magnesium acceptor states in gan n.
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Magnesium acceptor states in GaN . Daniel Wolverson, Department of Physics, University of Bath. Peter Parbrook Tao Wang. John Davies Shanshan Zeng Stephen Bingham Gazi Aliev Lowenna Glover Wang N Wang Sergei Stepanov. supported by EPSRC , Royal Society, Arima UK, Universities UK.

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magnesium acceptor states in gan

Magnesium acceptor states in GaN

Daniel Wolverson, Department of Physics, University of Bath

Peter Parbrook

Tao Wang

John Davies

Shanshan Zeng

Stephen Bingham

Gazi Aliev

Lowenna Glover

Wang N Wang

Sergei Stepanov

supported by EPSRC, Royal Society,

Arima UK, Universities UK

the problem
The problem
  • Doping of GaN with Mg produces a range of acceptor states
  • These include relatively “shallow” acceptor states (150 meV) but also a whole range of much deeper acceptor states
  • What are these states? Are they formed by a whole range of different centres? How do the growth methods and conditions affect their production?
  • One good way to identify different types of acceptor centre is by magneto(optical) spectroscopies:
    • Zeeman spectroscopy
    • Electron Spin Resonance
    • optically-detected magnetic resonance (ODMR)
optical detection of magnetic resonance
Optical detection of magnetic resonance




subject to spin

selection rules




PL intensity monitored

Magnetic resonance changes the spin distribution in excited states, and hence changes the PL intensity

Ground state

schematic odmr system



Microwave switch




Function generator





Superconducting magnet







Schematic ODMR system
donor acceptor recombination
Donor acceptor recombination



spin selection rules imply

weak photoluminescence



dap recombination and odmr
DAP recombination and ODMR

Apply microwave radiation:

When magnetic resonance occurs in either the donor or the acceptor, the PL intensity increases.

Simplest case: one electron





the g values
The g-values
  • g-value depends on the nature of the state in which the electron or hole is localised.
  • If spin-orbit coupling is neglected, the ground state will be an orbital singlet L=0, for which there is no orbital contribution to the g-value, which is therefore 2.00
  • However, spin-orbit coupling mixes excited states into the ground state, causing g-shifts
  • Usually, g-shifts are negative for electrons,positive for holes
  • The g-values are often anisotropic and reflect the local symmetry
odmr from gan mg annealed1
ODMR from GaN:Mg (annealed)


Left-hand band moves as the field direction is changed


dependence of acceptor g values on detection wavelength
Dependence of acceptor g-values on detection wavelength

For the acceptors, g|| depends on the recombination energy, i.e, on the acceptor depth


g values for mg related acceptors
g-values for Mg-related acceptors
  • We find g||~2.04 to 2.10 and g =2.00. Note:
  • (i) g|| > g
  • (ii) g||shifts with detection wavelength and therefore with the acceptor depth
  • For shallow acceptors, expect:
  • g|| > 2.00 and g = 0
  • Closeness of both g-values to 2.00 therefore confirms we are seeing well-localised holes: deep acceptors.
first approach to the g values
First approach to the g-values
  • Let the hole occupy a pz-like orbit on the magnesium or adjacent nitrogen atom

To a first approximation, perturbation theory gives:



px,, py

D is the crystal field; l is the spin-orbit coupling constant for the hole and is negative

This gives g|| < g , which is wrong.

reverse the crystal field
Reverse the crystal field?

The hole now lies in the

orbitally-degenerate px, py states

px,, py



In practice, the orbital degeneracy will be removed

first by the spin-orbit coupling l

then by the effect of any low symmetry fields U

effects of spin orbit coupling and of low symmetry crystal fields
Effects of spin-orbit coupling and oflow symmetry crystal fields

low symmetry crystal field U

spin-orbit coupling l

We find the g-values are very sensitive to the ratio U/l


Now have g// > g

  • Have a dependence of
  • g// on acceptor depth:


where U is the splitting due to the low symmetry crystal field introduced by strain or nearby defects and aU is the accompanying change in the c-axis crystal field. We find a= 3.5


  • Note also that for small U, g tends to zero

The Mg acceptor state is first split by the wurtzite crystal field, such that an orbital doublet lies energetically lowest.The perturbation due to nearby defects or to strain splits and shifts this doublet

Large perturbation: large U, PL energy lower, g-values approach 2.00

Small perturbation: U tends to zero, acceptor is shallow, PL energy approaches the bandgap, g approaches zero

  • Model is consistent with all the observed magneto-optical data for acceptors in GaN
  • Implies that the acceptor depth is extremely sensitive to the presence of other defects or to strain and is therefore not well-defined
  • Hence shallow acceptor formation requires good material quality