Embed Size (px)
Citation preview
Semiconductor Optoelectronic Devices
Cheng Wang
Phone: 20685263 Office: SIST 401E
Part II Semiconductor Lasers
Lecture 13 3
Light emitting diodes
LED and Laser 4
Two solid-state optical sources are currently available, the light-emitting diode (LED)
and the laser diode (LASER stands for light amplification by the stimulated emission
of radiation). LEDs have poor spectral purity and low speed under direct modulation, and are
therefore unsuited to long-haul or high-speed communication systems.
Lasers, on the other hand, have at least one order of magnitude narrower linewidth
than LEDs and, under direct modulation, can reach bit rates in excess of 10 Gbps
(albeit with some deterioration of the spectral purity due to the spurious frequency
modulation or chirp associated with the amplitude modulation). Lasers are therefore
well suited for long-haul and high-speed applications, although indirect modulation
is required to achieve bit rates in excess of 10 Gbps over long distances (e.g., L > 10 km).
LEDs 5
Light-emitting diodes (LEDs) are based on electron–hole (e-h) pair recombination in a forward-
biased pn junction or heterojunction, leading to spontaneous photon emission. Due to the
emission mechanism, the LED output spectrum is comparatively broad (with a total width at
half power of the order of 1.8kBT ≈ 47 meV at ambient temperature), or, in terms of wavelength,
about 50 nm (or 500 Å) with respect to a central wavelength around 1μm. The spectral purity of
LEDs is therefore low with respect to lasers, whose linewidth is at least one order of magnitude
narrower. At the same time, the LED maximum modulation speed is of the order of 100 Mbps,
about two orders of magnitude slower than the laser direct modulation response. From the
standpoint of optical communication systems (operating in the near infrared), the LED is
therefore confined to short-distance, low-speed links. However, a number of important
applications exist for visible and also UV light LEDs, such as displays and lighting (automotive
and domestic). Developments in the latter area have been fostered by GaN-based blue light
LEDs, which have in turn allowed for the development of white-light LED-based sources.
LED structures 6
Homojunction LEDs have low efficiency, because the emitted photons can be absorbed by the substrate and top side materials, since the photon energy is larger than the bandgap.
Heterojunection LEDs have higher efficiency, because the photon can not be absorbed, due to the higher bandgap of cladding layers. Photons emitted toward the substrate can be recovered by through mirrors, thus improving the device efficiency.
LED structures 7
LEDs can be classified into vertical emitting LEDs and edge-emitting LEDs. Vertical emitting LEDs are well suited to coupling with wide-core multimode optical fibers
(50-100 um) due to the large emission area. Edge-emitting LEDs need lateral coupling and alignment with the optical fiber. In comparison
with lasers, LED has no mirrors, so the quality factor is low. However, high injection LEDs can have high gain, and the emitted photonics undergo amplification through stimulated emission. This is called superadiant LED or superluminescent (超发光) LED, which shows an increase in the optical power and also spectral narrowing.
Homojunction LED 8
The homojunction LED is a pn junction where radiative recombination dominates over nonradiative effects.
Assume the LED p side is on the surface, and the n side is on the substrate. Following the Schockley model, the total diode current includes the current contribution from electron injection from the substrate into the surface layer (minority electron current) In0, the current contribution from the hole injection from the top layer into the substrate Ih0, and the current arising from generation and recombination in the space-charge or depletion region IGR.
Since photons emitted in the substrate side are mostly lost by absorption, only In0 is a useful LED current component. The LED injection efficiency is defined as the ratio of the useful current (injected into the surface p side) to the total current.
Thus, the injection efficiency can be maximized by making the doping in the substrate side (ND) larger, ND>>NA.
0 0 0 0D n h GR n hI I I I I I
0 1
1
n
i
D h h A
n n D
I
I D N
D N
D is the diffusivity, tau is the total carrier lifetime, N is the doping density
Homojunction LED 9
Now, consider the optical generation associated with the current component In0, since the photon generation rate coincides with the excess minority carrier (electron) radiative recombination rate in the surface p side.
i D
out r
IP
q
The radiative efficiency is defined as the ratio between the optical power generated by the LED and the optical power the device would generate if recombination were entirely radiative.
