Field and related semiconductor-surface and equilibrium-step-junction variables in terms of the general solution

A depletion-approximation replacement offered recently employs one of two asymptotic functions of a universal curve of potential versus position to define a spatial origin, which is then used to write approximate-analytic expressions of simple form for the universal curve. Here we extend analogous treatment to additional functions, writing expressions as a function of normalized potential and of normalized position.     

Determination of the oxygen precipitate-free zone width in silicon wafers from surface photovoltage measurements

A procedure has been developed for applying the surface photovoltage technique to the measurement of the width of the oxygen precipitate-free zone present at the surface of a thermally processed, Czochralski-grown silicon wafer. This procedure was developed through the use of a numerical simulation program which models the experimental determination of an effective diffusion lenght, L₀, from surface photovoltage measurements on silicon wafers. The program predicts L₀ for a given precipitate-free zone diffusion length and thickness and bulk diffusion length. Results of the simulations show that for bulk diffusion lengths of 2 μ or less and a precipitate-free zone diffusion length greater than the thickness of the zone, W, the W ≡ 2.5L₀. Experimental results are presented which support the numerical findings.     

A detailed analysis of the metal-semiconductor contact

A general quantum and electronic theory able to explain the electric and photoelectric experimental properties of the metal-semiconductor contacts is proposed. The theory consists firstly in calculating the electric space charge due to the quantum mechanical tunneling of the electrons from the metal into the semiconductor, and vice-versa, and to the metal and semiconductor bands bending. Then the electric charge so obtained is utilised to solve in an appropriate and complete way the Poisson equation so as to determine the electric field and potential as functions of the abscissa x. The electric field F(x) is employed to obtain a new expression for the junction capacitance C, holding in the general case of a non-uniform charge, whereas the electric potential ν_i(x) is used to calculate general expressions for the thermionic and photoelectric currents i and i_ph, respectively, taking into account in this both the tunneling probability through the energy barrier and the many-valley structure of the semiconductor energy bands. Finally, from ν_i(x), C, i and i_ph four new expressions of the energy barrier height of the contact are deduced. The theoretical results relative to the barrier height so determined (which hold for both n-and p-type semiconductors) are compared with published experimental values obtained, by means of capacitance and photocurrent measurements: (a) on contacts between n-type CdS and Au, Cu, Ag and Pt; (b) on contacts between n-type GaAs and Au, Ag, Cu, Sn, Al and Pt and; (c) on contacts between p-type GaAs and Au and Al. The agreement between the theoretical and experimental values is very good.     

Current-voltage and light-voltage relations for the linear-graded pn junction

For the linear-graded pn junction, as in the case of the abrupt junction, the injection current I₁ depends on the applied forward voltage V(? kT/q) as I₁ = I_s1 exp (qV/kT); if it is a light-emitting diode the generated photon rate L behaves in an analogous way as L = L₀ exp (qV/kT). In this paper the complete analytical expressions are given for the dependence of I_s1 and L₀ on the gradient of the net dopant concentration, and on the diffusion coefficient and lifetime of the injected minority carriers. These expressions cover the various possible cases of band-to-centre and band-to-band recombination. For comparison the corresponding expressions for the abrupt junction are also presented.     

On the evaluation of first passage time densities for Gaussian processes

A detailed study of first- and second-order approximations to the first passage time conditional probability density function (p.d.f.) of a stationary Gaussian process with differentiable sample paths is provided both theoretically and numerically. An evaluation of mode and peak value of this function is also given and asymptotic expressions are derived for the functions W_n(t₁, t₂, …, t_n|;x₀) (n ⩾ 1) appearing in the series expansion of the first passage time probability density function.     

A percolation study of RTS noise amplitudes in nano-MOSFETs by Monte Carlo simulation

A high efficiency 2D percolation model of RTS amplitudes in nanoscale MOSFETs based on the numerical results of potential and carriers density distributions in the channel obtained by solutions of coupled 2D Schrodinger and Poisson equations was presented. Using this model the dependences of relative RTS amplitudes ΔI_D/I_D on device geometry L_eff × W_eff, t_ox bias conditions I_D, V_G and trap locations along the channel were simulated and analyzed for a set of square n-MOSFETs. The results show reasonable agreement with published numerical or experimental data.     

