Defects Maria Berdova maria.berdova@aalto.fi Postgraduate Course in Electron Physics I

Outline Types of Defects Generation-Recombination Statistics Mathematical Description Detection Methods Postgraduate Course in Electron Physics I

Types of defects 1) Foreign interstitial (e.g. Oxygen in silicon) 3) Vacancy 4) Self interstitial 2) Foreign substitutional (like dopant atom) 5) Stacking fault When a particle is missing at one or more lattice sites we get a vacancy. When a particle forces its way into a hole between lattice sites, we get an interstitial impurity.  Substitutional impurities result from replacing the particle that should occupy a lattice site with a different particle, such as substituting a K+ ion for a Na+ ion in NaCl. Dislocations are one-dimensional defects caused by holes that are not large enough to be a vacancy. 6) Edge dislocation 7) Precipitate Postgraduate Course in Electron Physics I

Defects Vacancy Stacking fault Interstitial http://open.jorum.ac.uk/xmlui/handle/123456789/5649 Interstitial Stacking fault Postgraduate Course in Electron Physics I

Metallic impurities Degradation of gate integrity Degradation of the device (at high stress point and in junction space charge region) Postgraduate Course in Electron Physics I

Effect of contamination Fe in Si, and Cu in Si Postgraduate Course in Electron Physics I

Defects Shallow defects Deep defects Energy levels close to the valence or conduction band Acting as dopants Deep defects Energy level away from the band edges Short range part of the potential determines energy level Normally non-wanted defects E  ~ 150 meV (from the conduction band or valence band edges) Postgraduate Course in Electron Physics I

Generation-Recombination Statistics Trapping Trapping Traps or G-R centers Deep level impurities (metal impurities, crystal imperfections) Postgraduate Course in Electron Physics I R G

Mathematical Description G-R center is occupied by hole or by electron, which are recombined or generated Time dependence of electron or hole density (electron/hole time rate of change due to G-R mechanisms) Center occupancy rate thermal velocity Postgraduate Course in Electron Physics I electron capture cross-section of the G-R center

Mathematical Description Solution nT(0) is the density of G-R centers occupied by electrons at t = 0 the steady-state density n-type substrate

Schottky diode a) nT = NT Capture dominates emission b) t ≤𝟎 G-R centers are initially occupied by electrons 𝒕>𝟎 electrons are emitted from G-R centers Near the edge of scr the mobile electron density tails of from qnr to scr – captures compete with emissions Postgraduate Course in Electron Physics I

Mathematical Description from zero bias to reverse bias Emission period Capture period from reverse bias to zero bias Postgraduate Course in Electron Physics I

Capacitance measurements Capacitance of the Schottky diode Nscr - ionized impurity density in the SCR time dependence of nT (t ) or pT (t ) capacitance at t = 0 and t = ∞ time – varying capacitance Postgraduate Course in Electron Physics I

Capacitance measurements the steady-state density Plot 1/C2 vs V nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases S (t) – slope Postgraduate Course in Electron Physics I

Capacitance measurements Transient Measurements time-varying W is detected as time-varying capacitance C0 is the capacitance of a device with no deep-level impurities at reverse bias -V nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases Postgraduate Course in Electron Physics I

Capacitance measurements Emission—Majority Carriers: During the reverse bias pulse, majority carriers are emitted as a function of time nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases As majority carriers are emitted from the traps , W decreases and C increases until steady state is attained Postgraduate Course in Electron Physics I

Capacitance measurements Reverse biased capacitance change The capacitance increases with time for majority carrier emission whether the substrate is n- or p-type and whether the impurities are donors or acceptors. nT(t) is “-” charged when occupied by electrons. With time, as electrons are emitted and the traps become neutral, (ND − nT(t)) increases and 1/C2 decreases Intercept on the ln-axis gives ln[nT(0)Co/2ND] Postgraduate Course in Electron Physics I

Emission minority carriers During the forward-bias phase, holes are injected into the n-substrate and capture dominates emission. (p+n junction) forward bias reverse bias Lower half of the band gap pulses minority carrier charge changes from neutral to negative Postgraduate Course in Electron Physics I

Capture—Majority Carriers The density of traps able to capture majority carriers tf is ”filling” time tf>>τc tf <<τc 1. Reverse bias 2. Zero bias Postgraduate Course in Electron Physics I

Capture—Majority Carriers The reverse-bias capacitance depends on the filling pulse width τc can be determined by varying tf Postgraduate Course in Electron Physics I

Capture—Majority Carriers ln(∆Cc) versus tf has a slope of 1/τc = σnvthn an intercept on ln(∆Cc) axis of ln{[NT − nT (0)]C0/2ND} obtained by varying the capture pulse width during the capacitance transient measurement Postgraduate Course in Electron Physics I

Current Measurements The carriers emitted from traps can be detected as a capacitance, a charge, or a current. The integral of the I -t curve represents the total charge emitted by the traps. high temperatures is short is high time constant current low temperatures increases decreases Area under I -t curve remains constant C-t measurements at low temp & I-t measurements at high temp time constant data Postgraduate Course in Electron Physics I

