Band Diagram of a P-N Junction PVMD Miro Zeman Delft University of Technology
Learning objectives ▪ What does the band diagram of P-N junction at thermal equilibrium look like ? ▪ How thick is the depletion region?
Band diagram of isolated Si materials E C E C E F E F E V E V p -type n -type p = p p0 ≈ N A n = n n0 ≈ N D n = n p0 ≈ n 2 p = p n0 ≈ n 2 i /N A i /N D
Forming the band diagram E C E C E F E F E V E V p -type n -type
Forming the band diagram diffusion E C E C E F E F E V E V p -type n -type
Forming the band diagram diffusion drift E C E C E F E F E V E V p -type n -type
Thermal equilibrium Potential energy of water level ~ Fermi level
Band diagram diffusion drift p -type n -type E C E C E F E V E V Quasi-neutral region Depletion Quasi-neutral region region
Built-in voltage p -type n -type q V bi E C E G E Fn E Fp E F E V Built-in voltage V bi
Charge density in the depletion region p -type n -type ρ q N D l p l n x =0 x q N A p -type: n -type:
Electric field in the depletion region ψ: electrostatic potential ξ : the electric field Poisson’s equation: ϵ r : relative permittivity ϵ 0 : the permittivity of free space Electric field : p- type n- type ξ x =0 x l p l n ξ max
Potential across the depletion region p -type n -type ψ V bi l p l n x =0 x
Thickness of the depletion region
Learning objectives ▪ The band diagram of P-N junction at thermal equilibrium ▪ How thick is the depletion region?
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