PDF 3. Diodos de unión p-n 4. El MOSFET

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Curso propedéutico de Electrónica INAOE 2009 Dr. Pedro Rosales Quintero 95

3. Diodos de unión p-n

3.1 Diodo de unión p-n 3.2 Diodos túnel

3.3 Fotodiodos 3.4 LEDs y láseres 3.5 Transistor Bipolar de unión

4. El MOSFET

41 El capacitor MOS ideal 4.2 Efectos en superficies reales

4.3 Voltaje de encendido

4.4 Operación básica del transistor MOS 4.5 Control del voltaje de encendido

4.6 Fabricación del MOS

p-n Junction Diodes

¾ The diodes are designed to exploit specific junctions properties.

Rectifiers

¾ The most obvious property of a p-n junction is its unilateral nature; that this, to a good approximation its conducts current in only one direction.

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¾ From the theory derived in chapter 5 we can easily list the various requirements for a good rectifier diodes.

1. Band gap. Since n_i is small for large band gap materials, then Ir decreases with increasing Eg. On the other hand, the contact potential and E₀generally increases with increasing Eg.

2. The doping concentration on the each side of the junction influences the avalanche breakdown, the contact potential and the series resistance of diode.

Switching diodes

¾ A common technique for improving the switching speed of a diode is adding efficient recombination centers to the bulk material.

¾ Thus, for example, a p⁺-n silicon diode may have τ_p= 1µs and reverse recovery time of 0.1 µs before Au doping. If the addition of 1x10¹⁴ Au atoms reduces the lifetime to 0.1 µs and t_sd to 0.01 ns.

¾ The second approach to improving the diode switching time is to make the lightly doped neutral region shorter than a minority carrier diffusion length.

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The breakdown Diode

¾

When a diode is deigned for a specific breakdown voltage, it is called breakdown diode. Such diodes are also called Zener diodes.

¾

Breakdown diodes can be used as voltage regulators in circuits with varying inputs.

The Varactor Diode

¾

Term varactor is shortened form of variable reactor, referring to the voltage-variable capacitance of a reverse biased p-n junction. The equations in the previous section indicate that the junction capacitance depends on the applied voltage breakdown diode. Such diodes are also called Zener diodes.

¾

If the p-n junction is abrupt, the capacitance varies as the square root of the reverse bias. In a graded junction, however, the capacitance can be usually be written in the form:

V

0

V for V

C

_j

α

_r⁻ⁿ _r

>>

¾

When such a capacitor is used with an inductor L in a resonant circuit, the resonant frequency varies linearly with the voltage applied to the varactor.

r

V

LC α

ω = 1

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Curso propedéutico de Electrónica INAOE 2009 Dr. Pedro Rosales Quintero 101

3.1 Diodo de unión p-n 3.2 Diodos túnel

3.3 Fotodiodos 3.4 LEDs y láseres 3.5 Transistor Bipolar de unión

4. El MOSFET

Degenerated Semiconductors

¾

If the conduction band electron concentrations n exceeds the effective density of states

Nc

, the Fermi level is no longer within the band gap but lies within the conduction band. When this occurs, the material is called degenerate n-type

¾

The analog case of degenerate p-type material occurs when the

acceptor concentration is very high and the Fermi level lies in

the valence band.

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Tunnel Diode Operation

¾

In semiconductors, a forbidden energy gap exists between the

valence energy band (with maximum energy Ev) and the

conduction energy band (with minimum energy Ec). In most

devices, current flows when electrons are excited from the

valence band to the conduction band. In tunnel diodes,

electrons can tunnel through a potential barrier without changing

energy. This results in complex current-voltage curves that can

be explained by energy gap diagrams

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3.1 Diodo de unión p-n 3.2 Diodos túnel 3.3 Fotodiodos 3.4 LEDs y láseres 3.5 Transistor Bipolar de unión

4. El MOSFET

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Photodiodes

¾ Two-terminal devices designed to respond to photon absorption are called photodiodes.

Current and voltage in an illuminated Junction.

¾ If the junction is uniformly illuminated by photons with hν > Eg, and added generation rate g_op (EH/cm³-s) participates in this current.

¾ The resulting current due to collection of these optically generated carries by the junction is:I_op=qAg_op(L_p+L_n+W)

¾ If we call the thermally generated current described I_th, we can add the optical generation to find the total reverse current with illumination.

I= I_th(e^qV/kT-1) - I_op

I = qA(L_pp_n/

τ

_p+L_pn_p/

τ

_n)(e^qV/kT -1) - qAg_op(L_p+L_n+W)

¾ When the device is shortcircuit (V=0), the current is I_op_.

¾ When there is an open circuit across the device, and the voltage V₀ = V_oc is:

V_0C = kT/q ln[I_op/I_th+1]

V_0C ≈ (kT/q)ln[g_op/g_th] for g_op >> g_th

The appearance of forward voltage across an illuminated junction is known as the photovoltaic effect.

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Solar Cells

¾

Since the power can be deliberated to an external circuit by an illuminated junction, it is possible to convert solar energy into electrical.

