Basics of semiconductor, current equation

1. ELECTRONIC DEVICES & CIRCUITS
INTRODUCTION TO SEMICONDUCTOR
III Semester
Prepared By
Ms. Nidhee Bhuwal
Assistant Professor
Department of Electronics & Telecommunication

2. TOPICS
 Insulator, Semiconductor and Conductors
 Crystal structure of Ge and Si
 Intrinsic Semiconductor
 Extrinsic Semiconductor
 Mass Action Law & Law of electrical Neutrality.
 Comparison of N type and P type
 Mobility
 Drift Current Density
 Diffusion current Density
 Einstein’s Relationship
 Net Current Density
 Generation & Recombination of Charges
 Continuity Equation
 Injected Minority Carrier Charges
 Potential variation in a graded semiconductor
 Contact potential due to step Graded Junction

3. INSULATOR, SEMICONDUCTOR AND
CONDUCTOR
Valence Band (VB)= Outermost band filled with electrons
Conduction band (CB)= Next highest band empty or partly filled with electrons
Eg (Energy Band Gap)= Energy difference between VB and CB, no electron
resides here hence called forbidden band.

4.  Conductors (Metals):- Materials that are capable of
carrying electric current. Eg:-Copper, Silver, Iron etc.
Eg=0eV
 Insulators :- Materials that are not capable of carrying
electric current. Eg:-Glass, Quartz, Diamond. Eg =3eV to
6 eV
 Semiconductors:- Materials whose conductivity lies
between insulator and conductor. Eg:- 0.1 eV to 3 eV.
Eg:- Germanium (Ge & Silicon (Si)

5. SILICON & GERMANIUM
 Forms covalent bond (Sharing of electron), Consist of 4 electrons in its
valence shell.

6. INTRINSIC SEMICONDUCTOR
n=p=ηi ------(1)
n= electron concentration, p= hole concentration
ηi = intrinsic carrier concentration

7. EXTRINSIC SEMICONDUCTOR
N TYPE (PENTAVALENT IMPURITIES)
 ND :- Donor impurity concentration
 Example:- Arsenic (As), Antimony (Sb)

8. P TYPE (TRIVALENT IMPURITIES)
NA :- Acceptor Impurity concentration
Example:- Boron (B)

9. MASS ACTION LAW
 Under thermal equilibrium, product of free electron concentration
and hole concentration is a constant independent of impurity
doping. This is called mass action law.
--------(2)
n=electron concentration
P= hole concentration
ηi =intrinsic carrier concentration
LAW OF ELECTRICAL NEUTRALITY
ND :- Donor impurity concentration (becomes +ve charge after donating an electron
NA :- Acceptor impurity concentration (becomes - ve charge after accepting an
electron
ND+p=NA+n
According to this law, sum of positive charges is equal to sum of negative
charges.
-----------(3)

10. COMPARISON OF N TYPE AND P TYPE
Parameters N type P type
No. of electrons in
valence shell
5 electrons/ pentavalent 3 electrons / trivalent
Energy band Gap ED
Donor energy Band
formed just below the
conduction band
EF
Acceptor energy level formed
just above the valence band
Majority carriers Electrons (nn) Holes (pp)
Minority carriers Holes (pn) Electrons (np)
Impurity
Concentration
ND (Donor impurity
concentration)
NA (Acceptor impurity
concentration)
Condition n>>p p>>n
Majority carrier
concentration
nn≈ND pp≈NA
Minority carrier
concenration ----------(4) --------(5)

11. MOBILITY
 It is a speed with which particles moves in the presence
of electric field.
 As per gas theory, without external Electric field (E),
electrons are in random motion due to which net current
is zero.
 When E is applied, due to electrostatic force, electrons
will be accelerated and velocity will increase with time.
v=µE ------(6)
v= drift speed (cm)
E=electric field (V/cm)
µ=mobility (cm2/V sec)

