Strain-Induced Piezoelectric Field in a Quantum Dot

Dot Composition & Geometry

Indium fraction x (In_xGa_1-xN) 0.25

Dot height h (growth axis) 3.0 nm

Dot base radius r 5.0 nm

Live Readouts

Biaxial strain ε_xx

0.00%

Piezo field F_pz

0.0 MV/cm

e–h separation Δz

0.00 nm

QCSE redshift ΔE

0.0 meV

How it works

An In_xGa_1-xN quantum dot grown pseudomorphically on GaN has a larger relaxed lattice constant than its barrier, so it is compressed elastically to match GaN in-plane. This biaxial strain, in a wurtzite crystal lacking inversion symmetry, produces a piezoelectric polarization along the c-axis:

a(x)   = a_GaN + x(a_InN – a_GaN)        [relaxed dot lattice constant]
ε_xx   = (a_GaN – a(x)) / a(x)            [in-plane strain, compressive < 0]
P_pz   = 2 ε_xx ( e31 – e33 · C13/C33 )    [piezoelectric polarization, C/m²]
F_pz   = – P_pz / (ε0 εr)                   [internal field along c-axis]

e31, e33 are the piezoelectric coefficients and C13, C33 the elastic stiffness constants, both alloy-interpolated between GaN and InN end-point values. The field tilts the electron and hole confinement potentials in opposite directions — the quantum-confined Stark effect — pulling the electron and hole wavefunctions toward opposite faces of the dot:

Δz  ≈  h · tanh(κ F_pz h)          [charge separation, saturates near h]
ΔE  ≈  e F_pz Δz                    [emission redshift vs. unstrained dot]

Indium fraction — sets the lattice mismatch and interpolates the piezoelectric/elastic constants toward InN; higher x means larger strain and a stronger internal field.
Dot height — the field acts over this distance, so ΔE and Δz grow roughly with h even at fixed field strength.
Dot radius — sets the lateral size of the confining potential (shown for geometric reference; the polarization charge density scales with lateral area).
Field & charge overlay — toggles the sheet-charge markers (+σ top / −σ bottom, from the discontinuity in polarization at the dot–barrier interface) and the internal field arrows that separate the blue electron cloud from the red hole cloud.

This is the mechanism behind the well-known redshift and reduced oscillator strength of InGaN/GaN self-assembled quantum dots and quantum wells relative to non-polar or cubic growth directions — a real limitation LED and laser designers work around by using thin dots or non-polar substrates.

Electron cloud Hole cloud Internal field F_pz

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