, ,
, ,
1/ 1/
1/ 1/ 1/
n r n r
r
n n r n nr
Homojunction LED 10
Photon losses also arise because photons are reflected by the semiconductor-air
interface with power reflection coefficient R. The transmission efficiency is given by
2
1 2
1 2
1 ,t
r r
r r
R
n nR
n n
Finally, the power-current relation of LEDs is given by
D
out t r i
IP
q
Homojunction LEDs 11
sl
The internal efficiency
The external efficiency
The slope efficiency
in r i
ex t r i
t r iq
Some useful efficiency definitions,
For high power level, the linear relation no longer holds, mainly due to the device
heating, and Auger recombination. The power-current relation of LEDs saturates at
high current and power.
Modulation bandwidth 12
( )( )
1
1(0)
1
i
n
j t j tj t
i
n i
n
n
dN I N
dt q
Ie Nej Ne
q
IN
j q
Nj
If the biased LED is modulated by a small-signal current as
0
j tI I Ie
Then, the carrier response is of the form
0
j tN N N e
The rate equation
Modulation bandwidth 13
The modulation transfer function of the carrier is
2 2
10 10
( ) 1( ) 10 log 10log
(0) 1N
NH
N j
Because the optical power is proportional to the photon number, which is
linearly proportional to the carrier number through the spontaneous
emission process, then the modulation transfer function of the photon is the
same as the carrier,
2 2
10
( ) 1( ) 10 log
(0) 1
opt
opt
opt
PH
P j
Modulation bandwidth 14
The 3-dB modulation bandwidth is
3
1
2dB
n
f
The 3-dB bandwidth of LED is inversely proportional to the carrier lifetime, which is on
the order of nanosecond. Thus, the bandwidth is typically 100 MHz-1.0 GHz. So for
data communications, LEDs are confined to applications below 1 Gbps.
Modulation bandwidth 15
The carrier lifetime decreases with increasing current injection to reach a limiting
value of the spontaneous radiative lifetime, thus the modulation bandwidth depends
on the LED bias current.
3
max
3dB
0
1
2
n
D
dB D
K
I
f I
f
Heterojunction LED 16
In heterojunction LEDs, the total carriers are stored in the narrowgap active layer, so
the total LED current is approximated with the GR contribution in the active layer,
while diffusion current in the cladding layers have been neglected.
The diode current in heterojunction LED is mainly recombination current in the active
region, while the current in homojunction LED is mainly the diffusion current in the
cladding layers.
The current-power relation is the same as homojunction LEDs, while the injection
efficiency is almost 1.
The modulation dynamics and the modulation bandwidth are also the same as
homojunection LEDs.
Both relations hold for QW LEDs as well.
LED emission spectrum 17
For low injection conditions, the spontaneous emission spectrum is given by
( )spr
with
g
B
Ex
k T
LED emission spectrum 18
The low-injection LED FWHM is 1.8kBT, based on the derivation in pp. 262.
Example 5.1
LED emission spectrum 19
In high injection, the linewidth increases due to the onset of degeneracy.
Assuming the quasi-neutrality, the spontaneous emission spectrum is given by
Therefore, in high injection condition, the FWHM linewidth is given by
Which is much larger than the low-injection value. (294 meV)
2/3
2 2
2/3
max *
3
2g
r
E E E nm
LED spectrum 20
At high injection, however, the LED may become superradiant or
superluminescent, implying that part of the spontaneous emission spectrum
is affected by the gain, and that the resulting total spectrum will follow the
narrower gain spectrum. Other effects, such as nonparabolic bands, can play a
role in narrowing the LED emission.
In QW LEDs, the emission spectrum follows a staircase density of states,
where exciton peaks are also present. In low-injection conditions, the
emission spectrum is proportional to the absorption spectrum through the
Roosbroeck-Shockley relation,
LED spectrum 21
A similar behavior with marked emission peaks is observed in Qdot LEDs.
