V. A. Gergel

A discrete model of the development and relaxation of a local microbreakdown in silicon avalanche photodiodes operating in the Geiger mode

A new discrete theoretical model of the development and relaxation of a local microbreakdown in silicon avalanche photodiodes operating in the Geiger mode is developed. It is shown that the spreading resistance in the substrate profoundly affects both the amplitude of a single-photon electrical pulse and the possibility of attaining the steady-state form of the avalanche breakdown excluding the Geiger mode of the photodiode’s operation. The model is employed to interpret the experimental data obtained using test single-photon cells of avalanche photodiodes fabricated on the basis of the 0.25-μm silicon technology with the use of deep implantation to form the region of avalanche multiplication for the charge carriers. Excellent functional properties of the studied type of the single-photon (Geiger) cell are noted. A typical amplitude characteristic of the cell for optical radiation with the wavelength λ = 0.56 μm in the irradiance range of 10−3–102 lx is presented; this characteristic indicates that the quantum efficiency of photoconversion is extremely high.

A mathematical simulation of the effect of the bistability of current characteristics in nanosized multiple-layer heavily doped heterostructures

Simulation methods based on the energy-balance equation are used to study the electrical conductivity of layered nanosized heterostructures in high electric fields. A quasi-hydrodynamic description of the electron drift is used with regard to the diffusion and thermal-diffusion components of the current, the divergence of the electron heat flux, and the temperature dependence of the electron mobility and energy relaxation time. Current-voltage characteristics are obtained for a layered heterostructure with a barrier height of 0.3 eV and with lengths of both the narrow-and wide-gap layers equal to 50 nm. Depending on the doping level in the range (5–1) × 1017 cm−3, the characteristics exhibit either a sharp peak of the differential conductivity or a bistability loop corresponding to the thermal-injection instability. A physical model is suggested that attributes the shape of the calculated current-voltage characteristics to the cumulative effect of the electrostatic lowering of the heterobarrier height and the increase in electron temperature near the injecting heteroboundaries.

Quasi-hydrodynamic simulation of the features of electrical conduction in nanosized multilayer heavily doped heterostructures

The electrical conduction in nanosized layered heterostructures in the presence of strong electric fields is studied via mathematical simulation based on the energy-balance equation and the quasi-hydrodynamic description of electron drift with allowance for the diffusion and thermal diffusion components of the current, the divergence of the thermal electron flow, and the temperature dependences of the mobility and energy-relaxation time. For the doping level in the range (5−1) × 1017 cm−3, the resulting I−V characteristics of heterostructures with a barrier height of 0.3 eV and equal widths of the narrow-and wide-band-gap components (50 nm) exhibit either a sharp peak of the differential conductivity or a bistability loop. A physical model that interprets the shape of the calculated characteristics on the basis of the cumulative effect of the electrostatic decrease in the height of heterobarriers and an increase in the electron temperature in the vicinity of the injecting heteroboundaries is proposed.

Boron distribution profiling in asymmetrical n+-p silicon photodiodes and new creation concept of selectively sensitive photoelements for megapixel color photoreceivers

Experimental results on spectral photo responsivity obtained for silicon n+-p photodiodes with implanted p+ layer in a silicon substrate are represented. It is demonstrated, that such p+ doping effectively shifts long-wave edge of the photodiodes spectral sensitivity in optical range of light spectrum, depending on the p+ layer bedding depth. A new concept of selectively sensitive photoelements development was stated for megapixel color photoreceivers on the basis of n+-p photodiode structures, containing one or more different (in depths) implanted layers, which form color separation potential barriers and lateral diffusion channels required for collecting of minority carriers generated by quanta of different wavelength.

Analytical model of the electrical instability mechanism in multibarrier heterostructures with tunnel-opaque barriers

Through mathematical modeling of the conductivity of multibarrier heterostructures, the steady-state current-voltage characteristics, the S-shaped behavior of which is indicative of electrical instability, are obtained. To study its dynamic parameters, an analytical model of instability is developed using known approximations of the physics of semiconductor devices. In the steady-state case, the model yields an S-shaped current-voltage characteristic close to numerical simulation results. This fact is considered as confirmation of the adequacy of the developed analytical model. In the small-signal case, the latter is generalized to the situation with harmonic electrical perturbation. The resulting formula for the frequency dependence of the small-signal impedance indicates the possibility of dynamic-resistance negativity up to terahertz frequencies. A clear physical interpretation of the instability in terms of positive feedback in the unit cell of the multibarrier heterostructures under study is proposed. The results of measurements of the quasi-stead-state current-voltage characteristics of fabricated test multibarrier GaAs/AlGaAs structures with a pronounced portion of negative differential resistance are also presented.

