Junction Theory & Different Types of Diodes & Their Characteristics - 1 | Electronic Devices - Electronics and Communication Engineering (ECE) PDF Download

Semiconductor Diode Characteristic

Thus, the drift and diffusion current densities components cancel each other for both carrier types. 

Electrostatic Equations

The potential distribution in the junction satisfies the Poisson equation inside the depletion region:

where $\rho \backslash rho$ is the charge density and $\epsilon \backslash varepsilon$ is the permittivity of the semiconductor.

Outside the depletion region, where the charge density is zero, the potential satisfies the Laplace equation:

A schematic diagram of a p - n junction, including the charge density, electric field intensity, and potential - energy barriers at the junctions, (not drawn to scale.)

The P-N Junction as a Diode

Diode permits the easy flow of current in one direction but restrains the flow in die opposite direction.

Forward Bias:

• Suppose we apply a voltage V such that n-side is negative and p-side is positive.
• The applied voltage V (or bias V) is opposite to the junction barrier potential V
• The consequences of this are:
  (i) The effective barrier potential becomes (Vo — V) and hence the energy barrier across the junction decreases.
  (ii) more majority carriers will be allowed to flow across the junction.
  (iii) the junction width decreases.
• The current flow is principally due to majority charge carriers and is large (mA).

Reverse Bias:

• The applied voltage V on the n-side is positive and is negative on the p-side.

• The applied bias V and the barrier potential V# are in the same direction making the effective junction potential as V + V_o. As a result, the junction width will increase.

• The higher junction potential would restrict the flow of majority carriers to a much greater extent.

• However, such a field will favour the flow of minority carriers (as they have opposite charges).

• So, the reverse bias current will be due to the minority carriers only.

• Since, the number of minority carriers is very small as compared to the majority carriers, the reverse bias current is small (≈ μA).

The short-circuited and open-circuited P-N Junction

• If the voltage V applied to the p-n junction is set equal to zero, the p-n junction would be short-circuited.
• Under this condition, no current can flow (I = 0) and the electrostatic potential Vo remains uncharged and equal to the value under open circuit conditions.
• The sum of the voltages around the closed loop must be zero, the junction potential V0 must be exactly compensated by the metal to semiconductor contact potentials at the ohmic contacts.
• It is not possible to measure contact difference of potential directly with a voltmeter across an open-circuited p-n junction diode and the voltmeter would read zero voltage.

Band AND Structure Of An Open-Circuited PN Junction

• The Fermi level must be constant throughout the specimen at equilibrium.
• The Fermi level E_F is closer to the conduction band edge E_cn in the n-type material and closer to the valence band edge E_vp in the p-side.
• The conduction band edge E_cp in the p material cannot be at the same level as E_cn, nor can the valence band edge E_vn in the n-side line up with E_vp. Hence the energy bandagram for a p-n junction appears as shown in fig.2 Where a shift in energy levels E₀ is indicated. Note that
  E₀ = E_cp - E_cn = E_vp - E_vn = E₁ + E₂

This energy E₀ represents the potential energy of the electrons at junction.

Band diagram for a p-n junction under open-circuit conditions. This sketch corresponds to fig (le) and represents potential energy for electrons. The width of the forbidden gap is E_g in electron volts.From figure,
E_F - E_vp - 1/2 E_G - E₁ and E_Cn - E_F - 1/2 E_G - E₂ E_G = forbidden energy gap
By adding the above equations
E₀ = E₁ + E₂ = E_G - (E_Cn - E_F) - (E_F - E_Vp)

E_G = kT In |(N_CN_v) / ni²] ....(1)

E_cn - E_F = kT ln (N_C/N_D) ....(2)    ∴ KT = 26 meV

E_F - E_vp = kT ln (N_v/N_A) ....(3)

The E’s are expressed in electron volts and-k has the dimensions of electron volts per degree Kelvin. The Contact difference in potential V₀ is expressed in volts and is numerically equal to E₀ and it is depends only upon the equilibrium concentrations, and not at all upon the charge density in the transition region(space charge region).

