FYS3410 Condensed matter physics

Transcription

1 FYS3410 Condensed matter physics Lecture 23 and 24: pn-junctions and electrooptics Randi Haakenaasen UniK/UiO Forsvarets forskningsinstitutt and

2 Outline Why pn-junctions are important Physics of pn-junction What does a pn-junction look like? Three electrooptic applications LED, IR detector, solar cell Demo IR detector, modulated-led-sound-transmitter Excess carriers Most SC devices operate by creation of charge carriers in excess of thermal equil. values Optical excitation Electron bombardement Injected in forward biased pn-junction Steady state: nonequil condition in which all processes are constant and are balanced by opposing processes (eg a sample with a constant current or optical generation of EHPs just balanced by recombination)

3 Thermodyn. equilibrium: no net flows of matter, charge or energy, no phase changes, and no unbalanced potentials (or driving forces) within the system. (a sample at constant temperature, in the dark, with no fields applied). A system in thermodyn. equil. experiences no changes when isolated from its surroundings

4 Importance of pn-junction pn-junctions have diode characteristics Conduct current well in one direction: exp with V Conduct current poorly in the other direction Used as rectifier, two pn-junctions back-to-back make a transistor (used as electrical amplifiers and switches), basic building block of all integrated circuits (ICs), advanced microprosessor can have > 3 billion transistors Billions of pn-junctions in computer, phone, Ipod. about 60 million transistors made per person on Earth (2002) Electrooptics Light emitting diodes LEDs Lasers Photodetectors Solar cells

5 Physics of the pn-junction Abrupt junction at equilibrium (no external excitation, no net currents flowing in the device) Large carrier concentration gradients at the junction: diffusion of majority electrons from n- to p side where they become minority carrier and recombine with a majority carrier hole Same for holes but opposite direction Ionized donor atoms (Nd+) are left uncompensated on the n-side and ionized acceptor atoms (Na-) on p-side Ɛ This space charge is fixed in place, and it gives an Ɛ - field from n-side to p-side (positive to negative charge) The Ɛ -field opposes J diff for both electrons and holes and only the majority carriers with enough energy to overcome the E-field will make it across Any minority carrier that enters the depletion region will immediately be swept across by the Ɛ -field and create a drift current J drift in the opposite dir. of J diff The field builds up until J drift exactly cancels J diff and no net current flows in the junction at equilibrium

6 Junction characteristics (equilibrium) The Ɛ-field appears in a narrow region around the junction called the space charge region or the depletion region W An equilibrium potential difference called the contact potential V 0 across W (Ɛ = - dv/dx) is a built-in potential barrier (does not imply an external potential). No net (external) current can result from it. The contact potential separates the bands: they are higher on the p side by qv 0 (Fermi level constant at equilibrium)

7 Einstein relation at equilibrium (need this for calculation of V 0 ) In a SC with a carrier gradient and an electric field, the current density for holes is dd x J p x = qμ h p x ℇ x qd h dd drift diffusion At equilibrium, no net current flows. Thus a fluctuation which starts a diffusion current also sets up an electric field which redistributes carriers by drift J p x = 0 ℇ x = D h μ h 1 p x dd x dd = D h n i e (E i EF) kk 1 μ h n i e (E i E F ) kk kk de i de F dd dd = D h μ h 1 kk de i dd de F dd 0 D h = D e = k BT μ h μ e q = V D: cm2/s µ: cm2/vs = D h μ h 1 kk qq x

8 Electron energy levels in ℇ -field Electrons drift in direction opposite to field -> Potential energy increases in direction of field The electrostatic potential V x = E x q The electric field ℇ x = dd x dd Relate ℇ x to the electron potential energy in band diagram, choosing E i as reference ℇ x = dd x dd = d dd E i q = 1 q de i dd To remember: e- drift downhill in an ℇ -field, while holes float up like bubbles

9 Doping concentrations and the contact potential No net current can flow across the junction at equilibrium: J drift and J diff cancel Furthermore no net buildup of electrons or holes on either side as function of time -> J drift and J diff cancel for each carrier type. For holes: D: cm2/s µ: cm2/vs Einstein relation D μ = kk q V and p functions of x only V and p at edges of depl reg Step junction: use equil. values for p and n outside depletion region

10 Contact potential in terms of doping concentrations and n i Contact potential in terms of equilibrium hole or electron concentrations outside junction

11 Equilibrium Fermi levels E F constant through device in equilibrium The energy bands on either side of the junction are separated by qv 0 When bias is applied to the junction, the potential barrier is raised or lowered from V 0, and the Fermi levels on either side are shifted by energy q*v f

