1. ACADEMIC AND SCIENTIFIC WORK ROBERTO PINEDA GÓMEZ
MODULATION DOPING
ACADEMIC AND SCIENTIFIC WORK ROBERTO PINEDA GÓMEZ

2. CONTENT INTRODUCTION MODULATION DOPING
SCATTERING PHENOMENA AND CRITERIA TO CHARACTERIZE A 2DEG
RESULTS AND CONCLUSION

3. SUPERLATTICE Periodic structure of layers of two or more materials.
Diffusion of materials was not able to fabricate a lightly doped layer on a heavily doped substrate.
70’s: Proposal of synthetic superlattices by Esaki and Tsu.
Modulation doping concept, the doping is modulated as a whole when different materials form a stack.

4. HOW TO MAKE SUCH A SYSTEM?
Techniques which can be used to grow two semiconductors alternately to form a one dimensional sandwich like structure.
Keywords: High degree of control and reproducibility.
Techniques:
MBE (Molecular Beam Epitaxy)
MOVPE (Metal Organic Vapours Phase Epitaxy)

5. MBE
Substrate.
Effusion cells.
Heating coils.

6. MOVPE OR MOCVD Flow ultra pure gases. Injection units.
Combination at elevated T to cause chemical interaction.
Surface chemical reaction.

7. FEATURES Which one is better? MBE : MOVPE :
Low growth rate 1 monolayer per second.
Low growth temperature 550ºC for GaAs.
MOVPE :
High throughput.
Gas flow and surface chemical reaction.
Higher temperature 500ºC-1500ºC.
Which one is better?

9. 2DEG
Scientific model.
Electron gas free to move in 2D.

10. 2DEG
Conventional doping introduces ionized impurity scattering reducing the carrier mobility.
Advantage of a 2DEG?
Get rid of the dopant scattering. In a 2DEG we can separate electrons from the dopants.

11. HOW TO CHARACTERIZE A 2DEG?

12. CHARACTERIZATION OF 2DEG
Aim: Understand and quantify the electrical transport characteristics of low-dimensional structures in order to get reliable data.

13. ANALYSIS Ohm’s law: 𝐽= 𝜎𝐸 Mean free path 𝑙(mfp)≈ 𝜇 𝑛
Mobility of charge carriers μ
Relaxation time τ
Drift velocity – independent of collisions, determines the electric current density: 𝐽=−𝑛𝑞 𝑣 𝑑𝑟𝑖𝑓𝑡
n: free electron carrier concentration
Effective mass m*
𝜇= 𝑞𝜏 𝑚 ∗

14. POISSON’S EQUATION
Describes electrostatic potential as a function of charge density distribution: defines band bending
Poisson’s equation: 𝛻 2 𝜙 𝑥 = − 𝜌(𝑥) 𝜀
𝐸 = −𝛻𝜙(𝑥
𝜙(𝑥 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑓𝑖𝑒𝑙𝑑
𝛻𝐸 = 𝜌(𝑥 ε
𝜌(𝑥) 𝐶ℎ𝑎𝑟𝑔𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

15. SCHRÖDINGER EQUATION 𝐻𝜓(𝑥)= 𝐸𝜓(𝑥
Time-independent Schrödinger equation:
Eigenfunctions & eigenvalues: information on the position of charge carriers
𝐻𝜓(𝑥)= 𝐸𝜓(𝑥
[− ℏ 2 2 𝑚 ∗ 𝛻 2 +𝑉(𝑥)]𝜓(𝑥)= 𝐸𝜓(𝑥)
𝑉 𝑥 = −𝑞𝜙 𝑥 + ∆𝐸𝑐(𝑥

16. SELF CONSISTENT P-S THEORY
Spatial density of e-: 𝑛 𝑥 = 𝑘=1 𝑚 𝜓 𝑘 (𝑥) 2 𝑛 𝑘
𝑛 𝑘 - average occupation number of state k
Charge density: 𝜌 𝑥 = 𝑞( 𝑁 𝐷 𝑥 −𝑛(𝑥))

17. ITERATION METHOD
Start with a trial potential ϕ1(x) and solve Schrödinger’s equation.
Calculate spatial density of e- from the obtained wavefunction.
Calculate ϕ2(x) using Poisson’s equation (using calculated spatial density of e-).
A new potential V(x) is obtained from the newly found value for ϕ2(x).
Iterate in this manner until a certain error criteria is satisfied: 𝜙 𝑖 𝑥 − 𝜙 𝑖−1 𝑥 < 𝛼 , ∀𝑥.

18. SCATTERING PHENOMENA

19. SCATTERING MECHANISMS
There are different kind of scattering mechanism. Each of them can be or not predominant under certain circumstances:
Interface
Imperfections between layers of materials, interface roughness.
Random alloy at the interface.
Coulomb interactions
Phonons

20. RUTHERFORD SCATTERING
Potential seen by an e- is screened by other e- in the system, inelastic approach.
The carrier interaction contributing to a deviation of trajectory of the carriers.

21. PHONONS
Are movements of atoms of the lattice out of the equilibrium position.
Displacement of atoms causes a change in the band structure.
Two kinds of phonons:
Acoustic: Coherent movement
Optical: Out of phase movement time varying electrical dipole moment

22. SUPERLATTICE LAYERS
Developing of a superlattice made out of heterostructures of 2 semiconductors periodically arranged.
Lattice periodic crystal.
Superlattice.

23. SUPERLATTICE LAYERS Conduction channel layer GaAs, undoped.
AlGaAs doped n-type puts mobile electrons into its conduction band. These electrons will migrate.
Where?
There’s a (+) charge left on the donor impurities which attracts these e-s to the interface and bends the bands in the process.

24. WHY GaAs / AlGaAs?

25. RESULTS AND CONCLUSION

26. RESULTS 𝜎=𝑞𝑛𝜇 To extract the mobility from the Hall measurement:
Scattering phenomena depends on the system’s conditions.

27. RESULTS At Low T: ionized impurity scattering At RT: phonons
Mobility varies depending on the spacer thickness

28. MESSAGE The conductivity of Increased by 1 order of magnitude.
Ultra-clean AlGaAs/GaAs heterostructures with mobility >10^7 cm^2/Vs.
The advantage of using such structure is to get rid of the dopant scattering. In a 2DEG we can separate electrons from the dopants.
High mobility enhancement. HEMT

29. THANKS FOR YOUR ATTENTION

30. References
- H. L. Strömer, A. Pinczuk, A. C. Gossard, W. Wiegmann; “Influence of an undoped (AlGa)As spacer on mobility enhancement in GaAs-(AlGa)As superlattices”; Appl. Phys. Lett. 38 (9); 1 May 1981
Lidia Łukasiak and Andrzej Jakubowski, History of Semiconductors.
Magneto/characterization of a 2DEG Ivan Sytsevich et Al.