Non-traditional methods of material properties and defect parameters measurement Juozas Vaitkus on behalf of a few Vilnius groups Vilnius University, Lithuania
Outline: Definition of aims Photoconductivity kinetics Free carrier diffusion and capture process measurement Photo-Hall and magnetoresistance Photo-ionization spectroscopy
A few general words: Profile of our group self-formed 40 years ago as: measurement of properties of high resistivity and wide bandgap materials. These materials have many different type of local levels and, usually, different non-uniformities. Therefore it was developed or modified a few of methods for exclusion or activation of a definite level or non-uniformity. The modification of methods was oriented on: Exclusion of an origins of nonlinearities; Avoiding an influence of contacts; Creation of scenario that allows to understand the process.
Free carrier kinetics
Direct measurement of trapping and recombination: photoconductivity decay (short pulse excitation) 1 τ M =1/γ nm (M-m) 3 1 2 E C E M E R 2 τ N =1/γ nm Ν CM Θ I = 1/[γ nm Ν CM + γ nm (M-m)] Θ II = 1/[γ nm Ν CM ] 4 E V τ 3 τ R =1/γ nr (R-r) 4 τ P =1/γ pr r asymp τ 1 + M m 0 = R 2 ( N + ) CM n 0 Measurement of this dependence: E.Gaubas talk!
Limitations and possibilities Excitation pulse duration: ~10 ps, ~10 ns and longer pulses or mosulated dc light. Generation of carriers direct band-band or extrinsic (via deep levels or from/to deep level) Problems appears in high quality samples due to influence of the recombination at the surface (if the diffusion is significant)
Transient gratings Free carriers change the refractive index of semiconductor, therefore if the excitation is by the light interference pattern, then semiconductor become as a periodical grating. The incident or probe beam pulse will diffract in it.
Transient gratings - contactless, non-destructive semiconductor homogeneity control parameters (D, S, τ and etc.) measurement method I λ sample I -1 I I 0 Λ I +1 Also allows to indicate the internal electric field related to impurities if the optical symmetry allows the effect.
Two step excitation spectroscopy: generation of carriers via deep centers G.G.Macfarlane et al, J.Phys.Chem.Solids 8,(1959) 388-392. Diff. Efficiency a. u. 10-1 10-2 10-3 10-4 10-5 Ι 0 = 0.7 mj/cm 2 -p 17 (irradiated) -p 17 Reference Si Ι 0 = 0.7 mj/cm 2 -p 17 (irradiated) -p 17 Reference 0 50 100 150 200 250 300 Temperature, K Identification if the centre is localized or Hydrogen-type
Free carrier lifetime (trapping time and diffusion) measurement by transient grating method I λ sample I -1 I I 0 Λ I +1 1 1 4 π = + 2 τ τ Λ G R 2 D
