletion region are ~0. Diffusion xample Linear concentration profile constant diffusion current x p N1 L Non-linear concentration profile varying diffusion current x p N exp L d J p, diff dp qdp dx N qdp L J p, diff dp qdp dx qdpn x exp L L d d 13
ollector urrent A qd N W S exp n n 2 i exp where 1 S A qd n n N W 2 i he equation above shows that the J is indeed a voltage dependent current source; thus it can be used as an amplifier. mitter urrent Applying Kirchhoff s urrent Law to the J, we can easily find the emitter current. 1 1 14
Summary of J urrents S 1 exp S 1 exp S exp 1 Parallel ombination of ransistors When two transistors are connected in parallel and have the same terminal voltages, they can be considered as a single transistor with twice the emitter area. 15
Simple J Amplifier onfiguration Although the J converts an input voltage signal to an output current signal, an (amplified) output voltage signal can be obtained by connecting a load resistor (with resistance R L ) at the output and allowing the controlled current to pass through it. J as a onstant urrent Source deally, the collector current does not depend on the collector to emitter voltage. his property allows the J to behave as a constant current source when its base to emitter voltage is fixed. 16
onstraint on Load Resistance f R L is too large, then X can drop up to below ~0.8 so that the collector junction is forward biased. n this case, the J is no longer operating in the active mode, and so here exists a maximum tolerable load resistance. J haracteristics 17
xample J Large Signal Model A diode is placed between the base and emitter terminals, and a voltage controlled current source is placed between the collector and emitter terminals. 18
J vs. ack to ack Diodes Figure (b) presents a wrong way of modeling the J. Notes on PN Junctions ypically, pn junctions in devices are formed by counter doping. he equations provided in class (and in the textbook) can be readily applied to such diodes if N A net acceptor doping on p side (N A N D ) p side N D net donor doping on n side (N D N A ) n side D (A) D S S Aqn qd k ( e 1) 2 i Dn Ln N A L D p p N D D () 19
ransconductance, g m he transconductance (g m ) of a transistor is a measure of how well it converts a voltage signal into a current signal. t will be shown later that g m is one of the most important parameters in integrated circuit design. g g g m m m d d 1 S d d exp S exp isualization of ransconductance g m can be visualized as the slope of the vs. curve. he slope (hence g m ) increases with. 20
ransconductance and For a given swing (), the resulting current swing about 2 is larger than it is about 1. his is because g m is larger when = 2. ransconductance and mitter Area When the J emitter area is increased by a factor n, S increases by the factor n. For a fixed value of, and hence g m increase by a factor of n. 21
Derivation of Small Signal Model he J small signal model is derived by perturbing the voltage difference between two terminals while fixing the voltage on the third terminal, and analyzing the resultant changes in terminal currents. his is done for each of the three terminals as the one with fixed voltage. We model the current change by a controlled source or resistor. Small Signal Model: hange 22
Small Signal Model: hange Small Signal Model: hange deally, has no effect on the collector current. hus, it will not contribute to the small signal model. 23
Small Signal Model: xample 1 he small signal model parameters are calculated for the D operating point, and are used to determine the change in due to a change in. Small Signal Model: xample 1 he small signal model parameters are calculated for the D operating point, and are used to determine the change in due to a change in. g r m g m 1 3.75 375 24
Small Signal Model: xample 2 n this example, a resistor is placed between the power supply and collector, to obtain an output voltage signal. Since the power supply voltage does not vary with time, it is regarded as ground (reference potential) in smallsignal analysis. Small Signal Model: xample 2 n this example, a resistor is placed between the power supply and collector, to obtain an output voltage signal. Since the power supply voltage does not vary with time, it is regarded as ground (reference potential) in smallsignal analysis. 25
he arly ffect n reality, the collector current depends on : For a fixed value of, as increases, the reverse bias on the collector base junction increases, hence the width of the depletion region increases. herefore, the quasineutral base width decreases, so that collector current increases. arly ffect: mpact on J Due to the arly effect, collector current increases with increasing, for a fixed value of. 26
arly ffect Representation arly ffect and Large Signal Model he arly effect can be accounted for, by simply multiplying the collector current by a correction factor. he base current does not change significantly. 27
arly ffect and Small Signal Model r o S A exp A Summary of J oncepts 28
J in Saturation Mode When the collector voltage drops below the base voltage, the collector base junction is forward biased. ase current increases, so that the current gain ( / ) decreases. Large Signal Model for Saturation Mode 29
Large Signal Model for Saturation Mode J Output haracteristics 30
xample: Acceptable Range n order to prevent the J from entering very deeply into saturation, the collector voltage must not fall below the base voltage by more than 400 m. R ( 400 m ) xample: Acceptable Range n order to prevent the J from entering very deeply into saturation, the collector voltage must not fall below the base voltage by more than 400 m. R ( 400 m A linear relationship can be derived for and R and an acceptable region can be chosen. ) 31
Deep Saturation n deep saturation, the J does not behave as a voltage controlled current source. is ~constant. Review of J Operation (Active Mode) he emitter junction is forward biased. arriers diffuse across the emitter junction; thus, minority carrier concentrations are enhanced (by D e / ) at the edges of the emitter junction depletion region. More minority carriers are injected into the base vs. emitter, because the emitter is more heavily doped than the base. he collector junction is reverse biased (or not strongly forward biased). / Minority carrier concentrations are ~0 (since e D 0) at the edges of the collector junction depletion region. he minority carrier concentration gradient in the quasi neutral base region (of width W ) results in minority carrier diffusion toward the collector junction. f W is much shorter than the minority carrier diffusion length, then most of the minority carriers injected from the emitter will reach the collectorjunction depletion region, and then drift into the quasi neutral collector. he collector current is primarily due to carriers collected from the base. 32
33 ommon mitter urrent Gain, Assuming that no minority carrier recombination occurs within the quasi neutral base region: he collector current is equal to the current due to minority carrier injection from the emitter into the base: he base current is equal to the current due to minority carrier injection from the base into the emitter: 1 / 2 i e W N n qd A i e n qd A 1 / 2 he current gain can thus be expressed as a function of the J physical parameters: e W N 1 W N D W N D mpact of arly ffect on J urrents For a fixed value of, W decreases with increasing (because the width of the collector junction depletion region increases with increasing reverse bias), so that the minoritycarrier concentration gradient in the quasi neutral base region increases. hus, increases (slightly) with increasing. he base current is not impacted: n qd A 2 A i e W N n qd A 1 / 2 hus, the current gain increases with increasing. i e W N n qd A / S A e / 0 0 1 A A W N D W N D 0
What next J Amplifiers 34