¾

The voltage is restricted to values less than the contact potential, which in turn is generally less than the bandgap voltage Eg/q. For silicon the voltage V

_0C

is less than about 1 V.

¾

To utilize a maximum amount of available optical energy, it is

necessary to design a solar cell with a large area junction

located near to surface of the device.

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Photodetector

¾

When a photodiode is operated in the third quadrant of its I-V characteristic, the current is essentially independent of voltage but is proportional to the optical generation rate. Such a device provides a useful means of measuring illumination levels or converting time-varying optical signals into electrical signals.

¾

In the most optical detection applications the detector's speed of response is critical.

¾

When the carries are generated primarily within the depletion layer W, the detector is called a depletion layer photodiode.

3.1 Diodo de unión p-n 3.2 Diodos túnel

3.3 Fotodiodos 3.4 LEDs y láseres 3.5 Transistor Bipolar de unión

4. El MOSFET

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Light Emitting Materials

¾

An LED is a special type of semiconductor diode. Like a normal diode, it consists of a chip of semiconducting material impregnated, or doped, with impurities to create a structure called a p-n junction.

¾

When an electron meets a hole, it falls into a lower energy level, and releases energy in the form of a photon as it does so.

The wavelength of the light emitted, and therefore its color, depends on the band gap energy of the materials forming the p-n junction. In silicon or germanium diodes, the electrons and holes recombine by a non-radiative transition which produces no optical emission, because these are indirect bandgap materials.

The materials used for an LED have a direct band gap with energies corresponding to near-infrared, visible or near-ultraviolet light.

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Laser

¾

A laser diode is a laser where the active medium is a semiconductor similar to that found in a light-emitting diode.

When an electron and a hole are present in the same region, they may recombine by spontaneous emission—that is, the electron may re-occupy the energy state of the hole, emitting a photon with energy equal to the difference between the electron and hole states involved.

¾

These injected electrons and holes represent the injection current of the diode, and spontaneous emission gives the laser diode below lasing threshold similar properties to a LED.

¾

Spontaneous emission is necessary to initiate laser oscillation, but it is a source of inefficiency once the laser is oscillating.

Under suitable conditions, the electron and the hole may coexist

in the same area for quite some time (on the order of

microseconds) before they recombine.

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¾

Then a nearby photon with energy equal to the recombination

energy can cause recombination by stimulated

emission.

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3.1 Diodo de unión p-n 3.2 Diodos túnel

3.3 Fotodiodos 3.4 LEDs y láseres 3.5 Transistor Bipolar de unión

4. El MOSFET

This tiny triangle of plastic, gold and germanium was the first solid-state amplifier

The bipolar transistor was invented in 1947 at Bell labs by Bardeen &

Brattain consisting of metal points contacting a germanium substrate.

It was later explained by Shockley in 1949 and the three shared the Nobel prize for their work.

Base Collector

Emitter

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Modern devices

Modern bipolar transistors (so called as both holes and electrons participate in the conduction) are based on silicon substrates with two closely coupled p-n junctions.

Introduction

The goal of a transistor is to use a small input to control a large output e.g.

a small input signal to be amplified.

A bipolar transistor controls the flow of current through the device by using the base current to modify the potential profile in the channel…like water flowing over a bump in the ground…

Water flowing freely over flat ground

Water flow stopped by a bump in the ground

Water flow controlled by the height of the

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BJTs

(a) Idealized one-dimensional schematic of a p-n-pbipolar transistor and (b) its circuit symbol. (c) Idealized one-dimensional schematic of an n-p-nbipolar transistor and (d) its circuit symbol.

Modes of operation

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Thermal equilibrium

The device consists of a heavily doped p⁺emitter, a doped nbase region and a lightly doped pcollector region.

All regions are grounded.

Note the widths of the depletion regions, and the position of the valence and

conduction bands in relation to the Fermi level.

The results obtained for the p-n junction are equally applicable to the emitter- base and base-collector junctions here.

Note the ‘bump’ in the band diagram.

Active mode

The transistor is biased in the common- base configuration (base lead is common to both input & output circuits).

Note the widths of the depletion regions now under bias.

This is because the EB junction is forward biased and the BC junction is reverse biased.

Since the EB junction is forward biased, holes are injected or emitted from the p⁺ emitter into the base and electrons are injected from the n base region into the emitter.

Under ideal conditions there is no generation-recombination in the depletion region, so these two current

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Since the BC junction is reverse biased a small reverse saturation current will flow across the junction (as seen for p-n junctions).

If the base is narrow compared to the diffusion length, holes injected from the emitter can diffuse through the base to the BC depletion region edge, where they are swept into the collector by the reverse bias.

