A fast method of calculating avalanche breakdown voltage of semiconductor p-n junction

A fast method of calculating the avalanche breakdown voltage of semiconductor p-n junction is described. A simple technique of calculating the integral from the stored values of the integrand is illustrated for Silicon step junctions. This results in considerable saving of computational time.     

Safety drain voltage avoiding avalanche breakdown in MOSFET

It has been found that the avalanche breakdown voltage of MOSFET is independent of substrate bias and increases linearly with gate voltage in an operation regime. Applying this body-effect independency of breakdown, we obtain a maximum safety drain bias, below which avalanche breakdown is completely avoided. This safety drain voltage can be expressed in an empirical form ofgL_{eff}^{nu}where Leffis the effective channel length andgand ν are coefficients, dependent upon device architecture.     

Zener and avalanche breakdown in As-implanted low-voltage Si n-p junctions

Implanted-diffused As layers in Si have been well-characterized and have been used in fabricating low-voltage n-p junctions. It is shown that these As layers form linearly graded junctions with a uniform B-doped background (ρ ≃ 0.006 Ω.cm). The grade constant of the As profile at the junction is known sufficiently well as a function of As dose, diffusion time, and temperature to allow quantitative use of existing tunneling and avalanche theories for the calculation of the reverse I-V curves. Following a verification of the calculated I-V curves and their temperature dependence as a function of grade constant, calculated curves are presented which correlate As implant dose and diffusion with junction breakdown voltage, breakdown impedance, and temperature coefficient of reverse voltage. The temperature coefficient is shown to change from negative to positive as the transition from tunneling to avalanche occurs. In addition, the relative importance of tunneling and multiplied-generation current as a function of current density is elucidated for any particular As layer grade constant.     

High-speed photodiode signal enhancement at avalanche breakdown voltage

It has previously been found that when photons are injected into a photodiode biased to the avalanche region, that there is a multiplication of the signal over the usual bias-voltage signal level. This multiplication is due to the created electron-hole pairs colliding with the lattice and creating more electron-hole pairs under the influence of the large biasing field. This paper presents a circuit analysis of this effect when using a high-speed silicon (Si) P-I-N photodiode and shows what the SNR bandwidth and Noise Equivalent Power (NEP) are under both normal bias conditions and avalanche bias conditions. It is shown that there is a substantial improvement in the NEP and SNR ratio at high frequencies when operating at avalanche so that the device may be made nearly shot noise limited if the multiplication factorMis sufficiently large. Microwave measurements on such a high-speed diode gave gains greater than 30 dB with a SNR improvement of 13 dB at 1.45 Gc/s. The effect was observed at frequencies as high as 2.54 Gc/s and appeared to follow a linear 1/M law with bias voltage in the avalanche region with some deviation at large values ofM. The device SNR ratio at moderately high light levels is determined by the signal-to-shot noise ratio. A high modulation depth is found to be essential to reduce shot noise. Analysis of the diode circuit reveals that the detected signal power bandwidth product is a constant. The NEP is found to vary directly with the bandwidth in a pulse type system. Avalanche operation increases the signal power by M²and decreases the NEP byMat high frequencies. The photodiode appears to nearly provide the solid-state analog of the photomultiplier tube.     

On the avalanche initiation probability of avalanche diodes above the breakdown voltage

In the calculation of the turn-on probabilities per unit time of avalanche diode microplasmas, or of the single-photon detection probabilities of avalanche photodiodes used in the photon-counting mode, it is desirable to know how the avalanche initiation probability varies with voltage above the breakdown voltage. It is shown that the two coupled differential equations derived by Oldham et al. for the probabilities that a self-sustaining avalanche will be initiated in an avalanche diode biased above the breakdown voltage by an injected electron or by an injected hole (avalanche initiation probabilities) can be combined to provide a single integral equation for each of the electron, hole, and electron-hole pair initiation probabilities. These equations can be integrated for the special case in which the electron and hole ionization rates αeand αhare related byalpha_{h} approx kalpha_{e}wherekis a constant. A method of computing an effective value ofkfor other cases in which this approximation is not a good one is presented. The resulting expressions are shown to be consistent with previously published calculations by McIntyre of the breakdown probabilities both for the casek = 1and for the more general casek neq 1.     

The breakdown voltage of double-sided p-n junctions

The avalanche breakdown voltage of an abrupt double-sided junction is a function only of Neff(the doping obtained from capacitance-voltage analysis) in a material in which the ionization rates for electrons and holes are equal or maintain a constant ratio. This doping parameter, together with the published breakdown voltage data for single-sided junctions, immediately gives the breakdown voltage of the more complex structure.     

Avalanche breakdown voltage of diffused junctions in silicon

A semi-theoretical relationship has been developed between the avalanche breakdown voltage and the product of the junction depth and background impurity concentration for plane, cylindrical and spherical diffused junctions. This has been confirmed experimentally for plane and cylindrical junctions, over the voltage range $\text{10 < V}{}_{\mathrm{B}}\text{< 9000}\text{V}$.     

Avalanche breakdown voltage of GaAs hyperabrupt junctions

The avalanche breakdown voltage of a GaAs hyperabrupt junction diode is calculated by using unequal ionization rates for electrons and holes, and shown graphically as a function of the parameters which characterize the impurity profile of the diode. The breakdown voltage decreases abruptly at the critical point of the characteristic length L_c which varies in accordance with the impurity concentration N₀ at X = 0. For example, the critical length L_c is 7.7 × 10⁻⁶ cm and 3.3 × 10⁻⁵ cm for N₀ = 1 × 10¹⁸ cm⁻³ and 1 × 10¹⁷ cm⁻³, respectively. The breakdown voltage of a diode with extremely short or long characteristic length can be estimated from the results for corresponding abrupt junctions. The experimental results agree well with the calculated ones.     

