1. Theory
- Definition: Deep-level transient spectroscopy fills traps in the depletion region of a junction or Schottky diode with a voltage pulse and records the capacitance transient as they emit, while scanning temperature (Khan and Yamaguchi).
- Emission: Each trap emits with a rate , so its time constant changes rapidly with temperature (Khan and Yamaguchi).
- Spectrum: A rate window turns the transients into a peak at the temperature where the emission rate matches the window; Arrhenius plots of several windows give the activation energy and capture cross section (Khan and Yamaguchi).
- Sign: Majority-carrier and minority-carrier traps give peaks of opposite sign (Khan and Yamaguchi).
2. Working Principle
- Pulse sequence: A quiescent reverse bias, a filling pulse toward zero bias for majority traps or into forward bias for minority traps, then the transient (Khan and Yamaguchi).
- Capacitance meter: A fast capacitance meter records C(t) after each pulse; the Boonton meter long popular for DLTS works at a fixed 1 (Zurich Instruments).
- Rate window: A boxcar, lock-in or correlation filter weights the transient; the signal peaks at one emission rate (Khan and Yamaguchi).
- Laplace DLTS: Isothermal transients are averaged and inverse-Laplace transformed to separate close emission rates (Dyba et al.; Capan).
3. Applications
- Contamination: Detection of electrically active defects down to about (Capan, citing Peaker et al.).
- Radiation damage: Vacancy and interstitial defects after irradiation (Khan and Yamaguchi).
- Solar cells and III-V materials: Recombination centres in InGaP, AlInGaP and InP-based layers (Khan and Yamaguchi).
- Wide-gap devices: Deep levels in GaN junctions (Dyba et al.).
Emission and Capture
| Name | Formula | Related Formulae | Variables/Constants |
|---|---|---|---|
| Thermal emission rate | |||
| Arrhenius plot | |||
| Capture and filling |
Rate Window
| Name | Formula | Related Formulae | Variables/Constants |
|---|---|---|---|
| Boxcar rate window | |||
| Peak height |
Concentration and Resolution
| Name | Formula | Related Formulae | Variables/Constants |
|---|---|---|---|
| Trap concentration | |||
| Transition-region (lambda) correction | |||
| Laplace DLTS |
Important Questions
Ques: How does DLTS detect traps?
By watching the capacitance of a reverse-biased junction relax after the traps are filled. A pulse toward zero bias fills traps in part of the depletion region with majority carriers; when the bias returns, the trapped charge reduces the capacitance, which recovers as while the traps emit with time constant . Because depends exponentially on temperature, a trap 0.4 deep with a cross section in silicon has at 200 (computed), and the transient becomes milliseconds or seconds over a modest temperature range. Introduced by Lang in 1974, the method resolves several traps in one temperature scan and detects concentrations of order . Reference: A. Khan and M. Yamaguchi, ‘Deep Level Transient Spectroscopy: A Powerful Experimental Technique…’, in Solar Cells - New Approaches and Reviews, IntechOpen 2015 (some symbols lost in extraction) (fetch-tool summary).
Ques: How does a rate window turn transients into a spectrum?
By sampling each transient at two times and plotting the difference against temperature. The boxcar signal is near zero when the trap emits too fast (both samples after the decay) or too slowly (no decay between them), and peaks when . For gates at 1 and 10 that is 3.91 , an emission rate of 256 (computed). Each trap therefore gives a peak at its own temperature. The peak height depends only on the gate ratio: 0.697 of the transient amplitude for a ratio of 10 and 0.25 for 2 (computed). Repeating the scan with several windows gives emission rate against peak temperature for the Arrhenius plot. Reference: A. Khan and M. Yamaguchi, ‘Deep Level Transient Spectroscopy: A Powerful Experimental Technique…’, in Solar Cells - New Approaches and Reviews, IntechOpen 2015 (some symbols lost in extraction) (fetch-tool summary).
Ques: How are activation energy and capture cross section obtained?
From an Arrhenius plot of emission rates. Since thermal velocity rises as and the density of states as , , so against is a line with slope , -4642 for 0.4 (computed), and intercept ; Zurich Instruments writes , for (computed). Khan and Yamaguchi describe plotting log e or against the inverse peak temperature. The intercept gives only an apparent cross section, because a temperature-dependent cross section changes both slope and intercept (Vasilev et al.). A direct value comes from the filling-pulse width: with (Khan and Yamaguchi; the density n from Schleich). Reference: Zurich Instruments blog, ‘Deep Level Transient Spectroscopy with the HF2LI Lock-in Amplifier’, 2015: ln(e_n/T^2) = -dE/(k_{B}T) + ln(sigma_n) + ln(16 pi m* k_{B}^2/(g h^3)), Boonton meter at a fixed 1 MHz, Laplace and Fourier DLTS named (fetch-tool summary); A. Khan and M. Yamaguchi, ‘Deep Level Transient Spectroscopy: A Powerful Experimental Technique…’, in Solar Cells - New Approaches and Reviews, IntechOpen 2015 (some symbols lost in extraction) (fetch-tool summary); A. A. Vasilev et al., ‘Observation of Temperature-Dependent Capture Cross-Section for Main Deep-Levels in beta-Ga2O3’, arXiv:2410.20509: temperature-dependent capture changes slope and intercept, Arrhenius cross sections overestimated by 1 to 3 orders of magnitude (fetch-tool summary); C. Schleich, PhD thesis, TU Wien, section 4.2 ‘The Shockley-Read-Hall Model’, Eq. 4.13: capture rate proportional to n C_n with C_n = v_T sigma_n (fetch-tool summary).
