P-n Junction Basics
Semiconductor
The conduction properties of a semiconductor can be precisely controlled by doping an element with less or more valency
For Si (or Ge), doping a pentavalent impurity such as Phosphorus or Arsenic, makes conduction electron concentration much higher than the hole concentration
These are called n(negative)-type Semiconductors and the impurities are called donor impurities
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N-Type Semiconductors
In n-type semiconductors, impurity levels are created slightly (few tens of meV) below the conduction band and are occupied by the extra electrons attached to the impurity ions
Due to thermal energies, a large number of them go to the conduction band, increasing $n_e$. Intrinsic concentration is of the order of $10^{10} {cm}^3$, but the impurity electrons forpm type doping could be around $10^{16} {cm}^3$
$n_e n_h=n_i^2$ (Independent of doping)
For Si (or Ge ), doping a trivalent impurity such as Boron or Aluminium, makes hole concentration much higher than conduction electron concentration
These are called p-type Semiconductors and the impurities are called acceptor impurities
In p-type semiconductors, impurity levels are created slightly (few tens of meV) above the valence band and are vacant
Due to thermal energies, valence electrons can jump to these impurity levels making holes in the valence band, increasing $n_h$. Intrinsic concentration is of the order of $10^{10} {cm}^3$, but the hole concentration for_ppm type doping could be around $10^{16} {cm}^3$
$n_e n_h = n_i ^2$
$n_i$ = Concentration of e or h when no dopping is done
$n_e = n_h = n_i$
Charge density itself = 0
Charged carrier density can be changed
When an electric field is applied in the semiconductor, the electrons and holes move systematically and an electric current is generated
$I = I_h + I_e,$ the two currents are proportional to the concentiations of the charge carriers
Drift Velocity
Drift velocity $v_d \propto E$
Collision time $=\tau$
$a=\frac{e E}{m} , v=\frac{e E}{m} \tau$
$v_d=\frac{e \tau}{m} E \rightarrow$ Mobility
Density of conduction electron = n
Drift velocity is $v_d$
Charge crossing the cross-section = $n A (v_d \Delta t)e$
$ I = A n e v_d$
$ J= \frac{I}{A} = n e v_d = n e \mu E$
Ohm’s Law
$J = n e \mu E$
n e $\mu$ = $\sigma$ ($\sigma$ is conductivity)
J = $\sigma$ E (Ohm’s Law)
$\mu = \frac{e \tau}{m*} $
m* = effcofine mass
Si $\Rightarrow m_e * = 0.26 m_e$
Holes
$J = (n_e \mu_e + n_h \mu_s) \times eE$
$I = I_e + I_h$
Impurity Levels
n-type semiconductors impurity levels are created slightly below the conduction band.
Hydrogen Atom
Ionization energy = 13.6 eV.
e = $\frac{m e^4}{2 (4 \pi \epsilon_0)^2 n^2 h^2}$
$\epsilon$ = K G (Dielectric constant K = 12)
P-n Junction
p-type impurities Acceptor impurities
Donar impurities p-type
Negative p
Positive charge density
Deplition Region
Charge density $\neq$0
Charge carrier density = 0
Potential Barrier
$N_A , N_D \leftarrow$ (width of depletion)
Potential Barrier (V)
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