EECS 105 Spring 2004, Lecture 20 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Context

This lecture will discuss Lecture 20: PN (forward z Currents in forward and bias), small signal model, BJTs reverse bias (6.1-6.3)

z Small signal models for diodes

And if we have some time, we will Prof J. S. Smith start: z BJTs (Bipolar Junction )

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EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Reading Lecture Outline

z The midterm covers chapters 1-4, plus phasors,

linear circuits, and Bode plots z Diode applications

z Today we will be covering the material in chapter z Forward currents in diodes 6, PN diodes z Diode Small Signal Model z Wednesdays lecture will be review, example z Diode Charge Storage (6.4.4) problems, and answers to any last minute questions. z Types of diodes z After the midterm, we will be covering chapter 7, Bipolar Junction Transistors (BJT’s) z The BJT (7.1) z BJT Physics (7.2)

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1 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Diode applications More Diode applications

z Varactor Tuner z High frequency up-converter mixers

z Rectification z Down-conversion mixers

z Envelope Detector (AM demodulator, for instance) z oscillator

z Phase modulator z oscillator

z Voltage reference/Limiters/Regulators z Light emitting diodes

z Diode Clamp z Laser diodes

z ESD (electrostatic discharge) protection circuits z Light detectors

z Voltage multipliers (doublers, etc) – Solar cells – PIN diodes – Avalanche diodes

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EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Minority carrier injection Generation and Recombination

z In the last lecture, we discussed the ideal diode z The processes which cause the electron and hole equation, and how it treats the minority carriers as populations to come into equilibrium with each if they always make it all the way across the other are rather slow in , so we can make junction, but then disappear once they have gotten some approximations: across (we didn’t account for the possibility that z Generation and recombination will be neglected they wandered back, for instance) inside the depletion zone, for one.

z Now, we will more accurately account for the transport of the minority carriers. Sidebar: Conduction band Including: It is possible to add atoms to silicon which greatly enhance generation and recombination, z Diffusion such as gold and copper. The are called traps. Trap, ex: Gold atom Except for very pure silicon, impurities will z Recombination/Generation dominate carrier recombination Valence band

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2 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Minority Carriers at Junction Edges

minority carrier concentration at boundaries of depletion The minority carrier concentrations at the edges of region increase as barrier lowers. This is called minority the will then be given by: carrier injection. If we neglect generation and recombination inside the depletion regions, the number −q(φB −VD ) / kT of carriers function is approximately the density of pn (x = xn ) = N Ae carriers on the other side of the barrier at the equivalent energy: −q(φB −VD ) / kT n p (x = −x p ) = N De p (x = x ) (minority) hole conc. on n-side of barrier n n = p (x = −x ) (majority) hole conc. on p-side of barrier p p Note: NA and ND are the majority carrier concentrations on = e−(Barrier Energy) / kT the other side of the junction, with the assumption that p << N and n << N p (x = x ) n D p A n n = e−q(φB −VD ) / kT N A Department of EECS University of California, Berkeley Department of EECS University of California, Berkeley

EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Quasi-Neutrality Diffuse and Recombine

z Since the regions outside the depletion regions are z Once the minority carriers have been injected going to be very close to electrically neutral (called across the depletion region, they will diffuse, and quasi-neutrality) the number of majority carriers they will recombine. 2 will increase slightly as well (slightly because there z They will recombine, because now pn > n i are usually many more majority carriers than and since recombination is proportional to pn, it minority carriers anyway) will now cause carriers to recombine at a rate faster than they are generated.

Carrier Nd z They will also diffuse into the other side, because concentrations there are more of them (the minority carriers) at the

Minority carriers edge of the depletion region than there are further in.