LED materials 22
Since the LED emission spectrum is concentrated around the semiconductor energy gap, the material of choice depends on the application. Visible LEDs (with emission between 400 and 700 nm) exploit materials with a comparatively large gap. Examples of visible LED materials are the GaAs1−xPx alloy, covering red, orange, and yellow colours, and GaN based alloys, covering green, blue, and violet. Since GaAs1−xPx is indirect bandgap for x > 0.5, the problem arises of exploiting indirect bandgap materials for spontaneous emission. Due to the high radiative lifetime and low radiative efficiency, indirect-bandgap materials are characterized by very low external efficiencies, unless the material is doped with an impurity (e.g., nitrogen) called an isoelectronic impurity (等电子杂质), whose effect is to improve radiative processes without leading to acceptor or donor behavior (isoelectronic means that the number of external electrons of the impurity is the same as for the hosting material). Isoelectronic doping improves the radiation efficiency of indirect-bandgap compound semiconductors by about two orders of magnitude, although this is always much lower than in direct bandgap alloys. While the InGaN alloy covers the visible range from green to blue, UV LEDs require AlGaN, with a wider bandgap. Applications of UV LEDs include monitoring of contaminants and ambient-temperature portable water purification systems. LEDs for optical communications operating in the first window exploit AlGaAs/GaAs/AlGaAs heterostructures. Long-wavelength operation is possible with InP-based alloys, such as InGaAsP; the resulting LEDs, often edge-emitting and superradiant, offer the best performance in this device class with 1.3μm and 1.5μm emission.
Lecture 14 23
Semiconductor laser modes
From LED to laser 24
Both the LED and the laser diodes exploit radiative recombination of electron–hole pairs in a forward-biased junction to emit light. However, LEDs are based on spontaneous emission, implying broad linewidth (of the order of 2kBT ) and narrow modulation bandwidth, well below 1 GHz. The dominant emission mechanism in lasers is stimulated emission: photons of a specific energy and wavenumber stimulate the emission of coherent photons (with the same energy and wavenumber), thus leading to EM wave amplification; all e-h pairs recombine to generate coherent photons, and narrow linewidth results. At the same time, the lifetime associated with stimulated emission can be shorter, for high photon density, than the spontaneous radiative lifetime τ0; thus, the laser can achieve modulation bandwidths as wide as 20–30 GHz. In summary, stimulated emission is the key to improving the LED spectral purity and modulation bandwidth or speed. To turn a LED into a laser, however, we need a mechanism able to foster stimulated rather than spontaneous recombination at a certain photon energy, i.e., a frequency-selective structure such as an optical resonator or cavity. The optical cavity is compatible with a discrete set of photon states, whose density is large within the cavity, and which operate as positive feedback with respect to stimulated emission.
Fabry-Perot cavity laser 25
The double heterostructure confines carriers in the active region due to the narrower bandgap
The double heterostructure confines photons in the active region due to the higher refractive index
The cleaved mirror face has a reflectivity of about 0.32, following the Fresnel Principle
The far-field laser pattern is narrow in the horizontal plane, while broad in the vertical plane, due to the diffraction.
Fabry-Perot cavity laser 26
The cavity feedback makes stimulated emission dominant only when the photon density in the cavity is large enough. The junction hosts two radiative recombination mechanisms, spontaneous and stimulated; we neglect for the moment other competing nonradiative processes, such as thermal and Auger recombination. The diode current injects carriers recombining in either radiative mechanism according to the relative lifetimes. For low current, the carrier density in the junction is small, and so is the phonon density in the cavity. In this region, spontaneous emission dominates over stimulated emission and the laser works as a LED, according to the flow scheme shown by the thick arrows The output power near the laser emission wavelength is small, because most photons are emitted on a broad spectrum.
Fabry-Perot cavity laser 27
Increasing the current density, the photon density in the cavity allowed modes increases. Correspondingly, the stimulated lifetime (inversely proportional to the cavity mode photon density) decreases, becoming smaller than the spontaneous lifetime. The feedback loop now becomes dominant and typical laser operation starts. Above the laser threshold – corresponding to self sustaining oscillations where the photons lost in one cycle are replaced by the photons generated by stimulated emission – the laser spectrum narrows. A small fraction of carriers still recombine spontaneously, emitting incoherent photons and thus contributing to the laser phase noise and finite linewidth.
