’07 7/23 memo
Relation between photoluminescence and
photoluminescence-excitation spectra in the linear response
regime measured on two-dimensional electron gas
T. Ihara, Akiyama group, ISSP
Outline
-
Target of this work
Optical setup and sample structure
Power/Energy dependence of PL and PLE spectra at 30K
Ratio of PL and PLE at Pex = 1.7mW (T = 30K)
PL/PLE at various temperatures (Pex = 16 mW )
PL with resonant/non-resonant excitation at 5K (Pex = 2 mW)
Summary
Target of this work
PLE (photoluminescence-excitation) spectra
: measurement of photoemission as a function of excitation photon energy
-> lineshape of absorption spectra
Using micro-PL technique, we can compare the lineshape of photo-absorption (PLE)
with photoemission (PL) at the same microscopic region of 1mm order.
Any general relation between PL and PLE spectra ?
’96 D. A. Sawicki and R. S. Knox, Phys. Rev. A 54, 4837 (1996).
Kennerd-Stepanov relation
W  
3
 h

 exp  
 DT     
 k BT

’04 S. Chatterjee, C. Ell, S. Mosor, G. Khitrova, and H. M. Gibbs, W. Hoyer, M. Kira, S. W. Koch, J. P.
Prineas, and H. Stolz, Phys. Rev. Lett. 92, 067402 (2004).
Kubo-Martin-Schwinger relation
eq
  
I PL
1
exp   m  / k BT   1
  
Required condition : Linear Response, quasi-equilibrium
PL : emission
PLE : absorption
Weak excitation power
  
PL

 exp  
PLE
 k BT 
!?
Optical setup and sample structure
PL and PLE measurement in a backscattering geometry.
Detect PL polarized with perpendicular to the polarization of excitation laser
2DEG density ( VDP measurement) : 6×1010 cm-2
Power/Energy dependence of PL and PLE spectra at 30K
Lineshape of PL are independent with excitation photon energy at Pex = 1.7 mW.
Lineshape of PL and PLE are independent with excitation power at Pex < 80 mW.
Our measurements at Pex < 80 mW are in the Linear Response regime.
Ratio of PL and PLE at Pex = 1.7mW (T = 30K)
Exponential decay against hv in the whole energy region.
Estimated temperature (T* = 30±2 K) agrees with the thermometer (30.8±1K)
-> Photo-excited quasi-equilibrium 2DEG at environmental temperature.
PL/PLE at various temperatures (Pex = 16 mW )
T* agree with the thermometer at various temperature.
  
PL
-> verification of general relation between PL and PLE

 exp  
in the linear response regime for quasi-equilibrium system : PLE
 k BT 
PL with resonant/non-resonant excitation at 5K (Pex = 2 mW)
In the case of resonant excitation, T* (= 6.2±0.3 K) agrees with the thermometer (5.6±1 K).
In the case of non-resonant excitation (+ 6.3 meV), T* (= 7.2±0.5 K) is higher than the thermometer
(5.6±1 K) and additional non-equilibrium component appears at higher energy side (ML fluctuation).
Summary
Low-temperature photoluminescence and photoluminescence-excitation spectra
of two-dimensional electron gas are measured at low-excitation power in the
linear response regime.
We found that the ratio between PL and PLE is proportional to exp(-hv/kT), where
T agrees with environmental temperature.
This should be the first verification of the general relation between photo-emission
and absorption in the linear response regime, or Kubo-Martine-Schwinger relation,
which is an exact solution under quasi-equilibrium condition.