PHYSICAL AND CHEMICAL CONSTANTS AND SOME MATHEMATICAL FUNCTIONS
CONTENTS 1 INTRODUCTION 1 1 CLASSIFICATION OF SEMICONDUCTORS: GRIMM?SOMMERFELD RULE 1 2 CRYSTAL STRUCTURE 1 2 1 ATOMIC BOND 1 2 2 CRYSTAL STRUCTURE 1 3 DIELECTRIC FUNCTION: TENSOR REPRESENTATION 1 4 OPTICAL DISPERSION RELATIONS 1 5 OPTICAL SUM RULES 1 5 1 INERTIAL SUM RULE 1 5 2 DC-CONDUCTIVITY SUM RULE 1 5 3 F-SUM RULE 1 6 OPTICAL SPECTRA 1 6 1 CLASSIFICATION INTO SEVERAL REGIONS 1 6 2 THE RESTSTRAHLEN REGION 1 6 3 THE TRANSPARENT AND INTERBAND TRANSITION REGIONS (A) CRITICAL POINT (B) THE TRANSPARENT REGION (C) THE INTERBAND TRANSITION REGION REFERENCES 2 ELEMENTAL SEMICONDUCTORS 2 1 GROUP-IV ELEMENTAL SEMICONDUCTORS 2 1 1 DIAMOND (C) 2 1 2 SILICON (SI) 2 1 3 GERMANIUM (GE) 2 1 4 GRAY TIN (?-SN) 2 2 GROUP-VI ELEMENTAL SEMICONDUCTORS 2 2 1 SELENIUM (SE) 2 2 2 TELLURIUM (TE) 3 VALENCE BINARY SEMICONDUCTORS I 3 1 IV?IV BINARY SEMICONDUCTORS 3 1 1 CUBIC SILICON CARBIDE (3C-SIC) 3 1 2 HEXAGONAL SILICON CARBIDES (4H- AND 6H-SIC) 3 1 3 RHOMBOHEDRAL SILICON CARBIDE (15R-SIC) 3 2 III?V BINARY SEMICONDUCTORS 3 2 1 CUBIC BORON NITRIDE (C-BN) 3 2 2 HEXAGONAL BORON NITRIDE (H-BN) 3 2 3 WURTZITE ALUMINUM NITRIDE (W-ALN) 3 2 4 CUBIC ALUMINUM NITRIDE (C-ALN) 3 2 5 ALUMINUM PHOSPHIDE (ALP) 3 2 6 ALUMINUM ARSENIDE (ALAS) 3 2 7 ALUMINUM ANTIMONIDE (ALSB) 3 2 8 WURTZITE GALLIUM NITRIDE (?-GAN) 3 2 9 CUBIC GALLIUM NITRIDE (?-GAN) 3 2 10 GALLIUM PHOSPHIDE (GAP) 3 2 11 GALLIUM ARSENIDE (GAAS) 3 2 12 GALLIUM ANTIMONIDE (GASB) 3 2 13 WURTZITE INDIUM NITRIDE (W-INN) 3 2 14 CUBIC INDIUM NITRIDE (C-INN) 3 2 15 INDIUM PHOSPHIDE (INP) 3 2 16 INDIUM ARSENIDE (INAS) 3 2 17 INDIUM ANTIMONIDE (INSB) 3 3 II?VI BINARY SEMICONDUCTORS 3 3 1 MAGNESIUM OXIDE (MGO) 3 3 2 ZINC OXIDE (ZNO) 3 3 3 WURTZITE ZINC SULPHIDE (?-ZNS) 3 3 4 CUBIC ZINC SULPHIDE (?-ZNS) 3 3 5 ZINC SELENIDE (ZNSE) 3 3 6 ZINC TELLURIDE (ZNTE) 3 3 7 CADMIUM OXIDE (CDO) 3 3 8 CUBIC CADMIUM SULPHIDE (C-CDS) 3 3 9 WURTZITE CADMIUM SULPHIDE (W-CDS) 3 3 10 CUBIC CADMIUM SELENIDE (C-CDSE) 3 3 11 WURTZITE CADMIUM SELENIDE (W-CDSE) 3 3 12 CADMIUM TELLURIDE (CDTE) 3 3 13 MERCURY SELENIDE (HGSE) 3 3 14 MERCURY TELLURIDE (HGTE) 4 VALENCE BINARY SEMICONDUCTORS II 4 1 IV?VI2 BINARY SEMICONDUCTORS 4 1 1 TIN DIOXIDE (SNO2) 4 1 2 TIN DISULPHIDE (SNS2) 4 