Closed-form analytical solutions for avalanche breakdown quantities in high-voltage diffused junctions

By using a particularly chosen exponential profile and depletion approximation, the analytical expressions for avalanche breakdown critical quantities in high-voltage diffused junctions are derived. The analytical results are in good agreement with those of the full numerical method obtained by Temple and Adler and much more accurate than the values obtained by using the one-sided abrupt junction and the linearly-graded junction depletion approximations.     

On multiplication and avalanche breakdown in exponentially retrograded silicon P-N junctions

An analysis of avalanche breakdown in exponentially retrograded p-n junctions results in simple criteria for avoiding breakdown in such structures. Breakdown voltages are shown to be extremely dependent on the surface concentration and grading constant of the retrograded region. The effect of background resistivity on breakdown is also analyzed. Unusual saturation effects in the multiplication voltage curves of retrograded p-n diodes are predicted theoretically. Experimental results point towards a confirmation of this theory.     

Negative resistance in p-n junctions under avalanche breakdown conditions, part I

A one-dimensional, small-signal analysis of the space-charge region of a p-n junction in which avalanche occurs uniformly is presented. The impedance is found to have a negative real part. The impedance is Well represented by a parallel connection of the depletion layer capacitance, an inductance, and a negative resistance. The admittance of the latter two is proportional to the bias current. The magnitude of the negativeQis below ten. The negative resistance is due to an intrinsic instability in the avalanching electron-hole plasma. A discussion of the instability and a traveling-wave tube-like amplification is given.     

Negative resistance in p-n junctions under avalanche breakdown conditions, part II

The small-signal impedance of the space-charge region of p-n junctions under avalanche breakdown conditions is calculated using reasonably realistic dependences of electron and hole ionization rates and drift velocities upon electric field. Two structures are analyzed: one is p⁺νn⁺structure which has a fairly uniform distribution of avalanche multiplication, and the other is a singly diffused junction which is a hybrid of an abrupt and a linear graded junction. Both structures show negative resistance when the transit time of carriers becomes appreciable. A computer program was evolved which requires, as input, the impurity profile and field dependences of ionization rates and drift velocities. The program first calculates the dc field and electron and hole currents and then solves the ac small-signal problem. Both the ac small-signal impedance and theQof the diode are calculated.     

Temperature dependence of breakdown voltage in silicon abrupt p-n junctions

Temperature dependence of breakdown voltage in silicon abrupt p⁺-n junctions has been calculated using a modified Baraff theory [1]-[3] and measured experimentally from 77°K to 500°K, with substrate doping from 10¹⁵cm^-3to 10¹⁸cm^-3. Experimental data are in good agreement with the results of theoretical calculations. These results strongly substantiate the validity of the modified Baraff theory which has been pointed out by Sze and Crowell.     

Calculation of the diffusion curvature related avalanche breakdown in high-voltage planar p-n junctions

Avalanche multiplication calculations are performed in high-voltage planar p-n junctions to determine breakdown voltage limitations imposed by curvature effects. The issue of choice of ionization coefficient for avalanche multiplication is discussed. From the calculations, a series of design curves and equations are generated which relate the breakdown voltage and peak electric field to those of an ideal junction of the same doping profile, the critical parameters being the substrate doping concentration, the diffusion profile, and the ratio of the radius of curvature to the substrate depletion width for the ideal one-dimensional case. With appropriate distance normalization, these curves and equations can be reduced to a single curve and a single equation. The agreement between theory and experiment is consistently good provided the correct ionization coefficients are used in the theory.     

The effect of photogenerated carriers on the mean time delay for avalanche breakdown in p-n junctions

Avalanche breakdown in p-n junctions is preceded by a delay time between application of an overvoltage and the actual initiation of an avalanche discharge. The mean of this delay time has been studied as a function of photogeneration in p-n junction devices. Results agree well with McIntyre's theory of breakdown probability. The data further indicate that the probability of any given carrier initiating breakdown is independent of carrier concentration over the three orders of magnitude investigated.     

Semiempirical determination of avalanche breakdown temperature parameters in p-n junctions

A method is proposed which permits the determination of the electric field dependence of the ionization coefficient at any temperature. Relative simple semiempirical expressions for the ionization coefficients α_n and α_p for electrons and holes as a function of electric field and temperature are derived. This is applied to express the avalanche breakdown voltage (U_B) and its temperature coefficient (β) as a function of impurity density or concentration gradient for abrupt and linearly graded p-n junctions, and of temperature. The results for U_B and β obtained from these expressions compare satisfactorily with exact numerical results. It is confirmed (both theoretically and experimentally) that β(T) exhibits a maximum at a definite temperature and that U_B (T) deviates significantly from a linear temperature dependence.     

Avalanche breakdown voltage of multiple epitaxial pn junctions

Calculation of the peak electric field at breakdown for two-sided step junctions with arbitrary doping levels on each side is presented. The theoretical predictions are compared with the results of experimental breakdown studies of a series of carefully prepared and characterized high voltage diodes. Calculations based upon the ionization coefficients determined by Van Overstraeten and De Man are shown to be in better agreement with experiment than those based on the ionization coefficients of Lee et al.