Semiconductor detectors properties of semiconductors p-i-n diode - PowerPoint PPT Presentation

Semiconductor detectors •properties of semiconductors •p-i-n diode •interface metal-semiconductor •measurements of energy •space sensitive detectors •radiation damage in detectors Literatura: W.R.Leo: Techniques for Nucear and Particle Physics Experiments H. Spieler: Semiconductor Detector Systems G. Lutz: Semiconductor Radiation Detectors S.M. Sze: Physics of Semiconductor Devices Glenn F. Knoll: Radiation Detection and Measurement V. Cindro and P. Križan, Semiconductor detectors 1 IJS and FMF

Why semiconductors? • Energy resolution of a detector depends on statistical fluctuation in the number of free charge carriers that are generated during particle interaction with the detector material • Low energy needed for generation of free charge carriers → good resolution • Gas based detectors: a few 10eV, scintillators: from a few 100 do to 1000 eV • Semiconductors: a few eV! V. Cindro and P. Križan, Semiconductor detectors 2 IJS and FMF

Comparison: radiation spectrum as measured with a Ge (semiconductor) in NaI (scintillation) detector V. Cindro and P. Križan, Semiconductor detectors 3 IJS and FMF

good energy resolution → easier signal/background sepairstion V. Cindro and P. Križan, Semiconductor detectors 4 IJS and FMF

Principle of operation: Semiconductor detector operates just like an ionisation chamber: a particle, which we want to detect, produces a free electron – hole pair by exciting an electron from the valence band: conduction band electron forbidden band, width E g E g hole valence band V. Cindro and P. Križan, Semiconductor detectors 5 IJS and FMF

Drift velocity in electric field: = µ ⋅ v d E µ mobility different for electrons and for holes! = µ × v d E V. Cindro and P. Križan, Semiconductor detectors 6 IJS and FMF

properties of semiconductors ρ [kg dm -3 ] ε µ e [cm 2 V -1 s -1 ] µ h [cm 2 V -1 s -1 ] E g [eV] Si 2.33 11.9 1.12 1500 450 Ge 5.32 16 0.66 3900 1900 C 3.51 5.7 5.47 4500 3800 GaAs 5.32 13.1 1.42 8500 400 SiC 3.1 9.7 3.26 700 GaN 6.1 9.0 3.49 2000 CdTe 6.06 1.7 1200 50 V. Cindro and P. Križan, Semiconductor detectors 7 IJS and FMF

Intrinsic (pure) semiconductor (no impurities) n - concentration of conduction electrons N(E) density of states p - concentration of holes 1 = F ( E ) E t − E E ∫ = + F 1 exp( ) n N ( E ) F ( E ) dE kT E c E F Fermi energy level Fermi-Dirac Pure semiconductor distribution Neutrality: n=p + E E 3 kT m = + c v h E ln( ) ratio of effective masses of holes F 2 4 m e and electrons V. Cindro and P. Križan, Semiconductor detectors 8 IJS and FMF

E c energy of the bottom of conduction band − E v energy of the top of the valence band ( E E ) = × − c F n N exp( ) c E g =E c -E v width of the forbidden band kT − N c , N v : effective density of states in the ( E E ) = × − F v p N exp( ) conduction and valence bands v kT E × = = − 2 g n p n N N exp( ) i c v kT E = − g n N N exp( ) i e v 2 kT n i number density of free charge carriers in an intrinsic semiconductor (only for electrons and holes) At room themperature: [ ] − = × 10 3 n 1 . 4 10 cm Si i [ ] − = × 13 3 n 2 . 4 10 cm Ge i Semiconductor detectors 9 − 22 3 out of 10 atoms cm

Properties of semiconductors are modified if we add impurities Donor levels → neutral, if occupied • charged +, if not occupied Acceptor levels → neutral, if not occupied • chargedi -, if occupied shallow acceptors – close to the valence band (e.g. three-valent atoms in Si – examples B, Al) shallow donors – close to the conduction band (e.g. five-valent atoms in Si – examples P, As) V. Cindro and P. Križan, Semiconductor detectors 10 IJS and FMF

n-tip semiconductor , with added donors p-tip semiconductor , with added acceptors Binding energy of a shallow donor state is smaller because of a smaller effective mass and because of the diectric constant m ⋅ 13 . 6 eV eff 0 ≈ m for Si 0 . 025 eV ε In most cases it can be assumed that all shallow donors (acceptors) are ionized since they are far from the Fermi level. Neutrality: + = + n N p N A D As a result, the Fermi level gets shifted: N − = if N D » N A , n type semiconductor D E E kT ln( ) F i n i N − = if N A » N D , p type semiconductor A E E kT ln( ) i F n i V. Cindro and P. Križan, Semiconductor detectors 11 IJS and FMF

