2.11. A uniform piece of GaAs (gallium arsenide) crystal is 18 mm long, 3 mm wid
ID: 1766076 • Letter: 2
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2.11. A uniform piece of GaAs (gallium arsenide) crystal is 18 mm long, 3 mm wide, and 4 mm thick. A current of 3.8 mA is forced through the length of the crystal, causing a voltage of 8.1 mV to develop along its length (a four-point measurement configuration is used so that contact resistance can be neglected) a) What is the conductivity of the material? b) If the electron concentration is 11x1022 m-3 in the material (the free carriers are assumed to be electrons), what is the carrier mobility? c) If the electrons behave in GaAs as if they had an "effective" mass 0.0665×m, (the usual electron mass), what is the mean time between collisions? d) Find the ratio of drift to rms thermal speeds for the electrons, using the above mass value and assuming T- 300 K. Comment on the relative magnitudes. e) What would you expect to measure for the Hall coefficient in this sample? f) Find the mean free path (i.e., distance traveled) between collisions. Use a reasonable assumption based on your comment in part (d) g) The conventional lattice constant of the zinc blende GaAs crystal structure is 5.65 A. If the electrons scattered from every nucleus they encountered (as assumed in the original theory of conductivity in solids), could they have a mean free path similar to that found in part ()? Explain.Explanation / Answer
area=395mm(AS PER THE RULE,(AREA=2*PI*R(R+H) ) (R=RADIUS,H=HEIGHT)
res=8.1/3.8=2.1315 ohm
(a) conductivity=LENGTH/(RES*AREA)=18/(2.1315*395)=0.0021MS/mm
(b) Actually, the mobility measures the ability of free carriers (electrons or holes) to move in the material as it is subjected to an external electric field. The magnitude of the mobility directly impacts on the device performance since it determines the operation speed through the transit time across the device, the circuit operating frequency or the sensitivity of magnetic sensors
MOBILITY=DRIFT VELOCITY/ELECTRIC FIELD
=(current/cross-sectional area of the conductor*number of charge carriers*chrge on each carrier)/ELECTRIC FIELD
=(3.8/0.395*1.1*10^(-23)*1.6*10^(-19))/EF
=17.3*10^(-42)/EF
= 11.89
(c)Mean free time is the average time between collisions with ions in the material.
MFT=0.065*9.10938356 × 10-31
(d)the ratio will be: 1:1
(e)The Hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. It is a characteristic of the material from which the conductor is made since its value depends on the type, number, and properties of the charge carriers that constitute the current.
here we can expect as no hall coefficient as a magentic field is absent here.
(g)No there will be no free path because of absent in collision between the molecular components,
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