Shot noise in back biased p-n silicon diodes

An earlier calculation of the noise due to generation of carriers in the space charge region in a p-n silicon diode by Lauritzen and by Scott and Strutt is corrected for the fact that the field distribution in the space charge region of a p-n junction is linear instead of uniform. If the noise is expressed as S_I(f) = 2eIΓ², we find $\text{Γ}{}^2\text{=}\text{11}\text{15}$ in a p⁺n or n⁺p junction, instead of $\text{Γ}{}^2\text{=}\text{10}\text{15}$ found previously.     

Hot electron noise effects in buried channel MOSFETs

Measurements are reported on a 2.0 μmeter buried channel MOSFET. Because of the short channel length, the device showed large hot electron effects. The noise reaches a limiting value above a few MHz; this is attributed to hot electron thermal noise. The parameter $\text{α = (}\text{q}\text{2kT}\text{)(}\text{I}{}_{\mathrm{eq}}\text{g}{}_{\mathrm{m}}\text{)}$ is plotted as a function of the absolute temperature T; it increases with decreasing temperature, as expected for hot electron effects.     

Thermal emission rates and activation energies of electrons at tantalum centers in silicon

The thermal emission rates and activation energies of electrons trapped at the two Ta donor centers in n-type silicon are determined from transient capacitance measurements on Schottky barrier diodes made on phosphorus and tantalum doubly doped silicon crystals. The thermal activation energies are 232 and 472 meV for the two donor levels below the conduction band edge and the pre-exponential factors, A, are both 1.5 × 10¹⁰ sec^?1 in the Ahrrenius equation for the emission rate, $\text{A (}\text{T}\text{300)}{}^2\text{exp}\text{(}\text{> ?ΔE}\text{k}{}_{\mathrm{B}}\text{T}\text{)}$.     

Hot electron noise in n-channel JFETs between 150 and 300°K

The noise parameter $\text{α}{}_{\mathrm{T}}\text{=}\text{S}{}_{\mathrm{I}}\text{(?)}\text{(4kTg}{}_{\mathrm{m}}\text{)}$ of n-channel JFETs was measured as a function of the voltage V_GS?V_P with the temperature T as a parameter between 150 and 300°K. It was found that α_T could be approximated by the formula $\text{α}{}_{\mathrm{T}}\text{? (}\text{300}\text{T}\text{)α}{}_{300}$, indicating the presence of hot electron effects.     

Equivalent temperature of hot electrons

The two extensions of the Einstein relation qD_par = kT_eμ_par and qD_par = kT′_eμ′_and define, in the case of hot electrons, two different electron temperatures T_e and T′_e. It is shown here that the two interpretations are fully equivalent in that they lead to the noise expressions $\text{S}{}_{\mathrm{I}}\text{(0)=4kT(}\text{I}\text{V}\text{and}\text{S}{}_{\mathrm{I}}\text{(0) = 4kT′}{}_{\mathrm{e}}\text{(}\text{d}\text{I}\text{d}\text{V}\text{)}$, respectively. The T′_e interpretation, however, is slightly favored, since it leads to the simple expression $\text{S}{}_{\mathrm{V}}\text{(0) = 4kT′}{}_{\mathrm{e}}\text{/}\text{d}\text{I}\text{d}\text{V}\text{)}$ for the open-circuit noise.     

Energy levels and concentrations for platinum in silicon

The energy levels and electrically active concentrations of platinum in silicon have been measured by Hall techniques. Analysis shows platinum to have two electrically active sites. The usual site N_PtI (assumed to be substitutional) predominates (>80%) and has two levels, a donor at E_v+0·28 eV, degeneracy γ_I⁺=2 in p-type material and an acceptor at E_c ?0·20 eV, $\text{γ}{}_{\mathrm{<mtext>I</mtext>}}{}^{\mathrm{?}}\text{=}\text{1}\text{6}$, in n-type material. However a second platinum site exists, and is present to a concentration N_PtII of about 10 per cent with an acceptor level at $\text{E}{}_{\mathrm{<mtext>v</mtext>}}\text{+ 0·42}\text{eV}\text{(γ}{}_{\mathrm{<mtext>II</mtext>}}\text{=}\text{1}\text{8}\text{)}$. The physical nature of this Pt associated site is unknown.Neutron activation analysis has been used to determine total atomic platinum concentrations for diffusions from 800 to 1250°C. These results, in conjunction with Hall measurements, show the electrical activity to be very high. Previous studies on platinum are reviewed and compared to the result of this work.     

