K.K. Thornber

Relation of drift velocity to low‐field mobility and high‐field saturation velocity

From an investigation of the behavior of the momentum distribution function of electrons or holes under scattering rate and momentum scaling transformations, a number of interesting results are derived concerning the parameterization of drift‐velocity–vs–electric‐field relations in terms of mobility and saturation velocity. Indeed it is determined that saturation velocity is invariant under scaling of the magnitude of the scattering rates, which alters mobility, while mobility is invariant under scaling of the magnitude of the momentum, which alters saturation velocity. This independence between mobility and saturation velocity is utilized to generalize to interfaces velocity‐field relations valid the the bulk. Using the transformation of drift velocity under both rate and momentum scaling, partial experimental data can be used to predict high‐field saturation velocities. These velocities need not be reduced due to higher scattering rates as much as their low‐field counterparts. Nonzero magnetic fields an...

Applications of scaling to problems in high‐field electronic transport

Utilizing changes in the carrier distribution function by magnitude and momentum scaling of scattering rates, the author a number of interesting results concerning ionization coefficients and transient drift and diffusion. Starting with a general definition of the ionization coefficient which includes nonlocal effects, the behavior of this coefficient under scaling is determined and used to find a simple analytical expression in terms of physical parameters valid for all field strengths. When fit to data for silicon, surprisingly large but consistent high‐field, effective ionization energies are found for electrons (3.6 eV) and holes (5.0 eV). This expression can also relate ionization near an interface to that in the bulk. Rate scaling is also used to predict changes in velocity overshoot and diffusion‐limited rise times between bulk and interface behavior. These comparisons are facilitated by a novel relationship between the time dependence of the spacial diffusion of a carrier pulse and it spacial disp...

Incomplete charge transfer in IGFET bucket-brigade shift registers

The time evolution of the charge transfer during one half-cycle of operation of an IGFET bucket-brigade dynamic shift register is calculated analytically for a smooth but otherwise arbitrary voltage driving function. Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) solutions to the charge transfer equation are matched to Airy-function solutions in the current cutoff region to determine the charge transferred as a function of initial charge. This directly gives several contributions to the incomplete transfer parameter α, the rate of change of the charge left behind on transfer with the initial charge. Although the increment of charge not completely transferred is less than 1 percent of the charge comprising the signal, the calculation is done so that no subtraction of nearly equal large numbers is necessary. We do not evaluate the actual loss of charge due to leakage, traps, recombination, etc. It is found that the finite dynamic drain conductance of an IGFET makes a major contribution to the parameter α, and that under many experimental conditions it will limit shift-register performance. It is also found that all contributions to α depend on the clock-voltage wave-form. Comparison is made with the results of preliminary experiments, and good qualitative and reasonable quantitative agreement is obtained.

Spectral density of noise generated in charge transfer devices

We calculate the spectral density of the noise added to an analog signal passed through a charge transfer device (CTD) in terms of the charge fluctuation associated with each transfer. A correlation between noise in neighboring elements substantially suppresses the energy content of the noise associated with charge transfer for frequencies much less than the clock frequency.

Comment on ’’Simulation of high‐field transport in GaAs using a Monte Carlo method and pseudopotential band structures’’ and on ’’Band‐structure dependent transport and impact ionization in GaAs’’

Recent theoretical work by Shichijo, Hess, and Stillman on a Monte Carlo simulation of high‐field transport and impact ionization in GaAs is examined. The failure of that calculation to reproduce the experimentally well‐documented orientation dependence of impact ionization can be directly related to the use of a phonon scattering rate that is unrealistically high. It is shown that such high scattering rates lead, by the uncertainty principle to a large collisional broadening (?0.3 to 0.6 eV) of the conduction band, thus invalidating the Monte Carlo simulation and rendering questionable any attempt to relate transport to the band structure. The important role played by the avalanche region width in the orientation dependence of impact ionization is also discussed.

Differential studies of dual‐dielectric charge‐storage cells

By means of novel differential techniques, we have studied the writing and erasing dynamics of DDC cells and, in the process, uncovered a number of unexpected phenomena which play an important role in these processes. For example, we find writing currents qualitatively similar to, but considerably in excess of, those predicted earlier by Fowler‐Nordheim studies on similar MOS structures. We find that these devices can be written with high and undiminished efficiency to 7–10 V of flatband shift depending on insulator thickness, and we determine the limiting source of efficiency degradation beyond these levels. In erase, we find an interesting enhancement due, we believe, to electron‐electron repulsion of the net stored charge. By studying the reversible motion of the stored‐charge centroid at high temperatures, we determine that the effect of the interfacial dopant on the outer insulator extends about 80 A into this layer. Other studies indicate an effect on the thin oxide to be less than 20 A. Low‐field l...

High-frequency, transient response of microstrip lines

Two expressions for the impulse response function of resistive microstrip transmission lines, including the effects of frequency-dependent field penetration (classical skin effect), are derived. One expression is complete in the sense that the three parameters on which it depends are expressed in terms of the material and geometrical properties of the stripline. The other expression is unexpectedly simple in form and depends on only two parameters, propagation delay and effective response time. At present, these parameters must be determined by matching the response predicted by both expressions to representative pulses. These then agree to +or-1% with each other and with recent transient experimental results of J.S. Loos and A.H. Endvik. These expressions should find application in the design and simulation of multi-gigabit-per-second, digital pulse transmission over microstrip lines. >