Diffraction efficiency (a. u.) 10 0 10-1 10-2 Λ = 4.0 µm = 1900 ps I excitation = 5 mj/cm 2 Si (CE2419) Λ = 9.5 µm = 300 ps Λ = 5.8 µm = 400 ps Λ = 4.9 µm = 480 ps Λ = 4.4 µm = 740 ps 0 500 1000 1500 Delay (ps) Λ = 4.4 µm = 640 ps Λ = 4.0 µm = 1310 ps I excitation = 5 mj/cm 2 Si (CH2259) Λ = 9.5 µm = 300 ps Λ = 5.8 µm = 370 ps Λ = 4.9 µm = 440 ps 0 500 1000 1500 Delay (ps)
1 1 CE 2419, ( phi_p [cm -2 ] 1.06 x 10 14 ), τ R > 15 ns CH 2210, ( phi_p [cm -2 ] 1.06 x 10 14 ), τ R > 15 ns Diffraction efficiency. (a. u.) CE 2437, ( phi_p [cm -2 ] 1.84 x 10 14 ), τ R > 15 ns CE 2458, ( phi_p [cm -2 ] 4.25 x 10 14 ), τ R = 11 ns 0,1 CH 2219, ( phi_p [cm -2 ] 1.84 x 10 14 ), τ R > 15 ns CH 2237, ( phi_p [cm -2 ] 4.25 x 10 14 ), τ R = 9 ns CH 2253, ( phi_p [cm -2 ] 6.36 x 10 14 ), τ R = 7 ns 0,1 CE 2459, ( phi_p [cm -2 ] 6.36 x 10 14 ), τ R = 9 ns CH 2259, ( phi_p [cm -2 ] 9.80 x 10 14 ), τ R = 6 ns 200 400 600 800 1000 1200 Delay time (ps) 200 400 600 800 1000 1200 Delay time (ps) I 0 = 0.2 mj/cm 2, grating period Λ=60 µm (decay time ~ recombination (trapping) time)
Diffraction efficiency. (a. u.) Diffraction efficiency. (a. u.) 1 0,1 0,01 1 0,1 0,01 1E-3 CE 2458, CE 2419, ( phi_p [cm -2 ] 1.06 x 10 14 ), = 370 ps, D = 17.6 cm 2 /s CE 2437, ( phi_p [cm -2 ] 1.84 x 10 14 ), = 395 ps, D = 16.5 cm 2 /s ( phi_p [cm -2 ] 4.25 x 10 14 ), = 390 ps, D = 16.3 cm 2 /s CE 2459, ( phi_p [cm -2 ] 6.36 x 10 14 ), = 390 ps, D = 16.2 cm 2 /s 200 300 400 500 600 700 CH 2210, ( phi_p [cm -2 ] 1.06 x 10 14 ), = 400 ps, D = 16.3 cm 2 /s CH 2253, ( phi_p [cm -2 ] 6.36 x 10 14 ), Delay time (ps) = 360 ps, D = 17.4 cm 2 /s CH 2259, ( phi_p [cm -2 ] 9.80 x 10 14 ), = 380 ps, D = 16.2 cm 2 /s CE 2419, I 0 = 0.12 mj/cm 2 I 0 = 0.25 mj/cm 2 ( phi_p [cm -2 ] 1.06 x 10 14 ), 1 = 450 ps, D = 14.4 cm 2 /s CE 2437, ( phi_p [cm -2 ] 1.84 x 10 14 ), I 0 = 0.12 mj/cm 2 CH 2219, ( phi_p [cm -2 ] 1.84 x 10 14 ), = 400 ps, D = 16.2 cm 2 /s CH 2237, ( phi_p [cm -2 ] 4.25 x 10 14 ), = 385 ps, D = 16.4 cm 2 /s 0,1 0,01 1E-3 1 0,1 0,01 1E-3 CE 2458, ( phi_p [cm -2 ] 4.25 x 10 14 ), = 455 ps, D = 14.2 cm 2 /s = 445 ps, D = 14.2 cm 2 /s CE 2459, ( phi_p [cm -2 ] 6.36 x 10 14 ), = 440 ps, D = 14.2 cm 2 /s 200 300 400 500 600 700 800 900 1000 1100 1200 Delay time (ps) CH 2210, ( phi_p [cm -2 ] 1.06 x 10 14 ), = 460 ps, D = 14.1 cm 2 /s CH 2253, ( phi_p [cm -2 ] 6.36 x 10 14 ), = 430 ps, D = 14.4 cm 2 /s CH 2219, ( phi_p [cm -2 ] 1.84 x 10 14 ), = 470 ps, D = 13.7 cm 2 /s CH 2259, ( phi_p [cm -2 ] 9.80 x 10 14 ), = 440 ps, D = 13.9 cm 2 /s I 0 = 0.25 mj/cm 2 CH 2237, ( phi_p [cm -2 ] 4.25 x 10 14 ), = 445 ps, D = 14.1 cm 2 /s 200 300 400 500 600 700 800 Delay time (ps) 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 Delay time (ps) Workshop on Defect Analysis in Radiation Grating Damaged period Λ=5 Silicon µm (diffusion Detectors, influence). Hamburg, 23./24. August 2006 J. Vaitkus
