Slide 2 - Massachusetts Institute of...

6.071Semiconductors 1

Ohm’s Law

σ = 1ρ

σ ≡ conductivity (mho/cm)

mho = 1ohm

= 1Ω

Look again at Ohm’s Law, V=IR, from a materials point of view. Restate as a law that is valid for every point inside a material, so we replace

voltage -> electric field, E,

current -> current density, J,

resistance -> resistivity.

R = ρ lA

ρ ≡ resistivity (ohm cm)A ≡ cross sectional areal ≡ lengthR ≡ resitance of object

Replace the object oriented equation with a point specific version,

E = JρJ = σE

To introduce semiconductors it is useful to start by reviewing conductors. There are two perspectives one can take in exploring conduction, We can think of devices and thus be interested in bulk properties (voltage, resistance etc) Or (2) We can think of materials and thus take a microscopic view in terms of electric field, current density etc. First we will look at the materials of semiconductors, so the second perspective is best. Then we will introduce devices composed of semiconductors.


Conductors, semiconductors and insulators

log scale of conductivity (S)

ρ = R Al

ρ ≡ resitivity (ohm cm)A ≡ cross sectional areal ≡ lengthR ≡ resitance of sample

σ = 1ρ

σ ≡ conductivity (mho/cm)1 siemen (S) = 1 mho/m

mho = 1ohm

= 1Ω

The DC electrical properties of materials can be expressed in terms of a conductivity, which is the inverse of the resistivity and reported in Siemens ( or mho/m). The plot on the right shows the range of conductivities for common materials. Here we are primarily interested in silicon which is a very poor conductor.


Band structure

• an insulator has all its electrons tied up as valence electrons and there is a large energy jump to make these free.

• a metal has a partially filled band that allows electrons mobility.

• a semi-conductor has a small band gap between the filled valence band and the conduction band. Thus for a small energy cost the material will conduct.

The conduction properties of a pure material can be directly related to the materials electron structure. As you recall from chemistry and physics classes, the electron structure is composed of a series of energy levels that electrons systematically fill. A metal has a partially filled band of energy levels thus providing the freedom for electrons to move between these and thus move through the material. An insulator has a completely filled band and then a large energy gap before the next lowest lying empty band. Electrons can only move if they acquire the energy necessary to jump to this set of empty levels. The larger the energy spacing, the harder this is to achieve and thus the better the insulator. Semiconductors have filled bands, like an insulator, but with a relatively small band-gap to the lowest lying unfilled levels. Thus some electrons can have the energy to provide mobility. Of course the average energy of an electron is a function of temperature and thus the conductivity is a function of temperature.


Silicon and semiconductors

• silicon is abundant and can be grown as a very pure, large crystal.

• The conductivity of pure silicon is quite low, all electrons are tied up as valence electrons.

• It is easy to form an oxide layer on Si and the conductivity of this glass is extremely low (it is a very good insulator).

• Si can be doped to add either electrons or holes as conductors.

Silicon is a wonderful material for semiconductor applications. First the conduction is quite low for pure silicon. It is not zero, but mostly you can think of silicon as an array of covalently bonded atoms. Also, silicon can be highly purified, so that any impurities that are intentionally placed in silicon will easily dominate unintentional defects. Finally, while pure silicon is a poor conductor, silicon dioxide (glass) is a very good insulator. Much of the advantages of using silicon are associated with the extremely precise processing of silicon that has been engineered over the past 50 years.


Intrinsic conductivity of Silicon• conductivity is expressed in terms of:the carrier densities, ni and pi

(intrinsic number of electron and hole carriers)e, the charge of the carriers (electron charge e = 1.6 x 10-19 Coulombs).µ, the carrier mobility.

J = e niµn + piµp( )E

V

+-

for Si : µn = 0.135m2 /(V ⋅ s), µp = 0.048m2 /(V ⋅ s)

at 300°K : ni = pi =1.5 ⋅1016

σ = 4.4 ⋅10−4 S

The intrinsic conductivity of silicon comes in two types: The motion of electrons, And the motion of holes (empty sites waiting for an electron). As an analogy you can think of the atoms as an array of buckets, and the electrons as balls placed in the buckets. If there are many empty buckets and only a few balls, then you would keep track of the distribution by noting the locations of the balls. On the other hand, if there are many balls and only a few buckets without, then it is more efficient to take note of which buckets are empty rather than trying to keep track of all the balls. In either case it is the balls that are moving however. Also notice that since the electrons are moving if there are only a few vacencies, then for an apparent motion of a hole many electrons must move and thus it is not surprising that the mobility of holes is lower than that of electrons. Clearly the full understanding of this requires quantum mechanics and you should not hold too firmly to this picture which is only given to motivate that the behavior is “reasonable.”


n-type doped siliconBy replacing a small amount of Si with another atomic species we can dramatically change the conductivity. For instance P or As (and other group V elements) have 5 valence electrons (rather than silicon’s four) and thus an extra electron (beyond that needed for bonding) is available for each atom replaced. Such doped materials are called n-type for negative charge carrier.

