= (n μ

_{n }+ p μ_{p}) q
If the semiconductor is intrinsic, then the concentration of free
electrons n and holes p is same at any time and given by n

_{i}which is called intrinsic concentration.
n

_{i}= n = p for intrinsic semiconductor
Using the expression of conductivity, we get the expression for the conductivity of intrinsic semiconductor denoted as.

σ

σ

_{i}= n_{i}( μ_{n }+ μ_{n }) q ..........(1)**Note**: Note that the mobilities of electron and hole are different, through the concentration semiconductor n and p are same in intrinsic semiconductor.

__1.1 Temperature Dependence of n__

_{i}and σ_{i}.
The intrinsic concentration depends on temperature, due to thermal
generation. As temperature increases, more number of electrons-hole
pairs are generated. Hence the free electron concentration n and hole
concentration p increases by same amount. Hence intrinsic carrier
concentration n

_{i}also increases.
As temperature increases,

i) Intrinsic carrier concentration n

_{i}increases.
ii) Intrinsic conductivity σ

_{i}increases.
iii) Intrinsic resistivity ρ

_{i}= 1/σ_{i}decreases
where A

_{0}= Constant independent of temperature
T = Absolute temperature expressed in

^{o}K
E

_{G0}= Forbidden energy gap at absolute zero temerature
k = Boltzmann's constant expressed in eV/

^{o}K = 8.620 x 10^{3}eV/^{o}K
B = √A

_{0}= Constant independent of temperature
The equations (2a) and (2b) show that the charge carrier concentration
increases as the temperature increases. The effect of temperature on
charge carrier concentration is shown in the Fig. 1.

Fig 1. Effect of temperature on n _{i} |

The values of E

_{G0}and B for various materials are given in the table 1.Table 1 Constants of semiconductors |

**Note**: The concentrations can be expressed in the units /m^{3}or /cm^{3}and accordingly B must be used in m^{-3}^{o}K^{-3/2}or cm^{-3}^{o}K^{-3/2}.__1.2 Effect of Light on Semiconductor__

The effect of light on a semiconductor is exactly similar to the effect
of heat on a semiconductor. Just as thermal energy causes electrons to
break their covalent bonds, similarly the light energy also causes
electrons to break their covalent bonds. Under the influence of light
energy, electron-hole pairs get generated in a semiconductor, increasing
its conductivity.

When not illuminated there are few free electrons in a semiconductor and
its resistance is high called dark resistance. As the light is incident
on a semiconductor and it is illuminated it imparts light energy to the
electrons. The electrons breaking their bonds move from valence band to
conduction band and the conduction can take place readily. Thus there
is decreases in resistance of a semiconductor. When illumination
increases, a semiconductor may behave comparable to a conductor.

The effect of light on a semiconductor is to cause increase in the conductivity of a semiconductor.**Note**: Both heat and light are responsible to generate electron-hole pairs and hence to increase the conductivity of a semiconductor.

__1.3 Effect of Temperature on Mobility (μ)__

^{o}K, the mobility changes as T

^{-m}.

where value of m is ,

**Note**: The mobility decreases with increase in temperature.

Similarly the mobility also changes with electric field intensity E. It remains constant for E less than 10

^{3}V/m. For value of e between 10^{3}to 10^{4}V/m, μ changes as E^{-1/2}. While for high values of E, μ changes inversely as E.__1.4 Effect of Temperature on Conductivity (σ__

__)__

The conductivity is directly proportional to mobility and concentration
of charge carriers. The mobility decreases while the concentration of
charge carriers increases with the temperature.

But change in concentration of charge due to the temperature is more
dominating in intrinsic materials than the change in due to temperature.

**Note**: Thus the conductivity of intrinsic semiconductor increases with increase in temperature.

The temperature dependence of conductivity (σ) is given by,

σ

_{2}= σ

_{1}{1+ α

_{1}ΔT}

where σ

_{1}= Conductivity at temperature T

_{1}.

σ

_{2}= Conductivity at temperature T

_{2}.

α

_{1}= Resistance temperature coefficient at .

ΔT = Temperature rise ( T

_{2 }- T

_{1})

__1.5 Effect on Energy Gap (E__

_{G})E

_{G}(T) = E

_{G0 }- βT

where E

_{G0 }= Energy gap at 0

^{o}K.

β = Constant depending on material

The value of β = 2.23 x 10

^{-4}for Ge while 3.6 x 10

^{-4}for Si.

While E

_{G0 }= 1.21 for Si and 0.785 for Ge.

**Note**: E

_{G }decreases as temperature increases.

**Example**: Find the resistivity of an intrinsic silicon at 300

^{o}K if intrinsic concentration of silicon at 300

^{o}K is 1.5 x 10

^{10}per cm

^{3}while μ

_{n }= 1300 cm

^{2}/V-sec and μ

_{p }= 500 cm

^{2}/V-sec. Assume q = 1.6 x 10

^{-19}C.

**Solution**: The given values are, n

_{i}= 1.5 x 10/cm

^{3}

**.**n

^{.}._{i}= (1.5 x 10

^{10})/10

^{-6}/m

^{3}= 1.5 x 10

^{16}/m

^{3}

And μ

_{n }= 1300 x 10

^{-4}m

^{2}/V-sec, μ

_{p}= 500 x 10

^{-4}m

^{2}/V-sec

Now σ

_{i}= ( μ

_{n }+ μ

_{p}) q = 1.5 x 10

^{16}{1300 + 500} x 10

^{-4}x 1.6 x 10

^{-19}

= 0.000432 (Ω-m)

^{-1}..............Conductivity

**.**ρ = 1/σ

^{.}._{i}= 1/0.000432 = 2314.8148 Ω-m .........Resistivity

**Sponsored links :**
## 0 التعليقات:

## Post a Comment