So holes, injected from a nearby emitter junction can result in a large current flow in a reverse-biased collector junction – transistor action.

emitter (p⁺) base (n) collector (p)

I_E I_C

I_B

Current gain

I_Ep

I_{EP -}I_CP

I_Cp

I_Cn I_En

I_BB

Hole current and hole flow Electron current

Electron flow En

Ep

E

I I

I = +

Cn Cp

C

I I

I = +

I I

I = −

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Current gain in the common-base configuration

An important parameter in the characterisation of the bipolar transistor is the common-base current gain,

γ

Emitter efficiency (a measure of the injected hole current compared with the total emitter current)

Base transport factor (a measure of how much of the hole current injected from the emitter reaches the collector)

γα

T

α

₀

=

For a well-designed transistor the common-base current gain is close to unity (typically 0.99)

α

T

⎟ ⎟

⎠

⎞

⎜ ⎜

⎝

⎛

⎟ ⎟

⎠

⎞

⎜ ⎜

⎝

⎛

= +

=

Ep Cp En

Ep Ep En

Ep Cp E

Cp

I I I

I α

0

Current gain in the common-base configuration

We can express the collector current in terms of the common-base current gain,

Cn E

Cn Ep

T Cn

Ep T Cn

Cp

C

I I I I

I I

I ⎟⎟ ⎠ + = +

⎜⎜ ⎞

⎝

= ⎛ +

= +

= α

₀

γα γ α

The collector-base current flowing with the emitter open-circuited (I_E= 0)

CBO E

C

I I

I = α

₀

+

I_C is the collector current for the common-base configuration I is the current between the collector and the base with the

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Current gain in the common-emitter configuration

The collector current for the common-emitter configuration is given by, Since,

C E

B

I I

I = −

(

_B _C

)

_CBO

CBO E

C

I I I I I

I = α

₀

+ = α

₀

+ +

0 0

0

1

1 α α

α

+ −

= −

_B ^CBO

C

I I I

CEO B

C

I I

I = β

₀

+

0 0

0

1 α

β α

= −

The common-emitter current gain, (typically high ~99).

So a small change in the base current gives rise to a much larger change in the collector current – amplification.

B B E

E E B

N W D

min min 0

=

β

Current gain in the common-emitter configuration

Since,

I

_C_B₀

⇒ 0

B C

I

= I β

0

t p B

C

I I

τ β

₀

= = τ

In a BJT Wb<< Lp. Thus, the average excess hole spend a time τ_t, defined as the transit time from the emitter to the collector. This transit time is much less than the average hole lifetime in the base.

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Static characteristics of the bipolar transistor

Since the bipolar transistor is simply two p-njunctions back-to-back we can apply to it the same quantitative analysis (with very similar simplifying

assumptions).

We also assume that holes are injected from the forward-biased emitter into the base and that these holes then diffuse across the base region to the collector junction.

Once we can determine the minority-carrier distribution we can obtain the current from the minority-carrier gradient…

Carrier distribution in the base region

The minority-carrier distribution (holes) in the neutral n-type base region is described by the field-free steady-state continuity equation.

2

0

2

− =

−

p no n

n p

p p

dx p D d

τ

The solution of this for p_n(x) where the width of the base region (W) is much smaller than the diffusion length (L_p) is

( ) ( ) ⎟

⎠

⎜ ⎞

⎝ ⎛ −

⎟ =

⎠

⎜ ⎞

⎝ ⎛ −

= W

p x W

e x p x

p

_n _no ^qV^EB ^kT

1

_n

0 1

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Emitter & Collector regions

The emitter and collector regions can be considered as semi-infinite

compared with the diffusion length of the injected electrons so the minority- carrier distributions decay exponentially into the bulk of the regions to their respective equilibrium concentrations…

( )

Eo Eo

(

^qV^EB ^kT

)

^x ^x^E ^L^E

E

x n n e e

n = + − 1

⁺

In the forward biased p⁺emitter region,

( )

_Co _Co ⁽^x ^x^C ^L^C⁾

C

x n n e

n = −

⁻ ⁻

In the reverse biased p collector region,

Ideal transistor currents

If we know the minority-carrier distributions, we can calculate the various current components flowing through the device…

kT no qV

p x

n p Ep

e

EB

W p qAD dx

qD dp A

I ⎟⎟ ≅

⎠

⎜⎜ ⎞

⎝

⎛ −

=

=0

The hole current injected from the emitter at x=0in the active mode of operation e.g. is proportional to the gradient of the minority carrier concentration at that point,

If we work through all of the current components and net current flows we obtain a set of general expressions applicable to all modes of operation of the bipolar transistor…

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Ideal transistor currents

( ) ( )

( ) ( 1 1 ) ( 1 ) ( 1 )

1 1

22 12

21 11

22 21

12 11

−

=

−

=

−

=

kT kT eV

eV B

kT eV kT

eV C

kT eV kT

eV E

CB EB

EB CB

e a a

I

e a e

a I

e a e

a I

Where,

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ +

⎟⎟ ≡

⎠

⎜⎜ ⎞

⎝

≡ ⎛

⎟⎟ ≡

⎠

⎜⎜ ⎞

⎝

⎛ +

≡ W

p D W

p eA D

W a p eA D

a L a

n D W

p eA D

a ^p ^no ^p ^no ^C ^Co

E Eo no E

p

22 21

12

11 , ,

The currents in the three terminals of the transistor are mainly determined by the minority-carrier concentration in the base region.

We can use these general equations to obtain the I-V characteristics of the transistor in the common-base configuration and the more often used

common-emitter configuration…