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…………………… 1.96



Therefore in semiconductors the mean free path will be the product of the thermal velocity and the mean free time. Mean free time is calculated from mobility of the mobile carriers which is determined experimentally.

From Table(1.10) we obtain the mobility values. In Table (1.11) the mobility, mean free time, thermal velocity and mean free paths are tabulated for Ge , Si and GaAs.

Table(1.11) Mobilities, Mean Free Times, Thermal Velocities and Mean Free Paths of Ge, Si and GaAs.

Semiconductor μ n (cm^ 2 / (V-sec)) τ (femtosec) v e (m/sec) L* (A°)
Ge 3900 2217 0.95×10^ 5 2106
Si 1350 767.6 0.95×10^ 5 729
GaAs 8600 4890 0.95×10^ 5 4645.5

As we see electron has much larger mobility in semiconductors as compared to that in metals. This implies that the mean free path of electrons is greater by one order of magnitude in semiconductor as compared to that in metal. But why is the scattering less in semiconductors as compared to that in metal.? This answer is obtained by determining the de Broglie wavelength of electron and by using wave optics.

We will determine the velocity of a conducting electron in Electron Microscope, in metal and in semiconductor. In these three cases the conducting electron gains Kinetic Energy equal to the Potential Energy it loses while falling through a potential difference of 10kV in case of Electron Microscope(because 10kV is the accelerating voltage in Electron Microscope), through a potential difference of 4V in case of metal(because average kinetic energy associated with conducting electron is (3/5)E F and E F is 7eV in copper) and through a potential difference 0.025V in case of semiconductor ( since thermal voltage at 300K Room Temperature is kT/q= 0.025V). From the kinetic velocity the de Broglie wavelength is determined. The set of equations are: Kinetic Energy gained =

Therefore momentum gained


Therefore de Broglie wavelength:


In Table (1.12) the de Broglie wavelengths are tabulated:

Table1.12. de Broglie wavelengths of conducting electron in Electron Microscope, Metal and Semiconductor.

V acc v e (m/sec) λ(m) Implications
Electron Microscope 10kV 59×10^ 6 10^ -11 m = (1/50)(5A°) λ<<a (lattice constant)
100kV 187.6×10^ 6 4×10^ -12 m
Metal 4V 10^ 6 6×10^ -10 m = (5A°) λ~ a (lattice constant)
Semiconductor 0.025V 10^ 5 7.75×10^ -9 m = (78A°) λ>>a (lattice constant)

As seen from Table(1.12), we see that de Borglie wavelength is much less than the lattice constant in case of Electron Microscope. For 100kV , theoretically the resolution should be (1/100)(4A°) This is like Sunlight falling through a broad aperture. Sun-ray will pass in a straight line and shadow of the aperture should fall on the screen behind the aperture. Hence in an Electron Microscope, a regular lattice array does not scatter an electron beam. The shadow of the crystal lattice should be imaged. But this theoretical resolution is never achieved since we are using magnetostatic focusing. Only 1A° is the resolution actually achieved. In case of 10kV, though the theoretical resolution (1/50)(5A°) but in practice only 10A° resolution is achieved. The electron beam can penetrate through a thin specimen and produce the image of its broad features without being influenced by the atomic details.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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