SOLID STATE PHYSICS IN OPTOELECTRONICS
SCHRODINGER EQUATION
POTENTIAL WELL
DIFFICULT TO FIND SOLUTIONS TO SCHRODINGER EQUATION FOR REALISTIC POTENTIAL DISTRIBUTION
THE POTENTIAL DISTRIBUTION CAN BE APPROXIMATED BY AN ELECTRON TRAPPED IN AN INFINITELY DEEP POTENTIAL WELL
THERE ARE 3 QUANTUM STATES OF ELECTRON IN A POTENTIAL WELL
ENERGY BAND
PAULI EXCLUSION PRINCIPLE
FORBIDS ANY TWO ELECTRONS HAVING THE SAME SET OF QUANTUM NUMBERS
IF THERE ARE SEVERAL ELECTRONS WITHIN A 3-D POTENTIAL WELL,EACH WILL HAVE DIFFERENT VALUES OF FOR QUANTUM NUMBERS.
AS INTERATOMIC SPACING DECREASING,ELECTRON WAVE FUNCTION BEGIN TO OVERLAP.
AVOID VIOLATING PAULI EXCLUSION PRINCIPLE,THE SPLITTING OF DISCRETE ENERGY LEVELS TENDS TO DEVELOP WHERE THESE ELECTRON WILL BE DISTRIBUTED
THESE SET OF BANDS VERY CLOSELY SPACED TOGETHER WITH FORBIDDEN ENERGY GAP BETWEEN THEM
THOSE LOWER ENERGY BANDS THAT ARE FULLY OCCUPIED WITH ELECTRONS ARE NOT IMPORTANT-COMPARED TO HIGHER ENERGY LEVELS
THE HIGHER ENERGY BANDS DETERMINES THE ELECTRICAL AND PHYSICAL PROPERTIES OF THE MATERIAL
TWO HIGHES ENERGY BAND THAT VERY IMPORTANT
VALENCE BOND
CONDUCTION BAND
ENERGY GAP IS THE FORBIDDEN ENERGY REGION BETWEEN THESE TWO HIGH ENERGY LEVELS
IN DIFFERENT SOLIDS, THE VALENCE BAND MIGHT BE COMPLETELY FILLED,PARTIALLY FILLED OR HALF FILLED WITH ELECTRONS WHILE CONDUCTION BAND IS SLIGHTLY FILLED.
DIRECT AND INDIRECT BANDGAP
TOP OCCUPIED BAND IS PARTIALLY FILLED - ELECTRONS CAN GAIN ENERGY FROM EXTERNAL FIELD QUITE EASILY,RESULTING HIGH CONDUCTIVITY
TOP OCCUPIED BAND IS PARTIALLY FILLED - ELECTRONS CAN GAIN ENERGY FOM EXTERNAL FIELD QUITE EASILY,RESULTING HIGH CONDUCTIVITY
CREATION OF ELECTRON-HOLE PAIR BY EXCITATION OF ELECTRON FROM THE VALENCE BAND TO THE CONDUCTION BAND
IF THE ELECTRIC FIELD IS APPLIED,ELECTRONS IN CONDUCTION BAND AND HOLES IN VALENCE BAND DRIFT IN OPPOSITE DIRECTIONS
BOTH CONTRIBUTE TO CURRENT FLOW BECAUSE OF OPPOSITE CHARGES.
ELECTRICAL CONDUCTIVITY
IN SEMICONDUCTOR - CURRENT FLOW DUE TO ELECTRONS AND HOLES MUST BE INCLUDED
INTRINSIC SEMICONDUCTOR
A PERFECT SEMICONDUCTOR CRYSTAL CONTAINING NO IMPURITIES OR LATTICE DEFECT IS CALLED AN INTRINSIC SEMICONDUCTOR
IN THIS MATERIAL, THERE IS NO CHARGE CARRIERS AT absolute zero K
BUT AS THE TEMPERATURE RISES ELECTRON-HOLE PAIR ARE GENERATED
AT A GIVEN TEMPERATURE, THERE IS A STEADY STATE OF CARRIER CONCENTRATION
THIS IS WHEN THE RECOMBINATION OF ELECTRON-HOLE PAIRS AT THE SAME RATE AS THE THERMAL GENERATION OCCURS
RECOMBINATION TAKES PLACE WHEN AN ELECTRON IN THE CONDUCTION BAND MAKES A TRANSITION INTO A VACANT STATE IN VALENCE BAND
ENERGY RELEASED IN THE RECOMBINATION MAY BE EMITTED AS A PHOTON OR HEAT TO THE CRYSTAL LATTICE TO FORM LATTICE VIBRATION CALLED PHONON
THE PROBABILITY OF AN ELECTRON RECOMBINATION IS PROPORTIONAL TO NUMBER OF HOLES PRESENT.
NUMBER OF CHARGE CARRIERS CAN BE INCREASED BY INTRODUCING IMPURITIES INTO CRYSTAL LATTICE.