1 3 TIN DISELENIDE (SNSE2) 4 2 II?VII2 BINARY SEMICONDUCTORS 4 2 1 CADMIUN DIIODIDE (CDI2) 4 2 2 MERCURY DIIODIDE (HGI2) 5 NON VALENCE BINARY SEMICONDUCTORS 5 1 IV?VI BINARY SEMICONDUCTORS 5 1 1 GERMANIUM SULPHIDE (GES) 5 1 2 GERMANIUM SELENIDE (GESE) 5 1 3 TIN SULPHIDE (SNS) 5 1 4 TIN SELENIDE (SNSE) 5 1 5 TIN TELLURIDE (SNTE) 5 1 6 LEAD SULPHIDE (PBS) 5 1 7 LEAD SELENIDE (PBSE) 5 1 8 LEAD TELLURIDE (PBTE) 5 2 III?VI BINARY SEMICONDUCTORS 5 2 1 GALLIUM SULPHIDE (GAS) 5 2 2 GALLIUM SELENIDE (GASE) 5 2 3 GALLIUM TELLURIDE (GATE) 5 2 4 INDIUM SELENIDE (INSE) 5 3 V2-VI3 BINARY SEMICONDUCTORS 5 3 1 ANTIMONY SELENIDE (SB2SE3) 5 3 2 ANTIMONY TELLURIDE (SB2TE3) 5 3 3 BISMUTH TELLURIDE (BI2TE3) 6 SEMICONDUCTING SILICIDES 6 1 INTRODUCTORY REMARKS 6 2 VIA-METAL SILICIDES 6 2 1 CHROMIUM SILICIDE (CRSI2) 6 2 2 MOLYBDENUM SILICIDE (MOSI2) 6 2 3 TUNGSTEN SILICIDE (WSI2) 6 3 VIIA-METAL SILICIDES 6 3 1 MANGANESE SILICIDE (MN15SI26) 6 3 2 RHENIUM SILICIDE (RE4SI7) 6 4 VIII-METAL SILICIDES 6 4 1 ORTHORHOMBIC IRON SILICIDE (?-FESI2) 6 4 2 IRIDIUM SILICIDE (IR3SI5) 7 MULTINARY SEMICONDUCTORS 7 1 I?III?VI2 TERNARY SEMICONDUCTORS 7 1 1 COPPER ALUMINUM SELENIDE (CUALSE2) 7 1 2 COPPER GALLIUM SULPHIDE (CUGAS2) 7 1 3 COPPER GALLIUM SELENIDE (CUGASE2) 7 1 4 COPPER INDIUM SULPHIDE (CUINS2) 7 1 5 COPPER INDIUM SELENIDE (CUINSE2) 7 1 6 SILVER GALLIUM TELLURIDE (AGGATE2) 7 1 7 SILVER INDIUM SELENIDE (AGINSE2) 7 2 II?IV?V2 TERNARY SEMICONDUCTORS 7 2 1 ZINC GERMANIUM PHOSPHIDE (ZNGEP2) 7 2 2 ZINC GERMANIUM ARSENIDE (ZNGEAS2) 7 2 3 CADMIUM GERMANIUM ARSENIDE (CDGEAS2) 7 2 4 CADMIUM TIN PHOSPHIDE (CDSNP2) 7 3 II?III2?VI4 TERNARY SEMICONDUCTORS 7 3 1 ZINC INDIUM TELLURIDE (ZNIN2TE4) 7 3 2 CADMIUM GALLIUM TELLURIDE (CDGA2TE4) 7 3 3 CADMIUM INDIUM TELLURIDE (CDIN2TE4) 7 4 I?IIIX?VIY TERNARY SEMICONDUCTORS 7 5 QUATERNARY SEMICONDUCTOR INTRODUCTION 1 1 CLASSIFICATION OF SEMICONDUCTORS: GRIMM?SOMMERFELD RULE THE PERIODIC LAW IS MOST COMMONLY EXPRESSED IN CHEMISTRY IN THE FORM OF A PERIODIC TABLE OR CHART AN IMPORTANT PART OF THIS TABLE IS SHOWN IN TABLE 1 1 THE SO-CALLED SHORT-FORM PERIODIC TABLE, BASED ON THE MENDELEEV TABLE, WITH SUBSEQUENT EMENDATIONS AND ADDITIONS, IS STILL IN WIDESPREAD USE THE ELEMENTS IN THIS TABLE ARE ARRANGED IN SEVEN HORIZONTAL ROWS, CALLED THE