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3 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Excess injected minority carriers Ambipolar diffusion

z The diffusion constant for minority carriers is complicated qVA kT pn0e by the fact that the minority carriers are dragged on (or

p side n side pulled!) by the majority carriers, in a mechanism called ambipolar diffusion qV A x nekT ⎛⎞qVA − p0 kT Lp z There is a small E field which keeps the excess holes and pnnn()xp=+00 pe⎜⎟ − 1 e ⎝⎠ electrons together. Minority Carrier z The ambipolar diffusion constant for minority carriers

pn0 Diffusion Length comes out to be the diffusion constant for the other, n p0 majority carriers, in the cases where the majority carriers -W -x x W p p n n greatly outnumber the minority carriers. In other words, Once the minority carriers are injected into the other side of the minority holes diffuse with Dn and electrons with Dp! junction, the minority carrier concentration in the bulk region z The minority diffusion length is a function of the ambipolar for forward bias is a decaying exponential. diffusion constant for the minority carriers, as well as the variability in the lifetime, etc. We will just take it to be a number!

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EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Steady-State Concentrations Diode Current Densities

qVA L >> W kT np,, np pn0e qVA In silicon, it is easy for the diffusion lengths to be kT p side n side dnpp n00 e− n p qVA kT ()x ≈ much longer than the distance to the contacts, if nep0 dx−−− xpp() W

none of the diffusing holes and electrons pn0 2 recombine until they get to the contactsÆ get a ni np0 np0 = Na linear concentration gradient. -Wp -xp xn Wn

qVA kT Under this linear approximation, we can calculate the current due to the holes pn0e diffusing into the N side, and the electrons diffusing into the P side. Notice that p side n side we are using the electron diffusion constant for the minority holes, The population is assumed qVA and visa versa. kT to be the equilibrium nep0 population at the contacts qV because of the many A diff dnp Dn ⎛⎞ traps (defects) there kT JqDnn= ≈− qne p0 ⎜⎟1 dx Wp xx=− p ⎝⎠ p qV n0 D ⎛⎞A np0 diff dpn p kT JqDqpepp=− ≈− n0 ⎜⎟1 − -Wp -xp xn Wn dx W xx= n n ⎝⎠ Department of EECS University of California, Berkeley Department of EECS University of California, Berkeley

4 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Net forward current (short device) Fabrication of IC Diodes

The total current is the sum of the currents carried by cathode anode the minority carriers on each side:

p+ p n+ n-well p-type ⎛⎞D D ⎛⎞qVA Jqndiff =+2 p n ekT −1 i ⎜⎟⎜⎟ p-type ⎝⎠NWdn NW ap⎝⎠

z Start with p-type substrate

z Create n-well to house diode

z p and n+ diffusion regions are the cathode and anode

z N-well must be reverse biased from substrate

z Parasitic resistance due to well resistance

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EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Diode large signal model Large-Signal Model

z It is inconvenient to use the exponential current model in a circuit, so a diode is often modeled with an approximation. One possible large signal model

is: The resistance R is the forward resistance i(t) → at large currents + The forward voltage drop Vf is about .7 volts R because that is about where the forward current goes from negligible to very large! v(t) The diode in the model is a perfect diode, C perfect conductor when forward biased, open when reverse biased

Vf The choice of capacitance C depends on − which is most important, the capacitance under forward or reverse bias conditions.

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5 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Diode Small Signal Model Forward Diode Capacitance

z The I-V relation of a diode can be linearized z We have already seen that a reverse biased diode acts like a since the depletion region ⎛⎞qV()dd+ v qV d qv d kT kT kT grows and shrinks in response to the applied field. IDD+=iIe S⎜⎟ −≈1 Iee S ⎝⎠ the junction capacitance in forward bias is given by 23 x xx ε S ex=+1 + + +L CAjj=≈1.4 C0 2! 3! X dep

z But another charge storage mechanism comes into ⎛⎞qv IiI+≈1 +d + play in forward bias: DD D⎜⎟kT L ⎝⎠ z Minority carriers injected into p and n regions must qVd qI kT D be built up, which takes current×time, and they I = I e ivgvD ≈=ddd D S kT must also be extracted as the voltage is lowered. The small signal model of a diode in forward bias is a resistance in parallel with a capacitance. In reverse, it is just a capacitance. (the z The effect is additional charge is stored in diode reverse leakage current is constant, thus no contribution to small signal)

Department of EECS University of California, Berkeley Department of EECS University of California, Berkeley

EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Charge Storage Symbols

qV()dd+ v kT pen0 p side n side qV()dd+ v kT nep0 Extra charge Stored in diode

pn0 np0

-Wp -xp xn Wn

z Increasing forward bias increases minority charge density 1 qI C = d τ z A detailed analysis yields: dT2 kT 1 Cg= τ Time to cross junction ddT2 (or minority carrier lifetime) Department of EECS University of California, Berkeley Department of EECS University of California, Berkeley

6 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith The PIN Diode

z The PIN diode has heavily doped p-type and n-type z Metal junction with a (typically) n-type regions separated by an intrinsic region. When semiconductor.

reverse biased, it acts like an almost constant z Mainly used in high frequency circuits or high capacitance and when forward biased it behaves as speed digital circuits. a variable . z There are no holes (minority carriers), so the z The built in field stretches over the intrinsic region, conduction quickly stops upon change to reverse causing minority carriers to be swept out by the bias. field over a larger volume. It is often used for light z Schottky diodes find application as for detectors, and some high efficiency solar cells. high frequency signals.

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EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Zener diodes

z In the step-recovery diode the level is z Diodes which are called Zener diodes do not use the Zener gradually decreased as the junction is approached. effect (tunneling) but are avalanche breakdown devices. z With the application of sufficient reverse voltage, a p-n z This reduces the switching time since the smaller junction will experience a rapid avalanche breakdown and amount of stored charge near the junction can be conduct current in the reverse direction. released more rapidly when changing from forward z Under a high electric field, high energy carriers can cause the generation of more electron hole pairs, and the to reverse bias. subsequent collisions quickly become an avalanche. When z The forward current can also be established more this process is taking place, very small changes in voltage rapidly than in the ordinary junction diode. can cause very large changes in current. z Zener diodes can be made which break down at precise z This diode is used in fast switching applications, voltages from about 4 volts to several hundred volts. The such as high frequency mixers avalanche breakdown occurs at a particular field strength, so the high field region just needs to be the correct length

z Avalanche breakdown does not damage the diode as long as power dissipation limits are not exceeded. Department of EECS University of California, Berkeley Department of EECS University of California, Berkeley

7 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Bipolar Junction (BJT) Ideal BJT Structure + z A BJT is physically just two back to back PN IC IE diodes, with three contacts, but the current between VEB Collector (N) IB + Emitter (P) + the emitter and the collector is a minority carrier − + V V current in the base. Base (P) CE Base (N) EC VBE − IB − z Essentially, a forward biased diode is used to create −I −I a minority current, most of which then goes all the Emitter (N) − E Collector (P) C way across to the depletion region of another, reverse biased diode. z NPN or PNP sandwich (Two back-to-back diodes) z The geometry can be such that almost all the current goes across to the second diode, so that the z How does current flow? Minority carriers diffusing controlling electrode doesn’t have to supply much across the base, which is thin so most go across I ≈ −I of the current, maybe 1:100 to 1:400 z A good BJT satisfies the following CE

qVBE I >> I kT CB IIeCS≈ Department of EECS University of California, Berkeley Department of EECS University of California, Berkeley

EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith Actual BJT Cross Section BJT Layout

z Vertical npn sandwich (pnp is usually a lateral structure)

z n+ buried layout is a low resistance contact to collector

z Base width determined by vertical distance between emitter z Emitter area most important layout parameter diffusion and base diffusion z Multi-finger device also possible for reduced base resistance

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8 EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith BJT Schematic Symbol Simple NPN BJT model

ICB= β I z A simple model for a NPN BJT:

qVBE C kT IIeCS≈ IB +

+ VCE I (t) → B B VBE − −I The arrow on the symbol + − E shows the controlling diode. βiB (t) C

VBE (t) IB + z Collector current is control by base current linearly, a

typical value would be β = 100 , because only one in 100 − + VCE electrons would stop in the base instead of making it across Real diode, not E VBE − to the collector −I an ideal diode − E z Collector is controlled by base-emitter voltage exponentially

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EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith EECS 105 Spring 2004, Lecture 20 Prof. J. S. Smith

BJT Collector Characteristic Collector Characteristics (IB)

z Ground emitter Saturation Region Breakdown (Low Output Resistance) z Fix VCE

z Drive base with Linear Increase Reverse Active fixed current IB (poor Transistor)

z Measure the collector current

Forward Active Region (Very High Output Resistance)

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