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

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

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.

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)

MBE Substrate. Effusion cells. Heating coils.

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

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?

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

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.

HOW TO CHARACTERIZE A 2DEG?

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

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 ∗

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

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

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))

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.

SCATTERING PHENOMENA

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

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.

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

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

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.

WHY GaAs / AlGaAs?

RESULTS AND CONCLUSION

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

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

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

THANKS FOR YOUR ATTENTION

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. https://en.wikipedia.org/wiki/Poisson%27s_equation https://en.wikipedia.org/wiki/Superlattice https://en.wikipedia.org/wiki/Molecular_beam_epitaxy