PERIODS, IN ORDER OF INCREASING ATOMIC WEIGHT, AND IN 18 VERTICAL COLUMNS, CALLED THE GROUPS THE FIRST PERIOD, CONTAINING TWO ELEMENTS, H AND HE, AND THE NEXT TWO PERIODS, EACH CONTAINING EIGHT ELEMENTS, ARE CALLED THE SHORT PERIODS THE REMAINING PERIODS, CALLED THE LONG PERIODS, CONTAIN ELEMENTS, AS IN PERIODS 4 AND 5, OR 32 ELEMENTS, AS IN PERIOD 6 THE LONG PERIOD INCLUDES THE ACTINOID SERIES, WHICH HAS BEEN FILLED IN BY THE SYNTHESIS OF RADIOACTIVE NUCLEI THROUGH ELEMENT 103, LAWRENCIUM (LR) HEAVIER TRANSURANIUM ELEMENTS (ATOMIC NUMBERS 104 TO 118) HAVE ALSO BEEN SYNTHESIZED THE ELEMENTAL SEMICONDUCTORS IN COLUMN IVB OF THE PERIODIC TABLE ARE DIAMOND (C), SI AND GE, AND THEY ARE OF SOME IMPORTANCE IN VARIOUS DEVICE APPLICATIONS GRAY TIN (?-SN) IS ALSO A SEMICONDUCTOR WITH THE LOWEST BAND-GAP ENERGY OF ?0 EV BUT PB IS A METAL SIC IS THE ONLY COMPOUND SEMICONDUCTOR FORMED BY COLUMN IVB ELEMENTS THE III?V, II?VI AND I?VII SEMICONDUCTORS POSSESS A CRYSTAL STRUCTURE SIMILAR TO EITHER ONE OF THE CUBIC MINERAL, SPHALERITE OR TO HEXAGONAL WURTZITE THERE ARE III?V, 18 II?VI AND 5 I?VII COMPOUND SEMICONDUCTORS WITH THIS CRYSTAL STRUCTURE THE FIVE I?VII COMPOUND SEMICONDUCTORS ARE: CUF, CUCL, CUBR, CUI AND AGI INTRODUCTION TABLE 1 1 PERIODIC TABLE * ELEMENTS IN THE GRAY BOXES ARE OF INTEREST IN THIS BOOK A SUBSTANTIAL DEVELOPMENT IN THE SEARCH FOR SEMICONDUCTING MATERIALS WITH NEW COMBINATIONS OF PHYSICAL AND CHEMICAL PROPERTIES WAS REACHED WHEN GORYUNOVA USING THE IDEAS OF HUGGINS [1] AND GRIMM AND SOMMERFELD [2], DEVELOPED A METHOD OF PREDICTION OF THE COMPOSITION OF CHEMICAL COMPOUNDS WITH THE TETRAHEDRAL AND OCTAHEDRAL (NACL-TYPE) COORDINATION OF ATOMS IN THEIR CRYSTAL LATTICE [3] HIS METHOD IS BASED ON THE CONSIDERATION OF THE NUMBER OF VALENCE ELECTRONS IN THE ELEMENTS AND IS ASSUMED TO BE EQUAL TO THE NUMBER OF THE GROUP IN THE PERIODIC TABLE TO WHICH THEY BELONG (SO-CALLED FULL OR NORMAL VALENCY) AND CAN BE EXPRESSED IN THE FORM OF THE EQUATION SYSTEM [4] ( ) ? ? ? ? = + = = = = ? = = A I I A N I I I N I I I A I I I X X B X B X B (1 1) FOR CALCULATING THE CONTENT OF THE REPRESENTATIVES OF DIFFERENT GROUPS OF THE PERIODIC TABLE IN A COMPOUND CONTAINING A COMPONENTS, N OF WHICH ARE CONSIDERED AS CATIONS, WHERE BI IS THE NUMBER OF THE