Wish you all Very Happy New Year
Course: Basic Electronics (EC21101) Course Instructor: Dr. S.K. Varshney (Sec. 4) Contact Email: [email protected] [email protected]: N. Vijay Kumar, A. Maity, P. Mondal, A. Bag, A. Das, I. Das, S. Chowdhury
Course contents Introduction to electronics and electronic systems, Semiconductor and devices like diodes, BJT, FET, MOSFET, Rectifier and Filters, Transistor biasing. Small signal transistor amplifiers, Operational amplifiers, Feedback and Oscillators, Digital circuit and combinational logic, Sequential logic and flip-flops, ADC & DAC, Data acquisition systems, Memory systems Case studies of electronic systems like microprocessors, radio & TV broadcasting, Mobile & cellular telephones, fiber optics & networking.
References Donald A Neamen, Electronic Circuits-Analysis and Design Text book Sedra and Smith, Microelectronics Text book (some portion). Raza Vi, Fundamentals of Microelectronics, Reference book Milliman and Halikas, Microelectronics, Reference book
Variation of bandgap with temperature
Extrinsic semiconductors (adding impurities to intrinsic semiconductors) Group V elements P, As, Sb (donor) free electrons: majority Group III elements B, Al, (acceptor) holes: majority
n-type
p-type
Rough sketch of bandgap for n-type
Rough sketch of bandgap for p-type
Fermi-Dirac distribution Electrons in solids obey Fermi-Dirac statistics tells the probability of an available energy state E to electron
f (E ) = 1+ e
1( E EF )kT
f(E)
Intrinsic semiconductor
n-type semiconductor
p-type semiconductor
Fermi distribution function can be used to know the carrier concentration at thermal equilibrium.
In case of intrinsic semiconductor Fermi energy level EF lies at some intrinsic level Ei (middle of bandgap)
Product of n0 and p0 is constant for a particular material and temperature (even if the doping is varied) Eg n0 p0 = N c N v exp kT
If we compute product of ni and pi (in case of intrinsic semiconductor), it will be, Eg ni pi = N c N v exp kT As ni=pi;
Important relation
Effective carrier densities at 300 K Ge Nc (cm-3) Nv (cm-3) 1.02 1019 5.64 10183/ 2
Si 2.81 1019 1.83 1019
GaAs 4.35 1017 7.57 1018
T N c (T ) = N c (300 K ) 300
Another way of writing n0 and p0
Ge Eg(0) eV (meV/K) 0.7437 0.477 235
Si 1.166 0.473 636
GaAs 1.519 0.541 204
(K)
T 2 E g (T ) = E g (0) T +Calculate the energy bandgap of Ge, Si, GaAs at 300 K, 400 K, 500 K and 600 K?
Temperature dependence of intrinsic carrier concentration
Example: A Si sample is doped with 1017 As atoms/cm3. what is equilibrium hole concentration at 300 K? Where is the EF relative to Ei? Draw bandgap diagram.
Transport of free carriers in semiconductorsDrift
Random motion of carriers in semiconductors with and without field o Thermal motion of an individual electron impurities, other electrons, and defects) random scattering (lattice vibration,
o no net motion of group of n electrons/cm3 over any period of time
Problems: Show that the minimum conductivity of a semiconductor sample occurs whenn0 = ni
p n
A Si sample is doped with 1017 Boron atoms/cm3. What is the electron concentration at 300 K? What is the resistivity?
Find out the expression of minimum conductivity. Calculate min for Si at 300 K and compare it with intrinsic conductivity.
Diffusion Flow from region of high concentration to low concentration - concentration gradient
Charge carriers in absence of electric field move toward region of low concentration More nonuniform the concentration, the larger the current
n : carrier concentration at given point along x Concentration gradient
If each carrier has charge q, and the semiconductor has cross-section area A
Dn: diffusion constant (cm2/s)
Dn = 34 cm2/s (for electrons); Dp=12 cm2/s (for holes)Current density (electrons) Current density (holes)
With both electron and hole gradients present, the total current density is
Consider a situation as shown in figure below. Suppose the electron concentration is N at x=0 and falls linearly to zero at x=L. Determine the diffusion current.
Ld is constant
Make an analysis of both gradient profiles (linear and exponential)Exercise
At what value of x does the current density drops to 1% of its maximum value?
Now, we can FINALLY write down the TOTAL current in a semiconductor:
For electrons:
JN = JN,drift + JN,diff = qnnFor holes:
dn + qDN dx
JP = JP,drift + JP,diff = qppAnd TOTAL current:
dp qDP dx
Under equilibrium, or open circuit conditions, total current must always be zeroJdrift = -Jdiffusion
J N = qn n + qDN
dn =0 dx
Leads to the Einstein Relationship:
D
=
kT q
This is very, very important because it connects diffusivity with mobility, which we already know how to look up
pn junction Simplest semiconductor device Flow of current freely when p region has external positive voltage (forward bias) No current in reverse bias mode This asymmetry in current flows makes pn junction diodes useful as rectifier. Biased pn junction can be used Voltage variable capacitors Photocells Light emittters
What are we going to study ..
No external connections Terminals are open
A pn junction employs following doping levels, Na=1016 cm-3, Nd=51015 cm-3. Calculate the electron and hole concentrations on the two sides.
p-type electrons holes
n-type
Evolution of junction with timet =0
-
+ +
t =t1
- - Ein
+ + + +
t =Junction reaches equilibrium once the electric field is strong enough to stop diffusion
Can you measure the built-in potential with a voltmeter?