MTLE-6120: Advanced Electronic Properties of Materials 1 Semiconductor transistors for logic and memory Reading: Kasap 6.6-6.8
Vacuum tube diodes 2 Thermionic emission from cathode Electrons collected at anode with positive bias Anode not heated: cannot emit electrons no reverse current Nominally similar characteristics to pn-junction diode Images: Wiki: Vacuum tubes
Vacuum tube triodes 3 Control plate / grid between cathode and anode Negative bias repels electrons; reduces current Small changes in voltage large changes in current Acts as a switch or amplifier Images: Wiki: Vacuum tubes
Vacuum tube computers 4 Each triode in own separate tube ENIAC computer in 1946: 17468 such tubes Key characteristic required: three terminal device where third terminal controls current between first two In principle: computer made entirely of hydrualically or pneumatically-controlled valves! Images: Wiki: Vacuum tubes
Bipolar Junction Transistor (BJT) 5 Heavily doped emitter E (like cathode in triode) Thin lightly-doped base B (like control plate / grid) Lightly-doped collector C (like anode) Either pnp (shown above) or npn (polarities reversed) Which one does the vacuum tube triode correspond to?
BJT: junction potentials 6 Two pn-junctions: E-B and C-B Normal (active) operation: forward-bias E-B and reverse-bias C-B E-B junction: depletion region mostly in base C-B junction: comparitively symmetrical Potential drop across depletion regions; negligible field in interiors Hole concentration at B-end of E-B junction: p n (0) = n2 i N d exp ev EB k B T Hole concentration at B-end of C-B junction: p n (W B ) 0
BJT: current flow 7 Diffusion current across base: I E I C = ead h p n0 W B = ead hn 2 i N d W B exp ev EB k B T Current out of n-type base has to be electrons: two factors in α I C /I E Electron current in E-B: small due to asymmetric doping γ = 1 1+ N d W B µe NaW E µ h Recombination: small for thin lightly-doped base α T = 1 W 2 B /(2D h) τ h Current transfer ratio α = γα T 0.99 for typical BJTs Current gain β I C /I B = α 1 α 102 10 3
BJT: IV characteristics 8 Ideal characteristic: I C = I E independent of V CB Leakage current in reverse-biased C-B junction, I CB0 At high V CB, I C = αi E + I CB0 and I B = (1 α)i E I CB0 But slope of I C vs V CB increases for finite I E (beyond I CB0 ) Early effect: C-B depletion width increases with V CB This reduces W B, making hole diffusion easier, and therefore I E
BJT: common base amplifier 9 Small changes in E-B potential strongly affect I C I E = I E0 exp ev EB k B T Convert amplified current to voltage using resistor Collector potential V CB = V CC + R C I C Voltage gain (controlled by selecting I E and R C ): V CB I C = R C = I ER C V EB V EB k B T
BJT: common emitter amplifier 10 Note npn-transistor: polarities reversed Current amplifier: input I B amplified by β to output I C With leakage current, I B = (1 α)i E I CB0 and I C = I E I B = βi B + I CB0 1 α }{{} I CE0 Operate at V CE > V BE, else saturation: I C limited by I E
Junction Field-effect Transistor (JFET) 11 n-jfet: narrow n channel between p+ gates (reversed for p-jfet) Width of n channel determined by depletion regions Basic idea: control channel width and conduction using gates Always operate with channel potential > gate reverse bias
JFET: channel IV characteristics 12 First consider applied V DS with V GS = 0 Voltage of channel-gate junction increases from S to D Correspondingly increasing depletion width narrows channel Increase V DS, current I D increases, but channel narrows At V sat DS, channel pinches off at D end, I D saturates
JFET: gate effects 13 Apply negative gate potential: V DG increases Narrower depletion region, earlier pinch off V sat DS = V P + V GS, where pinchoff voltage V P = V sat DS at V GS = 0 Therefore, gate potential controls channel current and effective resistance Strong-enough V GS shuts off channel completely V off Empirical behaviour: I DS = I DSS [ 1 VGS /V off GS ] 2 GS