12 Qualitative description of current flow at junction Apply an external voltage to junction almost all voltage appears across transition region Forward bias - Vf is positive on the p-side Potential barrier at junction is lowered to V 0 -V f the Ɛ-field decreases The transition width W decreases J diff increases because more majority carriers have enough energy to cross the potential barrier Majority carriers-> large currents Reverse bias Vr is positive on the n-side Potential barrier at junction is raised to V 0 +V r the Ɛ-field increases The transition width W increases Almost no majority carriers have enough energy to cross the potential barrier, so J diff negligible Left with J drift which is indep of Ɛ-field, it is minority carriers that wander into transition region and are swept across

13 Biasing the junction changing the diffusion current The diffusion current J diff depends strongly on the bias voltage The drift current J drift is independent of bias voltage - It is minority carriers generated by thermal excitation of EHP pairs. If they diffuse to the depletion region they are swept across by the Ɛ-field. It is also called generation current J gen For electrons at zero bias: J dddd,e 0 = J drrrr,e 0 = J ggg,e An applied bias voltage V f increases the probability that a carrier can diffuse across the junction by e (qv f) kk J dddd,e V f = J dddd,e 0 e (qv f kk ) = J ggg,e e (qv f kk)

14 Diode equation - IV curve For each type of carrier: J dddd V f = J dddd (0)e qv f kk= J ggg e qv f kk Total current each carrier is J dddd J ggg total current J = (J ggg,e + J ggg,h )(eqv kk 1) qv kk J = J ggg (e 1) The total current must be constant through the device. There is a flow of electrons from the negative battery terminal to the junction. These supply the extra electrons that diffuse across the junction as well as resupply the electrons lost by recombination in the excess hole distribution near the junction (on the n-side). In the p-material the current is carried by holes that flow from the positive battery terminal. Since the electrons and holes flow in opposite direction, the current throughout the device is in the same direction.

15 Variation in diffusion current with applied bias V f We expect the minority carrier conc. next to junction on each side to vary with V because of variations in diffusion across junction. When more carriers diffuse across, there will be a higher concentration of these immediatelty on the other side, but further away from the junction they decrease to the equilibrium values. For junction without bias we found This becomes with bias V For low-level injection (not too large increase in diffusion current) we neglect changes in majority carrier concentrations which vary only slightly with bias. p p p x nn = p ne qv0 kk p x nn = e q(v 0 V) kk In forward bias, increased p(x n0 ) minority carr injection steady state injection of holes In reverse bias, V is negative, p(x n0 ) reduced below equilibrium value Same for electrons on p-side of junction n(-x n0 )

16 What does a pn-junction look like? Electroplated Au bonding pad Sputtered Au Schematic drawing ZnS (0.3 µm) CdTe passivation (0.5 µm) n CMT (9-10 µm) CZT (211)B substrate p SEM cross-section EBIC image of current through diode R. Haakenaasen et al., J. Electron. Mater. 29, 849 (2000). R. Haakenaasen et al., J. Appl. Phys. 91, 427 (2002).

17 Demonstration of photodiode applications

18 Qualitative description of current flow at junction no light I = I ggg (eqq kk 1) I positive I negative

19 pn-junction At equilibrium, V ext = 0 Diode with built-in contact potential V 0 For electrons I diff from n to p I drift from p to n these cancel in equilibrium: no net current Non-equilibrium: add a constant photocurrent I ph Get new higher level of carriers and gen/recomb current I ph is a minority carrier current same direction as I drift proportional to incident light V=0, get short circuit I sc = - I ph open circuit I = 0, V = V oc (max V 0 ) I = I ggg (eqq kk 1) becomes I = I ggg (eqq kk 1) I pp

20 pn-junction photodiode and 3 applications qq kk I = I ggg e 1 I pp Short-circuit current I oo and open circuit voltage V oo In 1st quadrant, V and I positive -> LED, laser In 3rd quadrant, V and I are negative -> photodetector In 4th quadrant, V positive and I negative -> solar cell When P=VI is positive, power delivered from external circuit to junction When P=VI is negative, power delivered from junction to external circuit

21 Light emitting diode LED Photodiode with I ph in forward bias V f The carriers that diffuse through the junction recombine radiatively in or near the depletion region Almost all the current is converted into light

22 Photodiode in reverse bias - photodetector In reverse bias dark current is small and constant (IR: A) It comes from generation currents in depletion zone + within diffusion length of junction Signal current proportional to optical generation rate ( A) Proportional to incoming light intensity Fast reponse time: high mobility or wide depletion layer qq kk I = I ggg e 1 I pp Short-circuit current I oo and open circuit voltage V oc Important characteristics: Large signal/dark current ratio RA ( Ω cm 2 ), quantum efficiency (100%), noise equivalent temperature difference NETD (10 mk), response time (µs) Small power dissipation, can have many detector elements

23 Solar cell Voltage V oc V 0 generally E g /q Si: V oc 1V, I op ma for A=1cm 2 But use many devices to generate enough power to run electronics or charge batteries

24 No light