7.7 Deep Levels
213
(a)
(b)
Fig. 7.35 a Population of states of a negative-U defect (neutral: black, single ionized: red, double ionized: blue)
according to (7.64a–c) as a function of the Fermi level. The ionization energies have been chosen as E 1 = −0.4 eV
and E 2 = −0.2 eV (cmp. Fig. 7.30) and are indicated by dashed lines (kT = 25 meV). The occupancy level E(0, 2) is
indicated with a dash-dotted line. The conduction band edge is taken as zero energy. b depicts the according number of
electrons ionized from the defect
c(V
++
)
c(V 0 )
= exp
E(1, 2) + E(0, 1) − 2E F
kT
= e
2 exp
E(0, 2) − E F
kT
.
(7.72)
The occupancy level E(0, 2) is thus again given as
E(0, 2) =
E(0, 1) + E(1, 2)
2
,
(7.73)
and is shown in Fig. 7.33. V
++ dominates if E F < E(0, 2) and V
0 dominates for E F > E(0, 2).
V
+ is, for no position of the Fermi level, the dominating charge state of the Si vacancy. We note that
for n-doped Si the V
− and V
−− can also be populated. The population of the V
0 state with an extra
electron introduces another Jahn–Teller splitting (Fig. 7.34) that has trigonal symmetry.
Generally, the Jahn–Teller effect can make the addition of an electron cause an effectively negative
charging energy; in this case the center is termed a negative-U center. We note that the single vacancy in
germanium is not a negative-U center due to smaller Jahn–Teller distortion and smaller electron-lattice
coupling [668].
7.7.6 DX Center
The DX center is a deep level that was first investigated for n-doped (e.g. Si-doped) Al x Ga 1−x As. It
dominates the transport properties of the alloy for x > 0.22. For smaller Al concentrations and GaAs
the DX level lies in the conduction band. DX-type deep levels have also been found for other alloys
and dopants, e.g. GaAsP:S.
It is experimentally found that the capture process of electrons into the DX center is thermally
activated. The capture energy E c depends on the AlAs mole fraction (Fig. 7.36). The (average) barrier
for electron capture has a minimum of 0.21 eV for x ≈ 0.35, near the crossover point between direct
and indirect band gap (cf. Fig. 6.24). For lower Al concentrations, the capture barrier increases to 0.4 eV
for x = 0.27; for x > 0.35 the capture barrier increases to about 0.3 eV for x around 0.7 [669]. The
barrier for thermally releasing carriers from the DX center has been determined to be about 0.43 eV,
independent of the Al mole fraction [669].
213
(a)
(b)
Fig. 7.35 a Population of states of a negative-U defect (neutral: black, single ionized: red, double ionized: blue)
according to (7.64a–c) as a function of the Fermi level. The ionization energies have been chosen as E 1 = −0.4 eV
and E 2 = −0.2 eV (cmp. Fig. 7.30) and are indicated by dashed lines (kT = 25 meV). The occupancy level E(0, 2) is
indicated with a dash-dotted line. The conduction band edge is taken as zero energy. b depicts the according number of
electrons ionized from the defect
c(V
++
)
c(V 0 )
= exp
E(1, 2) + E(0, 1) − 2E F
kT
= e
2 exp
E(0, 2) − E F
kT
.
(7.72)
The occupancy level E(0, 2) is thus again given as
E(0, 2) =
E(0, 1) + E(1, 2)
2
,
(7.73)
and is shown in Fig. 7.33. V
++ dominates if E F < E(0, 2) and V
0 dominates for E F > E(0, 2).
V
+ is, for no position of the Fermi level, the dominating charge state of the Si vacancy. We note that
for n-doped Si the V
− and V
−− can also be populated. The population of the V
0 state with an extra
electron introduces another Jahn–Teller splitting (Fig. 7.34) that has trigonal symmetry.
Generally, the Jahn–Teller effect can make the addition of an electron cause an effectively negative
charging energy; in this case the center is termed a negative-U center. We note that the single vacancy in
germanium is not a negative-U center due to smaller Jahn–Teller distortion and smaller electron-lattice
coupling [668].
7.7.6 DX Center
The DX center is a deep level that was first investigated for n-doped (e.g. Si-doped) Al x Ga 1−x As. It
dominates the transport properties of the alloy for x > 0.22. For smaller Al concentrations and GaAs
the DX level lies in the conduction band. DX-type deep levels have also been found for other alloys
and dopants, e.g. GaAsP:S.
It is experimentally found that the capture process of electrons into the DX center is thermally
activated. The capture energy E c depends on the AlAs mole fraction (Fig. 7.36). The (average) barrier
for electron capture has a minimum of 0.21 eV for x ≈ 0.35, near the crossover point between direct
and indirect band gap (cf. Fig. 6.24). For lower Al concentrations, the capture barrier increases to 0.4 eV
for x = 0.27; for x > 0.35 the capture barrier increases to about 0.3 eV for x around 0.7 [669]. The
barrier for thermally releasing carriers from the DX center has been determined to be about 0.43 eV,
independent of the Al mole fraction [669].