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ECSE-6230 Semiconductor Devices and Models I Lecture 5
Prof. Shayla Sawyer Bldg. CII, Rooms 8225 Rensselaer Polytechnic Institute Troy, NY Tel. (518) Fax. (518) June 23, 2018 June 23, 2018 1
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Lecture Outline Carrier Concentration vs. Temperature
Non-Equilibrium Processes Recombination and Generation Mechanisms Carrier Lifetimes Shockley-Read-Hall Recombination Process Derivation (also online)
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Carrier Concentration vs. Temperature
At room temperature, all the shallow dopants are ionized. (Extrinsic region) When the temperature is decreased sufficiently (~100 K), some of the dopants are not ionized. (Freeze out region) When the temperature is increased so high that the intrinsic carrier conc. approaches the active dopant conc. (T Ti, > 450K for Si), the semiconductor is said to enter the intrinsic region.
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Fermi Level vs. Temperature
When the temperature is decreased, the Fermi level rises towards the donor level (N-type) and eventually gets above it. When the temperature is increased, the Fermi level moves towards the intrinsic level.
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Non-Equilibrium Processes
Whenever the thermal-equilibrium condition of a semiconductor system is disturbed pn ≠ ni2 processes exist to restore the system to equilibrium Recombination mechanisms np>ni2 Generation mechanisms np<ni2 Recombination Processes
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Recombination Mechanisms
Direct or Band to Band Basis for light emission devices Photon (single particle of light) or multiple phonons (single quantum of lattice vibration – equivalent to saying thermal energy) Recombination Processes
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Recombination Mechanisms
R-G Center Also known as Schockley-Read-Hall (SRH) recombination Photon (single particle of light) or multiple phonons (single quantum of lattice vibration – equivalent to saying thermal energy) Note: Trap level Two steps: 1st Carrier is trapped at a defect/impurity 2nd Carrier (opposite type) is attracted to the RG center and annihilates the 1st carrier Energy loss can result in a Photon but more often multiple Phonons Recombination Processes
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Recombination Mechanisms
Auger Requires 3 particles Two steps: 1st carrier and 2nd carrier of the same type collide instantly annihilating the electron hole pair (1st and 3rd carrier). The energy lost in he annihilation process is given o the 2nd carrier. 2nd carrier gives off a series of phonons until it’s energy returns to equilibrium energy (E~Ec) Recombination Processes
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Generation Mechanisms
Direct of Band to Band Does not have to be a direct bandgap material Mechanism that results in ni Basis for light absorption devices such as semiconductor photodetectors, solar cells, etc. Recombination Processes
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Generation Mechanisms
R-G center Two steps: A bonding electron is trapped at an unintentional defect/impurity generating a hole in the valence band This trapped electron is then promoted to the conduction band resulting ina new electron-hole pair Almost always detrimental to electronic devices Recombination Processes
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Generation Mechanisms
Impact Ionization Requires 3 particles and typically high electric fields 1st carrier is accelerated by high electric fields Collides with a lattice atom Knocks out a bonding electron Creates an electron hole pair What is it called when this process repeats and what device is it useful for? Recombination Processes
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Non-Equilibrium Processes
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Non-Equilibrium Processes: Direct
Band to band transitions are more probable for direct bandgap semiconductors For this type of transition, the recombination rate is proportional to the product of electron and hole concentrations Rec is the recombination coefficient Rec is related to the thermal Generation rate (Gth). When temperature is raised, Gth increases so ni must increase
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Non-Equilibrium Processes: Direct
In thermal equilibrium, since pn=ni2 , Re=Gth and the net transition rate U(=Re-Gth) = 0 Under low level injection, where the disturbance from equilibrium is so small majority carrier concentration is not affected significantly Excess carriers are far fewer than majority carriers
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Non-Equilibrium Processes: Direct
Minority carrier lifetime: the average time a minority carrier spends before it recombines.