Analysis of the interaction of an electron beam with a solar cell—II

In continuation of previous work, the short circuit current I_SC generated by a collimated electron beam impinging on an N-P junction (solar cell) is investigated in a configuration in which the beam scans the front surface of a solar cell crossing the ohmic contact strips. The analysis employs Fourier and Wiener-Hopf techniques and shows that even in the idealized case of uniform doping in both the N-material and the P-material the scanning electron beam gives little information about junction parameters (diffusion lengths, surface recombination velocities etc.). A recently proposed method for measuring the surface recombination velocity by means of changing the beam energy is inapplicable for shallow junctions (junction depth ≈ 0.1 μm). The reason for this state of affairs is the fact that the radius of the beam-semiconductor interaction volume is larger than or comparable to the characteristic lengths, junction depth, depletion layer width and diffusion length of minority carriers in the N-material. The uncertainties of the distribution in space of excess carriers generated by the electron beam prevent an accurate determination of junction parameters. If, however, the ohmic contact on the back surface of a solar cell is partially removed, scanning across the free surface toward the ohmic contact yields useful information about the bulk diffusion length.     

Analysis of the interaction of an electron beam with a solar cell—II

In continuation of previous work, the short circuit current I_SC generated by a collimated electron beam impinging on an N-P junction (solar cell) is investigated in a configuration in which the beam scans the front surface of a solar cell crossing the ohmic contact strips. The analysis employs Fourier and Wiener-Hopf techniques and shows that even in the idealized case of uniform doping in both the N-material and the P-material the scanning electron beam gives little information about junction parameters (diffusion lengths, surface recombination velocities etc.). A recently proposed method for measuring the surface recombination velocity by means of changing the beam energy is inapplicable for shallow junctions (junction depth ≈ 0.1 μm). The reason for this state of affairs is the fact that the radius of the beam-semiconductor interaction volume is larger or comparable to the characteristic lengths, junction depth, depletion layer width and diffusion length of minority carriers in the N-material. The uncertainties of the distribution in space of excess carriers generated by the electron beam prevent an accurate determination of junction parameters. If, however, the ohmic contact on the back surface of a solar cell is partially removed, scanning across the free surface toward the ohmic contact yields useful information about the bulk diffusion length.     

Photoconverters based on gallium arsenide diffused <Emphasis Type="Italic">p-n</Emphasis> junctions formed on a microprofile GaAs surface

The p-n junctions promising for photoconverters have been fabricated using diffusion from the gaseous phase and studied with the analysis of mass transport of the doping impurity (Zn) through the microprofile GaAs surface taken into account. Depending on the conditions of diffusion (the diffusant’s mass and diffusion duration), the formation of both a p-n junction in a microprofile and a planar p-n junction in the GaAs bulk with a heavily doped near-surface p ⁺ type layer is possible. Photoelectric characteristics of device structures with textured p-n junction and a thin wide-gap Al _x Ga_{1 ? x} As window obtained by liquid-phase epitaxy are reported.     

Performance analysis of LRT/GLRT-based array receivers for the detection of a known real-valued signal corrupted by noncircular interferences

A performance analysis of likelihood ratio test (LRT)-based and generalized likelihood ratio test (GLRT)-based array receivers for the detection of a known real-valued signal corrupted by a potentially noncircular interference is considered in this paper. The distribution of the decision statistics associated with the LRT and GLRT is studied. This allows us to give exact closed-form expressions of the probability of detection (P_D) and false alarm (P_FA) for two LRT-based receivers. Then, asymptotic (with respect to the data length) closed-form expressions are given for P_D and P_FA for four GLRT-based receivers. Finally, in order to strengthen the obtained results, some illustrative examples are presented.     