Current Measurements Emission current Displacement current Junction leakage current I1 Postgraduate Course in Electron Physics I

Drawbacks of Current Measurements Leakage current might be sufficiently high The instrumentation must handle the large current transients during the pulse The amplifier should be non-saturable, or the large circuit transients must be eliminated from the current transient of interest No distinction between majority and minority carrier emission Postgraduate Course in Electron Physics I

Current Measurements is applied When difficult to make capacitance measurements Low capacitance of small-geometry MOSFETs When possible to detect the presence of deep-level impurities by pulsing the gate voltage and monitoring the drain current as a function of time In devices in which the channel can be totally depleted Postgraduate Course in Electron Physics I Drain current ID and gate capacitance CG transients of a 100 μm × 150 μm gate MESFET.

Charge Measurements Switch S is closed to discharge the feedback capacitor CF At t = 0 the diode is reverse biased S is opened Current through the diode Postgraduate Course in Electron Physics I

Charge transient Measurements With the input current into the op-amp approximately zero, the diode current must flow through the RFCF feedback circuit, giving the output voltage Choosing the feedback network such that tF>>τe Postgraduate Course in Electron Physics I

Deep-level Transient Spectroscopy (DLTS) The measurements use a two stage carrier capture and emission process Quantitative (deduce absolute concentrations of electrically active defects) Sensitive (In 20 Ω-cm silicon detection of 1010 cm-3 electrically active defects) Trap Energy Level Carrier Capture and Emission Rates Trap density Spatial Distribution of Defects Postgraduate Course in Electron Physics I

Deep-level Transient Spectroscopy (DLTS) Pulse applied to change occupancy of deep states Pulse from reverse to zero for majority carrier traps Into forward bias to inject minority carriers capacitance changes as carriers are emitted from states (can also use current) ƒ Rate depends on temperature and binding energy Postgraduate Course in Electron Physics I J. Appl. Phys. 45, 3023 (1974)

Deep-level Transient Spectroscopy (DLTS) Conventional DLTS Rate window concept to deep level impurity characterization Conventional DLTS varies the temperature and produces a peak when the emission rate matches a ‘standard’ rate (the rate window) determined by the positions of t1 and t2 http://www.ph.unimelb.edu.au/~part3/notes/dlts02.pdf The magnitude of the peak ΔC gives the concentration of deep states: signal changes as a function of temperature when a single trap is present Postgraduate Course in Electron Physics I

Deep-level Transient Spectroscopy (DLTS) ‘Tutorial Day: DLTS’ 16th July 2011 Tony Peaker By repeating the temperature scan with different settings of t1 and t2 the system filters out different rates (rate windows) and so each Tmax corresponds to the temperature at which the trap emits carriers at that rate window. So by making an Arrhenius plot (plotting log en vs. 1/T) it is possible to determine the energy of the state from the slope Postgraduate Course in Electron Physics I

Arrhenius plot of emission rates Xn is an entropy factor plot log (en /T 2) vs 1/T en /T 2 slope gives -Ea intercept A is used to obtain Xnσn(∞) Postgraduate Course in Electron Physics I

DLTS: Conclusion Advantages Disadvantages Highly sensitive - Defect concentrations to 1010 cm-3 Requires electrically active defects Contact less, non-destructive relatively easy measurement Levels identification requires comparison with other techniques Identification of impurities is not always straightforward Inability to characterize high resistivity substrates (capacitance transient)

Thermally stimulated capacitance and current Capacitance steps or current peaks are observed as traps emit their carriers Appl. Phys. Lett. 22, 384 (1973) The trap density is from the area under the TSC curve or from the step height of the TSCAP curve From zero bias to reverse bias Postgraduate Course in Electron Physics I

Positron annihilation spectroscopy The spectroscopy of gamma (γ ) rays emerging from the annihilation of positrons and electrons positron wave-function can be localized in the attractive potential of a defect annihilation parameters change in the localized state (e.g. positron lifetime increases in a vacancy) lifetime is measured as time difference between appearance of start and stop quanta defect identification and quantification possible If voids are available, positrons will reside in them and annihilate less rapidly than in the bulk of the material, on time scales up to ~1 ns. Postgraduate Course in Electron Physics I AMERICAN JOURNAL OF UNDERGRADUATE RESEARCH, VOL. 2, NO. 3 (2003)

Positron annihilation spectroscopy - Positron lifetime is measured as time difference between 1.27 MeV quantum (β+ decay) and 0.511 MeV quanta (annihilation process) - PM…photomultiplier; SCA…single channel analyzer (constant-fraction type); TAC…time to amplitude converter; MCA… multi channel analyzer Postgraduate Course in Electron Physics I

Positron annihilation spectroscopy Reinhard Krause-Rehberg, Martin-Luther-University Halle-Wittenberg, Germany Postgraduate Course in Electron Physics I (Polity et al., 1997)

Thank you Postgraduate Course in Electron Physics I