GROUP OF THE PERIODIC TABLE TO WHICH THE ITH COMPONENT OF THE COMPOUNDS BELONGS, AND XI IS ITS CONCENTRATION IN THE COMPOUND THE FIRST EXPRESSION IN EQUATION (1 1) REPRESENTS THE CONDITION THAT THE AVERAGE NUMBER OF VALENCE ELECTRONS PER ATOM IS EQUAL TO FOUR (TETRAHEDRAL RULE) THE SECOND EQUATION 1 1 CLASSIFICATION OF SEMICONDUCTORS: GRIMM ? SOMMERFELD RULE STATES THAT IN THE COMPOUND, THE NUMBER OF VALENCE ELECTRONS WHICH ‘CATIONS’ GIVE TO ‘ANIONS’ IS EQUAL TO THE NUMBER OF ELECTRONS THE ANION NEEDS TO FORM THE OCTET (I E , THE NORMAL VALENCY CONDITION) THE QUOTATION MARKS HERE ARE USED TO REMIND US THAT IN THE SOLIDS WITH DOMINATING COVALENT BONDS, WHICH FACTUALLY FORM THE CLASS OF SEMICONDUCTOR, THE ION CONCEPT IS QUITE CONDITIONAL BASED ON THESE CRITERIA, IT IS POSSIBLE TO OBTAIN ALL PROBABLE TYPES OF TETRAHEDRAL SUBSTANCES, TAKING INTO CONSIDERATION ONLY THE LOCATION OF THEIR COMPONENTS IN ONE OR ANOTHER GROUP OF THE PERIODIC TABLE IN TABLE 1 2, THESE RESULTS ARE BRIEFLY SUMMARIZED [5] IN ANALYZING THE NORMAL VALENCY COMPOUNDS, NOT ONLY TETRAHEDRAL PHASES BUT ALL COMPOUNDS OF THIS CATEGORY CAN BE GROUPED, FIRST OF ALL, IN ACCORDANCE WITH THE AVERAGE VALENCE ELECTRON CONTENT PER ATOM OF A COMPOUND, Z WE LIST IN TABLE 1 3 ALL POSSIBLE TYPES OF THE BINARY VALENCE COMPOUNDS [4] IF A AND B ARE THE CATION VALENCIES IN A BINARY COMPOUND, THE ATOMIC RATIO OF COMPONENTS IN A VALENCE COMPOUND AXBY IS WRITTEN AS A B Y X ? = (1 2) AND THE VALENCE ELECTRON CONCENTRATION PER ATOM IN THE CORRESPONDING BINARY COMPOUND IS ( ) ( ) B A A A B A Z ? + = ? ? = II2?V?VII II?VI CDTE (ZB) III III2?IV?VI AL2CO (W) III3?IV2?VII III?V GAAS (ZB) IV IV?IV SIC (ZB, W, H, RH) INTRODUCTION AS FOLLOWING FROM EQUATION (1 1) IN TABLE 1 3, THERE ARE 22 TYPES OF BINARY VALENCE COMPOUNDS [5] GORYUNOVA [3] CONCLUDED FROM THE AVAILABLE EXPERIMENTAL DATA THAT THE PHASES POSSESSING SEMICONDUCTING PROPERTIES ARE THOSE WITH Z BETWEEN TWO AND SIX; THE PHASES SMALLER THAN TWO ARE EITHER METAL ALLOYS OR THE COMPOUNDS WITH TYPICAL METALLIC CRYSTAL STRUCTURE AND PROPERTIES GORYUNOVA ALSO SHOWED THAT THERE ARE 148 TYPES OF TERNARY COMPOUNDS WHICH ARE THE ELECTRON ANALOGS OF THE BINARY VALENCE COMPOUNDS [4] AMONG THEM, THERE ARE 10 TYPES OF TERNARY COMPOUNDS WHICH SATISFY THE