I 3 Characteristics of Si

7/27/2019 I 3 Characteristics of Si

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Professor Nathan Cheung, U.C. Berkeley EE143 Lecture # 4

Characteristics of Si ( a semiconductor)

Pure Si has a relatively high electrical resistivity

By adding ppm level of special impurities (dopant), resistivity

can be lowered by many orders of magnitude

There are two types of mobile carriers (electrons and holes)

in Si : Donor dopants will increase the electron concentration ;Acceptor dopants will increase the hole concentration.

The work function of Si depends on mobile carrier concentrations

Regions of Si with different work function will develop a built-in

electric potential difference ( 1volt)

Mobile carrier concentration can be modulated many orders of

magnitude with built-in or applied electric field


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TheThe SiSi AtomAtom TheThe SiSi CrystalCrystal

High performance semiconductor devices require defectHigh performance semiconductor devices require defect--free crystalsfree crystals


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Representation of Crystallographic Planes by Miller Indices


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Silicon Crystal

Viewing Direction


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Intrinsic Si

ni (Si) ~ 1.5 E10 /cm3 at room temp


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nn--typetype pp--typetype

Silicon Electrical Properties Modified bySilicon Electrical Properties Modified by DopantsDopants

P, As ,Sb B, Al, Ga


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Dopants in Semiconductors


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Energy Band Description of Electrons and Holes

Contributed by Donors and Acceptors

EC = bottom of conduction bandEV = top of valence band

ED = Donor energy level

EA = Acceptor energy level

At room temperature,the dopants of interest

are essentially fully ionized

Donors

Acceptors


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Carrier Concentrations

n: electron concentration (cm

-3

)p: hole concentration (cm-3)

ND: donor concentration (cm-3)

NA: acceptor concentration (cm-3)

ND + p= NA + n Charge Neutrality Condition

At thermal equilibrium, np= ni2 Law of Mass Action :

Carrier conc depends on

(ND - NA) !!!


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Carrier Mobility

Mobility depends on (ND + NA) !!!

Electron current density

Jn = ( -q)nv = qnnE

|Velocity ( v) | = Mobility()) Electric Field (E)

Hole current density

Jp = (+q)pv = qppE

n

p


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Note

This chart assumes

the starting Si

contains no dopant

= 1/ (qnn +qpp)

1/ qpp for p-type

1/ qnn for n-type

Electrical Resistivity

(in ohm-cm)


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Example (1) 1015/cm3 Boron added to pure Si

NA = 1015/cm3 , ND = 0 Si is p-typeTherefore p 1015/cm3 , n 2 105/cm3

Resistivity = 1/ (qnn +qpp) 1/ qpp = 1/ (1.6 E-19 1E15 470)

= 13.3 -cm

Here , we use p = 470 cm2/volt-sec from the p vs total conc curve

Example (2) 1017/cm3 Arsenic added to sample described in Example (1)

NA = 1015/cm3 , ND = 10

17/cm3 Si is n-type

Therefore n 1017/cm3 , p 2 103/cm3

Resistivity = 1/ (qnn +qpp) 1/ qnn = 1/ (1.6 E-19 1E17 720)= 0.087 -cm

Here , we use n = 720 cm2/volt-sec from the n vs total conc curve

The p-type Si is converted to n-type by adding more donors than original acceptors

Dopant Compensation


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Resistance

R = L / (W t) where = resistivity

V+ -

L

tW

I

Sheet Resistance(in ohms/square)

Rs / t is the resistance when W = L

* if is homogeneous


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1mile

1mile

WLRR s =

L

1 mW

Resistance and Sheet Resistance

(1/2 )Rs

2Rs

R=4Rs

1 mR=R

sR=Rs

R~ 2.6Rs


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How to find n, p and Ef when all the donors and acceptors are fully ionized

B, As and P are essentially 100% ionized at room temperature.

Since Nd and Naare given (they are fixed by the device fabrication procedures) ,the following approach will give n, p and Ef .

Solve for p and n

n p = Nd -Na (1)

pn = ni2 (2)

(i) If Nd -Na > 10 ni :

n Nd -Na

(ii) If Na - Nd > 10 ni :

p Na- Nd

No ne ed to use

Equations (1) and (2)

Find E ffrom either of the

following relationship:

Ef- Ei = kT ln(n/ ni)Ei -E f = kT ln(p/ ni)

Ec

Ev

E i

Ef(n-type)

Ef

(p-type)

q|F|

Ef

is called the Fermi level

Ei

is the Fermi level for

pure Si


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Dependence of Fermi Level with Doping Concentration


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Built-in Potential Difference across a PN Junction

The Fermi level Ef is spatially invariant at thermal equilibrium


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Summary of Semiconductor Terminology

intrinsic semiconductor: undoped semiconductor

electrical properties are native to the material

extrinsic semiconductor: doped semiconductor

electrical properties controlled by the added impurity atoms

donor: impurity atom that increases the electron concentration

group V elements (P, As)

acceptor: impurity atom that increases the hole concentration

group III elements(B)

n-type material: semiconductor containing more electrons than holes

p-type material: semiconductor containing more holes than electrons

majority carrier: the most abundant carrier in a semiconductor sample

minority carrier: the least abundant carrier in a semiconductor sample


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(1) PN Junction Isolation

n

p-sub

p p p

n

nn

n

pTop Vi ew

depletionreg

ion

Cross-section

n

Device 1 Device 2

DEV I CE I SO LAT I ON M ETHODS

I

V

conducting

Non-conducting

p n+ -

+-


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SiO2

n SiO2

n SiO2

p-sub

(2) Oxide Isolation

(3) Silicon-on-Insulator (SOI)

Dielectric Substrate. e.g. SiO2, Al

2O

3

Device 1 Device 2

Device 2Device 1

pn junction


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Con tacts to Si

(a) Tunneling Ohmic Contact

SiO2

metal

n+

n-Si

e 1020 - 1021/cm3

SiO2

Al

p+

p-Si

Ec

Ev

I

V

h

M

n+ Si

Very narrow

depletion region width

Quantum

tunneling


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(b) Schottky Contacts

SiO2

Al

p-Si

SiO2

Al

n-Si

I

V

Schottky

Rectifying

contact

SchottkyOhmic

contact

I

V

conducting

Non-conducting

Moderate

conductive

Moderate Conductive

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I 3 Characteristics of Si