The ƒT Characteristics of epitaxial NPN Transistors in upward operation

The gain-bandwidth products $\text{?}{}_{\mathrm{T}}$ of specially designed planar npn transistors were measured in upward operation at different operating current levels. It was found that the increase of $\text{?}{}_{\mathrm{T}}$ at high current levels cannot be accounted for by the variation of the factor (kT/qI_cxC_je. In fact, a plot of the delay time $\text{τ}{}_{\mathrm{T}}\text{( =}\text{1}\text{2}\text{π?}{}_{\mathrm{T}}$ against (1/√I_c) gives a straingth line at high current levels. Such observations can be explained by assuming that the lightly doped epi-emitter is operating at high injection levels. The high current limit of $\text{?}{}_{\mathrm{T}}\text{or}\text{τ}{}_{\mathrm{T}}$ depends on the epi-thickness w_epi and on the ratio between the volume of the parasitic region in the epi-emitter V_Ep and the collector area A_c     

Use of a Schottky barrier to measure impact ionization coefficients in semiconductors

The use of a Schottky barrier to determine the impact ionization coefficients of electrons and holes in semiconductors has been studied analytically and also evaluated experimentally by comparing the results for silicon with those already available in the literature.The Schottky barrier offers several advantages over a diffused p-n junction in such measurements. Pure electron initiation and pure hole initiation can be separately achieved. The abrupt barrier provides an accurately known electric field, and the linearity of the field distribution simplifies the problem of extracting the ionization coefficients from the multiplication data.We present a general solution of the charge multiplication equation and derive expressions for the ionization coefficients for the particularly simple conditions that can be achieved in a Schottky-barrier junction. Our results for silicon in the range 2 × 10⁵ < E < 4 × 10⁵V/cm can be expressed in the form $\text{α = α}{}_{\mathrm{\infty }}\text{exp}\text{(}\text{?b}{}_{\mathrm{n}}\text{E}\text{)}$ for electrons and $\text{β = β}{}_{\mathrm{\infty }}\text{exp}\text{(}\text{?b}{}_{\mathrm{p}}\text{E}\text{)}$ for holes, with α_∞ = 9·2 × 10⁵ cm^?1, β_∞ = 2·4 × 10⁵ cm^?1, b_n = 1·45 × 10⁶ V/cm and b_b = 1·64 × 10⁶ V/cm.     

Measurements of bandgap narrowing in Si bipolar transistors

Theory predicts appreciable bandgap narrowing in silicon for impurity concentrations greater than about 10¹⁷ cm^?3. This effect influences strongly the electrical behaviour of silicon devices, particularly the minority carrier charge storage and the minority carrier current flow in heavily doped regions. The few experimental data known are from optical absorption measurements on uniformly doped silicon samples. New experiments in order to determine the bandgap in silicon are described here. The bipolar transistor itself is used as the vehicle for measuring the bandgap in the base. Results giving the bandgap narrowing (ΔV_g0) as a function of the impurity concentration (N) in the base (in the range of 4.10¹⁵–2.5 10¹⁹ cm^?3) are discussed. The experimental values of ΔV_g0 as a function of N can be fitted by:

$\text{δV}{}_{\mathrm{g0}}\text{= V}{}_1\text{ln}\text{N}\text{N}{}_0\text{+}\text{ln}{}^2\text{N}\text{N}{}_0\text{+C}$

where V₁, N₀ and C are constants.It is also shown how the effective intrinsic carrier concentration (n_ie) is related with the bandgap narrowing (ΔV_g0).     

Lattice interaction noise of hot carriers in single injection solid state diodes

The spectral noise density of the a.c. open circuit voltage fluctuations (S_V) due to lattice interaction (thermal noise) is calculated for a single injection solid state diode operating in the hot carrier regime. Only acoustical phonon interaction is considered, giving rise to a Druyvesteyn velocity distribution in the case of very strong electric field strengths. This implies

$\text{μ}{}_0\text{V}{}_0\text{L}\text{u?1}$

, where V₀ is bias voltage, μ₀ low field mobility, L contact spacing and u sound velocity. It turns out that S_V is proportional to the imaginary part of $\text{Z}\text{ωτ}$, where Z is the a.c. small signal impedance and τ the carrier transit time. For ωτ?1 this expression is independent of frequency and can be described by an equivalent noise temperature T_n given by

$\text{T}{}_{\mathrm{n}}\text{=}\text{0·58T}\text{μ}{}_0\text{V}{}_0\text{L}\text{u}$

where T is the lattice temperature.Fair agreement exists between the calculated noise and noise data on hot holes in Ge injection diodes by Nicolet et al.     

