Home
Class 12
PHYSICS
The band gap in germanium is (Delta E=0....

The band gap in germanium is `(Delta E=0.68eV.)`.Assuming that the number of hole-electron pairs is proportional to `e^(-Delta E//2kT),find the percentage increase in the number of charge carries in pure germanium as the temperature is increased form 300K to 320K.

Text Solution

Verified by Experts

The number of charge carries in an intrinsic semiconductor is double the number of hole-electron pairs. If `N_1` be the number of charge carries at temperature`T_(1)`and `N_(2) at T_(2)`,we have
`N_(1)=N_(0)e^(-Delta E//2kT_(1))`
`N_(2)=N_(0)e^(-Delta E//2kT_(2))
the percentage increase as the temperature is raised form `T_(1) to T_(2)`is
`f=(N_(2)-N_(1))/(N_(1))xx100=((N_(2))/(N_(1))-1)xx100`
`100[e^((Delta E)/(2k))((1)/(t_(1))-(1)/T_(2))-1].
Now, `(Delta E)/(2k)((1)/(t_(1))-(1)/T_(2))`
`(0.68eV)/(2xx8.62xx10^(-5)eVK_(-1))((1)/(300K)-(1)/320K))`
`=0.82.`
`Thus,f=100xx[e^(0.82-1]~~127.`
Thus ,the number of charge carries increases by about 127%.
Promotional Banner

Topper's Solved these Questions

  • SEMICONDUCTOR AND SEMICONDUCTOR DEVICES

    HC VERMA|Exercise Question for short answer|10 Videos

  • SEMICONDUCTOR AND SEMICONDUCTOR DEVICES

    HC VERMA|Exercise objective I|15 Videos

  • SEMICONDUCTOR AND SEMICONDUCTOR DEVICES

    HC VERMA|Exercise exercises|35 Videos

  • PHOTOMETRY

    HC VERMA|Exercise All Questions|44 Videos

  • SPEED OF LIGHT

    HC VERMA|Exercise Exercises|3 Videos

Similar Questions

Explore conceptually related problems

The conductivity of a pure semiconductor is roughly proportional to T^(3/2) e^(-Delta E//2kT) where (Delta)E is the band gap. The band gap for germanium is 0.74eV at 4K and 0.67eV at 300K.By what factor does the conductivity of pure germanium increase as the temperature is raised form 4K to 300K?

Let (Delta)E denote the energy gap between the valence band and the conduction band.The population of conduction electrons (and of the holes)is roughly proportional to e^(-Delta E//2kT). Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room tempareture 300K. (Delta E) for silicon is 1.1 ev and for diamond is 6.0eV.How many conduction electrons are likely to be in one cubic meter of diamond ?

When a semiconducting meterial is doped with an impurity,new acceptor levels are created .In a particular thermal collision,a valence electrons recives an energy equal to 2kT and just reaches one of the acceptor levels. Assuming that the energy of the electron was at the top edge of hte valence band and that the temperature T is equal to 300K, find the energy of the acceptor levels above the valence band.

K.E. of a body is increased by 300%. Find the % increase in its momentum.

The conductivity of an intrinsic semiconductor depends on temperature as (sigma)=(sigma_0)e^(-Delta E//2kT), where (sigma_0) is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T=300 K .Assume that the gap for germanium is 0.650 eV and remains constant as the temperature is increased.

find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium.The band gap in germanium is 0.65eV.

The energy of a photon of sodium light (lambda=589 nm) equal the band gap of a semiconducting material.(a)Find the minimum energy E requried to create a hole-electron pair.(b)Find the value of E//kT at a temperature of 300K.

In an intrinsic semiconductor , the energy gap E_(g) is 1.2 eV . Its hole mobility is much smaller than electron mobility and independent of temperature . What is the ratio between conductivity of 600 K and that at 300 K ? Assume that the temperature dependence of intrinsic carrier concentration n_i is given by n_(i)=n_(0) exp ((-E_(g))/(k_T)), where n_(0) is a constant and k_=8.62xx10^(-5)eV//K.

The concentration of hole-electron pairs in pure silicon at T=300K is 7xx10^(15) per cubic metre, Antimony is doped into silicon in a proportion of 1 atom in 10^7 atons. Assuming that half of the impurity atons contribute electrons in the conduction band, calculate the foctor by which the number of silicon atoms per cubic metre is 5xx10^(28)

The current-voltage characteristic of an ideal p-n junction diode is given by i=i_0(e^eV//kT-1) where the drift current i_0 equals 10(mu)A .Take the temperature T to be 300K.(a)Find the voltage v_0 for which e^(eV//kT)=100 .One can neglect the term 1 for vlatages greater than this value (b)Find an expression of the dynamic resistance of the diode as a function of V for VgtV_0 .(c)Find the voltage for which the dynamic resistance is 2.0 (Omega)