1/ (ps -1 ) 3 2 Si (CH2259) D = 12.5 cm 2 /s ( D = 0.1 cm 2 /s) τ R = 5.7 ns ( τ R = 0.3 ns) I excitation = 5 mj/cm 2 1 0 Si (CE2419) D = 13.6 cm 2 /s ( D = 0.1 cm 2 /s) τ R > 30 ns 1 2 3 4 5 6 1/Λ (µm -2 ) Excitation Si (CE2419) Si (CE2459) Si (CH2259) (mj/cm 2 ) 1.06 10 14 cm -2 6.36 10 14 cm -2 9.80 10 14 cm -2 0.7 D (cm 2 /s) 16 (± 0.1) 15.7 (± 0.1) 17.2 (± 0.1) τ R (ns) > 30 >30 20 (± 2) 5.0 D (cm 2 /s) 13.6 (± 0.1) 13.1 (± 0.1) 12.5 (± 0.3) τ R (ns) > 30 > 30 5.7 (± 0.3)
Photo-Hall effect I t Intense laser pulse An influence of impurities on free carrier mobility. The indications of scattering on impurities, clusters and etc.: According the scattering coefficient value According the different dependence on temperature B Magnetic field up to 2 T Digital processing: High input impedance, small capacitance!
E H 2 ( 1) eini ( t) Ai µ i ( t) i () t = BEx i e i n ( t) µ ( t) i i () t = w[ E E ( t) ] B = r web U µ H Transient Photo-Hall and photo-magnetoresistance effects 1. Basic relationships: r H H 0 H 2 < τ > = m 2 < τ > H (4) (2) (3) µ = ρ ρ ( t) = T ( B) B M µ B T M e < τ m > m eff 3 2 < τ m >< τ m > < τ m > = 4 < τ > m 2 2 (1) (5) (6) < 1 1 >= τ m i < τ m > Matthiessen s rule i 1 µ H () t = 1 µ 0 + βvs () t N() t (7) (8)
1 µ H () t Transient Photo-Hall and photo-magnetoresistance effects 2. Practical considerations: = 1 µ 0 + βvs () t N() t 1 1 1 1 1 (9) wbe U 0 ( ) 0 0 1 0 () H = = = + U SN S N SN H 0 β v µ µ t βvu H 0 ± U () 1 H (10) Y t = + (11) U H S t N t = const Y t (12) [ ( ) ( )] ( ) (8) µ s µ ion. i. ~ T 3 2 ( ) * 1 /2 = 2 e N m kt S s 1 Further analyze depends on the model and a number of re-chargeable centers µ. ~ T 1 barr
Photo-Hall effect If the sample has micro/nano nonuniformities, then the signal is more complex dependent on parameters. (That should be in a case of change of conductivity type) It changes an effective active volume therefore changes the effective Hallmobility (a lot of models, quite complicated expressions)
Photo-ionization spectrum Measurement of photoconductivity (possible effect also: quenching of photoconductivity, if additional excitation is used), photo-voltage, short circuit current. Possible regime of constant signal: varying of excitation. It excludes different non-linearities. Determination of defect optical ionization energy.
Si photoconductivity spectrum Example of data from literature: Sample from Hamburg: 10-6 10-7 Si CH2237 4,25e+14p T=79K I (A) 10-8 10-9 2006.06.24 0,8 1,0 1,2 1,4 1,6 1,8 ε (ev)
Conclusions: 1. It exists additional (time consuming) methods for carrier capture processes and defect parameters measurement. 2. It is most important to have the samples, that are interesting for supplier. Thank You for Your attention!