Thermal emission rates and capture cross-section of majority carriers at titanium levels in silicon

The thermal emission rates and capture cross-sections of majority carriers on the titanium associated levels in the depletion region of reverse biased silicon p⁺n and n⁺n junctions have been investigated using the admittance spectroscopy technique and the dark capacitance transient method. We have found three levels associated with titanium in silicon. Its thermal activation energies are E_c ?238 ± meV, E_c ?512 ± 5 meV and E_v + 320 ± 5 meV.For the E_c ?238 meV and E_v + 320 meV levels, the thermal capture cross-sections are independent of the temperature: σ_n = 1.01 × 10^?4 cm² and σ_p = 1.55 × 10^?15 cm². The electron capture cross-section on the E_c ? 512 meV levels shows a slight dependence with the temperature, $\text{σ}{}_{\mathrm{n}}\text{= 2.01 × 10}{}^{\mathrm{?16}}\text{(}\text{T}\text{300}\text{)}{}^{\mathrm{?(0.35\pm 0.1)}}\text{cm}{}^2$ in the [120–240 K] range, which can account for the nonradiative multiphonon emission process.     

Reverse recovery in p-n junction diodes with built-in drift fields

This paper extends the earlier analysis of Moll, Krakauer and Shen of the reverse recovery of a symmetrical p-n junction diode with built-in retarding drift field in the base to the diodes in which the effect of bulk recombinations in the base is important. It is shown that the effect of bulk recombination becomes important if $\text{J}{}_{\mathrm{f}}\text{J}{}_{\mathrm{R}}\text{? 0.5}$ (J_F and J_R are the forward and the reverse currents respectively) even when the drift field is very strong. For very strong retarding fields, t_s vs ln $\text{(1 +}\text{J}{}_{\mathrm{F}}\text{J}{}_{\mathrm{R}}\text{)}$ plot is linear and has a slope very close to the minority carrier lifetime τ_B in the base even for small values of time. Hence, τ_B can be conveniently determined by this method for such diodes. Expressions for the charge left in the base at the end of the storage phase and for the decay of the current in the second phase are also derived and discussed.     

Equivalent input spectrum and drain current spectrum for 1/ƒ noise in short channel MOS transistors

Flicker noise in MOS transistors can be evaluated by measuring the spectrum S_ID of the drain current fluctuation or the spectrum Sve of an equivalent gate fluctuation. We show here that experimental variations of are in good agreement with g_m² by considering a model of the transconductance g_m which takes into account the variations of the channel carriers mobility with the surface electric field. The model agrees with the experimental results obtained on short channel MOS transistors which exhibit large variations of mobility with the gate voltage. The validity of physical interpretations of noise data on MOS transistors is examined.     

The self-consistent analysis of the on-set of strong inversion in an MOS transistor with double-layer substrate impurity profile

A unique criterion of the surface potential at the onset strong inversion case is obtained from the extension of the single layer case. The criterion is clearly defined by setting of the increasing rate of the total minority carrier concentration Q_n equal to the increasing rate of the total depletion impurity charge Q_B. The same criterion then applies to analyze the on-set strong inversion case for the double layer profile. The expression for the surface potential ψ_s has the form of $\text{(}\text{kT}\text{q}\text{) {l}{}_{\mathrm{n}}\text{(}\text{N}{}_1\text{N}{}_2\text{n}{}_{\mathrm{i}}{}^2$3 ? l_n[1 ? (q(N₁ ? n₂)$\text{W}\text{Q}{}_{\mathrm{B}}\text{)]}}$. The first term is the same as 3 the conventional expression; however, the second term is new. The expression is a continuous function of the width W of first N₁ layer, and gives a consistent prediction in the limiting case for a single N₁ layer. Therefore, the inconsistent prediction of a discontinuity in $\text{ψ}{}_{\mathrm{s}}\text{[=(}\text{kT}\text{q}\text{)l}{}_{\mathrm{n}}\text{(}\text{N}{}_1\text{N}{}_2$)] from the 3 conventional expression in the single layer limit is then removed. The corrected magnitude to the conventional expression increases with the product of N₁N₂, the ratio of ($\text{N}{}_1\text{N}{}_2$) and ($\text{W}\text{x}{}_{\mathrm{<mtext>d</mtext><mtext>1</mtext><mtext>max</mtext>}}$), and the correction will give a positive M (negative) value as N₁ > N₂(N₂ > N₁).     

A simplified technique for measuring fast surface states

A technique is presented which measures the number of fast states (/cm²) between (flat band) φ_s = 0 and φ_s = 2φ_B using a high frequency C ? V and d.c. ramp I ? V tracing of any MIS capacitor. For cases where fast state densities near flat band are insignificant, the true flat band point V(φ_s = 0) is obtained from the high frequency C ? V curve. Then from the (I ? V) curve the V(φ_s = 2φ_B) point is obtained by graphically measuring off an area = I_max (2kT/q) ln (N_B/ni) between V = V_FB, V = V₁, I = Imax, and I ? V curve. Then the fast state density (N_FS(/cm²)), is obtained from the expression: $\text{Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 2φ}{}_{\mathrm{B}}\text{? Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 0 = 2φ}{}_{\mathrm{B}}\text{+}\text{q}\text{C}{}_{\mathrm{<mtext>ins</mtext>}}\text{[N}{}_{\mathrm{si}}\text{+ N}{}_{\mathrm{FS}}\text{]}$ where all values are known. For cases where significant fast states exist near flat band, the true flat band point can be obtained graphically from the I ? V tracing using any value of surface potential near mid gap calculated from the high frequency capacitance.     