Ques: How is the trap concentration calculated, and why is the lambda correction needed?
For small concentrations, : a transient of on doping is (computed). This assumes traps fill and empty across the whole depletion region, but near the depletion edge, within the distance where the trap level lies below the Fermi level, they stay filled. Khan and Yamaguchi’s silicon example, with and depletion widths of 3 and 1.6 , says the correction raises the concentration by a factor of 1.9; here is 0.16 to 0.30 of the depletion width (computed). Johnston et al. obtain the corrected density by equating the total trapped charge, and note that level shifts of up to 0.1 , possibly from Poole-Frenkel emission, can change correction factors by up to 30 per cent. Reference: A. Khan and M. Yamaguchi, ‘Deep Level Transient Spectroscopy: A Powerful Experimental Technique…’, in Solar Cells - New Approaches and Reviews, IntechOpen 2015 (some symbols lost in extraction) (fetch-tool summary); S. W. Johnston, S. R. Kurtz and R. S. Crandall, NREL/CP-520-38334, 2006: N_T about 2N_a dC/C for small trap density, corrected density by equating total charge, Poole-Frenkel variations up to 0.1 eV changing correction factors by up to 30 per cent (fetch-tool summary).
Ques: How are majority and minority traps distinguished?
By how they are filled and by the sign of the peak. Majority-carrier traps are filled by a pulse toward zero bias, which brings free majority carriers into the previously depleted region; their emission increases the capacitance back to its steady value. Minority-carrier traps need forward-bias injection, or optical excitation, to fill them, and their peaks have the opposite sign (Khan and Yamaguchi). In a Schottky diode, minority injection is weak, so p-n junctions are used when minority traps matter. Khan and Yamaguchi’s examples include -2 quiescent bias with 2 filling pulses of 1 , and injection at 0.1 for annealing studies in InGaP. Dyba et al. resolved both trap types in a GaN junction with Laplace DLTS. Reference: A. Khan and M. Yamaguchi, ‘Deep Level Transient Spectroscopy: A Powerful Experimental Technique…’, in Solar Cells - New Approaches and Reviews, IntechOpen 2015 (some symbols lost in extraction) (fetch-tool summary); P. Dyba et al., ‘Deep Levels in GaN p-n Junctions Studied by DLTS and Laplace Transform Deep-Level Spectroscopy’, Acta Phys. Pol. A 119 (2011) (fetch-tool summary).
Ques: Why is Laplace DLTS used, and what does it resolve?
Because conventional rate windows broaden each trap into a wide peak. A boxcar weights the transient with a smooth filter, so traps whose emission rates differ by a small factor merge; for a trap 0.63 deep near 300 , a twofold rate difference shifts the peak by only about 8 (computed), and Capan notes the relatively limited energy resolution of conventional DLTS. Laplace DLTS holds the sample at a fixed temperature and inverts the transient, improving energy resolution by about an order of magnitude (Capan, after Peaker and Dobaczewski). Dyba et al. found a single broad peak near 300 in GaN junctions with conventional DLTS, while Laplace DLTS separated an electron trap at 0.63 and a hole trap at 0.66 , and showed the electron trap has a distribution of energies, attributed to metastability. Reference: P. Dyba et al., ‘Deep Levels in GaN p-n Junctions Studied by DLTS and Laplace Transform Deep-Level Spectroscopy’, Acta Phys. Pol. A 119 (2011) (fetch-tool summary); I. Capan, ‘Beyond Point-like Defects in Bulk Semiconductors: Junction Spectroscopy Techniques…’, arXiv:2602.20764: Laplace DLTS isothermal, energy resolution better by about an order of magnitude, after Peaker and Dobaczewski (2004); DLTS sensitivity about 1e10 cm-3; poor contacts distort transients (fetch-tool summary).
Ques: Which capture cross sections did Dyba et al. find for GaN, the table or the conclusion values?
