The radiative recombination of free excitons in diamond has been previously re- ported by Dean et al. /l/. They showed that the valence band splitting due to.
Short Notes
phys. stat. sol. (b) 96, K61 (1979) Subject classification: 13.5.1 and 20.3; 22.1 Laboratoire de Physique des Solides, associe au C . N. R. S., I. N. S. A . , D6partement de Physique, Toulousel) Luminescence Line ShaDe of Free Excitons in Natural Diamond BY J. MAZZASCHI, J. BARFUU, M. BROUSSEAU, J . COLLET, andH. MAAREF The radiative recombination of free excitons in diamond has been previously reported by Dean et al. /l/. They showed that the valence band splitting due to spin-orbit interaction must be taken into account for a good understanding of their line shape. Their experiments were performed a t high temperature (T > 77 K) and with a relatively low resolution. In our experiments we used a cathodoluminescence apparatus, working in pulsed mode, described in preceding publications /2, 3/. The main characteristics are briefly recalled: 2
rise time: z < 1 n s for 0 < I < 2 A/cm , 10 n s < 8 < 1000 ns, pulse length 8 : acceleration voltage U: 20 kV < U < 100 kV. We worked generally with the following experimental conditions: 2 I * 1.6 A/cm , U = 50 kV, repetition rate f = 800 Hz. High injection r a t e s can be reached, so that we could observe the free exciton luminescence a t low temperature, down to about 4.2 K. The intensity of this line decreases very quickly below 77 K. We worked with a sample of "natural diamond", type I1 b.
On Fig, 1 is reported the main emission line of free excitons a t 80 K. The maximum is situated a t 5.275 eV, as previously observed by Dean et al. /l/. The width a t half height is much l a r g e r than predicted when the valence band split off by the spin-orbit interaction is neglected.
1) 31077 Toulouse CBdex, France. 6 physica
(+)I
physica status solidi (b) 96
K62
Fig. 1. Comparison of the experimental and theoretical emission line shapes of free excitons in diamond.-.IA(E), --- lB(E - ) Y 0 IA(E) + IB(E - 6 ), experimental
'
-
This line is attributed to the annihilation of one exciton with simultaneous emission of one photon and one optical transverse phonon. The absorption coefficient associated to the creation of excitons in one excitonic band and corresponding to such indirect allowed transitions is 14, 5/ a(hY
)
w
K IDol" t h v
- Eg + Eex + fiwT0'
with 2
1
= 7for 1s excitons. 9f
a is the aohr radius of excitons. X -7 In diamond, the exciton lifetime is of the order of several 10 s, so that the detailed balance principle may be used to obtain the theoretical line shape of the exciton luminescence:
I(hv) = K IiDo12 I/hv
- Eg + Eex +
flw, -,exp(-
hv
-E
-t
Eex + fluTO kT
W e assume an experimental Gaussian broadening of this theoretical line,
due to the lihited resolution of our monochromator. The resulting experimental line is given by /6/ 00
I(hv) = K IDo12
0
sexp
(-
2
-
AE
(x - hv)2)dx
*
AE, the Gaussian width at half height, has been experimentally estimated to 3 meV.
K63
Short Notes Fig. 2. The ratio IA/IB v e r s u s reciprocal temperature
.
Actually, the two valence bands A and B of diamond, weakly split by the spin-orbit 07
0
-
03
02
l/kT (rneV)
interaction, give rise to L
w excitonic ~ bands,
o d which must be simultaneously considered.
These two bands produce two luminescence lines described by /l/, the B line is shifted
by the energy of the spin-orbit splitting 6 with respect to the A line, while the expected intensity ratio of these two lines is
B
gA, gB are the degeneracy of the bands and MA, M
their density of s t a t e s
masses. The best f i t s f o r any temperature between 30 and 200 K are obtained f o r
6
= (7.0
+-
-
O.2)meV and IA/IB = (1.1 + O.l)exp(d/kT)
,
A typical fit of the experimental lines by o u r model is reported on Fig. 1. The agreement is very satisfying o v e r a wide temperature range, as shown by log (I /I ) v e r s u s l / k T re The
rted on Fig. 2.
~at~b,x.",.3~~~/~~~ 3/2
depends only on the effective
m a s s e s and degeneracy factors. The effective m a s s e s are not accurately known in diamond. Taking the values given by Bauch /7/ f o r the valence band and m* = m /1/ f o r the conduction band, the predicted ratio is 1.25, close to o u r c o experimental result. To conclude, we have taken into account the spin-orbit splitting of the \
valence band to analyse the line shape of the free exciton luminescence in diamond We have deduced the energy 6 of the spin-orbit splitting f r o m a) the shift of the two lines resulting from the annihilation of excitons in the two excitonic bands; b) the ratio of the intensities of these two lines.
K6 4
physica status solidi (b) 96
Since the analysis was c a r r i e d out in a l a r g e temperature range we could improve the accuracy of the measurement of the spin-orbit splitting 6 = (7.0+
+- 0.Z)meV.
Compared to previous determinations (Deanetal. /l/: (7 2 1)meV
from luminescence a t 100 K by only a); Bauch /7/: 6 = (6 2 1)meV from cyclotron resonance) the accuracy is improved. References
/1/ P. J. DEAN, E.C. LIGHTOWLERS, and D.R. WIGHT, Phys. Rev. 140, A352 (1965). / 2 / H . MAAREF, J. BARRAU, M. BROUSSEAU, J. COLLET, and
J. MAZZASCHI, Solid State Commun. 22, 593 (1977). /3/ H. MAAREF, J. BARRAU, M. BROUSSEAU, J. COLLET, and J. MAZZA25, 601 (1978). SCHI, Solid State Commun. /4/ R. J. ELLIOTT, Phys. Rev. 102, 1384 (1957). /5/ J.O. DIMMOCK, in: Semiconductors and Semimetals, Vol. 3, Ed. R.K. WIL'LARDSON and A.C. BEER, Academic Press, New York 1967 (p. 270).
/6/ C. BENOIT A LAGUILLAUME andM. VOOS, Solid State Commun. 12, 1257 (1973).
/7/ C. J. BAUCH, Proc. Internat. C.onf. Semicond. Phys.
2, 276 (1963).
(ReceivedOctober 15, 1979)