Electron temperature dependences of nonradiative multiphonon hot-electron capture coefficients of deep traps in semiconductors—I: Small lattice relaxation

Generalizing the theory of nonradiative multiphonon capture of thermal electrons for cases where the effective temperature T_e of conduction electrons differs from lattice temperature T_L, we develop a corresponding theory of hot electron capture. Its principal novelty is due to an exponential decrease ∝ exp(?E/k_Bτ) of the efficiency of this energy loss mechanism, at increasing electron energy E, for the usual regime of small lattice relaxation characterized by a corresponding “capture extinction temperature” τ. The resulting T_e-dependences of hot electron capture coefficients at sufficiently low T_e (

τ, i.e. in the “Sommerfeld factor regime”) are controlled by the net charge of the centre which means C(T_e) ∝ C(T_e) ∝ $\text{T}{}_{\mathrm{e}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, ∝ T_e⁰, or ∝ $\text{T}{}_{\mathrm{e}}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ exp$\text{[?3·(θ/T}{}_{\mathrm{e}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{]}$ in cases of attraction, neutrality, and repulsion, respectively. At high T_e

τ, i.e. in the “energy-loss factor regime”) these relations reduce to the form C(T_e) ∝ $\text{T}{}_{\mathrm{e}}{}^{\mathrm{<mtext>?</mtext><mtext>3</mtext><mtext>2</mtext>}}$ which is simply due to an increasing depopulation of the relevant region of low-lying band states. This theory is applied to electron capture by a singly charged repulsive gold centre and a doubly charged repulsive copper centre in germanium. The corresponding theoretical maximum values C_max.^(?1) = 5.2 · 10^?11 cm³ s^?1 and ifC_(rnmax.)^(?2) = 2.4 · 10^?12 cm³ s^?1 of hot electron capture coefficients are in good agreement with experimen observations.     

Current transport mechanisms of electrochemically deposited CdS/CdTe heterojunction

The dark current transport mechanism in electrochemically deposited n-CdS/p-CdTe thin film heterojunctions is investigated. The forward current measured in the temperature range between 200° and 305°K can be expressed as J_f = J₀(T) exp (AV) and the reverse current can be expressed as $\text{J}{}_{\mathrm{r}}\text{= ?CV exp ?CV[?λ(V}{}_{\mathrm{d}}\text{?V)}{}^{\mathrm{<mtext>?(</mtext><mtext>1</mtext><mtext>2</mtext><mtext>)</mtext>}}\text{]}$. The current mechanisms are consistent with a multi step recombination-tunneling model.     

Reverse characteristics of rectifying TeSeCd structures

Current density j, measured as a function of reverse voltage V_R in rectifying TeSeCd structures, is found to be much lower under pulsed than steady voltage conditions. For pulsed voltages, it is observed that lnj is proportional to $\text{(V}{}_0\text{+ V}{}_{\mathrm{R}}\text{)}{}^{\mathrm{<mtext>l</mtext><mtext>n</mtext>}}$, with n between 2 and 3 and V₀ = 0.5 V. This form of dependence is consistent with reduction of the barrier potential by the electric field in the depletion layer. As the applied frequency is increased from 20 to 10⁶ Hz, the measured parallel junction capacitance is found to show an approximate 4 to 1 decrease, with the frequency-dependent portion varying as $\text{(}\text{frequency}\text{)}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ at higher frequencies. This is in accordance with theory in the literature for deep acceptors, which are thus considered to be dominant in the selenium of the structures. Trap release times, determined within the depletion layer, are found to decrease with increase in the total concentration of deep acceptors.     

The a.c. admittance of the p-n PbSSi heterojunction

The AC admittance (tY = G + jB) of the p-n PbSSi heterojunction was measured as a function of frequency, bias and temperature. Both the conductance and susceptance components were found to be frequency dependent. The measured admittance resulted in good agreement when used in conjunction with signal measurements, $\text{I}{}_{\mathrm{sc}}\text{= ¦Y¦V}{}_{\mathrm{oc}}$, as well as noise measurements, $\text{i}{}_{\mathrm{n}}\text{4KTG}$ and $\text{ν}{}_{\mathrm{n}}\text{4KTR}$. A small signal model was developed to explain the frequency dependence of the forward bias AC admittance. A good match resulted from fitting the model and experimental data to Shockley's theory for the p-n homojunction in the special case of retarding fields at the interface.