Electric instability in multibarrier heterostructures: Features of the RF impedance

By mathematical simulation of the electric conduction in multibarrier heterostructures, static voltage-current characteristics (VCCs) whose S-shape is indicative of the corresponding electric instability have been obtained. In order to analyze the dynamic parameters of this instability, an analytical model of the instability under investigation has been constructed with the use of the known approximations of semiconductor physics. The static version of the analytical model also provides an S-shaped VCC that is close to the corresponding results of the numerical simulation. With this closeness considered as a confirmation of the validity of the developed analytical model, the small-signal version of this model is generalized to the case of a harmonic electrical disturbance. A clear physical interpretation of the instability under consideration in terms of a positive feedback in a unit cell of the multibarrier heterostructures under study is proposed. The resulting formula for the frequency dependence of the small-signal impedance shows that the dynamic impedance is negative up to terahertz frequencies.

Ultraquasi-hydrodynamic electron transport in submicrometer field effect MIS transistors and heterotransistors

It is shown that electrons in the channel of submicrometer field effect transistors have no time to be heated to quasi-steady-state temperatures corresponding to a balance between the Joule heating and thermal relaxation. This “underheating” contributes to an increase in the effective mobility of charge carriers as compared to the value of μ(E) corresponding to the drift-diffusion approximation. Using a reduction of the thermal-balance equation by eliminating the relaxation-related term, a simple analytical expression is obtained for current-voltage characteristics. In particular, the saturation current in the developed ultraquasi-hydrodynamic model is found to be proportional to (VG-Vt)3/2. The results of measurements of characteristics of the test GaAlAs/InGaAs/GaAs P-HEMTs with the channel length of about 0.3 µm are reported; these results verify the adequacy of the developed model, the accuracy of which can only increase with a further decrease in the channel length.

On the temperature and field dependences of the effective surface mobility in MIS structures

A physical model establishing a relation between the surface density of the free electronic charge in an inversion layer and the surface density of stationary (localized) electrons trapped in surface states at a semiconductor-insulator interface is constructed. It is established that at moderately low temperatures this relation is close to a direct proportionality. The presence of surface states, which localize some of the surface electronic charge, is manifested as a decrease in the effective electron mobility in the channel of a MIS transistor. The well-known decrease of the surface mobility with increasing transverse electric field is attributed to field-induced variations in the position of the percolation level that separates bound electronic states from free states.

Electrical instability against thermal injection in multibarrier heterostructures: Theoretical model and experimental data

A simplified theoretical description of electrical instability under thermal injection in multibarrier heterostructures is given in terms of internal positive feedback in each elementary unit of the hetero-object. In the simplest case, which is a sequence of equally high heterobarriers, a pair of neighboring wide- and narrow-gap layers is taken for an elementary unit. Analytical dependences of the current and voltage in the structure on the electron temperature at the injecting boundary of the heterobarrier and the respective bistable I–V characteristics are derived. A typical I–V characteristic with a clear-cut negative resistance region is demonstrated. It is taken in quasi-static electrical measurements made on 12-μm test multibarrier GaAs/AlGaAs mesas.

Dynamics of local micro-breakdown in the Geiger mode of avalanche photodiodes

Mathematical modeling methods were used to study the dynamics of micro-breakdown development in structures of silicon avalanche photodiodes. The constructed model considers the locality of the avalanchexs multiplication region appearing during single photon absorption and the delay of the avalanchexs current spreading over the rear electrode of the diode. The calculations showed two different phases of transient process of the formation of the electrical signal, i.e., the rapid and slow ones due to current spreading and ordinary RC recharge, respectively. The load resistances required to implement the pulsed mode of operation of the structures of the avalanche photodiode were calculated for a series of actual diode capacitances and spreading resistances of the rear electrode.