Bulk moduli of PbSxSe1−x,PbSxTe1−x and PbSexTe1−x from a thermodynamical model compared to generalized gradient approximation approach

Very recently, first-principle technique of full-potential linearized augmented plane-wave method, by using for exchange-correlation potential the generalized gradient approximation (GGA), was employed for the study of the lead chalcogenide semiconductors’ alloys PbS_xSe_1−x, PbS_xTe_1−x and PbSe_xTe_1−x. These density functional calculations led to the determination of structural, electronic and optical properties, including the values of lattice constants and bulk moduli as a function of composition. Here, we investigate the latter properties, but by employing a thermodynamical model which has been suggested for the formation and migration of defects in solids including several recent applications in semiconductors. The following crucial difference emerges when comparing the present results with those deduced by density functional calculations: Among the alloys studied, GGA calculations identify that PbS_xTe_1−x exhibits the most evident non-linear variation of the bulk modulus versus the composition, while according to the thermodynamical model such an evident non-linear behavior – and maybe somewhat stronger – is also expected for PbSe_xTe_1−x. A tentative origin of this diversity is discussed.     

A comparison of simple and numerical two-dimensional models for the threshold voltage of short channel MOSTs

The threshold voltage for short channel MOSTs has been derived by two-dimensional numerical computation. The results can be expressed in normalised form with the reduced threshold voltage, V_T ? V_FB ? 2φ, given as a fraction of the reduced long-channel threshold voltage, V_T∞ ? V_FB ? 2φ, where V_FB and φ are the flat-band and bulk Fermi potentials respectively. An extremely good fit to the theoretical predictions is then given by

$\text{V}{}_{\mathrm{T}}\text{?V}{}_{\mathrm{FB}}\text{?2φ}\text{V}{}_{\mathrm{T\infty }}\text{?V}{}_{\mathrm{FB}}\text{?2φ}\text{=1?}\text{aW}{}_{\mathrm{sr}}\text{L}{}^{\mathrm{b}}$

where

$\text{a?0.94?0.17}\text{W}{}_{\mathrm{s}}\text{rj}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$

$\text{b?0.90?0.66}\text{log}{}_{10}\text{W}{}_{\mathrm{s}}\text{r}{}_{\mathrm{j}}\text{+0.37}\text{X}{}_{\mathrm{ox}}\text{W}{}_{\mathrm{s}}$

where the junction depth, r_j, and oxide thickness, x_ox, are expressed as fractions of the source depletion layer thickness, W_s, and where the channel length, L, is given as a fraction of the one-dimensional theoretical spread, W_sr, of a depletion region around a cylindrical step-junction.This empirical expression is valid over a wide range of normalised device geometries (0.4 < L/W_sr < 40, 0.1 < r_j/W_s < 10, 0.01 < x_ox/W_s < 0.2) and, except for very shallow junctions (r_j/W_s ? 1), differs only slightly from the simple model proposed by Yau. A comparison of the theory with experimental results shows good agreement for MOSTs fabricated with channel lengths between 2 and 5 μm using conventional photolithography.     

Bulk carrier lifetime measurement from transient diffusion photocurrent in semiconductor diodes

The theoretical analysis of the transient diffusion photocurrent i_D(t) created in the diode substrate, following weak carrier injection level by a homogeneous photoexcitation of short duration T, shows that the decay i_D(t) can be used in two ways to obtain the substrate bulk carrier lifetime τ_ν. Depending both on the decay times t considered and the values of the substrate parameters τ_ν, D (minority carrier diffusion constant), W (thickness), s (back contact carrier recombination velocity), β (carrier velocity ratio at the p?n junction boundary), then either (1)τ_ν may be deduced from the i_D(t) decay time constant τ if τ is measured at long enough times t>t₁, or else (2)τ_ν is given by the $\text{i}{}_{\mathrm{<mtext>D</mtext>}}\text{(t)×}\text{t}$ product decay time constant θ if θ measured at short enough times t.The numerical illustration of the accuracy and validity conditions of each of the above two ways of exploiting the decay of i_D(t) is given in the case of a P type silicon substrate with a resistivity of 0.2, 1 or 10 Ω cm, W from 50 to 500 μm, τ_ν from less than 0.1 μs to more than 100 μs and various pairs of s (0 or ∞) and β (0 to ∞) values.In practice, the use of a transient photocurrent decay to obtain the diode substrate carrier lifetime also implies a previous analysis of factors such as the device response time constant and transient bias modulation, and the carrier photoexcitation level in the substrate.Experimental results obtained with N⁺P silicon-cells (W = 460 μm and 200 μm) are given and discussed as an illustration of the above study.     