P

P

The real power of using silicon is derived from doping it, adding small amounts of other elements to dramatically change the conductivity. Silicon has four outer valence electrons and thus would like to participate in four covalent bonds. By doping this elements that have more or less valence electrons the extra electrons or holes (lack of electrons) provides a carrier for conduction. Phosphorous, and other group V elements, have five conduction electrons and thus when added as impurities into silicon introduces electron carriers. Such materials are called n-type since the majority carrier is negatively charged (an electron).


p-type doped siliconBy doping Si with a group III element, such as B or Ga (which have only 3 valence electrons we create a hole. The hole is a potential well that an electron can move in to. Such doped materials arecalled p-type for positive charge carrier. Note that the electrons are still moving, but the holes are what is unique and it is these that appear to move. Also note that both n and p type materials are charge neutral.

B

B

Boron, and other group III elements, have only 3 valence electrons and thus when added to silicon introduce hole (lack of electron) carriers. These are called p-type since the effective carrier type appears to be positively charged. It is important to recognize that while the impurities are adding carriers and thus significantly varying the conductivity of the composite material, they are not changing the charge. The dopants are added as neutrals and the overall material remains electrically neutral. This is in exactly the same way that a good conductor (say copper) is also neutral.


doped silicon

Doping a semiconductor introduces levels in the normally forbidden gap between the valence and conduction bands. The most interesting properties of these new materials arise from the interplay of the charge carries at the interface (junction) between n and p type materials.

From a solid state physics point of view the effect of doping is to introduce energy levels into the band gap between the filled valence band of silicon and the higher level conduction band. These donor or acceptor levels effectively reduce the band gap and make conduction easier. The term donor arises since in N-type materials each dopant atom donates an electron. Similarly acceptor arises since in P-type materials each dopant atom accepts an electron (or is a hole).


extrinsic (doped) semiconductorIn doped semiconductors the typical impurity concentration is 1022 donor or acceptor atoms per m3. This is 5 to 6 orders of magnitude higher concentrations than the intrinsic conductors insilicon. So the number of free carriers is very nearly the doping level.

An important relationship for any doped semiconductor is*:

(# electron carriers) x (# hole carries) = (# intrinsic electrons)2

Therefore, doping a semiconductor reduces the concentration of minority carries: the conduction is primarily by the impurity carrier.

* The demonstration of this is beyond this class, needing Boltzmann statistics and solid state physics.

σ = eNd µn ; n - type semiconductorσ = eNaµp ; p - type semiconductor

This is a small point, but the message to remember is that in doped semiconductors the action happens with the impurity carrier. Thus in n-type doped materials follow the electrons and in p-type doped materials follow the holes.


extrinsic (doped) semiconductor

Calculate the conduction of arsenic and indium doped silicon at 1022 atoms per m3.

Arsenic is a n-type dopant.

Indium is a p-type dopant.

recall that the intrinsic conductivity of silicon is much lower.

Also note that the atomic density of silicon is

σ = eNd µn = (1.6 ⋅10−19 )(1022 )(0.135) = 216S / m

σ = eNaµp = (1.6 ⋅10−19 )(1022 )(0.048) = 77S / m

σi = 4.4 ⋅10−4 S / m

5 ⋅1028 A / m3

The points to remember are: The conductivity is a function of the dopant concentration, Doped materials end up with conductivities of about graphite (good conductors about like a low value resistor). N and P type materials have different conductivities. Even in a heavily doped material the dopant is still only present in parts per million levels.


PN Junction

A junction of P- and N-type doped silicon.

bound acceptorion

freehole

bounddonorion

freeelectron

Unstable free charge distributionStable charge distribution

The opposite charges on either side of the junction combine and annihilate releasing some energy. The device is overall neutral, but now there is an electric field across the junction.

The interest in semiconductors is in how they behave when you put two or more together. By itself a doped semiconductor is just a resistor and there are much easier ways of constructing resistors. The device in the upper left is a PN junction (a P-doped material placed next to an N-doped material). This forms a diode. In the lower left is shown the configuration of dopants, electrons and holes that would be there if the two materials were placed side by side but not touching. When a PN junction is formed the charges and holes meeting at the interface combine and annihilate. This introduces a depletion zone around the junction where there is a net lack of carries. Again notice that since a negative electron annihilates with a positive hole, then net structure remains neutral. The annihilation of carriers releases some energy and this can be used to generate light photons (such as in the case of light emitting diodes - LEDs), and alternatively light can be used to create carriers, such as the case of photo-diodes and photo-transistors. These will be introduced latter.


