Diode Current Equation

ENT201-Electronic Devices�Lecture No. 10�Unit-1 �*�Quantitative Theory of the PN-Diode Currents�- Diode Current Equation.
Milliman's Electronic Devices and Circuits �

1. 1ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
ENT201-Electronic Devices
Lecture No. 10
Unit-1
*
Quantitative Theory of the PN-Diode Currents
-Diode Current Equation
V. R. Gupta
Assistant Professor
Department of Electronics Engineering
Shri Ramdeobaba College of Engineering and Management, Nagpur.

2. 2ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
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3. 3ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Quantitative Theory of the pn-Diode Currents
•Toderivetheexpressionforthetotalcurrentasafunctionof
theappliedvoltage(thevolt–amperecharacteristics),letus
assumethatthedepletionwidthiszero.
•Whentheforwardbiasisappliedtoadiode,holesare
injectedfromthep-sideintothen-side.
•Thustheconcentrationp
nofholesinthen-sideisincreased
aboveitsthermalequilibriumvaluep
no
•Where,Lpisthediffusionlengthforholesinn-type
semiconductor
�
′
�
(??????)=�
�(??????)−�
��=�
′
�
(�)�
−Τ??????????????????
∴�
�(??????)=�
��+�
′
�
(0)�
−Τ????????????
??????

4. 4ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Quantitative Theory of the pn-Diode Currents
•Theinjectedorexcess
concentrationatx=0is
•Thediffusionholecurrentinn-
sideisgivenby
�
′
�
(??????)=�
�(??????)−�
��=�
′
�
(�)�
−Τ????????????
??????
∴�
�(??????)=�
��+�
′
�
(0)�
−Τ????????????
??????
∴�
′
�
0=�
�0−�
��
൯??????
′
??????
(�
??????
��=−??????�??????
�
��
�
�??????
since
��
�
�??????
=
൯�
′
�
(0
??????
�
�
−Τ????????????????????????
��(??????)=
൯??????�??????
��
′
�
(0
??????
�
�
−Τ??????????????????

5. 5ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Quantitative Theory of the pn-Diode Currents
??????
��(??????)=
൯??????�??????
��
′
�
(0
??????
�
�
−Τ??????????????????
•Fromtheaboveequationitisevidentthattheinjectedhole
currentdecreasesexponentiallywithdistance.
•Similarly
•Sincetheinjectedconcentrationisafunctionofvoltageapplied
acrossthepn-diode,thuswecansaythatI
pndependsuponthe
appliedvoltageV.
??????
��(??????)=
൯??????�??????
��
′
�(0
??????
�
�
Τ??????????????????

6. 6ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Quantitative Theory of the pn-Diode Currents
•Letusnowfindthedependenceof൯�
′
�
(0uponV.
•FromtheBoltzmannrelationshipofkineticgastheory:
•where
–p
pandp
nareholeconcentrationsattheedgesofthespacechargeregion
inpandnmaterialrespectively.
–V
Bisthebarrierpotentialacrossthedepletionlayer
•Now,considerapn-junctionbiasedinaforwarddirectionbyan
appliedvoltageV.
•ThenthebarriervoltageV
Bisdecreasedfromitsequilibrium
valueV
obytheamountV,orV
B=V
o–V.
�
�=�
��
Τ??????B????????????

7. 7ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Quantitative Theory of the pn-Diode Currents
•Theholeconcentrationthroughoutthepregionisconstantand
equaltothethermalequilibriumvalue�
�=�
��
•Theholeconcentrationvarieswithdistanceintothen-sideas
showninfigurebelow
•Attheedgeofdepletionlayer
•i.e.atx=0
•Therefore,theBoltzmannrelationship
forthiscaseis
൯??????
′
??????
(�)�
�=�
�(0
�
�(0)=�
�(0)exp൫??????
�−??????Τ)??????
??????
∴�
�(0)=�
�(0)�
Τ????????????
??????
Refer next
slide to know
how this
equation has
come

8. 8ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Quantitative Theory of the pn-Diode Currents
•We know that, in an unbiased pn-junction diode, under equilibrium
condition
•Therefore by combining the equation obtained in previous slide with
the above equation, we obtain
�
��=�
��exp
??????
0
??????
??????
�
�(0)exp
??????
0−??????
??????
??????
=�
��exp
??????
0
??????
??????
�
�(0)exp
??????
0
??????
??????
exp−
??????
??????
??????
=�
��exp
??????
0
??????
??????
�
�(0)exp−
??????
??????
??????
=�
��
�
�(0)=�
��exp
??????
??????
??????
This boundary
condition is called the
Law of the junction

9. 9ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
•Thus, the hole concentration ൯�
′
�
(0injected into the n-side at the
junction is obtained as given below:
•Thus the hole current crossing the junction into n-side, with x=0, is
given by
•Similarly, the electron current crossing the junction into the p-side, with
x=0, is given by
Quantitative Theory of the pn-Diode Currents
�
′
�
(0)=�
��exp(Τ????????????
??????)−1
??????
��(0)=
??????�??????
��
��
??????
�
exp(Τ????????????
??????)−1
??????
��(0)=
??????�??????
��
��
??????
�
exp(Τ????????????
??????)−1

10. 10ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
•Finally, the total currentIis the sum of ??????
��0??????��??????
��(0).
•Therefore
•Where,
•I
ois the reverse saturation current.
Quantitative Theory of the pn-Diode Currents
൯??????=??????
��(0)+??????
��(0
??????=
??????�??????
��
��
??????
�
+
??????�??????
��
��
??????
�
exp(Τ????????????
??????)−1
??????=??????
0exp(Τ????????????
??????)−1
??????
0=
??????�??????
��
��
??????
�
+
??????�??????
��
��
??????
�

11. 11ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
•Notethat
–Throughoutthisdiscussion,wehaveneglectedcarriergeneration
andrecombinationinthespace-chargeregion.
–Suchanassumptionisvalidforagermaniumdiode,butnotfora
silicondevice.
–Ifweconsiderthecarriergenerationandrecombinationinthespace-
chargeregion,thegeneralequationofthediodecurrentis
approximatelygivenby
–Where,Forsiliconη=2andforGermaniumη=1.
Quantitative Theory of the pn-Diode Currents
??????=??????
�??????
Τ????????????????????????−�

12. 12ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Figure:Theminority(solid)andthemajority(dashed)currentsvs
distanceinaPN-diode.Itisassumedthatnorecombinationtakes
placeintheverynarrowdepletionregion.

13. 13ENT201-Electronic Devices Instructor-V. R. GuptaLecture No. 10
Reading Assignment
•Chapter-3ofMilliman'sIntegratedElectronics
(2
nd
edition)Book.
•section 3.3.
•AND
•Chapter-5 of Milliman's Electronic Devices and Circuits
(3
rd
or 4
th
edition) Book.
•section 5.4 and 5.5.