Ley de Distribución de Maxwell-Boltzmann.

𝑛𝑖 = 𝑁

𝑍𝑔𝑖𝑒−𝛽𝐸𝑖

Ley de Distribución de Fermi-Dirac.

𝑛𝑖 =𝑔𝑖

𝑒(𝐸𝑖−𝜖𝑓)/𝑘𝑇 + 1

Ley de distribución de Bose-Einstein

𝑛𝑖 =𝑔𝑖

𝑒𝛼+𝐸𝑖/𝑘𝑇 − 1

Nivel de Fermi

𝐹𝐷 = 1

𝑒𝐸−𝐸𝑓

𝐾𝑇+1

𝐹𝐷 = 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑑𝑎𝑑 𝑑𝑒 𝑞𝑢𝑒 𝑢𝑛 𝑛𝑖𝑣𝑒𝑙 𝑑𝑒 𝑒𝑛𝑒𝑟𝑔𝑖𝑎 𝑠𝑒𝑎 𝑜𝑐𝑢𝑝𝑎𝑑𝑜 𝑝𝑜𝑟 𝑢𝑛 𝑒𝑙𝑒𝑐𝑡𝑟ó𝑛

𝐸 = 𝐸𝑛𝑒𝑟𝑔𝑖𝑎 (𝑝𝑎𝑟𝑎 𝑢𝑛 𝑛𝑖𝑣𝑒𝑙)

𝐸𝑓 = 𝐸𝑛𝑒𝑟𝑔𝑖𝑎 𝑑𝑒 𝐹𝑒𝑟𝑚𝑖

𝐾 = 8.6𝑥10−5 𝑒𝑉𝐾⁄ = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑑𝑒 𝑑𝑒 𝐵𝑜𝑙𝑡𝑧𝑚𝑎𝑛

𝑇 = 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑎

𝐸𝑓 = (ℎ𝑐)2

32𝑚𝑐2 (

𝑁

𝐿)

2

𝐸𝑓 = 𝐸𝑛𝑒𝑟𝑔𝑖𝑎 𝐹𝑒𝑟𝑚𝑖 (𝑝𝑎𝑟𝑎 𝑢𝑛 𝑝𝑙𝑎𝑛𝑜 𝑢𝑛𝑖𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙)

ℎ = 6.63𝑥10−34 (𝐽𝑠) = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑒 𝑑𝑒 𝑃𝑙𝑎𝑛𝑐𝑘

𝑐 = 3𝑥108𝑚

𝑠= 𝑣𝑒𝑙𝑜𝑐𝑖𝑑𝑎𝑑 𝑑𝑒 𝑙𝑎 𝑙𝑢𝑧

𝑁

𝐿= 𝐷𝑒𝑛𝑠𝑖𝑑𝑎𝑑 𝑑𝑒 𝑢𝑛 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝐸𝑓 = (ℎ𝑐)2

8𝑚𝑐2 (

3

𝜋 𝑁

𝑉)

2/3

𝐸𝑓 = 𝐸𝑛𝑒𝑟𝑔𝑖𝑎 𝐹𝑒𝑟𝑚𝑖 (𝑝𝑎𝑟𝑎 𝑢𝑛 𝑝𝑙𝑎𝑛𝑜 𝑡𝑟𝑖𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙)

ℎ = 6.63𝑥10−34 (𝐽𝑠) = 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑒 𝑑𝑒 𝑃𝑙𝑎𝑛𝑐𝑘

𝑐 = 3𝑥108𝑚

𝑠= 𝑣𝑒𝑙𝑜𝑐𝑖𝑑𝑎𝑑 𝑑𝑒 𝑙𝑎 𝑙𝑢𝑧

𝑁

𝑉= 𝐷𝑒𝑛𝑠𝑖𝑑𝑎𝑑 𝑑𝑒 𝑢𝑛 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙

1 Amstrong = 1𝑥10−10 𝑚