Characterization Techniques for Deep Defects in Semiconductors

1. Lecture 17

2. RS OF DEFECT VIBRATIONAL MODES RS OF DEFECT VIBRATIONAL MODES • Vibrational Mode of Cl IN CdS= shaded broad peak centered at 113 cm-1. • The width of this Raman mode shows that it is not strongly localized around Cl. • The spectrum in (a) is excited when the Raman peak is closer to the I2 bound exciton peak in the luminescence. • The enhancement in the Raman mode is so strong that it is bigger than the luminescence.

3. - -U NATURE OF THE DX CENTER FROM U NATURE OF THE DX CENTER FROM HALL EFFECT HALL EFFECT • Hall carrier concentration in GaAs codoped with two donors:Ge and Te • In this experiment by Baj et al. pressure was used to convert the shallow donors Ge into DX centers. • The pressure for the conversion is ~1GPa. • Before the experiment, light is used to ionize the donors into the conduction band. • The carrier concentration is determined by Hall Effect.

4. • If the T is low (T=70K) electron cannot be captured into the DX state because of a capture barrier Ec. • Carrier can only be trapped at the shallow donor state which can capture only one e per Ge. • Hence n drops by [Ge]~1017cm-3. : e+d+=>d0 • At T=100K the Ge donor can overcome Ecand now capture 2 electrons per Ge into the deeper DX state: e+ d0 +Ec=>DX- • As long as there are carriers available from Te, • Ge will capture those electrons also due to its –U nature. • The drop in n should be equal to 2[Ge] or ~2x1017cm-3. • This is exactly what is observed experimentally proving that the DX state has a –U!

5. CAPACITANCE TRANSIENT TECHNIQUES CAPACITANCE TRANSIENT TECHNIQUES • M.F.Li M.F.Li and P. Y. Yu, and P. Y. Yu, Semicond • Capacitance transient techniques are important for characterizing deep defects in semiconductors especially those that are not optical active. • The disadvantage of the techniques is that the sample has to be fabricated into either a pn-junction or Schottky barrier diode. • When reverse biased these devices become a capacitor. Semicond. & Semimetals, 54, 457 (1998) . & Semimetals, 54, 457 (1998)

6. • The method was initially introduced by D. V. Lang in 1974. • DLTS is a capacitance transient thermal scanning technique, operating in the high frequency (Megahertz) range. • It uses the capacitance of a p-n junction or Schottky barrier as a probe to monitor the changes in charge state of a deep center.

7. p p- -n junction capacitance n junction capacitance • When voltage across a p-n junction (bias) is changed, • there is a corresponding change in the depletion region width. • Depletion region is a region in a P-N junction where only space charges are present. • With holes and electrons in the region compensated each other. • This change in width causes a change in the number of free charge carriers on both sides of the junction, resulting in a change in the capacitance.

8. • This change has two contributions; • a) the contribution due to change in depletion width known as the junction capacitance and • b) the contribution due to change in minority carrier concentration called the diffusion capacitance. • Junction capacitance is dominant under reverse biased conditions while diffusion capacitance is dominant under forward biased conditions.

9. • Consider a p-n junction with a deep level present having its energy as ET. • In steady state there is no net flow of charge carriers across the trap. • Also the electron and hole densities within the depletion region are negligible. Thus from Shockley and Reed and Hall (SRH), the relationship between the total density of deep sates NTand density of filled traps is given by, • epnt=(en+ep)Nt • where epis the hole emission rate, enis the electron emission rate, ntis the density of filled traps, and Ntis the total density of deep sates. • This is called a two-step recombination process, Shockley-Read-Hall recombination • conduction electrons can relax to the deep defect level and then relax to the valence band, annihilating a hole in the process.

10. • Now if the system is perturbed, this ntchanges and will thus cause the total charge in the depletion region to increase or decrease, leading to a corresponding change in the capacitance. • This change is only due to deep levels. • For example, we can study the capture of e’s by the deep centers in real time by performing two steps:

11. Filling phase Filling phase: • Filling Filling phase • Apply a forward biasing pulse of height Vpand time duration τ (known as a filling pulse) to lower the reverse bias, • so as to attract e’s to the depletion layer. • As deep levels in the depletion layer fill up with more e’s, W decreases. phase:

12. Emission phase Emission phase: • After the filling pulse, the bias is returned to original value. • This allows the captured e’s to return to the conduction band. • The process is usually referred to as emission. • Its rate is denoted by en. • The Δntas a function of time in this phase is given by: • Δ nt(t)=Nt [1-exp(-Cnτ)]exp(-ett); • assuming that the filling pulse is turned off at t=0, • Δ C/C is given by:

13. • For SRH to happen, In addition to the deep center (say a deep donor) the sample has to contain a source of free carriers eg shallow donor to provide e’s. • By applying a bias Vb, a depletion layer of width W can be created. • The capacitance C is given by: C= Aε/W, • A=area of cross-section of device and ε =permittivity of sample • If the shallow donor density is assumed to be constant, then the free carrier and the depletion width are related by the Poisson Equation: • Vb~ρW2 • Detailed dirivation skipped. We’ll revisit it later this semester. • These two relation shows that for a fixed Vb, W and hence C changes when ρ changes: • Δρ/ρ=-2(ΔW/W) =ΔC/C

14. STUDYING DEEP TRAPS BY STUDYING DEEP TRAPS BY CAPACITANCE TRANSIENTS CAPACITANCE TRANSIENTS • Suppose the sample contains Ndshallow donor while there are Nt deep traps. • When Nd>> Nt, ρ is determined mainly by Ndwhile Δρ (produced by a change in bias) is caused mainly by trapping or detrapping of e by the deep center. • In other words, Δρ =(-e) Δntwhere Δ ntis the change in the concentration of electrons trapped on the deep levels. • Combining with the previous result we get: • ΔC/C= - Δ nt/(2Nd) • This equation is the basis of the capacitance transient technique.

15. DEEP LEVEL CAPACITANCE DEEP LEVEL CAPACITANCE TRANSIENTS TRANSIENTS • Experimentally Cncan be measured by measuring ΔC as a function of the filling pulse width τ • while the emission rate encan be determined from Δ C/C as a function of time t. • The emission and the capture rates are related to each other by the principle of detailed balance: • where Ecand Ncare, respectively, the conduction band edge energy and effective density of states, and k is the Boltzmann constant. • The energy Ec-Et is the thermal ionization energy of the deep level.

16. • It is usual in the literature to define the capture rate in terms of a capture cross-section σnby: • Cn= n0<v>σn, where <v> and n0are, respectively, the thermal velocity and concentration of the free carriers.

17. • The capture cross section is usually assumed to be thermally activated and has the temperature dependence: • where EBis defined as the capture barrier heigh . • Combining these results we obtain:

18. • These two Eqns are commonly used to determine the capture and emission barrier heights by measuring the emission rate and capture crosssection as a function of t at constant temperatures. • The capacitance transient technique used to measure the capture and emission rates is quite time consuming since one has to measure many capacitance transient curves at many T. • An alternative is to scan T while keeping a “time window” constant. In this approach the capacitance is measured at two times t1 and t2 after a filling pulse.

19. • The corresponding capacitances are denoted by C1 and C2, respectively. • Their difference (C1 - C2 ) is then measured as a function of temperature. • The idea is that (C1 - C2 ) is non-zero only when there is significant change in the deep level occupation during the time window. • If t1 and t2 are both << 1/en(T), then both C1 and C2 are unchanged so their difference (C1 - C2 )~0. • If t1 and t2 are both >>1/en(T) then C1 and C2 are both almost equal to the equilibrium value and so again (C1 - C2 )~0. • A plot of (C1 - C2 ) versus temperature will exhibit a peak when 1/en (T) is approximately equal to the time window (t2 - t1 ). • This is the basis of the Deep Level Transient Spectroscopy or DLTS technique. • This technique is said to be “spectroscopic” since scanning T is analogous to scanning photon energy.

20. • Figure (a) shows the original DLTS spectrum of the DX center in GaAlAs. • The emission rate can be determined from the time window. • A plot of this rate vs 1/T (Aarhenius Plot) is required to obtain the emission rate.

21. • Fig. (b) illustrates the method of Thermally Stimulated Capacitance (TSCAP) which shows the variation of the capacitance vs T before (ii) after photo-excitation (i). • The difference is produced by the phenomenon known as persistent photoconductivity. • The sudden rise in C around 100 K in curve (ii) is due to thermally excited emission of carriers from the DX center • Nowadays DLTS has become the standard technique to measure capture and emission barriers of non-radiative deep centers

22. • The emission and capture rates determined by DLTS can be plot vs 1/kT to form an Arrhenius Plot. • The barrier heights for either capture or emission can be determined from the slope of thes plots. • For the DX center these barrier heights are ~300 meV.

23. OTHER TECHNIQUES OTHER TECHNIQUES • There are many other techniques which help to furnish pieces of a puzzle that is the defect in semiconductors: • Electron Paramagnetic Resonance • Position Annihilation Spectroscopy • Mӧssbauer Spectroscopy etc etc

24. SUMMARY SUMMARY • Defects alters the electronic and vibrational properties of the host crystal hence they can be detected via their effects on the optical and electronic properties of the host crystal • Optical techniques are well established and extremely sensitive techniques for studying defects. • Electrical measurements such as Hall Effect and DLTS are sensitive ways to study defects which cannot be detected optically. • Defects can have very complex structures and new techniques are still needed to detect and control them. • The Study of Defects has been a long and challenging trip but it has been exciting and the end is no where in sight!