We disagree with the exclusion of Newton's laws, Ohm's law and the energy conservation law from physics of primary schools in the Czech Republic!

Voltampere LED characterization
(approximate determination of Planck's constant)


Electroluminescent diode (LED)

source: File:Diodos_LED_foto.png

Light-emitting diodes are semiconductor lasers in addition to the basic optoelectronic light source. Features luminescent diodes (LED = Light Emitting Diode) is based on electroluminescent phenomenon, which we understand the emission of a photon in the field of semiconductor PN junction, through which the stream. By applying an external voltage on the PN junction in the forward direction occurs because the injection (injection) minority carrier current to conductive areas. Part P of the electrons and holes in the area of the bright N recombines with majority carriers and the energy released by emission of light occurs. This is also called just called injection electroluminescence.

The band spectrum of radiation diode is dependent on the chemical composition of the semiconductor. LEDs are made with bands from ultraviolet radiation, various colors of visible spectrum to the infrared band. Since the radiant recombination of an electron returns from belt to belt vodivostného valence, the energy quanta emitted light near the band gap width Eg.

Features of the luminescent diodes

Volt-ampere characteristics

Properties of Light-emitting diodes as components of electrical circuits voltampere describe their characteristics. For all luminescent diodes typically have diode waveform (see Figure 1).

V-A charakteristika

Fig. 1 - voltage characteristic red (RED) and yellow (YELLOW) electroluminescent diodes

oltampere characteristics in the forward direction, it can be quite difficult to express the analytical formula:

IF = I0 ·{ e
(  e·[UF – RS·IF )

 – 1}
that:  IF  [A]  - PN junction current flowing     RS  [Ω]  - diode series resistance
I0  [A]  - residual current     T  [K]  - Absolute temperature
e  [C]  - electron charge     n - see below
UF  [V]  - voltage on the diode     k  [J·K–1 - Boltzmann constant; k = 1,38.10–23 J·K–1

However, if the e.UF ≥ 4 k.T (ie if it is at room temperature for UF ≥ 100 mV) while UF >> IF.RS, simplify this equation to the shape:

IF = I0 · e
(  e·UF  )



Shape characteristics depends on the geometry and properties of transition, the characteristic of the material, manufacturing technology, etc. All these factors are included in the dimensionless constants n. The reciprocal value of n defines the constant α = 1/n, which characterizes the mechanism of charge transport transition (diffusion, recombination, tunneling).

Serial static and dynamic resistance

As with any other semiconductor diodes can also define the static serial resistance (working point UFo, IFo) as:

Rd =   UFo 



and serial dynamic (differential) resistance, which is defined by:

Rdi = (  dUFo  )

dIFo IFo= konst.


Static resistance is the order of 10 to 100 Ω, the dynamic resistance is < 1 Ω.

The threshold voltage

Another parameter is the threshold voltage U*, this stress is extrapolated from the linear part of the VA characteristics (red in Figure 1). When this voltage is linearized to break in the dependence of current flowing in the diode voltage is applied to the LED. This threshold voltage is dependent on the material from which the luminescent diodes made and is close to diffuse voltage Ud,thus the width of the band gap Eg/e. The reason for this is that it provides a voltage U* - roughly speaking - carriers of current energy necessary to overcome potential barriers e.Ud. The diodes of GaAs (Eg ≈ 1,4 eV) is the threshold voltage U* of about 1,4 V; of GaAsxP1-x (Eg ≈ 1,4 - 2,4 eV according to the composition) is U* = (1,4 - 2,3) V, the diodes of GaP (Eg ≈ 2,3 eV) is U* = 2,4 V.

The wavelength of light emitted

A similar relationship is also between the threshold voltage and the radiated frequency (wavelength) of emitted light. Shortening the wavelength of light emitted by the growing size of the required power and the resulting voltage. While the classical (lightless) silicon diode rectifying this voltage is about 0.6 V, the green LEDs of GaP 1,7 V and a blue LED from SiC even as early as 2,5 V.

Considering that the energy released during recombination is converted into energy of the emitted photon, we can write:

e·U* = h·f = h ·   c 



that:  e  [C]  - electron charge     λ  [m]  - wavelength of the emitted photon
U*  [V]  - threshold voltage     c  [m.s–1 - speed of light; c = 3.108 m.s–1
f  [Hz]  - frequency of the emitted photon     h  [J.s]  - Planck's constant; h = 6,625.10–34 J.s

 Color  λ / nm 
 red   656 - 768 
 yellow   568 - 585 
 green   495 - 535 
 blue   452 - 485 
Tab. 1 - wavelengths of LEDs colors

Usually, knowledge of threshold voltage U* determines the wavelength of the emitted radiation, which is compared with tabular values. Relationship (4) may be used both ways in order of magnitude estimates for the Planck constant. Knowing the threshold voltage and the approximate wavelength (see Table 1.) Can be expressed by Planck's constant:

 h =   e·U*·λ