The paper gives two sets. Its table lists for the electron trap and for the hole trap from Laplace DLTS, while its conclusions quote and , the electron value attributed to Arrhenius plots. The electron values differ by 45 per cent and the hole values by a factor of 2.8 (computed). Vasilev et al. show that ignoring temperature-dependent capture can overestimate Arrhenius cross sections by 1 to 3 orders of magnitude, so both sets are within normal uncertainty. The table values are more likely the authors’ final Laplace DLTS results (my reading), and either should be taken as an order of magnitude, not a precise number. Reference: P. Dyba et al., ‘Deep Levels in GaN p-n Junctions Studied by DLTS and Laplace Transform Deep-Level Spectroscopy’, Acta Phys. Pol. A 119 (2011) (fetch-tool summary); A. A. Vasilev et al., ‘Observation of Temperature-Dependent Capture Cross-Section for Main Deep-Levels in beta-Ga2O3’, arXiv:2410.20509: temperature-dependent capture changes slope and intercept, Arrhenius cross sections overestimated by 1 to 3 orders of magnitude (fetch-tool summary).
Ques: What can make a DLTS result misleading?
Several effects violate its assumptions. When the trap density is not small compared with the doping, the transient becomes non-exponential, following with (Khan and Yamaguchi), so the simple concentration and rate formulas fail. High fields can shift the apparent level by up to 0.1 , possibly through Poole-Frenkel emission (Johnston et al.); poor contacts distort the transients (Capan); and a temperature-dependent capture cross section biases both activation energy and cross section (Vasilev et al.). Traps near the depletion edge distort the apparent doping, (Khan and Yamaguchi). Checks include varying the filling pulse, the bias and the rate window, and confirming exponential transients. Reference: A. Khan and M. Yamaguchi, ‘Deep Level Transient Spectroscopy: A Powerful Experimental Technique…’, in Solar Cells - New Approaches and Reviews, IntechOpen 2015 (some symbols lost in extraction) (fetch-tool summary); S. W. Johnston, S. R. Kurtz and R. S. Crandall, NREL/CP-520-38334, 2006: N_T about 2N_a dC/C for small trap density, corrected density by equating total charge, Poole-Frenkel variations up to 0.1 eV changing correction factors by up to 30 per cent (fetch-tool summary); I. Capan, ‘Beyond Point-like Defects in Bulk Semiconductors: Junction Spectroscopy Techniques…’, arXiv:2602.20764: Laplace DLTS isothermal, energy resolution better by about an order of magnitude, after Peaker and Dobaczewski (2004); DLTS sensitivity about 1e10 cm-3; poor contacts distort transients (fetch-tool summary); A. A. Vasilev et al., ‘Observation of Temperature-Dependent Capture Cross-Section for Main Deep-Levels in beta-Ga2O3’, arXiv:2410.20509: temperature-dependent capture changes slope and intercept, Arrhenius cross sections overestimated by 1 to 3 orders of magnitude (fetch-tool summary).
References
- A. Khan and M. Yamaguchi, “Deep Level Transient Spectroscopy: A Powerful Experimental Technique for Understanding the Physics and Engineering of Photo-Carrier Generation, Escape, Loss and Collection Processes in Photovoltaic Materials,” in Solar Cells - New Approaches and Reviews, L. A. Kosyachenko, Ed. IntechOpen, 2015, doi: 10.5772/59419. Available: https://www.intechopen.com/chapters/47975
- Zurich Instruments, “Deep Level Transient Spectroscopy with the HF2LI Lock-in Amplifier,” blog, 2015. Available: https://www.zhinst.com/en/blogs/deep-level-transient-spectroscopy-using-hf2li-lock-amplifier/
- C. Schleich, Modeling of Defect Related Reliability Phenomena in SiC Power-MOSFETs, PhD thesis, TU Wien, section 4.2. Available: https://www.iue.tuwien.ac.at/phd/schleich/node-The-Shockley-Read-Hall-Model.html
- I. Capan, “Beyond point-like defects in bulk semiconductors: junction spectroscopy techniques for perovskite solar cells and 2D materials,” arXiv:2602.20764. Available: https://arxiv.org/abs/2602.20764
- A. A. Vasilev et al., “Observation of temperature-dependent capture cross-section for main deep-levels in beta-Ga2O3,” arXiv:2410.20509. Available: https://arxiv.org/abs/2410.20509
- S. W. Johnston, S. R. Kurtz and R. S. Crandall, “Characterization of a dominant electron trap in GaNAs using deep-level transient spectroscopy,” NREL/CP-520-38334, 2006. Available: https://www.nrel.gov/docs/fy06osti/38334.pdf
- P. Dyba, E. Placzek-Popko, E. Zielony, Z. Gumienny, S. Grzanka, R. Czernecki and T. Suski, “Deep Levels in GaN p-n Junctions Studied by Deep Level Transient Spectroscopy and Laplace Transform Deep-Level Spectroscopy,” Acta Physica Polonica A, vol. 119, no. 5, 2011. Available: https://przyrbwn.icm.edu.pl/APP/PDF/119/a119z5p29.pdf
Related pages in this vault: Charge Pumping, Lifetime Testers, Low-Frequency Noise Analyzer, LCR Meter and C-V, Metal Semiconductor Contacts, Radiation, Hall Effect System, Solar Cell Fundamentals, Generation-Recombination Models.