PN Junction

q

E

V

The annihilation of charge carriers across the junction leads to a charge separation, q(x).

This is turn lead to an electric field, E(x),

or

and a Voltage across the junction.

E ∝ q(x)dx∫

V = − E(x)dx∫

dE / dx = q / ε;ε ≡ permittivity

depletion zone

0.7 V*

* for Si, 0.2 V for Ge

The lack of charge carriers at the interface of a PN junction means that there is a charge separation across the junction (since the dopants are in no way effected by the carrier annihilation). The charge separation introduces an electric field across the junction and this a voltage. Notice that while there is a charge separation, there is not any excess charge, the device is electrically neutral. The area of the electric field (or charge separation) is called the depletion zone since the annihilation of charge carriers results in an area at the junction where there are no carriers. For silicon devices the charge separation results in a voltage of 0.7 V across the interface. This is the origin of the voltage needed to turn on a diode. For germanium based semi-conductors the charge separation leads to a small junction voltage (0.2 V).


Forward biased PN junction

V

A voltage connected across a PN junction with the positive terminal connected to the P- side will inject electrons into the n-region and remove them (inject holes) into the p-region. The result is an abundance of carriers. The carriers diffuse across the junction and annihilate permitting a current to flow. This annihilation is also called recombination.

P N

Id

Io

Id is the diffusion current (carriers diffusing across the junction)

Io is the minority current (minority carriers from the intrinsic carriers).

The essence of the action of a forward biased PN junction is that you can inject majority carriers. So a PN junction with a positive voltage across it has electrons being injected into the N-region and holes into the P region, so provided that the voltage across the device is sufficient to overcome the junction voltage current will flow. When the PN junction is forward biased the diffusion current is much larger than the minority current which can be ignored.


Reverse biased PN junction

P N

Id

Io

V

Under a reverse bias the depletion zone is increased and the diffusion current is reduced. The minority carrier current is unchanged. This reverse saturation current, or drift current, is typically 10-12 A in Si. It is somewhat larger in Ge, 10-6 A, which is why Si is more common for diodes and transistors.

A forward biased diode looks like a short and a reverse biased diode like an open circuit.

In the reverse biased case the junction becomes even more depleted of carriers and the important current is the minority carrier current (or reverse saturation current). This is small compared to the forward current in the forward biased case but for some applications it most be remembered. The minority carrier current is not influenced by the voltage across the junction and is simply a property of the material. For silicon this is low while for germanium it is about a micro-amp. This is the main reason that silicon is more common in diodes and transistors.


Rectifier and diode

V (volts)

I(A) 0.7V The diffusion and drift currents both follow a Boltzmann’s law dependence. The drift current is independent of applied voltage, while the diffusion current depends on the applied voltage. As we saw, these are in opposite directions.

I = Io(eeV / kT −1)

e / kT ≈ 39V −1 at 300°K

I = Io(e39V −1)

I = Id − I0 = Ke−e Vo −V( )/ kT − Ke−eVo / kT

Id = diffusion current; Io = drift current,K = constant depending on the geometry

e = electron charge (1.6 10-19 C)V = applied voltage; Vo junction voltage

k = Boltzmann' s constant (1.38 10-23 J / °K)T = °K

Here we provide a simple approximation for the current in a silicon diode. The important messages are: The IV curve is temperature dependent, The current has an exponential dependence on the voltage.


diode characteristics

Properties:

Si or Ge, determines the voltage drop across the diode and the drift current.

Maximum reverse voltage, PRV (peak reverse voltage) or

PIV (peak inverse voltage).

IF, maximum forward current

Junction capacitance, reverse recovery time.

Capacitance depends on the size and geometry of the junction, the capacitance can be thought of as in parallel with the junction.

A large IF typically means a large junction capacitance: what happens if you try to use this diode at high frequencies?

For every device there are defining characteristics that industry has found to be useful when describing them. Even for such a simple device as a diode there are many hundreds of types that have been specifically designed for: Switching Rectifying Power High frequency Low leakage Typically in choosing a diode you need to know the maximum ratings for voltage and current. In addition diodes have a significant capacitance and this must be included in high frequency designs.


diode datasheet

A typical general purpose diode’s data sheet. This is from the Fairchild web site which is a convenient place to find data sheets. All data sheets start with showing the various versions of the device, then give the maximum ratings followed by specifications and perhaps test configurations.


diode datasheet


characterizing a diode

If too much current is sent through a diode it becomes the equivalent of a blown fuse. How do we test for this?

Ohmmeter

Gx1

x100

-probe

+probe

The galvanometer is a current controlled electromagnet that torques a spring loaded needle.