JFET amplifier 14 Amplifier: gate voltage controls channel current Convert channel current to voltage through resistor R D Vaguely similar to common-emitter amplifier Set operating quiescent point at center of operating range Signal amplitudes small enough to stay in range Voltage gain V DS V GS = R D I DS V GS = 2I DSSR D V off GS [ 1 V ] GS VGS off
Metal-oxide-semiconductor (MOS) capacitor 15 Metal Oxide Semiconductor Metal Oxide Semiconductor Metal Oxide Semiconductor Metal and SC separated by an insulating oxide: why don t the bands bend? Apply potential: linear variation in oxide, typical bending in SC Vacuum level (potential) continuous, D continuous For p-sc and positive V metal, CB bends towards E F For V metal > V th (threshold), CB closer than VB to E F Inversion region: n > p in p-type semiconductor Analogous case with reversed potentials for n-type semiconductors
Metal-Oxide-SC Field-effect Transistor (MOSFET) 16 Enhancement n-channel MOSFET: metal-p capacitor surrounded by n+ MOS inversion: generates an n channel at surface Comparison with n-jfet: existing channel suppressed by gate junction Analogous depletion n-mosfet: replace p above with light n Flip n p and polarities enhancement and depletion p-mosfets
MOSFET: gate response 17 For V GS < V th, n+ contacts separated by depletion layer No channel I D = 0 irrespective of V DS One V GS > V th, inversion layer forms an n-channel For low V DS, channel behaves like an Ohmic resistor
MOSFET: drain response 18 Increasing V DS causes reduction in V GD Channel begins to narrow near drain; current starts to level off At V DS = V sat DS = V GS V th, channel pinches off at drain end Beyond this potential, I D does not increase with increasing V DS
MOSFET: IV characteristics 19 Saturation drain voltage V sat DS = V GS V th Saturation drain current I DS = K(V GS V th ) 2 (1 + λv DS ) Coefficient K Cµe 2L 2, where C = MOS capacitance, L = channel length Coefficient λ due to Early effect (exactly like in BJT, JFET) Similar characteristics to JFET similar amplifier circuits Switching: V GS > V th R DS small (on) vs V GS < V th R DS large (off) On-off ratio RDS off /Ron DS, switching time RC
Complementary MOS (CMOS) logic 20 Complementary MOS: combine p and n-mos transistors Inverter / NOT gate: V in < V th V out = V dd, V in > V th V out = V ss Digital logic: for input 0 and 1, output 1 and 0 respectively NOR (NOT OR) gate: output 0 (NOT 1) if any input 1 NAND (NOT AND) gate: output 0 (NOT 1) if all inputs 1 Any logic or arithmetic operation using just three gates!
Arithmetic circuits 21 XOR (exclusive OR) gate: output 1 if exactly one input 1 1-bit adder: sum bit = XOR, carry bit = AND 8-bit adder: chain bit additions together N-bit adder: requires N log 2 N gates N-bit multiplier: adder of N numbers with N-bits each
Example: Xeon Phi 7210 22 64 compute cores Each core: 8 64-bit multipliers Net: 10 12 64-bit math operations per second 8 10 9 CMOS transistors in 8 cm 2 of Si!
Bistable latches (flip-flops) 23 When R = S = 0: latch stores previous value Feedback loop between two inverters S = 1 sets value to 1, R = 1 resets it to 0 Volatile memory: data lost when circuit powered off Mechanism used in registers and static RAM Minimum 8 transistors / bit as shown above (low-density, high power)
Dynamic RAM 24 Bit = whether capacitor is charged Transistor in off state: capacitor isolated; retains charge To read, transistor in specific row and column switched on Reading destroys state; must be written back State lost due to leakage refresh circuitry Volatile: charge retention only 100 ms 1 transistor / bit: high-density, low power 8GB DDR4 memory: 8 10 9 transistors in < 10 cm 2 Si
Flash memory / SSD: floating-gate transistors 25 Floating gate transistor: bit = whether floating gate is charged Charge on floating gate affects V th Read bit by checking if transistor is on at specified V GS Write bit by hot-electron injection from channel Erase bit by Fowler-Nordheim tunneling to upper gate NOR-flash: closer to random-access; erase only in large blocks NAND-flash: all access in large pages / blocks (eg. SSD)