Properties of semiconductors with imputies (doped semiconductors) V. Cindro and P. Križan, Semiconductor detectors 12 IJS and FMF

Resistivity of semiconductors = µ × v d E Charge drift in electric fieldu E , µ mobility E = σ × = = ⋅ ⋅ + ⋅ ⋅ j E e v n e v p ρ 0 d 0 d e h 1 ρ = specific resistivity µ + µ e ( n p ) 0 e h at room temperatu re, intrinsic semiconduc tor : = Ω ρ 230k cm Si ρ = Ω 47 cm Ge V. Cindro and P. Križan, Semiconductor detectors 13 IJS and FMF

p-n structure At the p-n interface we have an inhomogenous concentration of electrons and holes  difussion of electrons in the p direction, and of holes into the n direction At the interface we get electric field (Gauss law) kT N N V = a d ln bi Potential difference 2 q n i V bi = built-in voltage difference , order of magnitude 0.6V To the signal only those charges can contribute that were produced in the depleted region with a non-zero electric field  The depleted region should cover most V. Cindro and P. Križan, Semiconductor detectors 14 of the detector volume! IJS and FMF

How to excrease the size of the depleted region: apply external voltage V bias + V bias • if the potencial barrier is increased, the depleted region increases  larger active volume of the detector – voltage in the reverse direction • if the potencial barrier decreases, the active volume is reduced, we get a larger current, voltage is in the conduction direction. The height of the potential barrier: V B = V bias + V bi How large is the depleted region ( x p +x n )? Neutrality: N a x p = N d x n ρ 2 e N d V = − = 0 a , d e εε εε 2 For the electric field we have the Poisson equation: dx 0 0 − dV e N = − ≤ ≤  0 d ( x x ) 0 x x εε n n  dx 0 The electric field varies linearly,  potential quadratically on the coordinate e N + − ≤ ≤  0 a ( x x ) x x 0 εε p p  0 V. Cindro and P. Križan, Semiconductor detectors 15 IJS and FMF

εε 2 V = 1 / 2 0 bias x ( ) + n e N ( 1 N / N ) 0 d d a 1 / 2   εε 2 V   = 0 bias x   + p   e N ( 1 N / N ) 0 a a d 1 / 2   εε + 2 V ( N N )   = + = 0 bias a d d x x   n p   e N N 0 a d 1 / 2   εε 1/2 increases as V bias 2 V   >> ⇒ ≈ ≈ 0 bias example : N N d x   a d n   e N 0 d ρ in terms of the spec. resistivit y : ( ) ≈ εε ρ µ 1 / 2 d 2 V 0 n e bias if ρ=20000kΩcm and  ρ µ 1 / 2  0 . 53 ( V ) m n - type = n bias  V bias =1 V → d ~75µm d example: silicon ρ µ  1 / 2 0.32( V ) m p - type  p bias V. Cindro and P. Križan, Semiconductor detectors 16 IJS and FMF

Leakage current = current in the reverse direction difussion current: • difussion of minority carriers into the region with electric field • current of majority carriers with large enough thermic energy, such that they overcome the potencial barrier generation current: generation of free carriers with the thermal excitation in the depleted layer V. Cindro and P. Križan, Semiconductor detectors 17 IJS and FMF

The probability of excitation is dramatically increased in the presence of intermediate levels. V. Cindro and P. Križan, Semiconductor detectors 18 IJS and FMF

generation current: E ∝ − g 2 j N T exp( ) N concentrat ion of traps gen t t 2 kT → high T – high generation current → wider forbidden band E g , lower generation current Consequence: some detectors have to be cooled (Ge based, radiation damaged silicon detectors) V. Cindro and P. Križan, Semiconductor detectors 19 IJS and FMF

metal-semiconductor interface (Schottky barrier) Χ electron affinity Φ work function Assumption Φ m > Φ s V bi = Φ m - Φ s V. Cindro and P. Križan, Semiconductor detectors 20 IJS and FMF

No external voltage voltage in the conduction direction voltage in the reverse direction Ohmic contact: high concentration of impurities → thin barrier → tuneling V. Cindro and P. Križan, Semiconductor detectors 21 IJS and FMF

Manufacturing of semiconductor detectorjev 1. manufacturing of monocrystals in form of a cylinder: • Czochralski (Cz) method Liquid silicon is in contact with the vessel – higher concentration of impurities V. Cindro and P. Križan, Semiconductor detectors 22 IJS and FMF

Float zone method: No contact of the liquid semiconductor with the walls – higher purity of the material. V. Cindro and P. Križan, Semiconductor detectors 23 IJS and FMF