In a tunnel diode, the degeneracy on the n-side can be expressed as
\(\dfrac{kT}{q}\left[\ln\left(\dfrac{N_D}{N_C}\right)+0.35\left(\dfrac{N_D}{N_C}\right)\right]\)
What "degeneracy" means here. A tunnel diode is made by doping both sides so heavily (1019–1020 cm−3) that the Fermi level moves into the bands — into the conduction band on the n-side and into the valence band on the p-side. The degeneracy is the amount by which the Fermi level penetrates, measured in volts:
\(V_n=\dfrac{E_F-E_C}{q}\)
Why the simple Boltzmann formula is not enough. For a lightly doped (non-degenerate) semiconductor,
\(E_F-E_C=kT\ln\!\left(\dfrac{N_D}{N_C}\right)\)
This is negative while \(N_D \lt N_C\) (the Fermi level lies below the band edge) and only turns positive once the doping approaches the effective density of states NC. But at such high doping the carriers obey Fermi–Dirac rather than Boltzmann statistics, so a correction term is added:
\(V_n=\dfrac{kT}{q}\left[\ln\!\left(\dfrac{N_D}{N_C}\right)+0.35\left(\dfrac{N_D}{N_C}\right)\right]\)
The constant 0.35 is the Joyce–Dixon coefficient \(1/\sqrt{8}=0.3536\), the leading term of the series that corrects the Boltzmann approximation as degeneracy sets in.
How to pick the right option without recalling the constant. Two structural checks do it:
The ratio must be ND/NC. Degeneracy grows with donor concentration, so ND belongs on top — that eliminates options 3 and 4.
The correction must be additive. Fermi–Dirac statistics place the Fermi level higher than Boltzmann predicts at high doping, so the correction adds — eliminating option 2.
Why this matters for the device. Both sides being degenerate is what puts filled states on one side directly opposite empty states at the same energy on the other, across a depletion layer only ~10 nm wide. That is what permits tunnelling at low forward bias and produces the negative-resistance region used in high-frequency oscillators.
Hence, the degeneracy on the n-side is \(\dfrac{kT}{q}\left[\ln\left(\dfrac{N_D}{N_C}\right)+0.35\left(\dfrac{N_D}{N_C}\right)\right]\).
Similar Questions
A PIN diode can not be used as
i. Microwave switch
ii. Microwave mixer
iii. Microwave detectorWhich is correct ?
________ diode is not used as a microwave mixer or detector.
Match the given lists :
List – I (Name of the Device) List – II (Application) a. Diode i. Rectification b. Tunnel diode ii. Microwave switching c. Zener diode iii. An oscillator d. PIN diode iv. Voltage regulation Codes :
Varacter diodes have the following properties :
A. Junction capacitance varies with bias voltage
B. Junction capacitance varies with time
C. Non linearity of varacter diodes makes them suitable for frequency multipliers
D. Linearity of varactor diode makes them suitable for frequency multipliers.
Choose the correct answer from the options given below:
The static current voltage characteristics of a tunnel diode consist of
(a) Tunneling current and thermal current
(b) Thermal current and excess current
(c) Tunneling current only
(d) Tunneling current, excess current and thermal current
Out of these which are correct ?
Match the following :
List – I List – II a. Gunn diode i. degenerate silicon b. Tunnel diode ii. n-type Ga As c. BJT iii. Silicon d. Diode (P-N junction) iv. \(I_o\left[\exp\left(\dfrac{qV}{kT}\right)-1\right]\) Choose the correct answer from the codes given below:
A TRAPATT diode has the doping concentration NA = 2 x 1015/cm3 and a current density of 20 kA/cm2. The value of avalanche zone velocity is given by :
Assertion (A) : The Gunn diode characteristics shows the region of negative resistance.
Reason (R) : The Gunn diode is made of n-type and p-type degenerate semiconductor.
Select your answer using the codes given below.
Which of the following statements are correct for Tunnel Diode ?
(a) 1 impurity atom in 103 atoms
(b) Very high doping in both p and n regions
(c) 1 impurity atom in 108 atoms
(d) used as a voltage controlled devices
Out of the above, the following is the correct answer :
Which of the following statements are true for a zener diode ?
(a) The voltage across the zener resistance is zero.
(b) The diode is used as a constant voltage device.
(c) The diode is used as a varactor diode.
(d) The diode is formed of heavily doped p and n-type semiconductor.
Options :
Important Questions from Types of Diode
A PIN diode can not be used as
i. Microwave switch
ii. Microwave mixer
iii. Microwave detectorWhich is correct ?
________ diode is not used as a microwave mixer or detector.
Match the given lists :
List – I (Name of the Device) List – II (Application) a. Diode i. Rectification b. Tunnel diode ii. Microwave switching c. Zener diode iii. An oscillator d. PIN diode iv. Voltage regulation Codes :
Varacter diodes have the following properties :
A. Junction capacitance varies with bias voltage
B. Junction capacitance varies with time
C. Non linearity of varacter diodes makes them suitable for frequency multipliers
D. Linearity of varactor diode makes them suitable for frequency multipliers.
Choose the correct answer from the options given below:
The static current voltage characteristics of a tunnel diode consist of
(a) Tunneling current and thermal current
(b) Thermal current and excess current
(c) Tunneling current only
(d) Tunneling current, excess current and thermal current
Out of these which are correct ?
