Drift Velocity with Elastic Scattering

Round 1

Reviewer 1 Report

The paper presents studies electron drift velocities in semiconductor materials based on a rudimentary mathematical model assuming only elastic scattering. It contrasts much more sophisticated models which include the band structure of materials, excitation of optical and acoustical phonons etc.  which were studied in many detail a long time ago (see Ref. [9]). It is hard to see how the physics of semiconductors or metals benefits from the results presented in the paper.

The physical significance of the results is not clear. In particular, the exclusion of a range of scattering angles in the direction of the applied force does not make much physical sense. The same can be stated about other "exclusion" models. What does the direction of the external force have to do with the scattering angle?

Some other comments.

The length and time scale chosen by the authors (for example, the distance of 1 m between the scatterers, the drift distance of thousands of meters) is completely irrelevant to the electron drift in matter.

Bottom of p. 3 and Fig. 1: what is the physical meaning of the different types of exclusion angles? Why don't the authors choose the scattering rate as a function of the scattering angle corresponding to a realistic physical system?

Eqs. (3), (4): isn't n=1/2 a natural choice? Why try other values of n? The exponential dependence, Eq. (5), seems completely unrealistic to me.

Eq. (8): should not v_0+at be in parenthesis?

line 235: the "-" sign is missing in front of 4.93.

Eq. (16): I think what is calculated here is not the average y position, but the average y displacement between two collision events. Calculation involving Eqs. (16)-(18) assumes that the y component of velocity after each collision event is 0, therefore Eq. (18) does not represent the drift velocity. My point is that even if "momentum is reset after every collision", it does not mean that its y-component is 0 after every collision.

Author Response

Please see the attachment (reviewer 1).

Author Response File: Author Response.pdf

Reviewer 2 Report

Drift of particles (in swarm-like ensembles) is a problem common to solid state physics, atomic physics, statistical physics in general.

Authors present some axiomatic, simple Monte Carlo methods to derive the drift velocity in a constant (gravitational) field. They present three models: time, space and energy dependent scattering. The results are clearly presented and one could leave them at this stage.

However, as the subject is important for infinity of applications, in order to increase the impact of the paper I suggest to make some (5-10) references to practical MC models in other fields. For example, a nice application reference would be theories of electron (or ion) scattering in rarefied gases. Depending on the kind of atom (He, Ar) the drift velocities change much. 

References to the practical applications of MC for drift velocities would be important in two aspects: 1) increase the impact of the paper, 2) show to researchers applying complex modelling that some of the results could be approximated by "axioms" used by present authors.

Minor: line 154 should read: where

It is the electrical current which is proportional to the electrical field; the opposite is mathematically correct, but disregards the chain cause - effect.

Figure 5 and 7 seem to show exponential / power dependencies. I suggest to add the plot in log-log or semi-log scale, to make it clear to the reader. 

Author Response

Please see the attachment (Reviewer 2)

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper presents a study on drift velocity under time-, space-, and energy- dependent scattering model. The present study has been able to obtain a constant drift velocity with elastic scattering. A well-known Monte-Carlo simulation technique has been used in this work to model a particle in a uniform force field, subject to randomly placed scatterers. The study shows that the space-dependent scattering and energy dependent scattering models do not arrive at a constant drift velocity. However, the study observes a decreasing drift velocity for space and energy dependent models.  Though the research topic is very old, this study looks interesting to me. In my opinion, the paper can be accepted for publication.

The quality of English language is fine. Minor editing of English language required.

Author Response

Please see the attachment (Reviewer 3)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The revised version is certainly an improvement. The authors emphasize that they are presenting model studies, rather than a realistic description of electron drift in semiconductors. On the other hand, they show now that the range of possible applications of their results could be pretty wide. I recommend publication in its present form.