Douglas Natelson
Nov14-04, 11:59 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nIgor Khavkine wrote:\n[regarding ballistic motion of electrons in solid state systems]\n>\n> I\'ve often heard the terms "ballistic transport" or "ballistic limit" or\n> "ballistic such and such", but never quite got what they meant. To me the\n> word "ballistic" evokes images of heavy projectile weaponry, not electron\n> transport.\n>\n> Would anyone care to explain the precise sense in which "ballistic" is\n> used in this context?\n\nFor electronic motion in solid state systems, two limiting cases\nare "ballistic" and "diffusive". In the former, the elastic mean\nfree path for the electrons is long compared to the size of your\ndevice (e.g. the spacing between voltage probes). In the latter,\nthe elastic mean free path is short compared to the size of your\nsystem, and you should think (semiclassically) of the electrons\nas executing a diffusive random walk with typical step size given\nby that mean free path.\n\nTo put it another way: in the ballistic limit, a (quasi)electron\nthat is placed into a Bloch state with a wavevector quantum number k\n(and a corresponding crystal momentum \\hbar k) will remain, in\nthe absence of external E and B fields, in that state. In the\ndiffusive limit, at some rate given by one over the elastic\nscattering time, the particle will scatter out of that state and\ninto another state labeled by k\' such that |k\'|=|k|.\n\nSo, in clean semiconductor systems like the 2d electron gas being\ndiscussed, the elastic mean free path can be hundreds of microns,\nbecause the material is so clean (i.e. free of impurities or\nstructural defects). If you start off an electron and it would\nfly through your device without scattering off into a different\ndirection due to disorder, one would say you\'re in the ballistic\nlimit. In contrast to the semiconductor 2deg, the typical\nelastic mean free path in a thin evaporated metal film (like Au or Cu)\nis something like 20 nm or so at low temperatures. Measuring\nballistic effects in metals is more challenging, though do-able.\n\nHope that helps.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Igor Khavkine wrote:
[regarding ballistic motion of electrons in solid state systems]
>
> I've often heard the terms "ballistic transport" or "ballistic limit" or
> "ballistic such and such", but never quite got what they meant. To me the
> word "ballistic" evokes images of heavy projectile weaponry, not electron
> transport.
>
> Would anyone care to explain the precise sense in which "ballistic" is
> used in this context?
For electronic motion in solid state systems, two limiting cases
are "ballistic" and "diffusive". In the former, the elastic mean
free path for the electrons is long compared to the size of your
device (e.g. the spacing between voltage probes). In the latter,
the elastic mean free path is short compared to the size of your
system, and you should think (semiclassically) of the electrons
as executing a diffusive random walk with typical step size given
by that mean free path.
To put it another way: in the ballistic limit, a (quasi)electron
that is placed into a Bloch state with a wavevector quantum number k
(and a corresponding crystal momentum \hbar k) will remain, in
the absence of external E and B fields, in that state. In the
diffusive limit, at some rate given by one over the elastic
scattering time, the particle will scatter out of that state and
into another state labeled by k' such that |k'|=|k|.
So, in clean semiconductor systems like the 2d electron gas being
discussed, the elastic mean free path can be hundreds of microns,
because the material is so clean (i.e. free of impurities or
structural defects). If you start off an electron and it would
fly through your device without scattering off into a different
direction due to disorder, one would say you're in the ballistic
limit. In contrast to the semiconductor 2deg, the typical
elastic mean free path in a thin evaporated metal film (like Au or Cu)
is something like 20 nm or so at low temperatures. Measuring
ballistic effects in metals is more challenging, though do-able.
Hope that helps.
[regarding ballistic motion of electrons in solid state systems]
>
> I've often heard the terms "ballistic transport" or "ballistic limit" or
> "ballistic such and such", but never quite got what they meant. To me the
> word "ballistic" evokes images of heavy projectile weaponry, not electron
> transport.
>
> Would anyone care to explain the precise sense in which "ballistic" is
> used in this context?
For electronic motion in solid state systems, two limiting cases
are "ballistic" and "diffusive". In the former, the elastic mean
free path for the electrons is long compared to the size of your
device (e.g. the spacing between voltage probes). In the latter,
the elastic mean free path is short compared to the size of your
system, and you should think (semiclassically) of the electrons
as executing a diffusive random walk with typical step size given
by that mean free path.
To put it another way: in the ballistic limit, a (quasi)electron
that is placed into a Bloch state with a wavevector quantum number k
(and a corresponding crystal momentum \hbar k) will remain, in
the absence of external E and B fields, in that state. In the
diffusive limit, at some rate given by one over the elastic
scattering time, the particle will scatter out of that state and
into another state labeled by k' such that |k'|=|k|.
So, in clean semiconductor systems like the 2d electron gas being
discussed, the elastic mean free path can be hundreds of microns,
because the material is so clean (i.e. free of impurities or
structural defects). If you start off an electron and it would
fly through your device without scattering off into a different
direction due to disorder, one would say you're in the ballistic
limit. In contrast to the semiconductor 2deg, the typical
elastic mean free path in a thin evaporated metal film (like Au or Cu)
is something like 20 nm or so at low temperatures. Measuring
ballistic effects in metals is more challenging, though do-able.
Hope that helps.