Why is there often a separate diode setting (in addition to the resistance setting)?

forward resistance ~ a few ohms

reverse resistance ~ megaohms

A problem to think about for the recitation section. If an ohm meter is sufficient to test for a diode’s function, why do many multi-meters have a separate setting for diodes?


Temperature Sensitivity of Diodes

V (volts)

I(A)

constant voltage

constant current

25 °C50°C The current through a forward biased diode is a function of temperature and thus a diode can be used as a temperature sensor.

We have two choices, constant current or constant voltage.

I = Io(eeV / kT −1)

In constant current mode, dV/dT ~ k/e ~0.002 V/°C.

currentsource

voltmeter


Is a junction a current source?A PN junction has a charge separation that looks like that of a capacitor. If you short this with a wire will a current flow? Or equivalently, is the junction voltage removed by a short?

q

V

Problem to think about for the recitation. With the charge separation across the junction of a diode it looks like a charged capacitor. We saw that when shorted a charged capacitor provided a dramatic source of energy, does a diode? In other words, if you short a diode does current flow?


Back to back diodes

• Used to avoid noise in radio frequency circuits.

.7V

-.7V

⇒

• Recall that diodes have an effective capacitance~4pF for switching diodes, 1N914’s

∴8pF

; tune out by

L


Back to back diodes (cont.)

z = 1ωC

@100MHz

12π ⋅108 ⋅8 ⋅10−12 =

1.5 ⋅10−2 ~ 200Ω

L = 1Cω2 ; ω2cL = 1


Voltage Regulator

Vin

Vout = VzenerREA simple voltage regulator.

Poor ripple suppression, requires a zener with high power rating, and variations with load impedance.

RealZener

IdealZener

I

V

Zeners are diodes that have variable resistance. Specifically,zeners have a constant currentoutput over a range of input voltages. Thus, by providing a constant current to a circuit,zeners can be used as voltageregulators.


Bipolar junction transistor

emitter

base

collector

A 2 junction, 3 terminal (base, emitter, collector) device.

Correctly biased the base emitter junction is forward biased andthe collector base junction is reverse biased.

The emitter is more heavily doped than the collector, and we canassume that the emitter provides all the carriers.

The base is thin and acts to control the emitter to collector current,

note: this is a current of electrons (npn case) and so the conventional current flows from collector to emitter.

Ie

Ib =Ie

(1+ β)

Ic =β

(β +1)Ie


Junctions of diodes and BJT

Forward biased the PN junction of a diode has a large recombination rate and thus supports a large current.

Forward biased in the BJT, the PN base to emitter junction has alow recombination rate (the base is thin and lightly doped), so the electron proceed to the collector where they are again the majority carrier.


Grounded emitter BJT

emitter

collector

base

Normally off,small input current at base and voltage relative to emitter turns it on, switching and amplifying

IC = βIB

IE = IC + IB = (1+ β)IB

VBE = VB −VE = +0.6V

β ~ 100


Temperature dependence of BJT


Grounded base BJT

The BJT is rarely used in the grounded base configuration, but it has the advantage of showing the emitter as the current carrier source.

Rload

Vbias

Rsource

Vsource

V

Vout

Vout = V − Ic Rload Ic

Vcb

IeIn this configuration the collector current is independent of the collector base voltage and varies linearly with the emitter current. Used as the input stage of a preamp

driven by a current source.

Ic =Ie


Transistor Tester Demonstration #1In this demonstration, a transistor tester will be used to generatecharacteristic current-voltage response curves for the 2N3904 BJTand the 2N5459 JFET. The tester works by applying a sawtoothvoltage pattern across the emitter/collector (or the source/drain forJFET), as well as applying a current step sequence to the base (gate).This is shown in the plot below.

VA

I

timeThe resulting collector (drain) current or voltage is then used to generate the characteristic curves with VA set as the x-axis on theoscilloscope.


Transistor Tester Demonstration #2

2N5459 JFET

VA

I

time

2N3904 BJT

Tester Input:

Vce

IbIcId

VDS

Vgs


Properties of Bipolar Transistors

β (current gain) is not a parameter, it varies with everything.

IC,max - maximum collector current rating.

BVCBO - maximum collector to base voltage.

BVCEO - maximum collector to emitter voltage.

VEBO - emitter to base breakdown voltage.

PD - maximum collector power dissipation.


Datasheet of 2N2222 (1 of 3)


Voltage Regulator

Vin

Vout = Vzener-0.6 V

R

Emitter follower configuration.

Base current is only 1/β of supply current.

RC filter reduces ripple.

VzenerC

Rload


Is a junction a current source? No

The short looks like you bent the junction around to form a second junction. Each junction has its own depletion zone and thus there is a voltage difference between the two sides of the structure.

q

V

q

V

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