Fabry-Perot cavity laser 28
Above threshold, the number of carriers injected per unit time (i.e., the junction current) is approximately equal (with unit quantum efficiency, i.e., neglecting nonradiative recombination processes) to the number of photons generated per unit time within the cavity; in steady-state conditions the photon density N remains constant because generated photons are lost at a rate N/τph where τph (the photon lifetime) is the average survival time of a photon before it leaves the cavity through the mirrors or is absorbed; we assume here that the first mechanism, called mirror or end loss, is dominant. Mirror loss is the source of the output optical power, which is therefore proportional to the input electric current. At very high input current densities, however, the radiative efficiency of the laser decreases, due to nonradiative (e.g., Auger) recombination processes competing with the stimulated recombination, self-heating, and gain compression, so that the laser output power finally saturates. Taking into account that the total number of photons generated is anyway proportional to the input current both in the LED-like and in the laser regime (below and above threshold), it is clear that the different slope of the laser power-current characteristics, also called slope efficiency, depends on the fact that the laser concentrates, around a narrow linewidth all the photons generated, which are emitted on a broader bandwidth in the LED. FP lasers have linewidths of the order of 2–3 nm (20–30 Å), at least one order of magnitude narrower than typical LED linewidths (>50 nm).
Resonant modes 29
Assume the FP cavity length is L along x axis, width is W along y axis, and the active region thickness is d along z axis. The front and back cavity facets are cleaved so as to act as a pair of flat parallel mirrors, while the lateral faces are treated to minimize lateral reflections.
The cavity only allow optical modes of some specific wavenumbers /wavelengths /frequencies to oscillate in the cavity, which are called longitudinal modes. The longitudinal modes are determined by the cavity length L.
The adjacent longitudinal mode spacing (Free spectral range, FSR) is
In addition, the cavity only allow optical modes of some specific spatial distributions to oscillate in the cavity, which are called transverse modes. The transverse modes are determined by the size of width W and thickness d. The fundamental mode is Gaussian mode, while larger size allows higher-order transverse modes.
2 r mn L m
2 r
cFSR f
n L
Resonant modes 30
The TE polarization is parallel to the active region, while the TM polarization is perpendicular to it. The cavity favors the TE polarization owing to better optical confinement factor and better reflectivity.
The laser field polarization is primarily determined by the gain, which is not polarized in bulk, while is polarized on the TE direction in QW.
Resonant modes 31
Photon confinement is achieved by the refractive index step, using differential materials in the active region and in the cladding region. An example is InP (substrate) and InGaAsP (active region).
Resonant modes 32
The longitudinal mode wavelength and frequency are
The mode wavelength and frequency spacing are
2= ; =
2
r
m m
r
n L cf m
m n L
For a cavity with typical length of 100 μm, effective refractive index neff ≈ 3, emission wavelength in vacum λ0 ≈ 1μm, this amounts to m ≈ 600. A high-order longitudinal mode is therefore excited in common (edge-emitting) lasers, while for vertical emission lasers (VCSELs) the mode order can be much lower due to the reduced cavity length.
2
2= ; =
2
=
r
m m
r
m m
m m
n L cf m
n Lm
f
f
Resonant modes 33
High-order transverse mode can appear if the width is large, and thus
can be suppressed by reducing the width.
Lecture 15 34
Effective refractive index & Optical confinement factor
Effective refractive index 35
The TE polarized (y direction) electric field’s propagation in z and x directions is expressed as
The electric field propagation along the z direction in the active region and in the cladding region is given by the wave equation,
The solution of the wave function is in the form
The refractive index in the active region is n1, in the cladding region is n2.
Effective refractive index 36
At the interface z=d/2, the TE field and its first derivative are continuous, thus the dispersion relation,
Introduce the normalized parameters
The mode effective refractive index is
0/eff effn k
Effective refractive index 37
Introduce the normalized frequency v and propagation constant b as
Then,
Therefore, the dispersion relation becomes
Effective refractive index 38
The effective refractive index is expressed as
The approximate solution for b is
Example 5.2
Optical confinement factor 39
The material gain achieves only in the active region, while the optical field extends also to the cladding, so the volume of the light is larger than the active region, which experiences losses. To account for this, an effective gain, called modal gain is defined as
The optical confinement factor is defined as
pmg g 2
0
p 2
d
op
op
E dz
E dz
Optical confinement factor 40
From the field symmetry, the optical confinement factor is given by
Optical confinement factor 41
Then, the optical confinement factor can be expressed by b and v,
When d is large, v is large, Gamma approaches 1. When d is small, v is small, and Gamma becomes,