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Non-Equilibrium Processes: Indirect
In indirect-bandgap semiconductors such as Si and Ge, the dominant transitions indirect recombination/generation via bulk traps of density Nt and energy Et present within the bandgap Single level recombination described by two proceses: Electron capture Hole capture Transitions are dominated by Shockley-Read-Hall statistics
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Non-Equilibrium Processes: Indirect
Rate of transitions for Shockley-Read-Hall statistics: The net transition rate is proportional to pn-ni2 and the sign determines whether there is net recombination or generation U is maximized when Et = Ei meaning for bulk traps, only those near the mid-gap are effective recombination/generation centers Therefore U is reduced to
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Non-Equilibrium Processes: Indirect
For low-level injection, change in minority carrier is most significant, n-type semiconductors: Minority carrier concentration now dependent on concentration of traps, capture cross section, and thermal velocity For p-type semiconductors
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Capture Cross-Section
Electrons with this thermal velocity must come within an area of the trap to be captured Electrons of momentum, p, captured within a circular neighborhood of the recombination center. n (p) - capture cross-section. The electron velocity, vn (= p / mn*), sweeps out a volume of (p / mn*) n (p) per second, which is the rate of electron capture. Including electrons of all energy (or momentum) range, the average rate of electron capture is < (p / mn*) n (p) > = vth n n n Similarly, the average rate of hole capture is < (p / mp*) p (p) > = vth p p p Au e-
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Example Problem Consider a sample of Si doped with 1015 cm-3 Boron, with a recombination lifetime of 10μs. It is exposed to light such that electron-hole pairs are generated throughout the sample at the rate of 1020 /s*cm3 Find: n0 and p0 Δn and Δp p,n, and the np product What is ni2 for Silicon and how does it compare with the np product?
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Non-Equilibrium Processes: Indirect
For high- level injection, Δn=Δp > n and p, the carrier lifetime for traps becomes Carrier lifetime is actually higher for high level injection with traps. Bottleneck: Like many cars trying to cross over a two lane bridge. Lifetime due to trap recombination increases with injection level for indirect recombination. (decreases for band-to band recombination)
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SRH Recombination Process
(1) Electron emission nT is the density of filled traps Rate of emission en proportionality constant defined as electron emission rate (2) Electron capture Rate of capture pT is the concentration of empty deep states σn is the capture cross-section <vn>th is the thermal velocity n number of electrons in the conduction band cn en cp ep
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SRH Recombination Process
(3) Hole emission pT is the concentration empty states Rate of emission ep proportionality constant defined as hole emission rate (2) Hole capture Rate of capture nT is the density of filled traps σp is the capture cross-section <vp>th is the thermal velocity p is the number of holes in the valence band cn en cp ep
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SRH Recombination Process
Kinetic equations: electron and hole densities in conduction and valence bands and also in deep levels at any time The net rate of electrons leaving the conduction band is given by: The net rate of holes leaving the valence band is given by: The net rate of increase of density of deep levels is given by: Using the total density of deep states NT = filled + empty = nT +pT
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SRH Recombination Process
Using the total density of deep states NT = filled + empty = nT +pT cn and cp are the capture rates of electrons and holes respectively Steady-state equation: no change in the occupancy of deep levels, hence dn/dt=0, solve for number of filled states over total number of states
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SRH Recombination Process
Detailed Balance Principle In thermal equilibrium, the rate of any physical process and its reverse must balance each other In this case, the rates for hole emission and capture must be equal Similarly the rates of emission of electrons and the corresponding capture rate must also exactly equal Therefore, Ra=Rb and Rc=Rb The probability of an electron occupying the energy level ET is given by the Fermi Dirac distribution function giving us the electron and hole emission rates
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SRH Recombination Process
Number of traps that are filled are given by the number of traps times the probability of occupation: Thermal emission rates for electrons and holes respectively
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SRH Recombination Process
Consider a situation when there is a generation of electron and holes (via illumination) Rate of electrons entering the conduction band has increased to G + Ra= Rb Rate of holes entering valence band to G + RC= Rd The probability of occupancy is given by:
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Shockley-Read-Hall Recombination Process
Recombination Through Multiple Levels Generally, recombination centers are associated with more than one level. Most transition metals have two or more impurity levels within the silicon bandgap. In particular, gold has two levels, one donor-like and one acceptor- like. SRH Recombination process through multiple levels can be generalized from the previous analysis on single recombination level. (See J.L. Moll, Physics of Semiconductors, pp ). 4 capture processes and 4 emission processes need to be considered.
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Recombination Levels in Si
Carrier Lifetime Control One level tends to dominate For gold, the carrier lifetime decreases linearly with gold concentration over th range of 1014 to 1017 cm-3 where τ decreases from about 2x10-6 s to 2x10-9 s. High energy particle irradiation, causes displacement of host atoms and damage to the lattice=energy levels in the bandgap
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Trapping Centers If the capture rate of one type of carriers is substantially smaller than that of the other, the recombination center becomes a trapping center. For example, such a site can capture an electron and holds it for some mean time, g, and then releases it to the conduction band. The rate equation is nt / t = nt n ( Nt - nt ) - nt / g Abrupt jumps or emissions are superimposed on the exponential decay of carriers during recombination. At least 4 trapping centers have been identified in Si, g as long as 1000s has been observed.
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