DTosi AE 2 Diodes

EEAE 239 Analog Electronics

![Lecture 2: Diodes]

Analog Electronics - Diodes - Daniele Tosi

pn junctionp-type (positive)n-type (negative)

Majority carriersElectron Hole


pn junction

pn junction

Apply bias to pn junction:

The excess of electrons (n) and holes (p) combine in the depletion region


(1) No bias

If 0V voltage is applied to pn junction: - Minority carriers (holes in p) pass

in n material - Majority carriers (electrons in n)

contrast the effect of minority carriers

- The net effect is ~0

The width of the depletion region determines the “resistance” of the diode to conducing current

In no-bias condition, the current through a diode is ~0


(2) Reverse bias

If negative voltage is applied to pn junction: - The barrier through conductance

increases: the majority current is ~0 - The minority current is the

dominant term, but is a very small term (uA-pA)

When VD<0V: The width of depletion increases

In reverse bias condition, the diode has a small negative saturation current (Is)


(3) Forward bias

If positive voltage is applied to pn junction: - The majority current overcomes

the effect of the minority carriers - Current flow from p to n - Barrier to conductance abated

When VD>0V: The width of depletion lowers

In forward bias condition, the diode has a large forward current (ID)


Shockley’s equationSolid state physics: Shockley’s equation

IS: Reverse saturation current (few pA) n: Ideality factor (~1-2) VT: Thermal voltage: VT = kT/q ≅ 26 mV at 27°C (300K) (k = Boltzmann’s constant, T = temperature in Kelvin, q = magnitude of electronic charge)

ID = IS{exp[VD/(nVT)]-1}


Diode characteristics

I(V) - IV characteristics



Active region High current for voltage > 0.7V



Very low saturation current for any negative V


“Knee” voltage

Knee: “discriminates” between reverse and forward mode !Knee voltage: 0.7 for Si diode


Zener region


SMC diodesGe⇾Si⇾GaAs !Knee voltage: Ge: 0.3V Si: 0.7V GaAs: 1.2V !Saturation current: Ge: ~uA Si: ~10pA GaAs: ~1pA


Temperature sensitivityID = IS[exp(VD/nVT)-1] Temperature ⬆:

!Knee V ⬇ Sat. current ⬆ |Zener V| ⬆ !Stability with T: GaAs > Si > Ge


Diode resistanceDiode resistance: 1) DC or static 2) AC or dynamic 3) Average

Static resistance is calculated with Ohm’s law: RD =VD/ID

VD = -5V ⇨ RD = 5e11Ω VD = -0.9V ⇨ RD = 9e10Ω VD = 0V ⇨ RD = 8e8Ω VD = 0.7V ⇨ RD = 9e2Ω VD = 1.3V ⇨ RD = 3e-4Ω VD = 2.5V ⇨ RD = 2e-17Ω


AC resistanceSmall input in AC - small-signal analysis We can approximate the IV as a linear curve, at the point of operation (Q-point) !The AC resistance is obtained then as rd =ΔVd/ΔId

Important to understand the process for the calculus of the rd value in small-signal conditions!


AC resistanceID = IS exp

VDnVT −1

⎛

⎝⎜⎜

⎞

⎠⎟⎟

dIDdVD

= IS expVDnVT ⋅ 1

nVT= 1nVT

IS expVDnVT −1

⎛

⎝⎜⎜

⎞

⎠⎟⎟+ IS

⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

dIDdVD

= 1nVT

ID + IS( )! IDnVT

Shockley:

Derivative:

ID

which can be rewritten as

in forward biasdVDdID

= rd =nVTID

≈ 26mVID

AC resistance: +rB


Average AC resistance

raverage =ΔVDΔID pt−pt

ΔId = 17mA - 2mA = 15 mA ΔVd = 0.725V - 0.65V = 75 mV rd = 75mV / 15mA = 5Ω

!


Resistance


Diode modelFor circuit analysis, diodes are replaced by a model, that simplifies the IV analysis.

Ideal diode Knee voltage Piecewise linear


Diode modelIdeal diode

Knee voltage

Piecewise linear


Diode circuit solving(1) Choose the appropriate diode model (2) For each diode, select a hypothesis on/off (N diodes, 2N

attempts) (3) Replace each diode with equivalent model (4) Solve the circuit using KVL, KCL and theorems (5) Measure voltage/current through diode (6) Compare the voltage/current with the hypothesis (7) If correct, the circuit is solved (8) If incorrect, reformulate hypotesis

KVL/KCL always correct! If hypotheses are not met, change hypothesis and/or diode model.


ExampleHypothesis: Diode OFF ID = 0A, VR = 0V Verify hypothesis: apply KVL E - VD - VR ⇒ VD = E = 6V Wrong! !Hypothesis: Diode ON VD = 0V, VR = 6V ID = VR / R = 3mA Ok! ID is okay with on mode

!

E=6V


Example (2)

Are both diodes on?


Example (AC)Si diode model !Diode ON - replace diode with 0.7V generator KVL: Vin - VD - VR = 0 ⇒ VR = Vin -0.7V When is diode on? ID = VR/R = (Vin - 0.7V)/R > 0A ⇒ Vin > 0.7V !Diode OFF - replace diode with open ID = 0A ⇒ VR = 0V When is diode off? KVL: Vin - VD = 0, VD = Vin ⇒ Vin < 0.7V !!


Diode capacitance

C = ε0εrAd

Closely related to the width of the depletion region

τ = RC CT = transition/depletion

CD = diffusion/storage


Reverse recovery time!tRR = reverse recovery time = Time required for a diode to stop conducting once it is switched from FW to REV bias.

!tRR, CD/T introduce frequency-dependent diode response


Commercial diodes

http://www.diodes.com/datasheets/ds12019.pdf

http://www.onsemi.com/pub_link/Collateral/BAS16XV2T1-D.PDF

http://www.diodes.com/datasheets/ds12019.pdf

http://www.onsemi.com/pub_link/Collateral/BAS16XV2T1-D.PDF


Other diodesOptical applications: - LED (also base for lasers) - Photodiode (pin and avalanche) !

Voltage regulations: - Zener diode - Schottky diode (optoelectronics) - Tunnel diode (optoelectronics) - Varactor diode - Thermal, varactor, varicap, …


LED diodes

LED case

Symbol

!LED: light emitting diode. When in forward mode, photons are emitted Applications: light (UV/VIS), telecom (NIR), … FW bias voltage is 2-3V, resistance is quite ideal ➭ connect a diode in a circuit to check whether the correct V is applied


Photodiode!Photodiode: Converts light into current with a p-i-n structure Responsivity: measured in A/W (Amps output per W optical input) Si (UV/VIS), InGaAs (NIR) For very high speed (10-100Gb/s telecom!) Photodiodes are 0- or reverse-biased (-3.3 to -12V): on top of a saturation current, there is the “optical” current

Active areaC = ε0εrAd

Big A: easier focusing on detection surface, high capacitance (no high speed) Small A: smaller capacitance (high speed), difficult focusing !


Zener diodeZener diodes operate in the breakdown (Zener) region

The characteristics is almost a vertical line, resistive element is negligible Zener voltage: 1.8V - 200V !

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DTosi AE 2 Diodes

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