High-Performance Ultraviolet Photodetectors Enabled by van der Waals Schottky Junction Based on TiO2 Nanorod Arrays/Au-Modulated Ti3C2Tx MXene

Two-dimensional transition metal carbides and nitrides (MXenes) show tremendous potential for optoelectronic devices due to their excellent electronic properties. Here, a high-performance ultraviolet photodetector based on TiO₂ nanorod arrays/Ti₃C₂T_x MXene van der Waals (vdW) Schottky junction by all-solution process technique is reported. The Ti₃C₂T_x MXene modulated by the Au electrode increases its work function from 4.41 to 5.14 eV to form a hole transport layer. Complemented by the dangling bond-free surface of Ti₃C₂T_x, the Fermi-level pinning effect is suppressed and the electric-field strength of the Schottky junction is enhanced, which promotes charge separation and transport. After applying a bias of −1.5 V, the photovoltaic effect is favorably reinforced, while the hole-trapping mechanism (between TiO₂ and oxygen) and reverse pyroelectric effect are largely eliminated. As a result, the responsivity and specific detectivity of the device with FTO/TiO₂ nanorod arrays/Ti₃C₂T_x/Au structure reach 1.95 × 10⁵ mA W⁻¹ and 4.3 × 10¹³ cm Hz^1/2 W⁻¹ (370 nm, 65 mW cm⁻²), respectively. This work provides an effective approach to enhance the performance of photodetectors by forming the vdW Schottky junction and choosing metal electrodes to modulate MXene as a suitable charge transport layer.     

Fractal character of the distribution of surface potential irregularities in epitaxial n-GaAs (100)

The fractal geometric properties of the relief of the surface potential of a heavily doped n ⁺-GaAs (100) wafer are studied by Kelvin’s method of atomic force microscopy. The average fractal dimensionalities determined by the triangulation method (D _f ), the method of horizontal cross sections (D _c ), and the method of similarity (D _s ) are rather close to each other, which is indicative of a unified nature of the fractal relief of the surface potential. In general, the fractal dimensionalities determined in the study suggest that the relative arrangement of local irregularities of the potential profile of the heavily doped n ⁺-GaAs (100) wafer subjected to chemical and dynamic polishing is similar to the pattern corresponding to the fractal curve known as Serpinsky’s napkin. It is found that the fractal irregularities of the potential vary much more gradually than it happens in the twodimensional case: the variations are proportional to linear dimensions to the power 2/D _c (1 < D _c < 2) rather than to the square of linear dimensions of the regions under study     

Impact of strain on the band offsets of important III–V quantum wells: InxGa1−xN/GaN,GaAs/InxGa1−xP and InxGa1−xAs/AlGaAs

Lattice strain has immense effect on the optoelectronic properties of III–V semiconductor quantum wells (QWs), since it introduces a pronounced change on the band properties of QWs and it is often purposefully introduced to improve device performance. In this paper we report the results of our experimental and theoretical studies on, how the important parameter, the band offset, changes with strain for In_xGa_1−xN/GaN, GaAs/In_xGa_1−xP and In_xGa_1−xAs/AlGaAs QWs. Experimentally the band offsets have been studied through capacitance transient measurements in the form of deep level transient spectroscopy (DLTS) on suitable QWs within a Schottky diode. The energy levels in a QW are considered to be analogous to a deep trap in the forbidden energy gap. From detailed balance between the emission and capture, Arrhenius type expressions were derived to analyze transient emission data, from which the band offsets were computed. Theoretically the band positions at the heterointerfaces have been calculated from the equations developed, which directly correlate the position of the bands with the strain at the interface. The strain is calculated from the In mole fractions and lattice constants. The parameters implicitly involved are the elastic stiffness constants (C₁₁ and C₁₂), the hydrostatic deformation potential of the conduction band (a′), the hydrostatic deformation potential (a) and the shear deformation potential (b) for the valance band. The results should be useful to research workers in the field of optoelectronics.     

