Formelsamling. Elektroner klassiskt. Vågutbredning. Fasta tillståndets fysik / Elektroniska material. Lorentzkraft. F = q(e + v B)

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1 Formelsamling Fasta tillståndets fysik / Elektroniska material Elektroner klassiskt F = q(e + v B) Lorentzkraft U = RI, J = E Ohms lag J = n( e)v d v d = e ee m drifthastighet m( d dt + 1 )v = F kollisionstid µ = e m rörelseekvationen = e2 n m J e = ed e dn dx J h = D = µ kt e ed h dp dx ( = 1 (elektroner) (hål) = enµ e + epµ h ) konduktivitet diffusionsström Einsteins relation Vågutbredning v p =! k v fashastighet grupphastighet 1

rörelseekvationen = e2 n m J e = ed e dn dx J h = D = µ kt e ed h dp dx ( = 1 (elektroner) (hål) = enµ e + epµ

2 Frielektronmodellen d 2 H = h2 2m dx = E 2 (x) e ikx E = h2 k 2 2m p = i h d dx = hk p = h Schrödingerekvationen för en fri elektron = H H = E (x,t) = (x)e iet/ h = 1 p L e i(kx Et/ h) Z(E)dE = C p EdE C = 4 L3 (2m) 3/2 2/3 E F = h2 3 2m 8 n F (E) = 1 e (E E F )/kt h 3 Tillståndstäthet i 3D Fermienergi (3D) FermiDirac fördelningsfunktion (E F är Ferminivån) x p = h Heisenbergs osäkerhetsrelation c V = 2 2 k 2 T E F värmekapacitet per elektron (E F är Fermienergin) 2

h2 3 2m 8 n F (E) = 1 e (E E F )/kt h 3 Tillståndstäthet i 3D Fermienergi (3D) FermiDirac fördelningsfunktion (E F är

3 Bandstruktur V (r) = e 2 4 " 0 r Coulombpotential a 0 = 4 h2 " 0 e 2 m Bohrradien E = me4 8" 2 0h 2 väteatomens grundtillstånd 2a sin = n h dk dt = F ext 1 m = 1 2 E 2 v g = 1 m < k p k >= Braggs lag rörelseekvationen effektiv massa elektronens hastighet Halvledare n = N C e (E C p = N V e (E F E F )/kt E V )/kt E F = E g m kt ln h 4 m e n p = N C N V e Eg/kT = n 2 i 2 m N C =2 e kt h 2 2 m N V =2 h kt h 2 3/2 3/2 elektronkoncentrationen hålkoncentrationen intrinsisk halvledare massverkans lag n = p N C N D e E d/2kt E d donatornsbindningsenergi 3

= N C e (E C p = N V e (E F E F )/kt E V )/kt E F = E g 2 + 3 m kt ln h 4 m e n p = N C N V e Eg/kT = n 2 i 2 m N C =2 e kt h 2 2 m N V =2 h kt

4 pnövergången de dx = ρ ε 0 ε r dψ dx = E w = x n + x p = J = J 0 (e eu/kt 1) 2ε 0 ε r (ψ 0 U) N A + N D e N A N D bristområdets vidd ideala diodekvationen J 0 = el hp n0 τ h + el en p0 τ e L h /L e diffusionslängd för hål/elektroner τ h /τ e livstid för hål/elektroner C j = A ε rε 0 w kapacitans n p0 = n n0 e eψ 0/kT elektronkoncentration på ömse sida i pnövergången 4

p0 τ e L h /L e diffusionslängd för hål/elektroner τ h /τ e livstid för hål/elektroner C j =

5 Konstanter c = m/s Ljushastigheten = Js Plancks konstant = evs h = Js = evs e = C Elementarladdningen a o = m Bohrradien m e = kg Elektronmassan m p = kg Protonmassan = m e m n = kg Neutronmassan k = J/K Boltzmanns konstant = ev/k N A = kmol 1 Avogadros konstant Ry = ev Rydbergs konstant Ry = cm 1 = 2 2 2ma o R = J/(kmol K) allmänna gaskonstanten R = N A k ε o = As/Vm dielektriska konstanen för vakuum µ o = Vs/Am permeabiliteten för vakuum = 4π 10 7 Vs/Am µ B = Am 2 Bohr magnetonen e µ B = 2m 1 T = 1 Vs m 2 1 F = 1 Vs A

380658 10 23 J/K Boltzmanns konstant = 0.861739 10 4 ev/k N A = 0.6022137 10 27 kmol 1 Avogadros konstant Ry = 13.6057 ev Rydbergs konstant Ry = 109 737.32 cm 1 = 2 2 2ma o R = 0.

6 kg m J = 1VAs = 1 s 2 = 0, ev 27 1 u = 1, kg Electrical resistivities of selected elements Element ρ / 10 8 Ωm 77 K 273 K 373 K ( ρ T) 373 K ( ρ T) 273 K Li Na melted K melted Rb melted Cs melted Cu Ag Au Be Mg Ca Sr 7 23 Ba Nb Fe Zn Cd Hg 5.8 melted melted Al Ga melted In Tl Sn Pb Bi Sb

84 1.02 Be 2.8 5.3 1.39 Mg 0.62 3.9 5.6 1.05 Ca 3.43 5.0 1.07 Sr 7 23 Ba 17 60 Nb 3.0 15.2 19.2 0.92 Fe 0.66 8.9 14.7 1.21 Zn 1.1 5.5 7.8 1.04 Cd 1.6 6.8 Hg 5.

