School

University of WaterlooDepartment

Electrical and Computer EngineeringCourse Code

ECE331Professor

C.R.SelvakumarLecture

1This

**preview**shows half of the first page. to view the full**3 pages of the document.**E&CE 231 Majority and Minority Carrier Density Page 1/3 C.R.Selvakumar

How to determine the thermal equilibrium Majority and

Minority Carrier Densities in extrinsic semiconductors ?

We want to consider a general situation in which we assume that both ND donors

and NA acceptors per unit volume are present in the extrinsic semiconductor. We

want to know how many electrons (n0) and how many holes (p0) per unit volume

will be there in this extrinsic semiconductor. This is easily determined by solving

two key equations: law of mass action and charge neutrality equations. Thus

solve the following two equations simultaneously to determine n0 and p0:

np n

i00 2

= (1)

nN pN

AD00

+=+

-+

(2)

nn

p

n

pNpN

pNNpn

p

i

iAD

AD i

0

2

0

2

00

0

202

0

0

=

+=+

-- -=

-+

-+

Substitute in (2):

Collecting the terms,

Solving for

()

,

pNN NN

AD AD022

1

2

1

24=-+ -+

-+ -+

()()n

i

---- (3)

The above equation is required to be used to calculate hole density only

in the rare cases where the doping density is so low as to be comparable to

intrinsic carrier density ni

Approximations

For example consider the case of silicon. The doping densities range usually

between 1015 to 1020 cm-3 . Clearly these dopant densities are much greater than

###### You're Reading a Preview

Unlock to view full version