Other expressions for E₀ are
....(4)
Rewriting the above equation (4) in another form

p_p0 = p_n0 e^v0/^v_T
n_n0 = n_{p0 e}^v_0/^v_{T ....(5)}

The hole and electron-current components vs, distance in a p-n junction diode. The space-charge region at the junction is assumed to be negligibly email

The Current Components in p-n Diode

• When a forward bias is applied to a diode, holes are injected into the n-side and electrons into the p-side.
• The number of these injected minority carriers falls off exponentially with distance from the junction as shown in fig.(3)
• The symbol I_pn(x) represents the hole current in the n material, and I_np(x) indicates the electron current in the p-side as a function of x.
• Electrons crossing the junction at x = 0 from right to left constitute a current in the same direction as holes crossing the junction from left to right. Hence the total current I at x = 0 is  I = I_pn(0) + I_np(0)
• Consequently, in the p-side, there must be a second component of current I_pp which, when added to I_up, gives.the total current I. Hence this hole current in the p-side I_pp(a majority carrier current) is given by I_pp(x) = I - I_np(x)
• This current is plotted as a function of distance as shown in fig.(3) as is also the corresponding electron current l_nn in the n material.
• For an un symmetrically doped diode, I_pn ≠ I_np.
• The current in a p-n diode is bipolar in character since it is made up of both positive and negative carriers of electricity.
• The total current is constant throughout the device, but the proportion due to holes and that due to electrons varies with distance.

Quantitative Theory of the P-N diode Currents

P_n(x) = P_no + P_n(0)e^-x/Lp ....(6)

Defining the several components of hole concentration in the n side of a forward - biased diode.

Where the parameter L_p is called the diffusion length for holes in the n material.
And the injected or excess concentration at x = 0 is

P_n(0) = P_n(0) - P_no
The diffusion hole current in the n-side is given by

junction

....(7)
Taking the derivative of equation (6) and substituting in equation (7) we obtain

.... (8)
This equation verifies that the hole current decreases exponentially with distance.
Where q = charge of an electron

The Law of the Junction

• If the barrier potential across the depletion layer is V_B, then
  P_p = P_ne^vB/^VT ....(9)
  This is the Boltzmann relationship of kinetic gas theory.
• If we apply above equation to the case of an open-circuited p-n junction, then
  P_p = P_po, P_n = P_n0 and V_B = V₀.
• Consider now a junction biased in the forward direction by an applied voltage V.
• Then the barrier voltage V_B is decreased from its equilibrium value V₀ by the amount or
  V_b = V₀ - V
  V₀ = equilibrium value
• At the edge of the depletion layer, x = 0, p_n = p_n(0), then the above equation(9) is
  P_p0 = P_n(0)e^(V₀ ^-V/^Vt] ....(10)
  Combining this equation with the above said equation(5), i.e., p_p0 = p_n0 e^V₀/V_T
  We obtain,
  P_n(0) = P_n0e^v/vT ....(11)
• This boundary condition is called the “law of the junction”. It indicates that, for a forward bias (V > 0), the hole concentration p_n(0) at the junction is greater than the thermal - equilibrium value p_n0.
• A similar equation, valid for electrons, is obtained by interchanging p and n itt above equation( II).
• The hole concentration P_n(0) injected into the n side at the junction is given by
  P_n(0) = P_n0(e^V/VT-1) ....(12)

The Forward Currents

• The hole current I_pn(0) crossing the junction into the n-side at x = 0 is given by
  
• The electron current I_np(0) crossing the junction into the p-side is obtained from above equation by interchanging n and p, or
  
  The total diode current I is the sum of I_pn(0) and I_np(0), or
  I = I₀(C^V/VT -1)
  
  Hence I₀ is called the "‘reverse saturation current!’ and depends on doping concentration.
  
