EE105 Fall 2011Lecture 6, Slide 1Prof. Salahuddin, UC Berkeley Lecture 6 OUTLINE PN Junction Diodes – Reverse Breakdown – Large and Small signal models.

EE105 Fall 2011 Lecture 6, Slide 1 Prof. Salahuddin, UC Berkeley

Lecture 6

OUTLINEPN Junction Diodes– Reverse Breakdown– Large and Small signal modelsReading: Chapter 2.2-2.3,3.2-3.4

Bipolar Junction Transistors: Chapter 4


Depletion Width at Equilibrium xa

qNE

si

A V(x)

xa-b

V0

0

bxqN

Esi

D

--(1)

--(2)

DA bNaN --(3)

V(a)=0 V(-b)=V0; Built in potential


Reverse Breakdown Mechanismsa) 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 E-field) in-between scattering events to cause electron-hole pair generation upon colliding with the lattice.


Reverse Breakdown• As the reverse bias voltage increases, the electric

field in the depletion region increases. Eventually, it can become large enough to cause the junction to break down so that a large reverse current flows:

breakdown voltage


Parallel PN Junctions• Since the current flowing across a PN junction is

proportional to its cross-sectional area, two identical PN junctions connected in parallel act effectively as a single PN junction with twice the cross-sectional area, hence twice the current.


Small and Large Signal Models- Basic Concept


Example: Diode DC Bias Calculations

S

XTXDXX I

IVRIVRIV ln11

mA 2.0XI

Vx=1 V


Constant-Voltage Diode Modelfor Large-Signal Analysis

• If VD < VD,on: The diode operates as an open circuit.

• If VD VD,on: The diode operates as a constant voltage source with value VD,on.


Example: Diode DC Bias CalculationsVx=1 V

Say, VD =V0

ND=1017

NA=1016


Large signal model: key points

• This 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 DC bias point by

perturbing the voltage by a small amount and observing the resulting linear current perturbation. – If two points on the I-V curve are very close, the curve in-

between these points is well approximated by a straight line:

1DD VVD

D

D

D

dV

dI

V

I

T

DVV

T

s

V

Ie

V

ITD 1/1


Diode Model for Small-Signal Analysis• Since there is a linear relationship between the

small-signal current and small-signal voltage of a diode, the diode can be viewed as a linear resistor when only small changes in voltage are of interest.

D

Td I

Vr Small-Signal Resistance

(or Dynamic Resistance)


Diode Model Summary


Bi-Polar Junction Transistors


Reverse-Biased PN Junction as a Current Source

• PN junction diode current is ~independent of the reverse-bias voltage. It depends only on the rate at which minority carriers are introduced into the depletion region.

Key Insight: We can increase the reverse current by injecting minority carriers near to the depletion region.


BJT Structure and Circuit Symbol• A bipolar junction transistor consists of 2 PN junctions

that form a sandwich of three doped semiconductor regions. The outer two regions are doped the same type; the middle region is doped the opposite type.


NPN BJT Operation (Qualitative)In the forward active mode of operation:• The collector junction is reverse biased.• The emitter junction is forward biased.

B

C

I

Icurrent gain:


Base Current• The base current consists of two components:

1) Injection of holes into the emitter, and 2) Recombination of holes with electrons injected from

the emitter.

BC II


BJT Design• Important features of a well-designed BJT (large ):– Injected minority carriers do not recombine in the

quasi-neutral base region.

– Emitter current is comprised almost entirely of carriers injected into the base (rather than carriers injected into the emitter).


Carrier Transport in the Base Region• The length of the quasi-neutral base

region (WB = x2-x1) is much smaller than the minority-carrier diffusion length, so that very few of the carriers injected (from the emitter) into the base recombine before they reach the collector-junction depletion region. Minority-carrier diffusion current is

~constant in the quasi-neutral base • The minority-carrier concentration at

the edges of the collector-junction depletion region are ~0.


Minority-Carrier Diffusion in theQuasi-Neutral (P-type) Base Region

B

VVq

B

iB

BBdiffn

We

N

nqD

dx

dnqDJ

TBE1

1

/2

,

BB

VVq

B

iB

BBdiffn

L

x

Le

N

nqD

dx

dnqDJ

TBE

exp1

1

/2

,

“Long Base”

LB ≡ diffusion length of minority carriers in the quasi-neutral base

“Short Base”

BB

VVqi

B L

x

N

enn

TBE exp

1/2

BB

VVqi

B W

x

N

enn

TBE

11/2

WB ≡ width of quasi-neutral base


Collector Current

• The equation above shows that the BJT is indeed a voltage-dependent current source; thus it can be used as an amplifier.

BB

iBES

T

BESC

T

BE

BB

iBEC

WN

nqDAI

V

VII

V

V

WN

nqDAI

2

2

whereexp

1exp


Common-Emitter Current Gain, • Assuming that no minority-carrier recombination occurs

within the quasi-neutral base region:– The collector current is equal to the current due to minority-carrier

injection from the emitter into the base:

– The base current is equal to the current due to minority-carrier injection from the base into the (short) emitter:

• The current gain can thus be expressed as a function of the BJT physical parameters:

1/2

TBE VV

BB

iBEC e

WN

nqDAI

CVV

EE

iEEB

Ie

WN

nqDAI TBE 1/

2

BBE

EEB

WND

WND


Emitter Current• Applying Kirchhoff’s Current Law to the BJT, we can

easily find the emitter current.

1

1CBCE IIII


Summary of BJT Currents

1

exp1

exp1

exp

T

BESE

T

BESB

T

BESC

V

VII

V

VII

V

VII

EE105 Fall 2011Lecture 6, Slide 1Prof. Salahuddin, UC Berkeley Lecture 6 OUTLINE PN Junction Diodes – Reverse Breakdown – Large and Small signal models.

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