Hall and photo-hall effect in semiconducting diamond. Zdenek Remes. TECHNION-Israel Institute of Technology, 2003

Transcription

1 Hall and photo-hall effect in semiconducting diamond Zdenek Remes TECHNION-Israel Institute of Technology,

2 Carrier transport properties of semiconducting diamond cm 3 B-doped p-type and N or P-doped n-type high activation energies: 1.7(N), 0.6(P) and 0.37 ev(b) low free carrier concentration at 300 K: cm 3 (B-doped), cm 3 (P-doped) > cm 3 compensating defects low Hall (DC) mobility ( cm 2 /Vs at 300 K) 2

3 Influence of charged defects on free carriers Defects induce localized states in energy gap trapping of free carriers compensate of dopants ionized dopants increase recombination rate of free carriers electrostatic scattering of free carriers deteriorate mobility 3

4 Carrier concentration and mobility from resistivity & Hall effect measurements Resistivity in Ωcm 1 ρ = (enµ) 1 Hall coefficient in cm 3 C 1 R H = r H /(en) elementary charge e = C n: density of free carriers in cm 3 µ: mobility of free carriers in cm 2 V 1 s 1 r H 1: the Hall factor Hall mobility µ H = R H ρ 4

5 Conf. const meas I (A) volt (V) V V V V V V V V ρ a = 1.133f ad I Van der Pauw resistivity measurements Q a = V 2 V 1, Q b = V 6 V 5 V 4 V 3 V 8 V 7 Q 1 Q + 1 = f arccosh(0.5 exp(0.693/f)) (V 2 + V 4 V 1 V 3 ), ρ b = 1.133f bd (V 6 + V 8 V 5 V 7 ) I thickness d (cm), ρ a and ρ b (Ωcm)should be within 10% of one another or the sample is not sufficiently uniform 5

6 Van der Pauw Hall effect measurements Conf. mag. f. const meas B (T) I (A) volt (V) V 1 +B V 2 +B V 3 +B V 4 +B V 5 -B V 6 -B V 7 -B V 8 -B n-type: V 1 > V 5 V 2 < V 6 V 3 > V 7 V 4 < V R Ha = 250d BI (V 5 V 1 + V 2 V 6 ), R Hb = 250d BI (V 7 V 3 + V 4 V 8 ) d (cm), I (A), V > 0 (V), B (Tesla), R H (cm 3 /C), R Ha and R Hb should be within 10% of one another or the sample is not sufficiently uniform 6

7 Basic High Impedance DC Hall System Equipment electromagnet 0.5 Tesla, water cooling Linkam THMS600 heating & freezing stage: K, ambient N 2 gas ( no vacuum needed), N 2 liquid cooling, water cooling at high T Keithley 220 DC Current Source: 1pA 100mA, max. output 100 TΩ, 100 V Keithley 6514 Electrometer: input resistance 200 TΩ, 10 µv 200 V triaxial cables max. 100 V, Ω, extensive manual switching! 7

8 Standard High Impedance DC Hall System Equipment Keithley 7001 switching mainframe: max. 1 A, 250 V Keithley 7065 Hall Effect Card: max. 8 V, Ω Keithley 2000 Multimeter to read voltage on #7065 Keithley 485 Picoampermeter to read current on #7065 8

9 Contacts in van der Pauw configuration Ohmic contacts: graphitization by ion bomb. (200 kev Ar/cm 2 ) or Ti/Au (25/200 nm), stabilize at 500 C Point contacts: small area small capacitance isolating substrate, no surface conductivity oxidize in boiling HNO 3 + H 2 SO 4 + HClO 4 (4:3:1) start measurement at high T or in vacuum to evaporate water condensed on surface 9

10 Symmetry of contacts and uniformity of layer: at low T enhance carrier concentration by photo-excitation 2 2 mm 1 µm P/cm 3 n-type homoepi CVD diamond, dark resistivity at 300 K: 1 MΩcm, 80V: 5 na at 300 K ( 10GΩ), 50 pa ( 1TΩ) background current at low T (hopping), 1 na photocurrent (IR,1 W) at low T, Hall effect measurable above 500 pa

11 Dark electron concentration in conduction band in n-type diamond 1. saturation at high temperature T: n N D (1 K) 2. N D K n N D n (βn c N D ) 1/2 exp ( ED 2k B T ) 3. n N D K n ( ) 1 Nc K 1 β exp ( ED k B T ) where effective density of conduction band states N c = 2(2πmk B T/h 2 ) 3/2, N D donor concentration, E D activation energy, β degeneracy (2 for electrons, 6 for holes), K = N + D /N D compensation ratio and m effective electron mass in lattice 10

12 Photo-excited electron concentration in n-type diamond photo-excitation = recombination: Iσ ph N 0 D = σ rn + D v n, n Iσ ph Kσ r (2k B T c /m) 1/2 n : concentration of photo-excited electrons with temperature T c n N D + = N DK ND 0 N D cm 3 I: IR photon flux density ( /cm 2 ) σ ph : photo-ionization cross section σ r : recombination cross section v = 2k B T/m average velocity of free carriers 11

13 Types of Scattering Centers lattice vibrations: Longitudinal acoustic phonons, optical phonons neutral point defects: vacancies charged point defects: ionized donors or acceptors, electrons or holes trapped on defect-induced localized states in energy gap extended defects: lattice distortions around point defects, dislocations, grain boundaries, surface, interfaces, atomic clusters, heterogeneous inclusions 12

14 Longitudinal acoustic phonon scattering µ = 8π eh 4 c l 3 m 5/2 (k B T ) 3/2 De 2 Bardeen and Shockley, 1950 D e : Deformation potential= change in band gap per unit strain c l : elestic constant for longitudinal deformation anisotropic in crystals (D e and c l are tensors) 13

15 Scattering on point defects µ = e mvσ s N i point defects with concentration N i and scattering cross section σ s neutral defects: scattering of electrons on H-like atom σ s cm 2 charged defects: Coulomb electrostatic scattering σ s cm 2 N i cm 3 µ 1000 cm 2 V/s at 300 K 14

16 Scattering on ionized impurities σ s = πr 2, e 2 4πε st ε 0 r mv2 2 k BT c µ = e mvσ s N i = 32π(εst ε 0 ) 2 (k B T c ) 3/2 e 3 KN D m N i = 2KN D conc. of ionized impurities, ε = 5.7 dielectric constant carrier temperature T c equals lattice temperature T L only in dark photo-excited carriers not fully thermalized T c > T L 15

17 Hole concentration and mobility in B-doped p-type diamond K 600 Carrier concentration (cm -3 ) p<<kn A E A =0.35eV photoexcited carriers /Temperature (1000/K) Mobility µ (cm 2 V -1 s -1 ) phonon sc ion.imp.sc Temperature (log K) dark measurements above 200 K, IR illumination below 200 K N A = cm 3, K 1% N i cm 3 at 270 K 16