THIS PROCESS IS CALLED DOPING
DOPING CAN BE MADE TO HAVE MORE ELECTRONS OR MORE HOLES
IT CAN BE MADE AS n-type (MAJOR CARRIERS ARE NEGATIVE ELECTRONS AND MINORITY CARRIERS ARE HOLES)
OR p-type WHERE MAJORITY CARRIERS ARE POSITIVE HOLES
THE CARRIER CONCENTRATION IN DOPE SEMICONDUCTOR ARE NO LONGER EQUAL = MATERIAL IS SAID TO BE EXTRINSIC
DOPING OF TETRAVALENT MATERIAL SUCH AS SILICON WITH PHOSPHORUS OR ARSENIC PRODUCE n-type SEMICONDUCTOR
DOPING WITH BORON ,ALUMINIUM OR INDIUM PRODUCE p-type SEMICONDUCTOR
SEMICONDUCTOR IN PERIODIC TABLE
SEMICONDUCTOR ELEMENTS
SEMICONDUCTOR MATERIALS
CARRIER CONCENTRATIONS
IMPORTANT IN ANALYSING SEMICONDUCTOR PROPERTIES AND DEVICE BEHAVIOUR
WHEN CALCULATIONG CARRIER CONCENTRATIONS,THESE PARAMETERS NEED TO BE KNOWN :-
DISTRIBUTION OF ENERGY STATES OR LEVELS
PROBABILITY OF EACH STATES OCCUPIED BY ELECTRONS
DENSITY OF STATES FUNCTION IS THE NUMBER OF ENERGY STATES PER UNIT ENERGY PER UNIT VOLUME
SINCE ELECTRON OBEY PAULI EXCLUSION PRINCIPLE,THE PROBABILITY OF AN ENERGY LEVEL BEING OCCUPIED AT TEMPERATURE T IS GIVEN BY FERMI-DIRAC STATISTIC
IN n-type MATERIAL, MORE ELECTRON IN CONDUCTION BAND - FERMI LEVEL LIE NEAR DONOR LEVELS
IN p-type MATERIAL, MORE HOLES IN VALENCE BAND - FERMI LEVEL LIE NEAR ACCEPTOR LEVELS
IS THE PRODUCT DENSITY OF STATES AND PROBABILITY OCCUPANCY OF ELECTRON OVER THE ENERGY RATE
SEMICONDUCTOR JUNCTIONS
FOCUS ON p-n homojunction, A JUNCTION FORMED BETWEEN p and n VARIANTS OF THE SAME SEMICONDUCTOR MATERIAL.
ASSUME THE JUNCTION IS ABRUPT,STEP CHANGE IN THE IMPURITY TYPE
FORWARD-BIASED p-n junction
IF THE EQUILIBRIUM SITUATION IS DISTURBED,THERE WILL BE A NET CURRENT FLOW.
THIS IS DONE BY CONNECTING A VOLTAGE SOURCE EXTERNALLY ACROSS THE p-n JUNCTION
IT IS FORWARD BIASED IF THE p-region IS CONNECTED TO POSITIVE TERMINAL OF THE VOLTAGE SOURCE
WHAT REALLY HAPPEN WHEN FORWARD-BIASED THE JUNCTION ??
THE DEPLETION REGION IS VERY SENSITIVE COMPARED TO BULK REGION
THE REDUCTION IS HEIGHT OF THE POTENTIAL BARRIER LEADS TO MAJORITY CARRIERS BEING INJECTED ACROSS THE JUNCTION
THESE CARRIERS IMMEDIATELY BECOME MINORITY CARRIERS
THE MINORITY CARRIERS CONCENTRATIONS NEAR TO THE JUNCTION RISE TO NEW VALUES n'p and p'n
THIS ESTABLISHES EXCESS MINORITY CARRIERS CONCENTRATION GRADIENTS AND INJECTED CARRIERS DIFFUSE AWAY FROM JUNCTION
AT THE n region, THE INJECTED HOLES DIFFUSE AWAY FROM THE JUNCTION AND RECOMBINING AS THEY DO SO
THE ELECTRON LOST IN THE RECOMBINATION ARE REPLACED BY THE EXTERNAL VOLTAGE SOURCE
SIMILARLY AS ABOVE FOR ELECTRONS IN p region
AS THE CONSEQUENCES OF THE INJECTION,MAJORITY CARRIER CONCENTRATIONS DOES NOT CHANGE MUCH
REVERSED-BIASED p-n JUNCTION
p-n region IS CONNECTED TO THE NEGATIVE TERMINAL OF THE VOLTAGE SOURCE
THIS HAS THE EFFECT OF INCREASING THE HEIGHT OF THE POTENTIAL BARRIER AND REDUCE DIFFUSION CURRENT TO NEAR ZERO
THE NET CURRENT FLOW IS THEREFORE THE DRIFT CURRENT WHICH IS IN THE REVERSED DIRECTION (FROM n TO p)
THE REVERSE CURRENT FLOW RESULTS IN CARRIER EXTRACTION RATHER THAN INJECTION
THIS IS BECAUSE THE MINORITY CARRIERS GENERATED NEAR THE JUNCTION DIFFUSE TO IT AND ARE SWEPT ACROSS THE DEPLETION REGION
THE NEARER THE CARRIERS ARE GENERATED TO THE JUNCTION , THE GREATED PROBABILITY OF OCCURING AND CONCENTRATION GRADIENT IS FORMED TOWARDS THE JUNCTION
IDEAL p-n JUNCTION
CURRENT-VOLTAGE CHARACTERISTIC FOR IDEAL p-n JUNCTION - IN FORWARD BIAS,CURRENT INCREASE EXPONENTIALLY WITH VOLTAGE
REVERSE BIAS,THE CURRENT SATURATES AT Jo TIMES THE JUNCTION CROSS-SECTIONAL AREA.