Measurement of space charge generation-recombination current in Hg1−xCdxTe photodiodes by deep level transient spectroscopy

Deep Level Transient Spectroscopy (DLTS) measurements have been used to characterize n⁺ ? pHg_1?xCd_xTe junction photodiode performance. Deep level results obtained on a x = 0.320 liquid phase epitaxial grown photodiode and a x = 0.219 bulk quench anneal-grown photodiode have identified deep Shockley-Read recombination centers. Detailed characterization of trap energy, trap density, and capture cross sections for these traps located within the diode depletion region have been used to predict a space charge generation-recombination current and dynamic resistance-area product at zero bias voltage. This paper presents for the first time a direct correlation of DLTS parameters with photodiode device performance.     

Effect of anion and cation substitution in tungsten disulfide and tungsten diselenide on conductivity and thermoelectric power

The temperature dependences of the conductivity and thermoelectric power for a series of samples W_1–x Nb _x S₂, W_1–x Nb _x Se₂, WS_2–y Se _y , W_1–x Nb _x S_2–y Se _y are studied at low temperatures. It is found that the cation substitution of W atoms with Nb leads to an increase in the conductivity and a decrease in the thermoelectric power. The anion substitution of S with Se atoms results in a simultaneous increase in the conductivity and thermoelectric power. The highest power factor among the samples studied is inherent to W_0.8Nb_0.2Se₂.     

Shallow acceptors in strained multiquantum-well Ge/Ge1−x Six heterostructures

Far infrared photoconductivity spectra due to excitation of shallow acceptors in strained multiquantum well Ge/Ge_1?x Si_x (x≈0.1) heterostuctures are investigated. It is shown that these spectra are shifted toward longer wavelengths in the far infrared region compared with those of bulk p-Ge, owing to “built-in” strain and size quantization, which lead to splitting of the light-and heavy-hole subbands in the Ge layers. Shallow acceptor spectra are calculated variationally for bulk germanium under uniaxial tension, which is “equivalent” to the strained Ge layers in the heterostructures. Although this method is only appropriate for wide quantum wells (d _Ge≈800 Å), the calculations are shown to qualitatively account for photoconductivity spectra obtained from narrower wells (d _Ge≈200 Å) as well.     

Mercury diffusion in Hg1−xCdxTe

A radiotracer technique has been used to measure both mercury self-diffusion and surface concentration values in bulk and liquid phase epitaxy, LPE, grown Hg_1−xCd_xTe. A high resolution sectioning technique has allowed profiling of thin epitaxial layers in submicron steps. Hg_1-xCd_xTe samples with composition values betweenx _Cd= 0.16 and 0.23 were isothermally annealed in carefully controlled and monitored diffusion con-ditions. Mercury reservoirs containing Hg²⁰³ were used to provide vapour diffusion sources during closed tube isothermal anneals in the temperature range 300° C to 400° C. Evidence has been found which may indicate the presence of two components in the radio-tracer profiles for both bulk and epitaxially grown material. In some cases it was possible to estimate two diffusion coefficients,D ₁andD ₂, from the near surface and deeply penetrating components, respectively. Our results forD ₁andD ₂are compared with other work. For bulk material annealed at 400° C under a saturated mercury pressureD ₁= 2.0 x 10^-12cm²s^-1 andD ₂= 1.1 x 10^-11cm²s⁻¹. Diffusion coefficients at 310° C under saturated mercury pressure, have been measured in bulk and epitaxial material. Close agreement was found between these results with an average value ofD ₁= 1.4 x 10⁻¹³cm²s⁻¹. We believe this to be the first time radiotracer results for epitaxial material have been presented. We have collated diffusion data, as a function of reciprocal temperature, from several workers and suggest there is evidence for a change in the activation energy for mercury diffusion around 350° C. This may be due to a change in the dominant diffusion mechanism.