7 Periodiska Systemet 1 H Fr (223) Li Na K Rb Cs Rn (222) Be Mg Ca Sr Ba Ra (226) Sc Y La Ti Zr Hf V Nb Ta Cr Mo W Mn Tc (97) Re Fe Ru Os Co Rh Ir Ni Pd Pt Cu Ag Au Zn Cd Hg He Ne Ar Kr Xe B Al Ga In Tl C Si Ge Sn Pb N P As Sb Bi O S Se Te Po (209) F Cl Br I At (210) Ac (227) Ce Th (232) Pr Pa (231) Nd U (238) Pm (145) Np (237) Sm Pu (244) Eu Am (243) Gd Cm (247) Tb Bk (247) Dy Cf (251) Er Fm (257) Tm Md (256) Yb No (254) Lu Lw (257) Ho Es (254) 2982 Symbol Atomic Weight electron configuration Atomic Number oxydation states Periodic Table of the Elements ,5, ,7 +4, ,6 +7,4,4,4,4,2,3, ,3,4 4,4 4,4,4,4,..,5 1,2,3,5 3,5 3,5 3,5 2 +4,6 2 +4,6 2 +4,6 2,4 1,5,7 1,5 1,5 +7,1, ,4,4 +5,6,4 +5,6,4 +5,6,4 +5,6,4

906 18121 73 Ta 180.948 32112 24 Cr 51.996 8131 42 Mo 95.94 18131 74 W 183.85 32122 25 Mn 54.938 8132 43 Tc (97) 18132 75 Re 186.2 32132 26 Fe 55.847 8142 44 Ru 101.07 18151 76 Os 190.

8 H Li Na K 5K Rb 5K Cs 5K Fr Be Mg Ca Sr Ba Ra Sc Y La Ac Ti Zr Hf Density in 10 3 kg m 3 Concentration in m 3 Nearestneighbor distance in Å V Nb Ta Cr Mo W Mn Tc Re Fe Ru Os Co Rh Ir Ni Pd Pt Ce Th Pr Pa Nd U Pm Np Sm Pu Eu Am Cu Ag Au Gd Cm Zn Cd Hg Tb Bk B Al Ga In Tl Dy Cf C Si Ge Sn Pb Ho Es N 20K 1.03 P As Sb Bi Er Fm O S Se Te Po Tm Md F Cl 93K He 2K (at 37 atm) Ne 4k Ar 4K Br 123K Kr 4K I At Xe 4K Rn Yb No Lu Lr Density and Atomic Concentration of the Elements The data are given atmospheric pressure and room temperature, or at the stated temperature in deg K.

13 Density in 10 3 kg m 3 Concentration in 10 28 m 3 Nearestneighbor distance in Å V 6.09 7.22 2.62 Nb 8.58 5.56 2.86 Ta 16.66 5.55 2.86 Cr 7.19 8.33 2.50 Mo 10.22 6.42 2.72 W 19.25 6.30 2.86 Mn 7.

9 Ionization energies of alkali metal atoms and electron affinities of halogen atoms Alkali metal Ionization energy (ev) Halogen Electron affinity (ev) Li 5.39 F 3.40 Na 5.14 Cl 3.62 K 4.34 Br 3.36 Rb 4.18 I 3.06 Cs 3.89 At 2.8 Fr 4.0 Values of the energy gap between the valence and conduction bands in semiconductors, at absolute zero and at room temperature E g in ev E g in ev Crystal Gap 0 K 300 K Crystal Gap 0 K 300 K Diamond i 5.4 HgTe d 0.30 Si i PbS d Ge i PbSe d αsn d PbTe d InSb d CdS d InAs d CdSe d InP d CdTe d GaP i ZnO GaAs d ZnS GaSb d ZnTe d AlSb i AgCl 3.2 SiC(hex) 3.0 AgI 2.8 Te d 0.33 Cu 2 O 2.17 ZnSb TiO Effective masses of electrons and holes Crystal E g in ev Electron Heavy hole Light hole mass, m e m mass, m hh m mass, m lh m InSb InAs GaSb GaAs

0 Values of the energy gap between the valence and conduction bands in semiconductors, at absolute zero and at room temperature E g in ev E g in ev Crystal Gap 0 K 300 K Crystal Gap 0 K 300 K Diamond

10 Acceptor ionization energies of trivalent impurities in germanium and silicon, in ev B Al Ga In Si Ge Donor ionization energies of pentavalent impurities in germanium and silicon, in ev P As Sb Si Ge Carrier mobilities at room temperature Mobility, m 2 Vs Mobility, m 2 Vs Crystal Electrons Holes Crystal Electrons Holes Diamond GaAs Si GaSb Ge PbS InSb PbSe InAs PbTe InP AgCl AlAs KBr (100 K) 0.01 Några materialparametrar Ge Si GaAs InAs m e m m h m ε r E g ev 0,22 0,26 0,066 0,026 0,31 0,69 0,56 0,40 16,3 11,8 12,4 12,2 0,66 1,12 1,42 0,35 I denna tabell ges medelvärden av de effektiva massorna, som är lämpliga att användas i uppgifter.

0096 Carrier mobilities at room temperature Mobility, m 2 Vs Mobility, m 2 Vs Crystal Electrons Holes Crystal Electrons Holes Diamond 0.180 0.120 GaAs 0.80 0.030 Si 0.135 0.048 GaSb 0.50 0.100 Ge 0.

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