  
  Where, σ_n = N_Dμ_nq and σ_p = N_Aμ_pq
  V_GO is a voltage which is numerically equal to the forbidden gap energy in electron volts. If we consider the recombination of carriers, then the total current I
  I = I₀(e^v/nVT -1) ....(13)
  Where η ≈ 2 for small (rated) currents and η ≈ 1 for large currents.
  η ≅ 2 for silicon
  η ≅ 1 for germanium
• I₀ depends on material and it is fixed for a given device. But varies with temperature
  I_o2 = I₀₁ x 2I(T₂ - T₁₎10l ....(14)
• Where I_o1 (I₀₂₎ is the reverse saturation current at a temperature T₁ (T₂).
• I₀ doubles for every 10°C rise in temperature. That is, it increases 7% / °C.
• I₀ is in the range of microamperes for a germanium diode andTVano amperes for a silicon diode.
• Since n = 2 for small currents in silicon, the current increases as e^v/2vT for the first several tenths of a volt and increases as e^v/vT only at higher voltages.

The Volt-Ampere Characteristic

For a p-n junction, the current I is related to the voltage V by the equation
I = I₀(e^v/ηvT -1) ....(13)
η ≅ 1 for Ge
η ≅ 2 for Si
V_T = T/11,600 = 26 m V at T = 300°K.
At room temperature,

(a) When the voltage V is positive and several times V_T , the unity in the parenthesis of equation (13) may be neglected, i.e., e^v/ηvT >>1,
∴ l = l₀ e^v/ηv T
Accordingly except for a small range in the neighborhood of the origin, the current increases exponentially with voltage.

(b) When the diode is reverse-biased and |V| is several times VT, I ≈ - I₀. The “reverse

current” is therefore constant, independent of the applied reverse bias. Consequently, I₀ is referred to as the “reverse saturation current”
At a reverse biasing voltage V_z, the diode characteristic exhibits an abrupt and marked departure from (13). At this critical voltage a large reverse current flows, and the diode is said to be in the “break down region”.

The volt-ampere characteristic for a germanium diode

The Cutin Voltage, Offset, break-point, or threshold voltage (V_y):
Below V_y the current is very small (say, less than 1 per cent of max. rated voltage).
Beyond V_y the current rises very rapidly. V_y = 0.2 V for Ge, 0.6 V for Si.
The reverse saturation current 10 in a Ge is normally larger by a factor of about 1000 than the 10 in a silicon diode of comparable ratings. Since n = 2 for small currents in Si, the 1 increases as e^V/2VT only at higher voltages.
The resistance R, cutin voltage Vy, power dissipation and noise margin of Germanium is less— than the silicon. But Germanium is not used in switching characteristics.
The temperature dependence of p-n diode characteristics:
The dependence of 10 on temperature T is given approximately by
I₀ = kT^m e^-v Go^/ηvT
Where k is a constant and qV_GO (q is the magnitude of the electron charge) is the forbidden gap energy in Joules:
For Ge : n = 1 m = 2 V_GO = 0.785V
For Si: n = 2    m = 1.5 V_{GO =} 1.21V
Taking the derivative of the logarithm of above equation, we find

At room temperature, d(l_nl₀)/dT = 0.08 /°C for Silicon and 0.11 / °C for Germanium.

The 10 increases approximately 7 percent / °C for both Si and Ge. Since (1.07)10 ≈ 2.0, we conclude that the “reverse saturation current(Io)” approximately doubles for every 10°C rise in temperature.
Consider a diode operating at room temperature (300°K) and just beyond the V_y.
Then we find,

Since these data are based on “average characteristics”, it might be well for conservative design to assume a value of

dV / dT = -2.5 mV/°C ....(14)
for either Ge or Si at room temperature.
For Germanium, an increase in temperature from room temperature (25°C) to 90°C increases the 10 to hundreds of microamperes, although in Silicon at 100°C the 10 has increased only to some tenths of a micro ampere.