12. DRIFT CURRENT DENSITY (JDRIFT )
• Occurs due to external electric field.
Jdrift = nqµnE+pqµpE ---------(7)
n= electron concentration
p= hole concentration
µn =electron mobility
µp =hole mobility
E= applied electric field
Jn(drift) = nqµnE
Jp(drift) = pqµpE
We know that,
------------------------(8)
Conductivity:-
----------------(9)
Resistivity :-
--------------(10)
Unit of resistivity:-Ω m

13. DIFFUSION CURRENT DENSITY(JDIFFUSION)
 Occurs due to non uniform concentration of electrons or holes in a
semiconductor.
 Movement occurs from higher concentration to lower concentration.
Dp= diffusion constant due to holes
dp/dx = concentration gradient due to holes
Dn=diffusion constant due to electrons
dn/dx = concentration gradient due to electrons
--------(11)
--------(12)

14. EINSTEINS RELATIONSHIP
 Diffusion constant (D) and mobility(u) are not
constant. They are related as:-
Dn:- Diffusion constant due to electrons (cm2/sec)
Dp:- Diffusion constant due to holes (cm2/sec)
µn:- mobility of free electrons (cm2/V sec)
µp:- mobility of holes (cm2/V sec)
VT:- Thermal voltage (Volts)
-------------(13)

15. NET CURRENT DENSITY
 Jtotal =Jdrift+Jdiffusion ------------(14)
Jtotal=Jn(drift)+Jp(drift) +Jp(diffusion) + Jn(diffusion)
In open circuited case,
Jtotal = 0

16. GENERATION AND RECOMBINATION OF
CHARGE CARRIERS
 Due to thermal agitation, new electron hole pairs appears.
This is called generation.
 Some electron hole pair recombine after completing their
lifetime. This process is called as recombination.
 Electrons (holes) will exists for particular time before
recombination. This is called mean lifetime of carrier(τn ).
 Consider N type semi conductor.
no = initial concentration of electrons (constant)
po = initial concentration of holes (constant)

17. After illumination,
By law of electrical neutrality, excess holes is equal to excess electrons,
% increase in Minority carriers (hole) >> % increase in majority carriers(electron).
--------------(15)

18.  Therefore, minority carrier concentration is studied in this case.
 g (generation rate )=increase in hole concentration due to
illumination.
 p/τp =Decrease in hole concentration due to recombination.
By law of conservation,
Increase in hole concentration/second=dp/dt
Under steady state condition,
g= po /τp
---------------(16)
---------------(17)
---------------(18)

19. CONTINUITY EQUATION
Increase in holes per unit
volume/sec dp/dt is given by
-------------------(19)

20. INJECTED MINORITY CARRIER CHARGES

21.  Low Level Injection condition:- Minority carrier is
much smaller than majority carriers
p<<n (in this case)
Jp(total)=Jp(drift)+Jp(diffusion)
Jp(total)=Jp(diffusion) [as Jp(drift) = pqµpE]
Using continuity equation and substituting Jp(diffusion)
we get,
Solving and substituting initial conditions,
-----------------(20)

22.  Hole Diffusion Current (Ip(diffusion) ):-
 Electron Diffusion Current (In(diffusion) ):-
 Electron Drift current (In(drift) ):-
 Hole Drift current (Ip(drift) ):-
----------------(21)
---------------(22)
---------------(23)
---------------(24)

23. POTENTIAL VARIATION WITHIN A GRADED
SEMICONDUCTOR
Assume,
No excitation and steady state
condition,
Since, doping is non uniform,
Therefore,
Ip(diffusion) ≠ 0
There must be Ip(drift) equal and
opposite to Ip(diffusion) .
Itotal = 0
Ip(drift) ∝ E ------(25)
Therefore, an electric field is generated to produce within an semiconductor due to
non- uniform doping.
-----------(26)

24. AN OPEN CIRCUITED STEP GRADED JUNCTION
From eq(26),
---------(27)
ppo = hole concentration at p side
pno = hole concentration at n side
for n type, n ≈ ND
------(28)
Substituting this value in eq(27),
ppo =NA
----(28)

25. THANK YOU