082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

2.4 Review of some common engineering functions and techniques 83
Engineeringapplication2.9
Thediodeequation
Adiodeisanelectronicdevicethatallowscurrenttoflowwitheaseinonedirection
andwithdifficultyintheother.Inplumbingtermsitistheequivalentofanon-return
valve.Itisconstructedbysandwichingtwodifferenttypesofsemiconductormaterial
together,knownasp-typeandn-typesemiconductors.Theresultantconstructionis
referred to as a p-n junction. These different types of semiconductors are created
by a procedure known as doping. The technical details are complex but it is one
of the most fundamental processes underpinning the electronics revolution that has
transformed society inrecent decades.
Asemiconductor diode can bemodelled by the equation
I=I s
(
e qV
nkT −1
)
whereV =applied voltage (V);
I =diode current (A);
I s
=reverse saturationcurrent (A);
k =1.38 ×10 −23 J K −1 ;
q =1.60 ×10 −19 C;
T =temperature (K);
n =idealityfactor.
This equation relates the current through the diode to the voltage across it. The idealityfactor,n,typicallyrangesbetween1and2dependingonhowthediodeismanufactured
and the type of semiconductor material used. We will consider the case
n = 1,whichcorrespondstothatofanidealdiode.Atroomtemperatureq/(kT ) ≈ 40
and sothe equation can be written as
I =I s
(e 40V −1)
Figure 2.31 shows a graph ofI againstV. Notice that for negative values ofV, the
equation may be approximated by
I≈−I s
since e 40V ≈ 0. The diode is said to be reverse saturated in this case. In reality,
I s
is usually quite small for a practical device, although its size has been exaggerated
in Figure 2.31. This model does not cater for the breakdown of the diode.
According to the model it would be possible to apply a very large reverse voltage
to a diode and yet only a small saturation current would flow. This illustrates an
importantpointthatnomathematicalmodelcoverseveryfacetofthephysicaldevice
orsystemitismodelling.Adifferentmodelwouldbeneededtodealwithbreakdown
characteristics.
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