Semiconductor Lasers
Comparison with LEDs
The light emitted by a laser is generally more directional, more intense and has a
narrower frequency distribution than light from an LED. The external efficiency of
a laser is much greater than that of an LED. Light emitted from a laser is
coherent.
Light power output (P)
External (differential) quantum efficiency
Number of additional photons emitted / number
of additional electrons injected
LED-like
Laser-like
e ⎛ ΔP ⎞
⎜
⎟
hν ⎝ ΔI ⎠
Current applied to device (I)
LASER – Light Amplification by the Stimulated Emission of Radiation
→ Need to understand the physics of stimulated emission
Consider a system with two electronic levels (1 and 2). There are 3 possible
electron-photon processes
2
Absorption – a photon of energy E excites an electron
photon
E
from level 1 to level 2. The photon is destroyed.
1
Spontaneous emission – An electron in level 2 relaxes
2
photon
1
2
1
to level 1. A photon of energy E is created. The relaxation is
a random process – the created photon has a random phase
and is emitted in a random direction.
Stimulated emission – An electron in level 2 is
stimulated into relaxing to level 1 by a passing photon. The
new photon has the same phase, energy and direction as the
original photon.
Absorption causes a beam of light (stream of photons) to be attenuated as it
passes through a material.
Stimulated emission causes a beam of light to be amplified as it passes through a
material.
Intensity (I)
Intensity (I)
Absorption
Distance (x)
Stimulated
emission
Distance (x)
In a real system a mixture of absorption and stimulated emission will occur
(spontaneous emission can be ignored once stimulated emission becomes
important as electrons will relax by stimulated emission before they have time
to relax spontaneously).
For laser action to occur, overall amplification is required
i.e. STIMULATED EMISSION > ABSORPTION
If there are n1 electrons in level 1 and n2 electrons in level 2:
Strength of absorption = Aabsn1
Strength of stimulated emission = Astimn2
(can be shown that Aabs=Astim)
Therefore laser action requires n2 > n1
Population Inversion
For thermal equilibrium
E
−
n2
kT
= e <1
n1
Hence n2 > n1 (a population inversion) is only possible under non-equilibrium
conditions
In a semiconductor a population inversion can be obtained if there are a large
number of occupied states (electrons) in the conduction band and unoccupied
states (holes) in the valence band.
electrons
holes
Such a condition is not easily obtained in a bulk
semiconductor but can be created and maintained
in a forward biased p-n junction:
p-type
A large density of electrons (holes)
are injected into the p-type (n-type)
material to create the population
inversion
n-type
Laser construction
Require a material in which a population inversion is maintained (this requires
constant energy input).
Generally require a very long optical path length through material for sufficient
amplification. Hence place material between 2 mirrors so that the light can keep
passing through the material:
Lasing material
High refl.
mirror
Partially reflecting mirror
allows some light to escape
from the cavity
Energy in to maintain
population inversion
Semiconductor laser:
Current flow
Coherent radiation
Optically flat
parallel faces
Variation of gain with carrier density and current
cb
vb
Low current and carrier density (n)
Absorption > stimulated emission
High current and carrier density (n)
Absorption < stimulated emission
LOSS
GAIN
g
nth (Ith)
n (or I)
ntrans (Itrans)
Point at which line passes through zero (g=0)
is known as TRANSPARENCY
- Gain balances absorption
- Light travelling along the cavity is
neither absorbed or amplified
Lasing does not occur at transparency. A positive non-zero gain is
required to overcome losses in the system. Lasing occurs at g=gth
where gth is the threshold gain (occurs when I=Ith, n=nth)
As light travels along the cavity it is amplified by the active region at a rate g per
unit length.
However, there will be some losses due to imperfections in the material, which
scatter the light, and also by absorption of the part of the light field which extends
beyond the active region. We describe these losses by α. Hence the
amplification per unit length is (g-α)
When light hits an end mirror only a fraction R, where R is the mirror reflectivity, is
reflected back into the cavity – the remainder escapes
After passing along a cavity of length L, the light is amplified by e(g−α )L
But only a fraction R is returned to the cavity. Hence, if the initial light intensity is
I0 after traversing one cavity length and hitting one mirror, the new intensity is
I1 = I0e(g−α )LR
Three cases ….
e(g−α )LR < 1
1. I1 < I0
L
L
L
I0
TOTAL LOSSES EXCEED GAIN → NO LASING
e(g−α )LR > 1
2. I1 > I0
L
L
L
I0
GAIN EXCEEDS TOTAL LOSS →
LIGHT LEVEL INCREASES INDEFINITELY
PHYSICALLY IMPOSSIBLE
e(g−α )LR = 1
3. I1 = I0
L
L
L
I0
GAIN EQUALS TOTAL LOSS → CONDITION FOR LASING TO OCCUR
Lasing condition:
e(g−α )LR = 1
∴
⇒
(g − α )L = ln⎛⎜ 1 ⎞⎟
⎝R⎠
1 ⎛1⎞
gth = α + ln⎜ ⎟
L ⎝R ⎠
gth is the gain required to achieve lasing. Known as the threshold gain.
Result shows that gth increases as cavity length decreases.
What happens to the carrier density at and above threshold?
At threshold, carrier density is just sufficient so that the resultant gain equals
all losses and lasing starts (g=gth)
If the carrier density increased as current increased further then gain would
increase above gth (case 2 above) – this is physically impossible
The gain of a laser can never exceed gth. This implies that the carrier
density can never exceed the threshold value nth.
Above threshold, both g and n are clamped (or saturate) to their threshold
values gth and nth:
nth
n
gth
g
n or g
Ith
I
Water analogy
I/eV
Ggen =
Current
leakage
ηiI
eV
Overflow Rst
nth
RL
Rnr
Rsp
Water level has reached the overflow and the depth of water (and hence escape
processes) is clamped to a value nth. Overflow provides an infinitely large
escape path. All additional water added to the tank leaves via the overflow.
Real Device
• At threshold n and g clamp to their threshold values
• Because carrier loss processes (spontaneous emission, leakage, non-radiative
recombination) have rates which are a function of n these processes must also
clamp / saturate at threshold
• Therefore, above threshold carrier loss mechanisms no longer increase
• Stimulated emission is the only process which can continue to increase
• All additional carriers injected into the active region must produce a photon by
stimulated emission.
External efficiency above threshold
Above threshold loss mechanisms are clamped to their threshold values
Above threshold additional carriers injected into the active region result in
photons produced by stimulated emission