3. 1. DEFINITION
Quantum well (QW) is a 2D structure: Electron is confined
in one direction and free in orther direction with :
Quantum well in semiconductor (heterostructure) consist of
One smaller bandgap layer like GaAs
Two larger bandgap layers like AlGaAs
𝐿𝑥 ≪ 𝜆𝐹
𝜆𝐹 =
2𝜋
3𝑁𝑒𝜋2
1
3
𝜆𝐹 𝐺𝑎𝐴𝑠 ~10 − 100𝑛𝑚
Fig 1. Schematic of growth layers and band
diagram of AlGaAs/GaAs quantum well.
(𝐹𝑒𝑟𝑚𝑖 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ)
KASAP, Safa O. Springer handbook of electronic and
photonic materials. New York: Springer, 2006.
3
4. 1.1 ELECTRONS IN QUANTUM WELL
The wave function of electron :
Energy of electron quantization in x direction
Energy in the y, z-direction represents an approximately
continuous
−
ℏ2
2𝑚∗
𝜕2
𝜕𝑥2
+
ℏ2
𝑘𝑙
2
2𝑚∗
𝜓𝑥 𝑥 = 𝐸𝜓𝑥 𝑥 𝑉 = 0, 0 ≤ 𝑥 ≤ 𝐿𝑥
Energy is obtained :
𝐸 =
ℏ2
2𝑚∗
𝑛𝜋
𝐿𝑥
2
+
ℏ2
2𝑚∗
𝑘𝑦
2
+ 𝑘𝑧
2
= 𝐸𝑛 +
ℏ2
2𝑚∗
𝑘𝑦
2
+ 𝑘𝑧
2
Fig 2. Confined states in a quatum
well. The wave function for the n=1
and n=2
n=2
n=1
𝐿𝑥
𝐸1
𝐸2
with
4
5. 1.2 ELECTRON TRANSPORT
One side of the barrier (AlGaAs) is n-type semiconductor
Another side (GaAs) is slightly doped with p type
Electron move to p-region, a electrostatic field is created
Band bending, Fermi level of two region line-up
Created a confining potential of carriers in one direction
Fig 3. Schematic energy band diagrams of a
selectively doped AlGaAs/GaAs heterostructure
before (a) and after (b) charge transfers have occurred
Source: Mitin, V. V., Kochelap, V. A., Stroscio, M. A. Introduction to
Nanoelectronics: Science, Nanotechnology, Engineering and Applications.
5
6. 1.3 OPTICAL PROPERTY OF QUANTUM WELL
When electron recombine with hole, they emitt a photon.
Various transitions can be occured with extent subband.
It is possible to tunning the absorbtion energy photon of
electron by adjust the well thickness or well material.
ℎ𝜔 = 𝐸𝑔 + 𝐸𝑛 + 𝐸𝑚 = 𝐸𝑔 +
ℏ2𝜋2
2𝑚ℎ
∗𝐿𝑥
2 𝑛2 +
ℏ2𝜋2
2𝑚𝑒
∗𝐿𝑥
2 𝑚2
ℎ𝜔 = 𝐸𝑔 +
ℏ2𝜋2
2𝑚𝑟
∗𝐿𝑥
2
Where 𝑚𝑟
∗ is the reduced mass, 𝑚𝑟
−1 = 𝑚𝑒
−1 + 𝑚ℎ
−1
Fig 4. schematic representation of the drift of the
injected carriers and their subsequent capture by
quantum well
=> Application for optoelectronic devices
(Photon energy at n = m=1)
KASAP, Safa O. Springer handbook of electronic and
photonic materials. New York: Springer, 2006.
6
8. MATERIALS FOR QUANTUM WELLS
- Significant restriction: the lattice constants of the materials in the heterostructure are very
similar.
- Lattice-matching reduces the number of dislocations in the epitaxial layer.
- AlAs and GaAs → What are III-V compounds?
- A partial list of materials used for quantum well structures includes: III-V's -
GaAs/GaAlAs, GaSb/GaAlSb, InGaAs/InAlAs, InGaAs/GaAs, …
8
9. FABRICATION TECHNIQUES
Basic principle of epitaxy: grow thin layers of very high
purity on top of a bulk crystal called the substrate.
