An optoelectronic notch (‘dip’) phenomenon in the heterodyne photocarrier radiometry frequency response of Si wafers: a route to quantitative trap-state dynamic processes in semiconductors

Abstract

An anomaly was observed in the heterodyne photocarrier radiometry (HePCR) frequency response of Si wafers in the form of a signal amplitude depression (‘dip’) accompanied by a 180° phase transition. This phenomenon resembles an electronic notch filter and was investigated experimentally and theoretically by invoking free-carrier-density-wave (CDW) kinetics in generic semiconductor systems. Both homodyne PCR and HePCR signals were obtained from n- and p-type wafers of different resistivities. Dynamic nonlinear rate-equation models with two bandgap carrier traps were introduced and analytical zeroth and first-order CDW solutions were obtained in the frequency domain. The experimental frequency responses of the HePCR optoelectronic notch phenomenon were found to be in very good agreement with the theory. Characteristic CDW recombination and trap capture and emission characteristic times were obtained and studied as functions of the illuminating laser intensity. The present newly observed HePCR notch phenomenon has revealed a new mechanism of nonlinear contributions due to trap-state-related CDW dynamics in semiconductors superposed on the well-known nonlinear electron-hole recombination interactions that give rise to non-zero HePCR signals. The implications of this notch phenomenon are discussed in terms of its importance in providing physical insights into photocarrier dynamic interactions with traps, leading to identification of active CDW trap-state numbers and precision measurements of their kinetic parameters, carrier capture and emission coefficients, and quantitative trap densities that determine the optoelectronic quality of semiconductors.

Quantitative Imaging of Defect Distributions in CdZnTe Wafers Using Combined Deep-Level Photothermal Spectroscopy, Photocarrier Radiometry, and Lock-In Carrierography

“…HeLIC was developed to allow high-frequency dynamic imaging of optoelectronic material and device properties, which require sampling rates orders of magnitude higher than those achievable by the frame rates of today's fastest NIR camera technologies. 23−26 Very recently, heterodyne PCR (HePCR) proved to be very sensitive to photocarrier emission/capture processes out of, and into, band-gap defect and impurity states: 27 a newly discovered HePCR phenomenon 27 giving rise to a frequency-domain heterodyne signal amplitude depression ("dip" or "notch") accompanied by a 180°phase transition was attributed to a nonlinear kinetic mechanism of laser-excited harmonic carrier density waves (CDW) interacting with trap or defect states in Si wafers. 27 and the associated activation energies, which can be used to identify the physical origin of the trap states, can be obtained using deep-level photothermal spectroscopy (DLPTS).…”

“…23−26 Very recently, heterodyne PCR (HePCR) proved to be very sensitive to photocarrier emission/capture processes out of, and into, band-gap defect and impurity states: 27 a newly discovered HePCR phenomenon 27 giving rise to a frequency-domain heterodyne signal amplitude depression ("dip" or "notch") accompanied by a 180°phase transition was attributed to a nonlinear kinetic mechanism of laser-excited harmonic carrier density waves (CDW) interacting with trap or defect states in Si wafers. 27 and the associated activation energies, which can be used to identify the physical origin of the trap states, can be obtained using deep-level photothermal spectroscopy (DLPTS). 28,29 The advantage of implementing DLPTS besides its noncontacting and nondestructive nature, as opposed to conventional electrical DLTS methods, is that of convenience as DLTPS may be easily and seamlessly integrated into the PCR and LIC instrumental setup.…”

“…Very recently, a much more spectrally resolved study of thermally stimulated current peaks (TSC) from CdZnTe crystals 34 4−6, with the temperature of the sample kept at 100 K for an optimal signal-to-noise ratio (SNR). A heterodyne PCR amplitude depression (notch or dip) phenomenon recently observed in Si wafers with origins in destructive interference among trap-captured and -released carrier density waves due to the nonlinear nature of eqs 1−3 27 appeared in the HeLIC image pixel frequency response in the intermediate frequency range over the entire area of the sample around 7.9 kHz, at I = I max , as shown in Figure 4. The phase images in Figure 4 exhibit values around 180°at low frequencies.…”

“…The nonlinear rate equations for p -type carrier kinetics (neglecting the minority n-type carriers for simplicity) in a semiconductor exhibiting two trap states (based on experimental evidence for our CdZnTe wafers, Section ) can be written as where p ( t ) is the photogenerated free-hole carrier density, G ( t ) is the optical generation rate, τ p is the hole recombination lifetime, e p1 and e p2 are the thermal emission rates from traps 1 and 2, respectively, N 1 ( t ) and N 2 ( t ) are the trapped carrier densities in the two traps, respectively, C p1 and C p2 are the respective trap-state capture coefficients, and N T1 and N T2 are the corresponding trap densities.…”

“…Most popular diagnostic methods in use are current deep-level transient spectroscopy (I-DLTS), transient current technique (TCT), current and capacitance vs voltage ( I – V and C – V ) measurements, γ-ray spectroscopy, Hall measurements, and optical and thermal measurements. − Beyond those methodologies, photocarrier radiometry (PCR) is a nondestructive and noncontacting spectrally gated frequency-domain dynamic semiconductor photoluminescence (PL) diagnostic modality, which allows for the simultaneous nondestructive determination of electronic transport parameters in semiconductor substrates and devices. − Subsequently, lock-in carrierography (LIC) was introduced as a near-infrared (NIR) imaging extension of PCR, aimed at constructing quantitative images of carrier transport parameters. − Next, two-beam heterodyne LIC (HeLIC) was introduced to address the need for high-frequency photocarrier excitation, eliciting fast enough signal responses required to measure short recombination lifetimes and other fast photocarrier relaxation processes. HeLIC was developed to allow high-frequency dynamic imaging of optoelectronic material and device properties, which require sampling rates orders of magnitude higher than those achievable by the frame rates of today’s fastest NIR camera technologies. − Very recently, heterodyne PCR (HePCR) proved to be very sensitive to photocarrier emission/capture processes out of, and into, band-gap defect and impurity states: a newly discovered HePCR phenomenon giving rise to a frequency-domain heterodyne signal amplitude depression (“dip” or “notch”) accompanied by a 180° phase transition was attributed to a nonlinear kinetic mechanism of laser-excited harmonic carrier density waves (CDW) interacting with trap or defect states in Si wafers . Important information about the number of trap/defect states involved in the carrier kinetics and the associated activation energies, which can be used to identify the physical origin of the trap states, can be obtained using deep-level photothermal spectroscopy (DLPTS). , The advantage of implementing DLPTS besides its noncontacting and nondestructive nature, as opposed to conventional electrical DLTS methods, is that of convenience as DLTPS may be easily and seamlessly integrated into the PCR and LIC instrumental setup.…”