TETRARAHEDRAL RULE Z = 4, AS LISTED IN TABLE 1 2 1 2 CRYSTAL STRUCTURE 1 2 1 ATOMIC BOND MOST SOLIDS ARE ESSENTIALLY CRYSTALLINE BUT THE CRYSTALS COMPOSING THEM ARE NOT PERFECT A PERFECT OR A NEARLY PERFECT CRYSTAL IS CHARACTERIZED BY ITS REGULAR THREE-DIMENSIONAL PERIODICITY IDENTICAL GROUPS OF ATOMS ARE REPEATED EXACTLY AT PRECISELY EQUAL INTERVALS QUALITATIVELY, THE PROTONS AND NEUTRONS OF THE ATOM ARE CLUSTERED TOGETHER IN A DENSE NUCLEUS OF DIMENSIONS ?10?15 M AND THE ELECTRONS SURROUND THE CORE IN A CLOUD WHICH EXTENDS OUT TO A DISTANCE OF THE ORDER OF 10?10 M THE ELECTRONS ARE IN CONSTANT MOTION AROUND THE NUCLEUS AND ARE DISTRIBUTED WITH A HIGH DENSITY NEAR THE NUCLEUS AND THIS DENSITY FALLS OFF WITH RESPECT TO DISTANCE ATOMS OF DIFFERENT ELEMENTS HAVE DIFFERENT SPATIAL DISTRIBUTIONS OF OUTER ELECTRONS 1 2 CRYSTAL STRUCTURE (2S22P2), WHEREAS THE HYBRIDIZED CONFIGURATION APPROPRIATE FOR THE DIAMOND-TYPE CRYSTAL STRUCTURE IS 3S13P3 (2S12P3) (TETRAHEDRAL COORDINATION) THE DIAMOND CUBIC LATTICE IS A CONSEQUENCE OF THE GROUP-IV ATOM VALENCY OF FOUR IN III?V (II?VI) COMPOUNDS, GROUP III (II) ATOMS HAVE THREE (TWO) ELECTRONS WITH AN S2P1 (S2) CONFIGURATION OUTSIDE A CORE OF CLOSED SHELLS AND GROUP V (VI) ATOMS FIVE (SIX) ELECTRONS IN AN S2P3 (S2P4) CONFIGURATION THE III (II) AND V (VI) ATOMS HAVE THEREFORE AN AVERAGE OF FOUR VALENCE ELECTRONS PER ATOM AVAILABLE FOR BONDING WE MIGHT THEN EXPECT THAT THE COVALENT BONDS ARE FORMED BETWEEN TETRAHEDRAL S1P3 HYBRID ORBITALS, E G , FOR GAAS AND ZNSE: GA (4S24P1) + AS (4S24P3) ? GA (4S14P3)? + AS (4S14P3)+ (1 4A) ZN (4S24P0) + SE (4S24P4) ? ZN (4S14P3)2? + SE (4S14P3)2+ (1 4B) FOR SUCH A COVALENT BONDING EACH V (VI) ATOM DONATES AN ELECTRON TO A III (II) ATOM, SO THAT V+ (VI2+) AND III? (II2?) IONS ARE FORMED, EACH WITH FOUR VALENCE ELECTRONS AN IONIC BOND IS DUE TO COULOMB ATTRACTION BETWEEN THE EXCESS POSITIVE AND NEGATIVE CHARGES ON IONS FORMED BY TRANSFER OF ELECTRONS FROM THE METALLIC TO THE NONMETALLIC ATOM IN THE SCHEME: GA (4S24P1) + AS (4S24P3) ? GA (4S04P0)3+ + AS (4S24P6)3? (1 5A) ZN (4S2) + SE (4S24P4) ? ZN (4S0)2+ + SE (4S24P6)2? (1 5B) TABLE 1 4 APPROXIMATE BINDING ENERGIES OF SOLIDS (IN KJ/MOL) BOND MATERIAL METALLIC AL COVALENT C (DIAMOND) IONIC NACL KCL AGCL HYDROGEN H2O