Molecular-beam epitaxy
Chemical vapor deposition
Das, Paul Masih. Nanostructure Engineering in
Two-Dimensional Materials Beyond Graphene.
Diss. University of Pennsylvania, 2020.
9
10. MOLECULAR - BEAM EPITAXY
Source: Mitin, V. V., Kochelap, V. A., Stroscio, M. A. Introduction to
Nanoelectronics: Science, Nanotechnology, Engineering and Applications.
This method can be realized in a high vacuum,
where molecular or atomic beams deliver the
necessary components onto a substrate for
growing the desired crystalline layer.
By controlling shutters, we can produce abrupt
changes in crystal compositions on the scale of
one monolayer.
10
11. CHEMICAL VAPOR DEPOSITION
For growth of AIII–BV compounds:
What is chemical vapor deposition? → using a relatively high temperature to activate the
gaseous precursors and subsequent gas-solid phase reactions on the substrate to form a thin layer.
Source: What is CVD? - ATL CVD
Extreme Coating Solutions_Youtube
11
13. - Quantum well (QW) devices are devices that use quantum well effects. The basic concept of a
quantum well is illustrated in Fig.1.
- The basis of a quantum well device is a situation where a thin semiconductor layer of lower band
gap material is sandwiched between two thick semiconductor layers of larger band gap.
13
Fig. 5. Schematic of a quantum well as function of distance in the growth direction Z.
14. Quantum Well Lasers
(QWL)
𝐽𝑡ℎ = 𝐽0 × 𝑒
𝑇
𝑇0
- It is also known as semiconductor lasers or improved lasers. QWL operate on the same basic
principle as a laser diode. Heterostructures are the main components of this device.
- The semiconductor material with the lower band gap will have a higher refractive index while the
larger band gap material will have lower refractive index.
where T is the device temperature, T0 is the threshold temperature coefficient and J0 is the initial
injected current.
- An interesting aspect of a QWL is the narrow nature of the well.
- One of the most important aspects of QWL is the fact that some of the lowest threshold
current has been measured in them.
- The threshold current density and the laser temperature are related by the expression:
14
15. - QWL with one active region (well) is called single QW (SQW) lasers and that with multiple active
regions is known as multi-quantum well (MQW) laser. The structure is optimized by choosing the
proper dimension of the active layer quantum well and the number of wells.
- Most common QWL are fabricated from
GaAs/AlGaAs and InGaAsP/InP structures.
- The lowering of threshold current due to quantum
size effects is largely offset by the small width of the
gain region in a SQW laser which causes the optical
confinement to be poor.
- The problem can be solved by using separate
confinement heterostructure (SCH) to enhance the
optical confinement factor.
15
Fig. 6.Schematic diagram of a quantum well laser (QW). (a) Gain-
guided QWL> Current flows through the Zn-diffused region of
GaAs and the injected carriers are thereby confined to the central
region of the well. The p-type AlGaAs and n-type AlGaAs layer
together with the sandwiched GaAs well forms the laser diode. (b)
Index-guided QWL.
B. R. Nag, Appl. Phys. Lett. 65, 1938 (1993)
16. Quantum Well Detectors
𝑉 =
𝜀𝑟𝜀0𝐸𝑀
2
2𝑞𝑁𝐷
where 𝐸𝑀 is the maximum field, q is the electronic charge, 𝑁𝐷 is the donor doping density on the n-
side, while 𝜀𝑟 and 𝜀0 are the relative permittivity of the doping material and permittivity of free space
respectively.
An avalanche photodiode (APD) is used to detect optical signal from the visible to the far-infrared of
the optical spectrum.
It operates on the basis of a reverse biased P-N junction with a relatively large voltage kept
substantially below the avalanche breakdown voltage.
This voltage can be calculated using Poison’s equation and expressed as
16
17. - A lot of improved new APD structures have been
made of recent with improved performance
characteristics by simply artificially increasing the ratio
of the ionization coefficient of electrons to holes
(αe/αh).
- In this structure, the absorption and multiplication
regions of APD is replaced with either multi-quantum
well (MQW) or superlattice structure having varying
sizes of wells and barriers
17
Fig. 7. Superlattice APD (Sze, 1990)
